CA2120624C - An optical grating and a method of fabricating an optical grating - Google Patents
An optical grating and a method of fabricating an optical gratingInfo
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- CA2120624C CA2120624C CA002120624A CA2120624A CA2120624C CA 2120624 C CA2120624 C CA 2120624C CA 002120624 A CA002120624 A CA 002120624A CA 2120624 A CA2120624 A CA 2120624A CA 2120624 C CA2120624 C CA 2120624C
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- grating
- sequence
- laser
- lines
- optical
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Classifications
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/02—Optical fibres with cladding with or without a coating
- G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
- G02B6/02076—Refractive index modulation gratings, e.g. Bragg gratings
- G02B6/0208—Refractive index modulation gratings, e.g. Bragg gratings characterised by their structure, wavelength response
- G02B6/02085—Refractive index modulation gratings, e.g. Bragg gratings characterised by their structure, wavelength response characterised by the grating profile, e.g. chirped, apodised, tilted, helical
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/02—Optical fibres with cladding with or without a coating
- G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
- G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
- G02B6/122—Basic optical elements, e.g. light-guiding paths
- G02B6/124—Geodesic lenses or integrated gratings
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/02—Optical fibres with cladding with or without a coating
- G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
- G02B6/02076—Refractive index modulation gratings, e.g. Bragg gratings
- G02B6/02123—Refractive index modulation gratings, e.g. Bragg gratings characterised by the method of manufacture of the grating
- G02B2006/02166—Methods of designing the gratings, i.e. calculating the structure, e.g. algorithms, numerical methods
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/02—Optical fibres with cladding with or without a coating
- G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
- G02B6/02066—Gratings having a surface relief structure, e.g. repetitive variation in diameter of core or cladding
Abstract
An optical grating includes a sequence of grating lines, the sequence being such that each grating line is centred on a position which is an integer multiple of a line spacing distance from a datum position on the grating, the sequence of grating lines is non-periodic and the sequence of grating lines is formed from N concatenated subsequences. Each subsequence comprising a series of one or more instances of a respective grating line pattern. Such an optical grating has a structure that is more amenable to calculation of the grating lines necessary to achieve a desired characteristic. A method of calculating and fabricating such a grating is also disclosed.
Description
AN OPTICAL GRATING AND A METHOD OF FABRICATION AN OPTICAL
GRATING
This invention relates to optical gratings.
An optical grating can be considered to be a sequence of grating lines. The lines modify the reflection and transmission characteristics of an optical transmission medium to which the grating is applied so allowing the characteristics to be tailored, to a greater or lesser degree, to a desired application. For example, an optical grating is used in a distributed feedback laser (DFB) to control the wavelength at which the laser is able to lace.
In another application, an optical grating is used to control the transmission characteristics of an optical waveguide, for example an optical fibre.
An article titled "D-Fibre Grating Reflection Filters", P. Yennadhiou and S A Cassidy, Optical Fiber Communications Technical Digest, 1990, page 27, ISBN 1-557-52113-1 describes a D-fibre mounted on a flat substrate to expose the optical field in the fibre core. A
holographically formed grating was placed on top of the substrate to give a periodic sequence of changes to the effective refractive index seen by the electric field. The changes in refractive index caused by the grating are very small but at each change in index there is a small amount of light reflected back down the fibre. At a certain resonant wavelength these small reflections build up through constructive interference to provide a large reflection whose magnitude is determined by the length of the grating and the size of the refractive index change.
For a periodic grating with an arbitrary index profile this resonance occurs where the grating period is an integer multiple of half the wavelength, 1~/2, divided by the mean effective index no. In the special case when the index profile is a sequence of discrete jumps, the resonance only arises when the period is an odd multiple of 1~/ (2no) .
At wavelengths around the exact resonance, the reflection has a characteristic "sin (1~) /?~" wavelength response profile of a finite-sized grating. The width of response peak is roughly inversely proportional to the grating length unless the reflectivity is very high. (see W4 93/14424 ~ ~ ~ ~ PCT/GB93/00043 Figures 1(a) and 1(b)). When the peak reflectivity is high then multiple reflections become important and the reflection profile no longer narrows with _ncreasing grating length. Instead the response flattens at around 100% reflectivity near the peak with very strong side lobes in the vicinity of the peak (see Figures 2(a) and 2(b)).
This characteristic profile is very di~ficult to change with conventional design methods. In particular, if the periodic change in effective refractive index is fixed i0 by the material properties, then it is not possible to adjust the width of the wavelength response independently of the peak reflection. Nor is it possible by explicit design to remove she side lobe structure of smaller resonances on either side of the peak (although minor errors in the exact periodicity in the grating will often wash these out in practice).
Requirements have emerged which need reflection profiles that differ qualitatively from known prior art gratings. The first is to obtain a reflection profile that is flat over a comparatively large wavelength range (greater than about lnm wide) but with no side lobe reflections in the immediate neighbourhood of this range.
The peak reflection in this case is not important but it needs to be at least 10%. Such an optical grating could be positioned within an optical fibre network so that the connection with a central control could be checked by monitoring the reflections from an interrogation signal sent from the control centre. The wavelength of the peak reflection would then be used to label the position of the grating and hence the integrity of the network could be checked at several places. A wide reflection is needed because the wavelength of the interrogation laser could not be accurately specified unless very expensive components were used. The side lobes need to be suppressed to prevent ?5 interference between different gratings in the network.
The second requirement is for a high reflection (as close to 100a as possible) in a narrow wavelength region, J
around O.lnm wide, with very low side lobes. This is for use as a wavelength selective mirror for use with a fibre laser to force it to operate in a narrow wavelength region only.
Other applications have been identi~ied for non conventional gratings where the wavelength response of the transmission and reflection properties could be specified.
In particular, distributed Braag reflectors (DBR) and distributed feedback lasers (DFB) appear to be very good i0 candidates for such gratings.
It is a fairly straightforward matter, in principle, to calculate the effect on light travelling in one dimension of a seauence of steps in the effective index seen by this light. In a weakly guiding fibre waveguide 15 both the electric field E and the magnetic field B are perpendicular to the. direction of travel. The reflecti on and transmission coefficients are determined completely by the relation of E and B after passing through the region of index steps to their values before the region.
20 If the light Gasses a distance dz through a region with a constant effective refractive index (i, then tB ~ / cos(xOz) ~x~z) I B
,a psin(xOz) coslxAz) or I BJe= =M(~il,x~zt~.~B~o where x is the effective wavenumber, 2n~3/~, and E
\B/ezi denotes the values of the electric and magnetic fields after a distance 0z.. Hence if the light passes a distance 0z, through a region of effective index Vii,, followed by a distance ~z2 through a region of effective index Vii' then E
and B are given by ~B,W..Gz. ~~~Z'1CAZ~). ,~~~I'K~Zt~~~8~0 The effect of a sequence of small steps through the regions of differing refractive index can therefore be calculated from a scattering matrix, given by the product of ail the small step matrices. Note that the matrix coefficients depend on the wavelength ~,. If the final i0 scattering matrix S is given by S1I SI2l \S21 S:2 then the reflection coefficient is given by ~R~Z and the transmission coefficient by ~T~' where no.(st t -szt ) - i.~no'-stz -sz: ~~
R 'no.(stt -s=z~ -i.lno=sl, *s=l~l 2n T. - o ~novsa ' S=z) - i.lno=stz +sm)~
n~ is the refractive index of the substrate and i=(-1)ii2 A Smm long grating With a pitch of say 0. 25~.m would have 20,000 steps and therefore the calculation for the scattering matrix would involve 20, 000 matrix products. If 20 the matrix were to be calculated at say 100 wavelengths in order to resolve the wavelength response of the grating, then the full scattering matrix of the grating would take several million arithmetic operations to calculate. This is therefore not a trivial calculation but one which would 25 pose no difficulty for a reasonably powerful computer.
;9hile the effect of a given sequence of steps in the effective index of the waveguide can easily be calculated, the converse task of designing the sequence to give the required properties to R and T is a different matter entirel:r. The problem lies in the number of calculations that have to be :jade. A crude approach of simply enumerating all the different possibilities, and testing each for its suitability, is out of the question: even if the grating pitch was constant and the changes were restricted to allowing a refractive index step or not, then the total number of ~ossibilities would be around 2~~'~~~ so no amount or computer power would help.
In order to make any kind of optimisation, the orating :zas to be defined ._. ~.erms of some tractable number of aarameters and repeated calculations made of how the :5 grating properties change with these parameters. This basic idea is known. Simple parameters that have been used ar a arati ng pi t ch whi c:~ may, f or exampl e, vary s 1 owl y al ong the grating's length ~o form a chirped grating or gratings -haz :piss out some c~ ~he steps in a regular or smoothly varying fashion. See nor example T Schrans, M Mitteistein and A Yariv "Tunabl a :active Chirped-Corrugation :daveguide Fil ters" Appl led Ph~-sics Letters 55, 212-214 ( I989 ) and D
J Reid and C M Raadale, _ Bennion, D J Robins, ~ Buus and W J Stewart "Phase-Shifted Moire Grating Fibre Resonators..
electronic Letters -c, 10-I2 (1990), respectively.
These known types of optical gratings are not amenable to approaches of computation that give enough degrees of freedom of device characterisation necessary to achieve the sort of wavelength response that are needed for many applications, for example as identified earlier in this application.
According to a Lirst aspect of the present invention an optical grating including a sequence of grating lines, the sequence being characterised in that:
a) each grating line is centred on a position which is an integer multiple of a line spacing distance from a datum position on the orating;
b) the sequence of grating lines is non-periodic;
and c) the sequence of grating lines is formed from a multiplicity of N concatenated subsequences, each subsequence comprising a series of one or more instances of a respective grating line pattern.
The present invention provides an optical grating having a structure that is more amenable to calculation of the grating lines necessary to achieve a desired effect as will be explained in more detail below. It is preferable that N=21~, where M i s a whol a number, al though a grati ng may comprise two or more such sequences with some decrease .n e~~iciency o~ calculation.
The number of subsequences can in effect be reduced by incorporating a number of null sections of zero length.
For example, in a preferred embodiment of the present invention, if two adjacent subsequences are found during calculation to be formed from the same grating line pattern they are combined into one larger subsequence for 'uture calculation, the number of subsequences being restored by insertion of a null subsequence.
The substrate may be an optical waveguide such as an optical fibre having a D-shaped cross-section. Other s ubs trates may be us ed as wi th known opti cal grab ngs .
The grating lines may be grooves in the substrate, for example, the grooves having a rectangular cross-section or having triangular cross-sections, for example. The grating lines may be also be defined by refractive index variations in a substrate or other medium.
The grating sequence is formed from a multiplicity of subsequences of the type described above in order to give the flexibility of design while allowing tractable calculation of the optical characteristics of a grating.
The sequence of grating lines is non-periodic so as to allow for non-periodic phase shifts between the grating lines which are necessary to achieve reflection profiles which are qualitatively different to those that can be achieved by conventional gratings. Thus use of a non periodic sequence of grating lines gives flexibility in the design process, while use of subsequences ensures that the design process remains tractable as will be explained bel ow.
Such considerations are of utmost importance in a design problem of this size as any optimisation method will involve repeated calculations of the total scattering matrix with different parameter values to see which one is the best.
The main consideration in the design algorithm is therefore concerned with providing an efficient method of calculating the total scattering matrix of a grating as efficiently as possible. As will be seen, the structure of grating according to the present invention allows such efficient calculation of the scattering matrix.
The design process of a grating according to the present invention involves determining the values of the parameters of the subsequences, ie the grating line pattern and the number of instances of each pattern in a given s ubs ea_uence, to obtai n des i red properti es i n the res ul rant optical grating. To do this it is necessary to change these parameters one or a few at a time, and compare the new calculated properties of the grating with the old ones to see if there has been any movement towards the desired characteristics.
Because the sequence of grating lines of the optical grating is made up of subsequences as described above it is possible to calculate the total scattering matrix of an optical grating more rapidly than if it was necessary to calculate all the properties of the grating from scratch.
Because the grating is split up into a number of sections N, where N is an exact power of 2, N=2M, then it can be shown that the effect of change in the grating in one of the sections can be calculated in log2(N) matrix multiplies rather than the N multiplies needed in a cruder algorithm which directly calculates the entire new matrix.
According to a second aspect of the present invention a method of fabricating an optical grating comprises the steps oz:
calculating the response of an optical grating including a sequence of grating lines, the grating lines being such that:
each grating line is centred on a position which is an integer multiple of a line spacing distance from a datum position on the grating;
the sequence of grating lines is non-periodic; and the sequence of grating lines is formed from N
concatenated subsequences, each subsequence comprising a series of one or more instances of a respective grating line pattern; and subsequently repeatedly altering a subsequence of the grating deciding whether to accept the alteration of the subsequence until some predetermined criterion is achieved;
and on achieving the predetermined criterion; forming the resultant optical grating sequence on a substrate.
The method preferably includes the additional prior steps of:
selecting a set of grating line patterns; and calculating the scattering matri:c of each member of a set of grating patterns.
The subsequence is preferably altered by either substituting the respective grating line pattern for a different grating line pattern from the set of grating line patterns or changing the number of instances of the grating line pattern in the subsequence. Other operations to change subsequences can be used; the grating line patterns of two subsequences may be interchanged, for example.
The decision whether to accept an alteration to one of the subsequences is preferably determined by an annealing algorithm. In particular an alteration to a subsequence is accepted if the change in a measure of fit of the grating profile to a desired profile is such that exp[-~8v~/TJ is less than a random number generated in the range 0 to 1 for some value of T and where v is a predetermined measure of the performance of the grating.
T preferably is monotonicaliy decreased between alterations to the sequence of grating lines.
It should be noted that the grating line patterns may include a null grating pattern of zero length.
In addition to requirements for optical gratings which have reflection profiles that differ qualitatively from known prior art gratings, as discussed above, there have emerged further requirements for gratings whose characteristic profile can be altered in use. For example, there is a requirement in wavelength division multiplexed ortical communications systems for both tunable lasers and tunable filters. Such a tunable laser can be achieved in a known manner by providing means for controlling the refractive index of the grating in a DBR or DFB laser. It will be understood that changing the refractive index of a grating means uniformly changing the refractive index across the whole of the grating, or a substantial part thereof, and does no~ affect the relative index variation which actually cons tituents the grating itself i. e. the small steps in refractive index whici~. form the grating lines.
The alteration of the characteristic profile of a grati ng can be achieved for example, i n a grating formed in a semiconductor material, by providing an electrical contact adj acent the grating for inj ecting current into the grating region so as to alter the refractive index of the material in which the grating is formed. A alternative method of altering the characteristic profile of a grating is to physically al ter the structure of the grating or a part thereof by for example employing piezo-electric transducers to stress or stretch the grating.
It has been found that the structure of a grating according to the present invention in addition being more amenable to calculation of a particular desired fixed characteristic pro=ile, is also more amenable to WO 93/14424 ~ ~ ~ PCT/GB93/00043 - lp -calculation of a characteristic profile which can be varied in a desired manner during use of the grating.
Thus the present invention also provides a grating in which a plurality of sub-uni is of the grating, each sub s unit formed from a plurality of subsequences, are separately addressable by means for altering a parameter of each grating sub-unit.
The multiplicity of sub-sequences from which the grating is formed again give flexibility in the design of, in this case, a variable characteristic profile of the grating, while at the same time enabling the calculation of the ~rofile to be tractable.
The design process required for such a grating, having a characteristic profile which can be varied in use, can be regarded as an extension of the design process for a grating having a fixed characteristic profile. The ability to vary a parameter, 'or example the refractive index, of a pi urali ty of s ub-~~nits o f the grati ng gi ves an extra degree of freedom is the design process so that any optimisation of the orating design must effectively be two dimensional, eg the physical structure of the grating sequence comprising ~!~e positioning of the grating lines must be optimised in conjunction with the choice of refractive indices =or each of the grating sub-units, as will be explained below.
The use of such a design process allows a grating to be designed which has for example four separately addressable sub-units whose refractive may be varied in use so as to provide a reflection profile which is tunable over a wider range of wavelengths than a conventional periodic grati ng.
The present invention will now be described, by way of example only, with =eference to the accompanying drawings in which:
~5 Figures 1(a) and 1(b) are graphs of the grating responses of prior art optical gratings having grating lines with a flat-triangle section groove;
- - L i -Figures 2(a) and 2(b) are graphs of the grating responses of prior art optical grati ngs having high peak reflectivity;
Fi gure _ i s a s chemati c bl ock di agram of an opti cal .. grating according to the present invention;
Figure 4 is a diagram of a set of grating line patterns suitable for optical gratings that are to be etched on an optical fibre waveguide;
Figure 5 is a diagram of a grating line patterns i0 suitable for an optical grating for a DFB/DBR laser grati ng;
Figure 6 is a representation of a grating according to the nres ent ~. nven ti on;
Figure 7 is a key to the representation of the grating '_ 5 s hown i n F i gure 5 s howl ng the grati ng 1 i ne pat terns employed;
Figure 8 is a graph cf the theoretical response of the optical grating of Figure 6;
Figure 9 is a graph of the measured response of the 20 optical grating of Figure 6; and Figure 10 is a scanning electron micrograph of a portion of the grating of Figure 6 at a transition between two subsequences;
Figure 11 shows ~ grating in 4 sub-units, the 25 refractive index n of each sub-unit may be varied by current injected via an electrode;
Figure 12 is a schematic flow diagram showing the stages of the method of designing a grating having a variable reflection response;
30 Figure 13 is a schematic diagram, similar to that shown ;n Figure , showing the sequence of scattering matrix calculations required when the refractive index of a grating sub-unit is changed; and Figure 14 a) and b) show the four theoretical 35 reflection responses from a single grating having four sub units of variable refractive index.
Figures 1(a), 1(b), 2(a) and 2(b) have already been di s cus s ed.
Referring to Figure 3 an optical grating 2 according to the present invention. is shown schematically to show its overall subsequence structure. The grating 2 is a sequence of grating lines formed, in ;.his particular =nstance, by a (=23) subsectuences =i, 6, 3, 10, i2, '4, 16 and 18. Each of the subseQUences is formed from a series of one or more instances of a respective grating line pattern. The particular grating 1 i ne pattern and the number of instances .0 of it in a particular subsequence will in general vary from one subsequence to another.
F figures 4 and 5 show sets of grating line patterns useful for subsequences 'or an optical fibre grating and DFB/DBR laser grating, respectively.
15 ~ typical set of grating line patterns comprising grooves 34 having a rectangular cross-section used for optical D-fibre grating designs for fabrication on a silica subst=ate are shown in Figure 4. This is an exemplary set of grating line utter.~.s - other sets could be chosen 20 instead. For a DBRiDFB laser grating which is written on an _nP substrate, the fabrication processes force a different type of grating line patterns to be chosen, eg ~rlangular cross-section grooves 35. On these substrates ;.. is very difricult to cut vertical walls, so discreet 25 steps in the refractive index profile cannot be easily achieved. The typical groove has a triangular cross-section, in this case with etch angles of around 55~, an exemplary set being shown in Figure 5.
Referring once again to Figure 3, the optical effect 30 of the subsequences 4 to 18 of the grating is calculated as follows. The scattering matrix for each grating line pattern is calculated beforehand in a known manner as described earlier. The scattering matrix for a given subseQUence ~, 6, 8, :0, 12, 14, 16 and 18 can then be calculated 'S by raising the appropriate grating line pattern scattering matrix to a power equal to the number of instances of that pattern in a subsequence. This is carried out for all the ,.~ ~ ~, ~ s z ~ ~~ ' 3 subseauences 4 to 18 of the grating line sequence.
The scattering matrices for consecutive pairs of the subseauences are then calculated by forming the product of the scattering matrices of the subsequences. These ., products form the second level scattering matrices 20, 22, 24 and 20 of the grating.
~n a similar fashion the level 2 scattering matrices are wired and the level 1 scattering matrices 28 and 30 are calculated. The two, 1 evel 1 scattering matrices 28 and 30 are ~inall~ combined to form the full, level 0 scattering matrix 32.
~f one of the level 3 subsequences is chanced during application of an Opti.~,:lZatlon algorithm, for example subsequence 12, then to calculate the new full grating scattering matrix one calculates the matrix product of subseauences 12 and ,'_.~ to form a new level 2 matrix, 24, which'is then multiplied with the existing level 2 matrix, 26, to form a new ~ evel y matrix number 30. This fi nally is multiplied with the other existing level 1 matrix 28 to form the full scatt~rina matrix 32 for this new sequence of aratina lines.
Referring now to :figure c, there is shown a tarticular optical grati.~.a calculated according to the method of the tresent invention comprising ten grating line patterns as 2~ shown by the key at Figure 7 and the theoretical response is shown at Figure o.
The basic pitch of the grating line patterns of Figure 7 are about 0. 5~m with a single smallest feature (one line) of about 0.25~m. The word patterns consist of 4 bits, each word being about lam long. The total length of the crating of Figure 6 is about 4mm with 64 subsequences including any null subsequences that may have been introduced when adj acent subsequences of the same grating line pattern were combined. The patterns were etched into a silica substrate to a depth of about 0. 25~tm.
Figure 9 is a graph of the experimentally measured reflection characteristics of the optical grating of Figure ~1~~~~4 6 after applying the optical fibre waveguide to the surface of a D-fibre optical _ibre waveguide.
The structure of the grating according to the present invention allows efficient calculation of changes to the scattering matrix and so allows efficient implementation of optimisation algorithms. The optimisation algorithm used in the present instance will now be described, by way of example.
The first step was to choose the shape of the desired reflection characteristics of the grating as a function of wavelength, RT(.1) and compare the actual reflection R~(n.) obtained from the grating with the desired one. The measure of the difference between the two was defi:~ed as pz = J~aIRT~z-;RA~~ZdA
where ~ a = J~ ~RT~2. ~Re ~2 dl~/ f ~ ~RT~4dl, a is, in effect, a measure of the scale of the reflection and ~ a measure of the fit to the desired shape. The aim was to minimise p and maximise a. Depending on the particular situation, a global measure v can be ~crmed from a weighted difference of the two numbers to give the parameter to be oat~:.msed ie setting v=( 1-w), a-w. Vii, where w is a weighting parameter between 0 and 1. A larger value of w means that more weight is being attached to the shape of the refraction profile at the possible expense of the total reflectivity.
We then sought to maximise v and used a version of a simulated annealing algorithm to determine the grating line seauence which led to a suitable maximum. In this algorithm a change was made to the grating either by changing one of the work patterns or changing the length or interchanging two of the subsequences. These changes were done sequentially to randomly chosen subsequences, one subsequence being changed or two interchanged before recalculating the response of the grating. Other more complicated changes may be made but at the expense of increased calculation. To simplify the scheme of this embodiment the interchange step may be eliminated.
Using this algorithm we then calculated the change 8v .. in the measure of the grating performance caused by the crrati na al ter ati on. I ~ 8v i ncreas ed, i a the new gra ti ng was "better" than the cld one, then the change to the grating was accepted. T_f 8v was decreased by the alteration to the subsequences, then the chance was only accepted ~_ exp[-IbW /"'; was less than a random number crenerated __. the ~.nterva 1 0 to ' , where T was a parameter that represents a _ictitious temperature.
T_f T was high, then ..~.early all the chances were accented and v wanders around almost randomly. As '?' was i5 decreased then the chances of accepting a change that decreases v gradually reduced and v was forced into a maxi mum.
Such a maximum is very probably a local maximum so there will in general be expected to be many solutions that result in the value of v very close to the best one obtained.
The strategy usually adopted, as here, was to make several independent calculations using different random seeds, and then pick the best orating line sequence that resulted. "_'he measure of the value of a particular grating was to some extent arbitrary and other measures of fitness of fit of crating could be used. In particular, if one is interested in the dispersion properties of a grating then one would use the full complex form of the target response RT (~, ) and the actual reflection RA (~, ) and the definitions of a and ~ rather than their moduii.
The calculated crating sequence was then used to fabricate a grating by forming the grating lines as a sequence of vertically walled, etched steps by electron-beam lithography directly onto a silica substrate. The experimentally measured response of the grating of Figure o i s s hown at Fi gure °.
- to -~'A~,4r ~' Fi gure i 0 s hows a porn on o f the grati ng o f Fi gure 6 at a transition between two subseauence 38 and 40.
The method of fabricating an optical grating according to the present invention has been described in terms of a grating line sequence which is made up of a whole number power of 2 subsequence. This structure obtains the full benefit of the tresent invention. However, it is also possible to obtain the principle benefit of the invention if a grating sequence comprises a small number of concatenated sequences each sequence being as described above. Ir. such a case there will be a small overhead in the calculation as two level 0 scattering matrices will need to be multiplied together. Thus a grating comprising a number of grating sequences each having 2~ subsequence according to the present invention in series can be calculated with slightly less efficiency than a grating having an exact power of two subsequence.
Figure 11 shows a grating whose characteristic profile can be altered in use. The grating is divided into four sub-uni is 41, 42, 43, 44, each of which is separately addressable throug:~ a electrode. Thus the refractive index of each of these sub-units can be controlled between two val ues whi c'.~. ar a gi ven, v n a known manner) by the properties of the semiconductor material used, by applying a voltage to each of the electrodes. The reflection profile of the grating can be switched between a number of different responses by applying different sets of voltages to the sub-units 41-44.
The design process for this grating must therefore specify a grating sequence, formed from sub-sequences of grating line patterns, and must also specify the particular refractive indices for each of t::e sub-units required to achieve switching between the desired characteristic responses.
Thus if four particular responses A, B, C, D are reauired from the grating then the design process must optimise both the grating sequence and the four sets of refractive indices n:, n" n~, n) required to achieve these four responses, so that the grating characteristic is A when { n" ~~, =:~, n, } is { a" a" a;, a, }
B whe n { .~., , a~, ::" n; } i s { b" b_, =c=, b~
}
J C when {n" n~, z" n,} is {cl, c" c"
c~}
D when { n" n~, _~.~, n) } i s { d" d2, d~, d, }
It should be noted that the grating line sequence remains fixed in each case, the only thing that changes is the seQUence of refractive indices. This sequence can be changed by appiyirg different voltages through the inden_ endent elect-odes.
The design method for a grating having a variable reflection characteristic thus differs =rom that for a grating having a fixed reflection characteristic in a number of respects. Firstly there is always a choice during the calculation of the design process of whether to change a grating subseQUence (as for the fixed response grating) or to change the refractive index of a sub-unit of the grating, this is shown schematically in the flow diagram of ~'i gore 1~- If the choice to change a grating subsecruence s made then the scattering mat-ices are recalculated in the same manner as for the fixed response grating as described above. ~F the choice is to chance the refractive index of a grating sub-unit then the recalculation is different as will be described below.
Secondly, a further difference for the variable response grating design method is that a set of scattering matrices corresponding to each of the different sequences (n,-y) of refractive index for the grating sub-units must be ~0 calculated. Thus if four different reflection responses are required from the grating, four sets of scattering matrices required to give the four different reflection coefficients as a function of wavelength, must be calculated.
Thirdly a different measure of fit between the WO 93/14424 .~ ~ ~ :~ ~ - 18 - PCT/GB93/00043 calculated matrices and the target response is required, since the target response is in fact a number of responses, each corresponding to one of the sequences of =efractive indices of the grating sub-units.
Referring to Figure 12 each of the stages of the design method will now be described in more detail, for a grating having s sub-units which is required to give R
different reflection characteristics.
The initialisation stage comprises:-i0 initialising the orating line patterns and R-refractive index seauences in the s sub-units (These could either be random seauences or values read in from a trey=ous cai cul ati or. j and;
pre-c: alculating the scattering matrices for each of :5 the grating line patterns at each of the allowed values of refractive indices.
The selection stage 46 comprises choosing at random a grating subsequence or a refractive index sub-unit in one of the switchable sequences (typically with the subsequence 20 being slightly more likely to be chosen?. Cycling the subseauence or =ndex value through all the possible choices, until either a change is accepted or all the possibilities are exhausted, and then choosing another subseauence or index sub-unit to change.
25 If a grating subsequence is chosen to be changed then the recalculation stage 47 is the same as for the fixed res pons a grab ng des i an method, i . e. onl y thos a matri ces i n the structure shown in Figure 3 which are affected by the change are recalculated. However as mentioned above, the 30 matrices need to be calculated N-times i.e. once for each of the N-target wavelength responses - corresponding to the N-switchable refractive index sequences of R-refractive index sections.
If a sub-unit refractive index is chosen to be changed 35 then the recalculating stage 48 must take account of the change in index affecting all the levels in Figure 3 below the level at which the index is changed. This is shown in ~~2Q~~~.
WO 93/14424 - 1 g - PCT/GB93/00043 Fi gure 13.
A change to the refractive index value of the sub-unit labelled 1 in level 4 of Figure 13 means that it is necessary to replace all of the scattering matrices affected at level 5 (numbers 8-15). Following this it is necessary to recalculate the matrices (4-7) at level (4) by pairwise multiplication in level (5), recalculate the matrices (2 & 3) at level (3) by 1 0 pairwise mui tiplication iz level ( 4 ), recalculate the matrix 1 at level 2 by multiplication of matrices 2 & 3 in level ( 3 ), Multiply the old matrix 0 wi t'.~. the new matri :c i to give a new matrix 0 at level (i).
Multiply the new matrix 0 with the old matrix 1 to give the new scattering matrix.
Thus 4+2+1+2=9=((32/4-1) + iog~(4) matrix operations are needed to update the scattering matrix as opposed to 31 with a more conventional algorithm.
In contrast to the calculation for a grating subsequence change, these matrices need only to be calculated once - as, in a refractive index change only one section (out of he R available) ,~n one refractive index sequence (of the M-available) is change at a time. The remaining matrices corresponding to the (N-1) sequences that were not changed at this point, are unaltered.
Having made a change, either of grating subsequence or of sub-unit index the next stage 48 is to decide whether to accept this change. This will depend on whether the change gives a better fit to the N-desired or target responses, hence the measure of difference used previously for the fixed grating response design method is modified to account for the R different refractive index sequences for the s s ub-uni is of the grati ng. Thus i N ( f (a ~~, (~'t) 12 ~ItA(~,t7 I2)Z d~) 'S
1 ~N (J ~~. ('~,t) ~z~ ~R.,(.l,c~ ~Zdl where a =
1 ~N ( J~~RT (~,y j'd~
the extra suffix, "i"' denotes the coefficients corresponding to the i' th refractive index sequence.
'~'he final measure of fit is formed from these two quanti ties: V - ( =-w) . a-w. ~ where w is a weighting parameter.
V is then used _n an optimisation or annealing algoritzm in prec~seiy t~!e same way as previously described in order to decide whether to accept the change (in grating subsequence or sub-unit index) or not.
If the change is accepted the current grating sequence and refractive index sequences are saved and the iteration is repeated by again choosing a grating sub-sequence or sub-unit index ~o change. Once a certain number of i5 iterations or a predetermined measure of fit has been reached the design process is stopped.
~_'he result of the design process is one sequence of gratira lines and R sequences of refractive indices for the s sub-units.
Figure 14 a) and b) show the four different theoretical reflection responses of a grating having s=4 (and T=4). Each response corresponds to a particular seauence of refractive index values for the grating sub-units. It can be seen that the reflection responses are separated by 4nm giving a total tuning range of l2nm. Fine tuning to give a reflection response intermediate between any of the four shown is achieved by altering the refractive index of all four sub-units uniformly, while tuning between eac:~ of the responses shown is achieved by switching from one of the sub-unit refractive index seauences determined by the design method to another such WO 93/14424 ~ ~~ ~ ~ ~' ~ ~ PCT/GB93/00043 s ecruence.
If the maximum index change utilised in the design of the grating of Figure 14 were applied to a conventional grating a tuning range of only 3-4nm would result, t?~.us the design achieves a significantly larger tuning range.
Although the design method for a grating having a variable reflection response has been described for gratings in which the response is changed by a change of refractive index, i t will be apparent to the skilled man, that, in the method, refractive index can be replaced by any other parameter which will affect the reflection response of the arati.~.g, ror example the local stressing or stretching of a sub-unit of the grating.
GRATING
This invention relates to optical gratings.
An optical grating can be considered to be a sequence of grating lines. The lines modify the reflection and transmission characteristics of an optical transmission medium to which the grating is applied so allowing the characteristics to be tailored, to a greater or lesser degree, to a desired application. For example, an optical grating is used in a distributed feedback laser (DFB) to control the wavelength at which the laser is able to lace.
In another application, an optical grating is used to control the transmission characteristics of an optical waveguide, for example an optical fibre.
An article titled "D-Fibre Grating Reflection Filters", P. Yennadhiou and S A Cassidy, Optical Fiber Communications Technical Digest, 1990, page 27, ISBN 1-557-52113-1 describes a D-fibre mounted on a flat substrate to expose the optical field in the fibre core. A
holographically formed grating was placed on top of the substrate to give a periodic sequence of changes to the effective refractive index seen by the electric field. The changes in refractive index caused by the grating are very small but at each change in index there is a small amount of light reflected back down the fibre. At a certain resonant wavelength these small reflections build up through constructive interference to provide a large reflection whose magnitude is determined by the length of the grating and the size of the refractive index change.
For a periodic grating with an arbitrary index profile this resonance occurs where the grating period is an integer multiple of half the wavelength, 1~/2, divided by the mean effective index no. In the special case when the index profile is a sequence of discrete jumps, the resonance only arises when the period is an odd multiple of 1~/ (2no) .
At wavelengths around the exact resonance, the reflection has a characteristic "sin (1~) /?~" wavelength response profile of a finite-sized grating. The width of response peak is roughly inversely proportional to the grating length unless the reflectivity is very high. (see W4 93/14424 ~ ~ ~ ~ PCT/GB93/00043 Figures 1(a) and 1(b)). When the peak reflectivity is high then multiple reflections become important and the reflection profile no longer narrows with _ncreasing grating length. Instead the response flattens at around 100% reflectivity near the peak with very strong side lobes in the vicinity of the peak (see Figures 2(a) and 2(b)).
This characteristic profile is very di~ficult to change with conventional design methods. In particular, if the periodic change in effective refractive index is fixed i0 by the material properties, then it is not possible to adjust the width of the wavelength response independently of the peak reflection. Nor is it possible by explicit design to remove she side lobe structure of smaller resonances on either side of the peak (although minor errors in the exact periodicity in the grating will often wash these out in practice).
Requirements have emerged which need reflection profiles that differ qualitatively from known prior art gratings. The first is to obtain a reflection profile that is flat over a comparatively large wavelength range (greater than about lnm wide) but with no side lobe reflections in the immediate neighbourhood of this range.
The peak reflection in this case is not important but it needs to be at least 10%. Such an optical grating could be positioned within an optical fibre network so that the connection with a central control could be checked by monitoring the reflections from an interrogation signal sent from the control centre. The wavelength of the peak reflection would then be used to label the position of the grating and hence the integrity of the network could be checked at several places. A wide reflection is needed because the wavelength of the interrogation laser could not be accurately specified unless very expensive components were used. The side lobes need to be suppressed to prevent ?5 interference between different gratings in the network.
The second requirement is for a high reflection (as close to 100a as possible) in a narrow wavelength region, J
around O.lnm wide, with very low side lobes. This is for use as a wavelength selective mirror for use with a fibre laser to force it to operate in a narrow wavelength region only.
Other applications have been identi~ied for non conventional gratings where the wavelength response of the transmission and reflection properties could be specified.
In particular, distributed Braag reflectors (DBR) and distributed feedback lasers (DFB) appear to be very good i0 candidates for such gratings.
It is a fairly straightforward matter, in principle, to calculate the effect on light travelling in one dimension of a seauence of steps in the effective index seen by this light. In a weakly guiding fibre waveguide 15 both the electric field E and the magnetic field B are perpendicular to the. direction of travel. The reflecti on and transmission coefficients are determined completely by the relation of E and B after passing through the region of index steps to their values before the region.
20 If the light Gasses a distance dz through a region with a constant effective refractive index (i, then tB ~ / cos(xOz) ~x~z) I B
,a psin(xOz) coslxAz) or I BJe= =M(~il,x~zt~.~B~o where x is the effective wavenumber, 2n~3/~, and E
\B/ezi denotes the values of the electric and magnetic fields after a distance 0z.. Hence if the light passes a distance 0z, through a region of effective index Vii,, followed by a distance ~z2 through a region of effective index Vii' then E
and B are given by ~B,W..Gz. ~~~Z'1CAZ~). ,~~~I'K~Zt~~~8~0 The effect of a sequence of small steps through the regions of differing refractive index can therefore be calculated from a scattering matrix, given by the product of ail the small step matrices. Note that the matrix coefficients depend on the wavelength ~,. If the final i0 scattering matrix S is given by S1I SI2l \S21 S:2 then the reflection coefficient is given by ~R~Z and the transmission coefficient by ~T~' where no.(st t -szt ) - i.~no'-stz -sz: ~~
R 'no.(stt -s=z~ -i.lno=sl, *s=l~l 2n T. - o ~novsa ' S=z) - i.lno=stz +sm)~
n~ is the refractive index of the substrate and i=(-1)ii2 A Smm long grating With a pitch of say 0. 25~.m would have 20,000 steps and therefore the calculation for the scattering matrix would involve 20, 000 matrix products. If 20 the matrix were to be calculated at say 100 wavelengths in order to resolve the wavelength response of the grating, then the full scattering matrix of the grating would take several million arithmetic operations to calculate. This is therefore not a trivial calculation but one which would 25 pose no difficulty for a reasonably powerful computer.
;9hile the effect of a given sequence of steps in the effective index of the waveguide can easily be calculated, the converse task of designing the sequence to give the required properties to R and T is a different matter entirel:r. The problem lies in the number of calculations that have to be :jade. A crude approach of simply enumerating all the different possibilities, and testing each for its suitability, is out of the question: even if the grating pitch was constant and the changes were restricted to allowing a refractive index step or not, then the total number of ~ossibilities would be around 2~~'~~~ so no amount or computer power would help.
In order to make any kind of optimisation, the orating :zas to be defined ._. ~.erms of some tractable number of aarameters and repeated calculations made of how the :5 grating properties change with these parameters. This basic idea is known. Simple parameters that have been used ar a arati ng pi t ch whi c:~ may, f or exampl e, vary s 1 owl y al ong the grating's length ~o form a chirped grating or gratings -haz :piss out some c~ ~he steps in a regular or smoothly varying fashion. See nor example T Schrans, M Mitteistein and A Yariv "Tunabl a :active Chirped-Corrugation :daveguide Fil ters" Appl led Ph~-sics Letters 55, 212-214 ( I989 ) and D
J Reid and C M Raadale, _ Bennion, D J Robins, ~ Buus and W J Stewart "Phase-Shifted Moire Grating Fibre Resonators..
electronic Letters -c, 10-I2 (1990), respectively.
These known types of optical gratings are not amenable to approaches of computation that give enough degrees of freedom of device characterisation necessary to achieve the sort of wavelength response that are needed for many applications, for example as identified earlier in this application.
According to a Lirst aspect of the present invention an optical grating including a sequence of grating lines, the sequence being characterised in that:
a) each grating line is centred on a position which is an integer multiple of a line spacing distance from a datum position on the orating;
b) the sequence of grating lines is non-periodic;
and c) the sequence of grating lines is formed from a multiplicity of N concatenated subsequences, each subsequence comprising a series of one or more instances of a respective grating line pattern.
The present invention provides an optical grating having a structure that is more amenable to calculation of the grating lines necessary to achieve a desired effect as will be explained in more detail below. It is preferable that N=21~, where M i s a whol a number, al though a grati ng may comprise two or more such sequences with some decrease .n e~~iciency o~ calculation.
The number of subsequences can in effect be reduced by incorporating a number of null sections of zero length.
For example, in a preferred embodiment of the present invention, if two adjacent subsequences are found during calculation to be formed from the same grating line pattern they are combined into one larger subsequence for 'uture calculation, the number of subsequences being restored by insertion of a null subsequence.
The substrate may be an optical waveguide such as an optical fibre having a D-shaped cross-section. Other s ubs trates may be us ed as wi th known opti cal grab ngs .
The grating lines may be grooves in the substrate, for example, the grooves having a rectangular cross-section or having triangular cross-sections, for example. The grating lines may be also be defined by refractive index variations in a substrate or other medium.
The grating sequence is formed from a multiplicity of subsequences of the type described above in order to give the flexibility of design while allowing tractable calculation of the optical characteristics of a grating.
The sequence of grating lines is non-periodic so as to allow for non-periodic phase shifts between the grating lines which are necessary to achieve reflection profiles which are qualitatively different to those that can be achieved by conventional gratings. Thus use of a non periodic sequence of grating lines gives flexibility in the design process, while use of subsequences ensures that the design process remains tractable as will be explained bel ow.
Such considerations are of utmost importance in a design problem of this size as any optimisation method will involve repeated calculations of the total scattering matrix with different parameter values to see which one is the best.
The main consideration in the design algorithm is therefore concerned with providing an efficient method of calculating the total scattering matrix of a grating as efficiently as possible. As will be seen, the structure of grating according to the present invention allows such efficient calculation of the scattering matrix.
The design process of a grating according to the present invention involves determining the values of the parameters of the subsequences, ie the grating line pattern and the number of instances of each pattern in a given s ubs ea_uence, to obtai n des i red properti es i n the res ul rant optical grating. To do this it is necessary to change these parameters one or a few at a time, and compare the new calculated properties of the grating with the old ones to see if there has been any movement towards the desired characteristics.
Because the sequence of grating lines of the optical grating is made up of subsequences as described above it is possible to calculate the total scattering matrix of an optical grating more rapidly than if it was necessary to calculate all the properties of the grating from scratch.
Because the grating is split up into a number of sections N, where N is an exact power of 2, N=2M, then it can be shown that the effect of change in the grating in one of the sections can be calculated in log2(N) matrix multiplies rather than the N multiplies needed in a cruder algorithm which directly calculates the entire new matrix.
According to a second aspect of the present invention a method of fabricating an optical grating comprises the steps oz:
calculating the response of an optical grating including a sequence of grating lines, the grating lines being such that:
each grating line is centred on a position which is an integer multiple of a line spacing distance from a datum position on the grating;
the sequence of grating lines is non-periodic; and the sequence of grating lines is formed from N
concatenated subsequences, each subsequence comprising a series of one or more instances of a respective grating line pattern; and subsequently repeatedly altering a subsequence of the grating deciding whether to accept the alteration of the subsequence until some predetermined criterion is achieved;
and on achieving the predetermined criterion; forming the resultant optical grating sequence on a substrate.
The method preferably includes the additional prior steps of:
selecting a set of grating line patterns; and calculating the scattering matri:c of each member of a set of grating patterns.
The subsequence is preferably altered by either substituting the respective grating line pattern for a different grating line pattern from the set of grating line patterns or changing the number of instances of the grating line pattern in the subsequence. Other operations to change subsequences can be used; the grating line patterns of two subsequences may be interchanged, for example.
The decision whether to accept an alteration to one of the subsequences is preferably determined by an annealing algorithm. In particular an alteration to a subsequence is accepted if the change in a measure of fit of the grating profile to a desired profile is such that exp[-~8v~/TJ is less than a random number generated in the range 0 to 1 for some value of T and where v is a predetermined measure of the performance of the grating.
T preferably is monotonicaliy decreased between alterations to the sequence of grating lines.
It should be noted that the grating line patterns may include a null grating pattern of zero length.
In addition to requirements for optical gratings which have reflection profiles that differ qualitatively from known prior art gratings, as discussed above, there have emerged further requirements for gratings whose characteristic profile can be altered in use. For example, there is a requirement in wavelength division multiplexed ortical communications systems for both tunable lasers and tunable filters. Such a tunable laser can be achieved in a known manner by providing means for controlling the refractive index of the grating in a DBR or DFB laser. It will be understood that changing the refractive index of a grating means uniformly changing the refractive index across the whole of the grating, or a substantial part thereof, and does no~ affect the relative index variation which actually cons tituents the grating itself i. e. the small steps in refractive index whici~. form the grating lines.
The alteration of the characteristic profile of a grati ng can be achieved for example, i n a grating formed in a semiconductor material, by providing an electrical contact adj acent the grating for inj ecting current into the grating region so as to alter the refractive index of the material in which the grating is formed. A alternative method of altering the characteristic profile of a grating is to physically al ter the structure of the grating or a part thereof by for example employing piezo-electric transducers to stress or stretch the grating.
It has been found that the structure of a grating according to the present invention in addition being more amenable to calculation of a particular desired fixed characteristic pro=ile, is also more amenable to WO 93/14424 ~ ~ ~ PCT/GB93/00043 - lp -calculation of a characteristic profile which can be varied in a desired manner during use of the grating.
Thus the present invention also provides a grating in which a plurality of sub-uni is of the grating, each sub s unit formed from a plurality of subsequences, are separately addressable by means for altering a parameter of each grating sub-unit.
The multiplicity of sub-sequences from which the grating is formed again give flexibility in the design of, in this case, a variable characteristic profile of the grating, while at the same time enabling the calculation of the ~rofile to be tractable.
The design process required for such a grating, having a characteristic profile which can be varied in use, can be regarded as an extension of the design process for a grating having a fixed characteristic profile. The ability to vary a parameter, 'or example the refractive index, of a pi urali ty of s ub-~~nits o f the grati ng gi ves an extra degree of freedom is the design process so that any optimisation of the orating design must effectively be two dimensional, eg the physical structure of the grating sequence comprising ~!~e positioning of the grating lines must be optimised in conjunction with the choice of refractive indices =or each of the grating sub-units, as will be explained below.
The use of such a design process allows a grating to be designed which has for example four separately addressable sub-units whose refractive may be varied in use so as to provide a reflection profile which is tunable over a wider range of wavelengths than a conventional periodic grati ng.
The present invention will now be described, by way of example only, with =eference to the accompanying drawings in which:
~5 Figures 1(a) and 1(b) are graphs of the grating responses of prior art optical gratings having grating lines with a flat-triangle section groove;
- - L i -Figures 2(a) and 2(b) are graphs of the grating responses of prior art optical grati ngs having high peak reflectivity;
Fi gure _ i s a s chemati c bl ock di agram of an opti cal .. grating according to the present invention;
Figure 4 is a diagram of a set of grating line patterns suitable for optical gratings that are to be etched on an optical fibre waveguide;
Figure 5 is a diagram of a grating line patterns i0 suitable for an optical grating for a DFB/DBR laser grati ng;
Figure 6 is a representation of a grating according to the nres ent ~. nven ti on;
Figure 7 is a key to the representation of the grating '_ 5 s hown i n F i gure 5 s howl ng the grati ng 1 i ne pat terns employed;
Figure 8 is a graph cf the theoretical response of the optical grating of Figure 6;
Figure 9 is a graph of the measured response of the 20 optical grating of Figure 6; and Figure 10 is a scanning electron micrograph of a portion of the grating of Figure 6 at a transition between two subsequences;
Figure 11 shows ~ grating in 4 sub-units, the 25 refractive index n of each sub-unit may be varied by current injected via an electrode;
Figure 12 is a schematic flow diagram showing the stages of the method of designing a grating having a variable reflection response;
30 Figure 13 is a schematic diagram, similar to that shown ;n Figure , showing the sequence of scattering matrix calculations required when the refractive index of a grating sub-unit is changed; and Figure 14 a) and b) show the four theoretical 35 reflection responses from a single grating having four sub units of variable refractive index.
Figures 1(a), 1(b), 2(a) and 2(b) have already been di s cus s ed.
Referring to Figure 3 an optical grating 2 according to the present invention. is shown schematically to show its overall subsequence structure. The grating 2 is a sequence of grating lines formed, in ;.his particular =nstance, by a (=23) subsectuences =i, 6, 3, 10, i2, '4, 16 and 18. Each of the subseQUences is formed from a series of one or more instances of a respective grating line pattern. The particular grating 1 i ne pattern and the number of instances .0 of it in a particular subsequence will in general vary from one subsequence to another.
F figures 4 and 5 show sets of grating line patterns useful for subsequences 'or an optical fibre grating and DFB/DBR laser grating, respectively.
15 ~ typical set of grating line patterns comprising grooves 34 having a rectangular cross-section used for optical D-fibre grating designs for fabrication on a silica subst=ate are shown in Figure 4. This is an exemplary set of grating line utter.~.s - other sets could be chosen 20 instead. For a DBRiDFB laser grating which is written on an _nP substrate, the fabrication processes force a different type of grating line patterns to be chosen, eg ~rlangular cross-section grooves 35. On these substrates ;.. is very difricult to cut vertical walls, so discreet 25 steps in the refractive index profile cannot be easily achieved. The typical groove has a triangular cross-section, in this case with etch angles of around 55~, an exemplary set being shown in Figure 5.
Referring once again to Figure 3, the optical effect 30 of the subsequences 4 to 18 of the grating is calculated as follows. The scattering matrix for each grating line pattern is calculated beforehand in a known manner as described earlier. The scattering matrix for a given subseQUence ~, 6, 8, :0, 12, 14, 16 and 18 can then be calculated 'S by raising the appropriate grating line pattern scattering matrix to a power equal to the number of instances of that pattern in a subsequence. This is carried out for all the ,.~ ~ ~, ~ s z ~ ~~ ' 3 subseauences 4 to 18 of the grating line sequence.
The scattering matrices for consecutive pairs of the subseauences are then calculated by forming the product of the scattering matrices of the subsequences. These ., products form the second level scattering matrices 20, 22, 24 and 20 of the grating.
~n a similar fashion the level 2 scattering matrices are wired and the level 1 scattering matrices 28 and 30 are calculated. The two, 1 evel 1 scattering matrices 28 and 30 are ~inall~ combined to form the full, level 0 scattering matrix 32.
~f one of the level 3 subsequences is chanced during application of an Opti.~,:lZatlon algorithm, for example subsequence 12, then to calculate the new full grating scattering matrix one calculates the matrix product of subseauences 12 and ,'_.~ to form a new level 2 matrix, 24, which'is then multiplied with the existing level 2 matrix, 26, to form a new ~ evel y matrix number 30. This fi nally is multiplied with the other existing level 1 matrix 28 to form the full scatt~rina matrix 32 for this new sequence of aratina lines.
Referring now to :figure c, there is shown a tarticular optical grati.~.a calculated according to the method of the tresent invention comprising ten grating line patterns as 2~ shown by the key at Figure 7 and the theoretical response is shown at Figure o.
The basic pitch of the grating line patterns of Figure 7 are about 0. 5~m with a single smallest feature (one line) of about 0.25~m. The word patterns consist of 4 bits, each word being about lam long. The total length of the crating of Figure 6 is about 4mm with 64 subsequences including any null subsequences that may have been introduced when adj acent subsequences of the same grating line pattern were combined. The patterns were etched into a silica substrate to a depth of about 0. 25~tm.
Figure 9 is a graph of the experimentally measured reflection characteristics of the optical grating of Figure ~1~~~~4 6 after applying the optical fibre waveguide to the surface of a D-fibre optical _ibre waveguide.
The structure of the grating according to the present invention allows efficient calculation of changes to the scattering matrix and so allows efficient implementation of optimisation algorithms. The optimisation algorithm used in the present instance will now be described, by way of example.
The first step was to choose the shape of the desired reflection characteristics of the grating as a function of wavelength, RT(.1) and compare the actual reflection R~(n.) obtained from the grating with the desired one. The measure of the difference between the two was defi:~ed as pz = J~aIRT~z-;RA~~ZdA
where ~ a = J~ ~RT~2. ~Re ~2 dl~/ f ~ ~RT~4dl, a is, in effect, a measure of the scale of the reflection and ~ a measure of the fit to the desired shape. The aim was to minimise p and maximise a. Depending on the particular situation, a global measure v can be ~crmed from a weighted difference of the two numbers to give the parameter to be oat~:.msed ie setting v=( 1-w), a-w. Vii, where w is a weighting parameter between 0 and 1. A larger value of w means that more weight is being attached to the shape of the refraction profile at the possible expense of the total reflectivity.
We then sought to maximise v and used a version of a simulated annealing algorithm to determine the grating line seauence which led to a suitable maximum. In this algorithm a change was made to the grating either by changing one of the work patterns or changing the length or interchanging two of the subsequences. These changes were done sequentially to randomly chosen subsequences, one subsequence being changed or two interchanged before recalculating the response of the grating. Other more complicated changes may be made but at the expense of increased calculation. To simplify the scheme of this embodiment the interchange step may be eliminated.
Using this algorithm we then calculated the change 8v .. in the measure of the grating performance caused by the crrati na al ter ati on. I ~ 8v i ncreas ed, i a the new gra ti ng was "better" than the cld one, then the change to the grating was accepted. T_f 8v was decreased by the alteration to the subsequences, then the chance was only accepted ~_ exp[-IbW /"'; was less than a random number crenerated __. the ~.nterva 1 0 to ' , where T was a parameter that represents a _ictitious temperature.
T_f T was high, then ..~.early all the chances were accented and v wanders around almost randomly. As '?' was i5 decreased then the chances of accepting a change that decreases v gradually reduced and v was forced into a maxi mum.
Such a maximum is very probably a local maximum so there will in general be expected to be many solutions that result in the value of v very close to the best one obtained.
The strategy usually adopted, as here, was to make several independent calculations using different random seeds, and then pick the best orating line sequence that resulted. "_'he measure of the value of a particular grating was to some extent arbitrary and other measures of fitness of fit of crating could be used. In particular, if one is interested in the dispersion properties of a grating then one would use the full complex form of the target response RT (~, ) and the actual reflection RA (~, ) and the definitions of a and ~ rather than their moduii.
The calculated crating sequence was then used to fabricate a grating by forming the grating lines as a sequence of vertically walled, etched steps by electron-beam lithography directly onto a silica substrate. The experimentally measured response of the grating of Figure o i s s hown at Fi gure °.
- to -~'A~,4r ~' Fi gure i 0 s hows a porn on o f the grati ng o f Fi gure 6 at a transition between two subseauence 38 and 40.
The method of fabricating an optical grating according to the present invention has been described in terms of a grating line sequence which is made up of a whole number power of 2 subsequence. This structure obtains the full benefit of the tresent invention. However, it is also possible to obtain the principle benefit of the invention if a grating sequence comprises a small number of concatenated sequences each sequence being as described above. Ir. such a case there will be a small overhead in the calculation as two level 0 scattering matrices will need to be multiplied together. Thus a grating comprising a number of grating sequences each having 2~ subsequence according to the present invention in series can be calculated with slightly less efficiency than a grating having an exact power of two subsequence.
Figure 11 shows a grating whose characteristic profile can be altered in use. The grating is divided into four sub-uni is 41, 42, 43, 44, each of which is separately addressable throug:~ a electrode. Thus the refractive index of each of these sub-units can be controlled between two val ues whi c'.~. ar a gi ven, v n a known manner) by the properties of the semiconductor material used, by applying a voltage to each of the electrodes. The reflection profile of the grating can be switched between a number of different responses by applying different sets of voltages to the sub-units 41-44.
The design process for this grating must therefore specify a grating sequence, formed from sub-sequences of grating line patterns, and must also specify the particular refractive indices for each of t::e sub-units required to achieve switching between the desired characteristic responses.
Thus if four particular responses A, B, C, D are reauired from the grating then the design process must optimise both the grating sequence and the four sets of refractive indices n:, n" n~, n) required to achieve these four responses, so that the grating characteristic is A when { n" ~~, =:~, n, } is { a" a" a;, a, }
B whe n { .~., , a~, ::" n; } i s { b" b_, =c=, b~
}
J C when {n" n~, z" n,} is {cl, c" c"
c~}
D when { n" n~, _~.~, n) } i s { d" d2, d~, d, }
It should be noted that the grating line sequence remains fixed in each case, the only thing that changes is the seQUence of refractive indices. This sequence can be changed by appiyirg different voltages through the inden_ endent elect-odes.
The design method for a grating having a variable reflection characteristic thus differs =rom that for a grating having a fixed reflection characteristic in a number of respects. Firstly there is always a choice during the calculation of the design process of whether to change a grating subseQUence (as for the fixed response grating) or to change the refractive index of a sub-unit of the grating, this is shown schematically in the flow diagram of ~'i gore 1~- If the choice to change a grating subsecruence s made then the scattering mat-ices are recalculated in the same manner as for the fixed response grating as described above. ~F the choice is to chance the refractive index of a grating sub-unit then the recalculation is different as will be described below.
Secondly, a further difference for the variable response grating design method is that a set of scattering matrices corresponding to each of the different sequences (n,-y) of refractive index for the grating sub-units must be ~0 calculated. Thus if four different reflection responses are required from the grating, four sets of scattering matrices required to give the four different reflection coefficients as a function of wavelength, must be calculated.
Thirdly a different measure of fit between the WO 93/14424 .~ ~ ~ :~ ~ - 18 - PCT/GB93/00043 calculated matrices and the target response is required, since the target response is in fact a number of responses, each corresponding to one of the sequences of =efractive indices of the grating sub-units.
Referring to Figure 12 each of the stages of the design method will now be described in more detail, for a grating having s sub-units which is required to give R
different reflection characteristics.
The initialisation stage comprises:-i0 initialising the orating line patterns and R-refractive index seauences in the s sub-units (These could either be random seauences or values read in from a trey=ous cai cul ati or. j and;
pre-c: alculating the scattering matrices for each of :5 the grating line patterns at each of the allowed values of refractive indices.
The selection stage 46 comprises choosing at random a grating subsequence or a refractive index sub-unit in one of the switchable sequences (typically with the subsequence 20 being slightly more likely to be chosen?. Cycling the subseauence or =ndex value through all the possible choices, until either a change is accepted or all the possibilities are exhausted, and then choosing another subseauence or index sub-unit to change.
25 If a grating subsequence is chosen to be changed then the recalculation stage 47 is the same as for the fixed res pons a grab ng des i an method, i . e. onl y thos a matri ces i n the structure shown in Figure 3 which are affected by the change are recalculated. However as mentioned above, the 30 matrices need to be calculated N-times i.e. once for each of the N-target wavelength responses - corresponding to the N-switchable refractive index sequences of R-refractive index sections.
If a sub-unit refractive index is chosen to be changed 35 then the recalculating stage 48 must take account of the change in index affecting all the levels in Figure 3 below the level at which the index is changed. This is shown in ~~2Q~~~.
WO 93/14424 - 1 g - PCT/GB93/00043 Fi gure 13.
A change to the refractive index value of the sub-unit labelled 1 in level 4 of Figure 13 means that it is necessary to replace all of the scattering matrices affected at level 5 (numbers 8-15). Following this it is necessary to recalculate the matrices (4-7) at level (4) by pairwise multiplication in level (5), recalculate the matrices (2 & 3) at level (3) by 1 0 pairwise mui tiplication iz level ( 4 ), recalculate the matrix 1 at level 2 by multiplication of matrices 2 & 3 in level ( 3 ), Multiply the old matrix 0 wi t'.~. the new matri :c i to give a new matrix 0 at level (i).
Multiply the new matrix 0 with the old matrix 1 to give the new scattering matrix.
Thus 4+2+1+2=9=((32/4-1) + iog~(4) matrix operations are needed to update the scattering matrix as opposed to 31 with a more conventional algorithm.
In contrast to the calculation for a grating subsequence change, these matrices need only to be calculated once - as, in a refractive index change only one section (out of he R available) ,~n one refractive index sequence (of the M-available) is change at a time. The remaining matrices corresponding to the (N-1) sequences that were not changed at this point, are unaltered.
Having made a change, either of grating subsequence or of sub-unit index the next stage 48 is to decide whether to accept this change. This will depend on whether the change gives a better fit to the N-desired or target responses, hence the measure of difference used previously for the fixed grating response design method is modified to account for the R different refractive index sequences for the s s ub-uni is of the grati ng. Thus i N ( f (a ~~, (~'t) 12 ~ItA(~,t7 I2)Z d~) 'S
1 ~N (J ~~. ('~,t) ~z~ ~R.,(.l,c~ ~Zdl where a =
1 ~N ( J~~RT (~,y j'd~
the extra suffix, "i"' denotes the coefficients corresponding to the i' th refractive index sequence.
'~'he final measure of fit is formed from these two quanti ties: V - ( =-w) . a-w. ~ where w is a weighting parameter.
V is then used _n an optimisation or annealing algoritzm in prec~seiy t~!e same way as previously described in order to decide whether to accept the change (in grating subsequence or sub-unit index) or not.
If the change is accepted the current grating sequence and refractive index sequences are saved and the iteration is repeated by again choosing a grating sub-sequence or sub-unit index ~o change. Once a certain number of i5 iterations or a predetermined measure of fit has been reached the design process is stopped.
~_'he result of the design process is one sequence of gratira lines and R sequences of refractive indices for the s sub-units.
Figure 14 a) and b) show the four different theoretical reflection responses of a grating having s=4 (and T=4). Each response corresponds to a particular seauence of refractive index values for the grating sub-units. It can be seen that the reflection responses are separated by 4nm giving a total tuning range of l2nm. Fine tuning to give a reflection response intermediate between any of the four shown is achieved by altering the refractive index of all four sub-units uniformly, while tuning between eac:~ of the responses shown is achieved by switching from one of the sub-unit refractive index seauences determined by the design method to another such WO 93/14424 ~ ~~ ~ ~ ~' ~ ~ PCT/GB93/00043 s ecruence.
If the maximum index change utilised in the design of the grating of Figure 14 were applied to a conventional grating a tuning range of only 3-4nm would result, t?~.us the design achieves a significantly larger tuning range.
Although the design method for a grating having a variable reflection response has been described for gratings in which the response is changed by a change of refractive index, i t will be apparent to the skilled man, that, in the method, refractive index can be replaced by any other parameter which will affect the reflection response of the arati.~.g, ror example the local stressing or stretching of a sub-unit of the grating.
Claims (30)
1. An optical grating including a sequence of grating lines, wherein the separation of any two adjacent lines of the sequence is an integer multiple of the smallest separation between adjacent lines occurring in the sequence and the separation of adjacent lines varies irregularly along the grating.
2. A grating as claimed in claim 1 in which the grating lines are defined by refractive index variations in a substrate.
3. A grating as claimed in claim 2 in which the substrate is an optical waveguide.
4. A grating as claimed in claim 3 in which the optical waveguide is an optical fibre having a D-shaped cross-section.
5. A grating as claimed in claim 4 in which the grating lines are walls of grooves in the substrate.
6. A grating as claimed in claim 5 in which the grooves have a rectangular cross-section.
7. A grating as claimed in claim 5 in which the grooves have triangular cross-sections.
8. A grating as claimed in claim 1, including control elements arranged for separately varying a parameter of discrete portions of the grating.
9. A grating as claimed in claim 8 in which said parameter is refractive index.
10. A grating as claimed in claim 8 in which said parameter is physical length.
11. A grating as claimed in claim 8 in which the control elements comprise electrodes.
12. A laser including a distributed feedback element which comprises an optical grating including a sequence of grating lines, wherein the separation of any two adjacent lines of the sequence is an integer multiple of the smallest separation between adjacent lines occurring in the sequence and the separation of adjacent lines varies irregularly along the grating.
13. A laser as claimed in claim 12 in which the lines are defined by refractive index variations in a substrate.
14. A laser as claimed in claim 13 in which the substrate is an optical waveguide.
15. A laser as claimed in claim 14 in which the optical waveguide is an optical fibre having a D-shaped cross-section
16. A laser as claimed in claim 13 in which the grating lines are walls of grooves in a substrate.
17. A laser as claimed in claim 16 in which the grooves have a rectangular cross-section.
18. A laser as claimed in claim 16 in which the grooves have a triangular cross-section.
19. A laser as claimed in claim 12 including control elements arranged for separately ~arying a parameter of discrete portions of the grating.
20. A laser as claimed in claim 19 in which said parameter is refractive index.
21. A laser as claimed in claim 19 in which said parameter is physical length.
22. A laser as claimed in claim 19 in which the control elements comprise electrodes.
23. A laser as claimed in claim 12, including a semiconductor laser active structure.
24. A method of fabricating an optical fibre grating comprising the steps of:
(a) storing a mathematical model of each of a plurality of different grating pattern elements;
(b) selecting a plurality of said models and calculating the grating response for a sequence, comprising the grating pattern elements represented by the selected models, from the selected models;
(c) comparing the calculated grating response with a target response and deriving a measure of the fit therebetween; and (d) forming a grating as claimed in said sequence in a substrate, wherein steps (b) and (c) are repeated until said fit conforms to a predetermined criterion before step (d) is performed.
(a) storing a mathematical model of each of a plurality of different grating pattern elements;
(b) selecting a plurality of said models and calculating the grating response for a sequence, comprising the grating pattern elements represented by the selected models, from the selected models;
(c) comparing the calculated grating response with a target response and deriving a measure of the fit therebetween; and (d) forming a grating as claimed in said sequence in a substrate, wherein steps (b) and (c) are repeated until said fit conforms to a predetermined criterion before step (d) is performed.
25. A method as claimed in claim 24 in which the second and subsequent performance of step (b) has an effect equivalent to an action selected from: replacing one pattern only, changing the number of contiguous repetitions of a pattern element and interchanging two runs of pattern elements.
26. A method as claimed in claim 24 in which calculating the grating response includes deriving a mathematical model of a subsequence comprising pattern elements and storing the subsequence mathematical model for use in subsequent performances of step (b) where said sequence includes said subsequence.
27. A method as claimed in claim 24 in which a change in the modelled sequence is retained if the resulting change in said measure of fit is such that exp(-¦.delta.v¦/T) is less than a random number generated in the range 0 to 1 for some value of T, where, T is a parameter representing a theoretical temperature and v is a predetermined measure of the calculated performance of the sequence.
28. A method as claimed in claim 27 in which T is decreased monotonically for each performance of step (b).
29. A method as claimed in claim 28 in which the measure of fit v=(1-w).alpha.-w.beta., where w is a weighting parameter between 0 and 1, R T is the desired reflection characteristic of the grating, R A is the actual reflection characteristic of the grating and .lambda. is a variable representing the wavelength of light.
30. A method as claimed in claim 28 in which the measure of fit v=(1-w).alpha.-w.beta., where w is a weighting parameter between 0 and 1, R T is the desired reflection characteristic of the grating, R A is the actual reflection characteristic of the grating, .lambda. is a variable representing the wavelength of light and i=~.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| GB929200616A GB9200616D0 (en) | 1992-01-10 | 1992-01-10 | An optical grating and a method of fabricating an optical grating |
| GB9200616.2 | 1992-01-10 | ||
| PCT/GB1993/000043 WO1993014424A1 (en) | 1992-01-10 | 1993-01-11 | An optical grating and a method of fabricating an optical grating |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2120624A1 CA2120624A1 (en) | 1993-07-22 |
| CA2120624C true CA2120624C (en) | 1999-10-12 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002120624A Expired - Fee Related CA2120624C (en) | 1992-01-10 | 1993-01-11 | An optical grating and a method of fabricating an optical grating |
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| Country | Link |
|---|---|
| US (2) | US5666224A (en) |
| EP (1) | EP0620924B1 (en) |
| JP (1) | JPH07502837A (en) |
| AU (1) | AU659528B2 (en) |
| CA (1) | CA2120624C (en) |
| DE (1) | DE69324236T2 (en) |
| GB (1) | GB9200616D0 (en) |
| WO (1) | WO1993014424A1 (en) |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US6819460B1 (en) * | 1995-03-13 | 2004-11-16 | University Of Washington | Apparatus and methods for routing of optical beams via time-domain spatial-spectral filtering |
| GB9722421D0 (en) | 1997-10-24 | 1997-12-24 | Univ Southampton | Optical grating |
| GB9722549D0 (en) * | 1997-10-24 | 1997-12-24 | Univ Southampton | Fabricating optical waveguide gratings and/or characterising optical waveguides |
| US6101301A (en) * | 1998-04-17 | 2000-08-08 | Lucent Technologies Inc. | Temperature-compensated optical fiber gratings with fine wavelength tuning |
| GB2385943B (en) * | 1999-03-05 | 2003-11-05 | Nanovis Llc | Mach-Zehnder interferometer with aperiodic grating |
| US6993222B2 (en) | 1999-03-05 | 2006-01-31 | Rj Mears, Llc | Optical filter device with aperiodically arranged grating elements |
| GB9905196D0 (en) * | 1999-03-05 | 1999-04-28 | Fujitsu Telecommunications Eur | Aperiodic gratings |
| KR100318903B1 (en) * | 2000-01-14 | 2001-12-29 | 윤종용 | Long period optical fiber grating |
| US6603904B1 (en) | 2001-03-28 | 2003-08-05 | Jaffalight Holdings Llc | All optical narrow pulse generator and switch for dense time division multiplexing and code division multiplexing |
| US6608690B2 (en) * | 2001-12-04 | 2003-08-19 | Timbre Technologies, Inc. | Optical profilometry of additional-material deviations in a periodic grating |
| US8043287B2 (en) * | 2002-03-05 | 2011-10-25 | Kimberly-Clark Inc. | Method of treating biological tissue |
| AUPS104402A0 (en) * | 2002-03-12 | 2002-04-11 | Redfern Optical Components Pty Ltd | Multi-layered structure characterisation |
| US7101226B1 (en) * | 2005-06-08 | 2006-09-05 | Wave Intellectual Property, Inc. | Compact contour electrical converter package |
| US9261632B2 (en) * | 2010-01-05 | 2016-02-16 | Hewlett Packard Enterprise Development Lp | Light emitting diode device |
| US8369664B2 (en) * | 2010-07-30 | 2013-02-05 | Hewlett-Packard Development Company, L.P. | Optical apparatus for forming a tunable cavity |
| US8452141B2 (en) * | 2010-07-30 | 2013-05-28 | Hewlett-Packard Development Company, L.P. | Optical waveguide coupling device and associated methods |
| FI128882B (en) * | 2017-12-22 | 2021-02-15 | Dispelix Oy | Optical waveguide and diffractive waveguide display |
| CN115185036B (en) * | 2022-07-18 | 2024-03-01 | 江苏师范大学 | Hollow fiber grating based on gas paramagnetic effect and implementation method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3814498A (en) * | 1972-05-04 | 1974-06-04 | Bell Telephone Labor Inc | Integrated optical circuit devices employing optical gratings |
| US4155056A (en) * | 1977-08-25 | 1979-05-15 | Bell Telephone Laboratories, Incorporated | Cascaded grating resonator filters with external input-output couplers |
| US4687286A (en) * | 1985-05-03 | 1987-08-18 | Gte Laboratories Incorporated | Methods of and apparatus for optical spatial scanning |
| US4740987A (en) * | 1986-06-30 | 1988-04-26 | American Telephone And Telegraph Company, At&T Bell Laboratories | Distributed-feedback laser having enhanced mode selectivity |
| JP2825508B2 (en) * | 1987-10-09 | 1998-11-18 | 株式会社日立製作所 | Semiconductor laser device and optical communication system |
| US4885752A (en) | 1988-03-28 | 1989-12-05 | Hughes Aircraft Company | Crystal modulated laser with improved resonator |
| DE3915625A1 (en) * | 1989-05-12 | 1990-11-15 | Standard Elektrik Lorenz Ag | SEMICONDUCTOR LASER |
| JP2966485B2 (en) * | 1989-07-15 | 1999-10-25 | 富士通株式会社 | Tunable coherent light source and method of manufacturing the same |
| JPH03251826A (en) * | 1990-01-25 | 1991-11-11 | Oki Electric Ind Co Ltd | Second harmonic generating element |
| US5048909A (en) * | 1990-07-27 | 1991-09-17 | At&T Bell Laboratories | Adiabatic reflection apparatus |
| US5113286A (en) * | 1990-09-27 | 1992-05-12 | At&T Bell Laboratories | Diffraction grating apparatus and method of forming a surface relief pattern in diffraction grating apparatus |
| US5091916A (en) * | 1990-09-28 | 1992-02-25 | At&T Bell Laboratories | Distributed reflector laser having improved side mode suppression |
| US5202775A (en) * | 1991-11-04 | 1993-04-13 | University Of North Carolina | Radically symmetric hologram and method of fabricating the same |
-
1992
- 1992-01-10 GB GB929200616A patent/GB9200616D0/en active Pending
-
1993
- 1993-01-11 AU AU32633/93A patent/AU659528B2/en not_active Ceased
- 1993-01-11 DE DE69324236T patent/DE69324236T2/en not_active Expired - Fee Related
- 1993-01-11 US US08/244,873 patent/US5666224A/en not_active Expired - Lifetime
- 1993-01-11 CA CA002120624A patent/CA2120624C/en not_active Expired - Fee Related
- 1993-01-11 WO PCT/GB1993/000043 patent/WO1993014424A1/en active IP Right Grant
- 1993-01-11 JP JP5512254A patent/JPH07502837A/en active Pending
- 1993-01-11 EP EP93901823A patent/EP0620924B1/en not_active Expired - Lifetime
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1997
- 1997-01-08 US US08/780,681 patent/US6172811B1/en not_active Expired - Lifetime
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| Publication number | Publication date |
|---|---|
| DE69324236D1 (en) | 1999-05-06 |
| AU659528B2 (en) | 1995-05-18 |
| GB9200616D0 (en) | 1992-03-11 |
| EP0620924B1 (en) | 1999-03-31 |
| CA2120624A1 (en) | 1993-07-22 |
| AU3263393A (en) | 1993-08-03 |
| US6172811B1 (en) | 2001-01-09 |
| US5666224A (en) | 1997-09-09 |
| JPH07502837A (en) | 1995-03-23 |
| WO1993014424A1 (en) | 1993-07-22 |
| EP0620924A1 (en) | 1994-10-26 |
| DE69324236T2 (en) | 1999-07-29 |
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