US 20050008044 A1
A laser utilizes a cavity design which allows the stable generation of high peak power pulses from mode-locked multi-mode fiber lasers, greatly extending the peak power limits of conventional mode-locked single-mode fiber lasers. Mode-locking may be induced by insertion of a saturable absorber into the cavity and by inserting one or more mode-filters to ensure the oscillation of the fundamental mode in the multi-mode fiber. The probability of damage of the absorber may be minimized by the insertion of an additional semiconductor optical power limiter into the cavity. To amplify and compress optical pulses in a multi-mode (MM) optical fiber, a single-mode is launched into the MM fiber by matching the modal profile of the fundamental mode of the MM fiber with a diffraction-limited optical mode at the launch end, The fundamental mode is preserved in the MM fiber by minimizing mode-coupling by using relatively short lengths of step-index MM fibers with a few hundred modes and by minimizing fiber perturbations. Doping is confined to the center of the fiber core to preferentially amplify the fundamental mode, to reduce amplified spontaneous emission and to allow gain-guiding of the fundamental mode. Gain-guiding allows for the design of systems with length-dependent and power-dependent diameters of the fundamental mode. To allow pumping with high-power laser diodes, a double-clad amplifier structure is employed. For applications in nonlinear pulse-compression, self phase modulation and dispersion in the optical fibers can be exploited. High-power optical pulses may be linearly compressed using bulk optics dispersive delay lines or by chirped fiber Bragg gratings written directly into the SM or MM optical fiber. High-power cw lasers operating in a single near-diffraction-limited mode may be constructed from MM fibers by incorporating effective mode-filters into the laser cavity. Regenerative fiber amplifiers may be constructed from MM fibers by careful control of the recirculating mode. Higher-power Q-switched fiber lasers may be constructed by exploiting the large energy stored in MM fiber amplifiers.
59. A multi-mode fiber amplifier system providing discrimination between a fundamental mode and undesired higher-order modes, said amplifier system comprising:
a light source for producing a light beam, and
a linear multi-mode fiber amplifier for receiving said light beam and comprising a multi-mode doped optical fiber having a V-number equal to or higher than 2.41 with respect to an input signal, capable of supporting a fundamental mode and higher-order modes, having a radius of curvature such that the higher-order modes of said input signal experience substantially increased bend losses as compared with the fundamental mode of said input signal.
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68. A linear multi-mode fiber amplifier comprising:
a cylindrical support member, and
a doped multi-mode optical fiber having a V-number equal to or higher than 2.4 with respect to an input signal, capable of supporting a fundamental mode and a plurality of higher-order modes, said fiber being wound onto said support with a radius such that said higher-order modes of said input signal experience substantially increased bend loss as compared with the fundamental mode of said input signal.
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This application is a continuation application of U.S. application Ser. No. 10/424,220 filed Apr. 25, 2003, which is a continuation application of U.S. application Ser. No. 09/785,944 filed Feb. 16, 2001, which is a continuation application of U.S. application Ser. No. 09/199,728 filed Nov. 25, 1998, now U.S. Pat. No. 6,275,512 issued Aug. 14, 2001.
The present invention relates to the amplification of single mode light pulses in multi-mode fiber amplifiers, and more particularly to the use of multi-mode amplifying fibers to increase peak pulse power in a mode-locked laser pulse source used for generating ultra-short optical pulses.
The present invention relates to the use of multi-mode fibers for amplification of laser light in a single-mode amplifier system.
1. Background Relating to Optical Amplifiers
Single-mode rare-earth-doped optical fiber amplifiers have been widely used for over a decade to provide diffraction-limited optical amplification of optical pulses. Because single mode fiber amplifiers generate very low noise levels, do not induce modal dispersion, and are compatible with single mode fiber optic transmission lines, they have been used almost exclusively in telecommunication applications.
The amplification of high peak-power pulses in a diffraction-limited optical beam in single-mode optical fiber amplifiers is generally limited by the small fiber core size that needs to be employed to ensure single-mode operation of the fiber. In general the onset of nonlinearities such as self-phase modulation lead to severe pulse distortions once the integral of the power level present inside the fiber with the propagation length exceeds a certain limiting value. For a constant peak power P inside the fiber, the tolerable amount of self-phase modulation Φnl is given by
As an alternative to single-mode amplifiers, amplification in multi-mode optical fibers has been considered. However, in general, amplification experiments in multi-mode optical fibers have led to non-diffraction-limited outputs as well as unacceptable pulse broadening due to modal dispersion, since the launch conditions into the multi-mode optical fiber and mode-coupling in the multi-mode fiber have not been controlled.
Amplified spontaneous emission in a multi-mode fiber has been reduced by selectively exciting active ions close to the center of the fiber core or by confining the active ions to the center of the fiber core. U.S. Pat. No. 5,187,759, hereby incorporated herein by reference. Since the overlap of the low-order modes in a multi-mode optical fiber is highest with the active ions close to the center of the fiber core, any amplified spontaneous emission will then also be predominantly generated in low-order modes of the multi-mode fiber. As a result, the total amount of amplified spontaneous emission can be reduced in the multi-mode fiber, since no amplified spontaneous emission is generated in high-order modes.
As an alternative for obtaining high-power pulses, chirped pulse amplification with chirped fiber Bragg gratings has been employed. One of the limitations of this technique is the relative complexity of the set-up.
More recently, the amplification of pulses to peak powers higher than 10 KW has been achieved in multi-mode fiber amplifiers. See U.S. Pat. No. 5,818,630, entitled Single-Mode Amplifiers and Compressors Based on Multi-Mode Fibers, assigned to the assignee of the present invention, and hereby incorporated herein by reference. As described therein, the peak power limit inherent in single-mode optical fiber amplifiers is avoided by employing the increased area occupied by the fundamental mode within multi-mode fibers. This increased area permits an increase in the energy storage potential of the optical fiber amplifier, allowing higher pulse energies before the onset of undesirable nonlinearities and gain saturation. To accomplish this, that application describes the advantages of concentration of the gain medium in the center of the multi-mode fiber so that the fundamental mode is preferentially amplified. This gain-confinement is utilized to stabilize the fundamental mode in a fiber with a large cross section by gain guiding.
Additionally, that reference describes the writing of chirped fiber Bragg gratings onto multi-mode fibers with reduced mode-coupling to increase the power limits for linear pulse compression of high-power optical pulses. In that system, double-clad multi-mode fiber amplifiers are pumped with relatively large-area high-power semiconductor lasers. Further, the fundamental mode in the multi-mode fibers is excited by employing efficient mode-filters. By further using multi-mode fibers with low mode-coupling, the propagation of the fundamental mode in multi-mode amplifiers over lengths of several meters can be ensured, allowing the amplification of high-power optical pulses in doped multi-mode fiber amplifiers with core diameters of several tens of microns, while still providing a diffraction limited output beam. That system additionally employed cladding pumping by broad area diode array lasers to conveniently excite multi-mode fiber amplifiers.
2. Background Relating to Mode-Locked Lasers
Both actively mode-locked lasers and passively mode-locked lasers are well known in the laser art. For example, compact mode-locked lasers have been formed as ultra-short pulse sources using single-mode rare-earth-doped fibers. One particularly useful fiber pulse source is based on Kerr-type passive mode-locking. Such pulse sources have been assembled using widely available standard fiber components to provide pulses at the bandwidth limit of rare-earth fiber lasers with GigaHertz repetition rates.
Semiconductor saturable absorbers have recently found applications in the field of passively mode-locked, ultrashort pulse lasers. These devices are attractive since they are compact, inexpensive, and can be tailored to a wide range of laser wavelengths and pulsewidths. Quantum well and bulk semiconductor saturable absorbers have also been used to mode-lock color center lasers
A saturable absorber has an intensity-dependent loss l. The single pass loss of a signal of intensity I through a saturable absorber of thickness d may be expressed as
Because the loss of a saturable absorber is intensity dependent, the pulse width of the laser pulses is shortened as they pass through the saturable absorber. How rapidly the pulse width of the laser pulses is shortened is proportional to |dq0/dI|, in which q0 is the nonlinear loss:
For a saturable absorber to function satisfactorily as a mode-locking element, it should have a lifetime (i.e., the lifetime of the upper state of the absorbing species), insertion loss l(I=0), and nonlinear loss q0 appropriate to the laser. Ideally, the insertion loss should be low to enhance the laser's efficiency, whereas the lifetime and the nonlinear loss q0 should permit self-starting and stable cw mode-locking. The saturable absorber's characteristics, as well as laser cavity parameters such as output coupling fraction, residual loss, and lifetime of the gain medium, all play a role in the evolution of a laser from startup to mode-locking.
As with single-mode fiber amplifiers, the peak-power of pulses from mode-locked single-mode lasers has been limited by the small fiber core size that has been employed to ensure single-mode operation of the fiber. In addition, in mode-locked single-mode fiber lasers, the round-trip nonlinear phase delay also needs to be limited to around ∂ to prevent the generation of pulses with a very large temporally extended background, generally referred to, as a pedestal. For a standard mode-locked single-mode erbium fiber laser operating at 1.55 μm with a core diameter of 10 μm and a round-trip cavity length of 2 m, corresponding to a pulse repetition rate of 50 MHz, the maximum oscillating peak power is thus about 1 KW.
The long-term operation of mode-locked single-mode fiber lasers is conveniently ensured by employing an environmentally stable cavity as described in U.S. Pat. No. 5,689,519, entitled Environmentally Stable Passively Mode-locked Fiber Laser Pulse Source, assigned to the assignee of the present invention, and hereby incorporated herein by reference. The laser described in this reference minimizes environmentally induced fluctuations in the polarization state at the output of the single-mode fiber. In the described embodiments, this is accomplished by including a pair of Faraday rotators at opposite ends of the laser cavity to compensate for linear phase drifts between the polarization eigenmodes of the fiber.
Recently the reliability of high-power single-mode fiber lasers passively mode-locked by saturable absorbers has been greatly improved by implementing non-linear power limiters by insertion of appropriate semiconductor two-photon absorbers into the cavity, which minimizes the peak power of the damaging Q-switched pulses often observed in the start-up of mode-locking and in the presence of misalignments of the cavity. See U.S. patent application Ser. No. 09/149,369, filed on Sep. 8, 1998, entitled Resonant Fabry-Perot Semiconductor Saturable Absorbers and Two-Photon Absorption Power Limiters, assigned to the assignee of the present invention, and hereby incorporated herein by reference.
To increase the pulse energy available from mode-locked single-mode fiber lasers the oscillation of chirped pulses inside the laser cavity has been employed. M. Hofer et al., Opt. Lett., vol. 17, page 807-809. As a consequence the pulses are temporally extended, giving rise to a significant peak power reduction inside the fiber laser. However, the pulses can be temporally compressed down to approximately the bandwidth limit outside the laser cavity. Due to the resulting high peak power, bulk-optic dispersive delay lines have to be used for pulse compression. For neodymium fiber lasers, pulse widths of the order of 100 fs can be obtained.
The pulse energy from mode-locked single-mode fiber lasers has also been increased by employing chirped fiber gratings. The chirped fiber gratings have a large amount of negative dispersion, broadening the pulses inside the cavity dispersively, which therefore reduces their peak power and also leads to the oscillation of high-energy pulses inside the single-mode fiber lasers.
See U.S. Pat. No. 5,450,427, entitled Technique for the Generation of Optical Pulses in Mode-Locked Lasers by Dispersive Control of the Oscillation Pulse Width, and U.S. Pat. No. 5,627,848, entitled Apparatus for Producing Femtosecond and Picosecond Pulses from Fiber Lasers Cladding Pumped with Broad Area Diode Laser Arrays, both of which are assigned to the assignee of the present invention and hereby incorporated herein by reference. In these systems, the generated pulses are bandwidth-limited, though the typical oscillating pulse widths are of the order of a few ps.
However, though the dispersive broadening of the pulse width oscillating inside a single-mode fiber laser cavity does increase the oscillating pulse energy compared to a ‘standard’ soliton fiber laser, it does not increase the oscillating peak power. The maximum peak power generated with these systems directly from the fiber laser is still limited to around I KW.
Another highly integratable method for increasing the peak power of mode-locked lasers is based on using chirped periodically poled LiNbO3 (chirped PPLN). Chirped PPLN permits simultaneous pulse compression and frequency doubling of an optically chirped pulse. See U.S. patent application Ser. No. 08/845,410, filed on Apr. 25, 1997, entitled Use of Aperiodic Quasi-Phase-Matched Gratings in Ultrashort Pulse Sources, assigned to the assignee of the present application, and hereby incorporated herein by reference. However, for chirped PPLN to produce pulse compression from around 3 ps to 300 fs and frequency doubling with high conversion efficiencies, generally peak powers of the order of several KW are required. Such high peak powers are typically outside the range of mode-locked single-mode erbium fiber lasers.
Broad area diode laser arrays have been used for pumping of mode-locked single-mode fiber lasers, where very compact cavity designs were possible. The pump light was injected through a V-groove from the side of double-clad fiber, a technique typically referred to as side-pumping. However, such oscillator designs have also suffered from peak power limitations due to the single-mode structure of the oscillator fiber.
It has also been suggested that a near diffraction-limited output beam can be obtained from a multi-mode fiber laser when keeping the fiber length shorter than 15 mm and selectively providing a maximum amount of feedback for the fundamental mode of the optical fiber. “Efficient laser operation with nearly diffraction-limited output from a diode-pumped heavily Nd-doped multi-mode fiber”, Optics Letters, Vol. 21, pp. 266-268 (1996) hereby incorporated herein by reference. In this technique, however, severe mode-coupling has been a problem, as the employed multi-mode fibers typically support thousands of modes. Also, only an air-gap between the endface of the multi-mode fiber and a laser mirror has been suggested for mode-selection. Hence, only very poor modal discrimination has been obtained, resulting in poor beam quality.
While the operation of optical amplifiers, especially in the presence of large seed signals, is not very sensitive to the presence of spurious reflections, the stability of mode-locked lasers critically depends on the minimization of spurious reflections. Any stray reflections produce sub-cavities inside an oscillator and result in injection signals for the cw operation of a laser cavity and thus prevent the onset of mode-locking. For solid-state Fabry-Perot cavities a suppression of intra-cavity reflections to a level <<1% (in intensity) is generally believed to be required to enable the onset of mode-locking.
The intra-cavity reflections that are of concern in standard mode-locked lasers can be thought of as being conceptually equivalent to mode-coupling in multi-mode fibers. Any mode-coupling in multi-mode fibers clearly also produces a sub-cavity with a cw injection signal proportional to the amount of mode-coupling. However, the suppression of mode-coupling to a level of <<I% at any multi-mode fiber discontinuities is very difficult to achieve. Due to optical aberrations, even well -corrected optics typically allow the excitation of the fundamental mode in multi-mode fibers only with maximum efficiency of about 95%. Therefore to date, it has been considered that mode-locking of a multi-mode fiber is impossible and no stable operation of a mode-locked multi-mode fiber laser has yet been demonstrated.
3. Description of the Related Art
Rare-earth-doped optical fibers have long been considered for use as sources of coherent light, as evidenced by U.S. Pat. No. 3,808,549 to Maurer (1974), since their light-guiding properties allow the construction of uniquely simple lasers. However, early work on fiber lasers did not attract considerable attention, because no methods of generating diffraction-limited coherent light were known. Man current applications of lasers benefit greatly from the presence of diffract on limited light.
Only when it became possible to manufacture single-mode (SM) rare-earth-doped fibers, as reported by Poole et al. in “Fabrication of Low-Loss Optical Fibres Containing Rare-Ear Ions”, Optics Letters, Vol. 22, pp. 737-738 (1985), did the rare-earth-doped optical fiber technology become viable. In this technique, only the fundamental mode of the optical fiber is guided at the lasing wavelength, thus ensuring diffraction-limited output.
Driven by the needs of optical fiber telecommunications for SM optical fiber amplifiers, nearly all further developments for more than a decade in this area were concentrated on perfecting SM fiber amplifiers. In particular, the motivation for developing SM fiber amplifiers stemmed from the fact that SM fiber amplifiers generate the least amount of noise and they are directly compatible with SM fiber optic transmission lines. SM fiber amplifiers also have the highest optical transmission bandwidths, since, due to the absence of any higher-order modes, modal dispersion is completely eliminated. In general, modal dispersion is the most detrimental effect limiting the transmission bandwidth of multi-mode (MM) optical fibers, since the higher-order modes, in general, have different propagation constants.
However, in the amplification of short-optical pulses, the use of SM optical fibers is disadvantageous, cause the limited core area limits the saturation energy of the optical fiber and thus the obtainable pulse energy. The saturation energy of a laser amplifier can be expressed as
As an alternative to SM amplifiers amplification in multi-mode (MM) optical fibers has been considered. See, for example, “Chirped-pulse amplification of ultrashort pulses with a multi-mode Tm:ZBLAN fiber upconversion amplifier” by Yang et al., Optics Letters, Vol. 20, pp. 1044-1046 (1995). However, in general, amplification experiments in MM optical fibers have led to non-diffraction-limited outputs as well as unacceptable pulse broadening due to modal dispersion, since the launch conditions into the MM optical fiber and mode-coupling in the MM fiber were not controlled.
It was recently suggested by Griebner et al. in “‘Efficient laser operation with nearly diffraction-limited output from a diode-pumped heavily Nd-doped multi-mode fiber”, Optics Letters, Vol. 21, pp. 266-268 (1996), that a near diffraction-limited output be can be obtained from a MM fiber laser when keeping the fiber length shorter than 15 mm and selectively providing a maximum amount of feedback for the fundamental mode of the optical fiber. In this technique, however, severe ode-coupling was a problem, as the employed MM fibers supported some 10,000 modes. Also, only an air-gap between the endface of the MM fiber and a laser mirror was suggested for mode-selection. Hence, only very poor modal discrimination was obtained, resulting in poor beam quality.
In U.S. Pat. No. 5,187,759 to DiGiovanni et al., it was suggested that amplified spontaneous emission (ASE) in a MM fiber can be reduced by selectively exciting any active ions lose to the center of the fiber core or by confining the active ions to the center of the fiber core. Since the overlap of the low-order modes in a MM optical fiber is highest with the active ions close to the center of the fiber core, any ASE will then also be predominantly generated in low-order modes of the MM fiber. As a result, the total amount of ASE can be greatly reduced in MM fiber, since no ASE is generated in high-order modes. However, DiGiovanni described dopant confinement only with respect to ASE reduction. DiGiovanni did not suggest that, in the presence of mode-scattering, dopant confinement can enhance the beam quality of the fundamental mode of the M fiber under SM excitation. Also, the system of DiGiovanni did not take into account the fact that gain-guiding induced by dopant confinement can in fact effectively guide a fundamental mode in a MM fiber. This further reduces ASE in MM fibers as well as allowing for SM operation.
In fact, the system of DiGiovanni et al. is not very practical, since it considers a MM signal source, which leads to a non-diffraction-limited output beam. Further, only a single cladding was considered for the doped fiber, which is disadvantageous when trying to couple high-power semi-conductor lasers into the optical fibers. To couple high-power semiconductor lasers into MM fibers, a double-clad structure, as suggested in the above-mentioned patent to Maurer, can be of an advantage.
To the inventors' knowledge, gain-guiding has not previously been employed in optical fibers. On the other hand, gain-guiding is well known in conventional semiconductor and solid-state lasers. See, for example, “‘Alexandrite-laser-pumped Cr3+:Li rAlF6” by Harter et al., Optics Letters, Vol. 17, pp. 1512-1514 (1992). Indeed, in SM fibers, gain-guiding is irrelevant due to the strong confinement of the fundamental mode by the wave-guide structure. However, in MM optical fibers., the confinement of the fundamental mode by the waveguide structure becomes comparatively weaker, allowing for gain-guiding to set in. As the core size in a MM fiber becomes larger, light propagation in the fiber structure tends to approximate free-space propagation. Thus, gain-guiding can be expected eventually to be significant, provided mode-coupling can be mad sufficiently small. In addition to providing high pulse energies, MM optical fiber amplifiers can also be used to amplify very high peak power pulses due to their increased fiber cross section compared to SM fiber amplifiers. MM undoped fibers and MM amplifier fibers can also be used for pulse compression as recently disclosed by Fermann et al. in U.S. application Ser. No. 08/789,995 (filed Jan. 28, 1997). However, this work was limited to the use of MM fibers as soliton Raman compressors in conjunction with a nonlinear spectral filtering action to clean-up the spectral profile, which may limit the overall efficiency of the system.
Compared to pulse compression in SM fibers, such as that disclosed in U.S. Pat. No. 4,913,520 to Kafka et al., higher-pulse energies can be obtained in MM fibers due to the increased mode-size of the fiber. In particular, V-values higher than 2.5 and relatively high index differences between core and cladding (i.e. a Δn>0.3%) can be effectively employed. In “Generation of high-energy 10-fs pulses by a new pulse compression technique”, Conference on Lasers and Electro-Optics, CLEO 91, paper DTuR5, Optical Society of America Technical Digest Series, #9, pp. 189-190 (1996), M. Nisoli et al. suggested the use of hollow-core fibers for pulse-compression, as hollow-core fibers allow an increase in the mode size of the fundamental mode. However, hollow-core fibers have an intrinsic transmission loss, they need to be filled with gas, and they need to be kept straight in order to minimize the transmission losses, which makes them highly impractical.
As an alternative to obtaining high-power pulses, chirped pulse amplification with chirped fiber Bragg gratings may be employed, as disclosed in U.S. Pat. No. 5,499,134 to Galvanauskas et al. (1996). One of the limitations of this technique is that, in the compression grating, a SM fiber with a limited core area is employed. Higher pulse energies could be obtained by employing chirped fiber Bragg gratings in MM fibers with reduced mode-coupling for pulse compression. Indeed, unchirped fiber Bragg gratings were recently demonstrated in double-mode fibers by Strasser et al. in “Reflective-mode conversion with UV-induced phase gratings in two-mode fiber”, Optical Society of America Conference on Optical Fiber Communication, OFC97, pp. 348-349, (1997). However, these gratings were blazed to allow their use as mode-converters, i.e., to couple the fundamental mode to a higher-order mode. The use of Bragg gratings in pulse-compression calls for an unblazed grating to minimize the excitation of any higher-order modes in reflection.
It has long been known that a SM signal can be coupled into a MM fiber structure and preserved for propagation lengths of 100s of meters. See, for example, “Pulse Dispersion for Single-Mode Operation of Multi-mode Cladded Optical Fibres”, Gambling et al., Electron. Lett., Vol. 10, pp. 148-149, (1974) and “Mode conversion coefficients in optical fibers”, Gambling et al., Applied Optics, Vol. 14, pp. 1538-1542, (1975). However, Gambling et al. found low levels of mode-coupling only in liquid-core fibers. On the other hand, mode-coupling in MM solid-core fibers was found to be severe, allowing for the propagation of a fundamental mode only in mm lengths of fiber. Indeed, as with the work by Griebner et al., Gambling et al. used MM solid-core optical fibers that supported around 10,000 or more modes.
In related work, Gloge disclosed in “Optical Power Flow in Multi-mode Fibers”, The Bell System Technical Journal, Vol. 51, pp. 1767-1783, (1972), the use of MM fibers that supported only 700 modes, where mode-coupling was sufficiently reduced to allow SM propagation over fiber lengths of 10 cm.
However, it was not shown by Gloge that mode-coupling can be reduced by operating MM fibers at long wavelengths (1.55 μm) and by reducing the total number of modes to less than 700. Also, in this work, the use of MM fibers as amplifiers and the use of the nonlinear properties of MM fibers was not considered.
The inventors are not aware of any prior art using MM fibers to amplify SM signals where the output remains primarily in the fundamental mode, the primary reason being that amplification in MM fibers is typically not suitable for long-distance signal propagation as employed in the optical telecommunication area. The inventors arc also not aware of any prior art related to pulse compression in multi-mode fibers, where the output remains in the fundamental mode.
All of the above-mentioned articles, patents and patent applications are hereby incorporated herein by reference.
This invention overcomes the foregoing difficulties associated with peak power limitations in mode-locked lasers, and provides a mode-locked multi-mode fiber laser.
This laser utilizes cavity designs which allow the stable generation of high peak power pulses from mode-locked multi-mode fiber lasers, greatly extending the peak power limits of conventional mode-locked single-mode fiber lasers. Mode-locking may be induced by insertion of a saturable absorber into the cavity and by inserting one or more mode-filters to ensure the oscillation of the fundamental mode in the multi-mode fiber. The probability of damage of the absorber may be minimized by the insertion of an additional semiconductor optical power limiter into the cavity. The shortest pulses may also be generated by taking advantage of nonlinear polarization evolution inside the fiber. The long-term stability of the cavity configuration is ensured by employing an environmentally stable cavity. Pump light from a broad-area diode laser may be delivered into the multi-mode fiber by employing a cladding-pumping technique.
With this invention, a mode-locked fiber laser may be constructed to obtain, for example, 360 fsec near-bandwidth-limited pulses with an average power of 300 mW at a repetition rate of 66.7 MHz. The peak power of these exemplary pulses is estimated to be about 6 KW.
It is an object of the present invention to increase the energy storage potential in an optical fiber amplifier and to produce peak powers and pulse energies which are higher than those achievable in single-mode (SM) fibers before the onset of undesirable nonlinearities and gain saturation.
Another object of the present invention is to achieve amplification of the fundamental mode within a multi-mode (MM) fiber while reducing amplified spontaneous emission (ASE).
A further object of the present invention is to employ gain-guiding within a MM fiber to improve the stability of the fundamental mode.
Yet another object of the present invention is to compress high peak power pulses into the range of a few psec to a fsec while preserving a near diffraction-limited output.
To achieve the above objects, the present invention employs a multi-mode (MM) optical fiber in an optical amplification system. According to the present invention, MM optical fibers, i.e., fibers with a V-value greater than approximately 2.5, provide an output in the fundamental mode. This allows the generation of much higher peak powers and pulse energies compared to SM fibers before the onset of undesirable nonlinearities and gain saturation. The increased fiber cross section equally greatly increases the energy storage potential in an optical fiber amplifier. The amplification system of the present invention is useful in applications requiring ultrafast and high-power pulse sources.
According to one aspect of the present invention, the gain medium is in the center of the MM fiber so that the fundamental mode is preferentially amplified and spontaneous emission is reduced. Further, gain-confinement is used to stabilize the fundamental mode in a fiber with a large cross section by gain guiding.
According to one embodiment of the present invention, the exploitation of self-phase modulation and other nonlinearities in (rare-earth) doped or undoped MM fibers allows the compression of high peak power pulses into the range of a few fsec while a near diffraction-limited output is pre-served.
According to another embodiment of the present invention, by writing chirped fiber Bragg gratings into MM optical fibers with reduced mode-coupling, the power limits for linear pulse compression of high-power optical pulses are greatly increased. Further, by employing double-clad MM fiber amplifiers, pumping with relatively large-area high-power semiconductor lasers is made possible.
According to yet another embodiment of the present invention, the incorporation of efficient mode-filters enables cw lasing in a near diffraction-limited single mode from (rare-earth) doped MM optical fibers.
According to yet another embodiment of the present invention, MM optical fibers allow the construction of fiber optic regenerative amplifiers and high-power Q-switched lasers. Further, MM optical fibers allow the design of cladding-pumped fiber lasers using dopants with relatively weak absorption cross sections.
These and other objects and features of the present invention will be apparent from the following detailed description of the preferred embodiments and the accompanying drawings.
The following description of the preferred embodiments of the invention references the appended drawings, in which like elements bear identical reference numbers throughout.
In this exemplary embodiment, the cavity 11 is formed between a first mirror 19 and a second mirror 21. It will be recognized that other cavity configurations for recirculating pulses are well known, and may be used. In this example, the mirrors 19, 21 define an optical axis 23 along which the cavity elements are aligned.
The cavity 11 further includes a pair of Faraday rotators 25, 27 to compensate for linear phase drifts between the polarization eigenmodes of the fiber, thereby assuring that the cavity remains environmentally stable. As referenced herein, the phrase “environmentally stable” refers to a pulse source which is substantially immune to a loss of pulse generation due to environmental influences such as temperature drifts and which is, at most, only slightly sensitive to pressure variations. The use of Faraday Rotators for assuring environmental stability is explained in more detail in U.S. Pat. No. 5,689,519 which has been incorporated by reference herein.
A polarization beam-splitter 29 on the axis 23 of the cavity 11 ensures single-polarization operation of the cavity 11, and provides the output 30 from the cavity. A half-wave plate 31 and a quarter-wave plate 33 are used to introduce linear phase delays within the cavity, providing polarization control to permit optimization of polarization evolution within the cavity 11 for mode-locking.
To induce mode-locking, the cavity 11 is formed as a Fabry-Perot cavity by including a saturable absorber 35 at the end of the cavity proximate the mirror 19. The saturable absorber 35 is preferably grown as a 0.75 μm thick layer of InGaAsP on one surface of a substrate. The band-edge of the InGaAsP saturable absorber 39 is preferably chosen to be 1.56 μm, the carrier life-time is typically 5 ps and the saturation energy density is 100 MW/cm2.
In this example, the substrate supporting the saturable absorber 35 comprises high-quality anti-reflection-coated InP 37, with the anti-reflection-coated surface 39 facing the open end of the cavity 11. The InP substrate is transparent to single-photon absorption of the signal light at 1.56 μm, however two photon absorption occurs. This two-photon absorber 39 is used as a nonlinear power limiter to protect the saturable absorber 35.
The mirror 19 in this exemplary embodiment is formed by depositing a gold-film onto the surface of the InGaAsP saturable absorber 35 opposite the two photon absorber 39. The combined structure of the saturable absorber 35, two photon absorber 37 and mirror 19 provides a reflectivity of 50% at 1.56 μm. The surface of the gold-film mirror 19 opposite the saturable absorber 35 is attached to a sapphire window 41 for heat-sinking the combined absorber/mirror assembly.
The laser beam from the fiber 15 is collimated by a lens 43 and refocused, after rotation by the Faraday rotator 25, by a lens 45 onto the anti-reflection-coated surface 39 of the two-photon absorber 37. The spot size of the laser beam on the saturable absorber 35 may be adjusted by varying the position of the lens 45 or by using lenses with different focal lengths. Other focusing lenses 47 and 49 in the cavity 11 aid in better imaging the laser signal onto the multi-mode fiber 13.
Light from a Pump light source 51, such as a laser source, with a wavelength near 980 nm and output power of 5 W, is directed through a fiber bundle 57 with an outside diameter of 375 μm. This pump light is injected into the end 53 of the multi-mode fiber 13 opposite the single-mode fiber 17. The pump light is coupled into the cavity 11 via a pump signal injector 55, such as a dichroic beam-splitter for 980/1550 nm. Lenses 47 and 48 are optimized for coupling of the pump power from the fiber bundle 57 into the cladding of the multi-mode fiber.
The M2-value of the beam at the output 30 of this exemplary embodiment is typically approximately 1.2. Assuming the deterioration of the M2-value is mainly due to imperfect splicing between the multi-mode fiber 13 and the single-mode mode-filter fiber 15, it can be estimated that the single-mode mode-filter fiber 15 excited the fundamental mode of the multi-mode fiber 13 with an efficiency of approximately 90%.
Mode-locking may be obtained by optimizing the focussing of the laser beam on the saturable absorber 35 and by optimizing the orientation of the intra-cavity waveplates 31, 33 to permit some degree of nonlinear polarization evolution. However, the mode-locked operation of a multi-mode fiber laser system without nonlinear polarization evolution can also be accomplished by minimizing the amount of mode-mixing in the multi-mode fiber 13 and by an optimization of the saturable absorber 35.
The pulses which are generated by the exemplary embodiment of
Due to the multi-mode structure of the oscillator, the pulse spectrum is strongly modulated and therefore the autocorrelation displays a significant amount of energy in a pulse pedestal. It can be estimated that the amount of energy in the pedestal is about 50%, which in turn gives a pulse peak power of 6 KW, about 6 times larger than what is typically obtained with single-mode fibers at a similar pulse repetition rate.
Neglecting the amount of self-phase modulation in one pass through the multi-mode fiber 13 and any self-phase modulation in the mode-filter 15, and assuming a linear increase of pulse power in the multi-mode fiber 13 in the second pass, and assuming an effective fundamental mode area in the multi-mode fiber 13 of 133 μm2, the nonlinear phase delay in the multi-mode oscillator is calculated from the first equation above as Φnl=1.45π, which is close to the expected maximum typical nonlinear delay of passively mode-locked lasers.
The modulation on the obtained pulse spectrum as well as the amount of generated pedestal is dependent on the alignment of the mirror 21. Generally, optimized mode-matching of the optical beam back into the fundamental mode of the multi-mode fiber leads to the best laser stability and a reduction in the amount of pedestal and pulse spectrum modulation. For this reason, optimized pulse quality can be obtained by improving the splice between the single-mode filter fiber 15 and the multi-mode fiber 13. From simple overlap integrals it can be calculated that an optimum tapered section of Coming SMF-28 fiber 15 will lead to an excitation of the fundamental mode in the multi-mode fiber 13 with an efficiency of 99%. Thus any signal in higher-order modes can be reduced to about 1% in an optimized system.
An alternate embodiment of the invention is illustrated in
In another alternate embodiment of the invention, Illustrated in
In the embodiment of
The use of two single-mode mode-filter fibers 15, 77 is also beneficial in simplifying the alignment of the laser. Typically, to minimize modal speckle, broad bandwidth optical signals need to be used for aligning the mode-filter fibers with the multi-mode fiber. The use of two mode-filter fibers 15, 77 allows the use of amplified spontaneous emission signals generated directly in the multi-mode fiber for an iterative alignment of both mode-filters 15, 77.
The chirped pulses generated in the cavity 75 with overall positive dispersion may be compressed down to approximately the bandwidth limit at the frequency doubled wavelength by employing chirped periodically poled LiNbO3 79 for sum-frequency generation, in a manner well known in the art. The chirped periodically poled LiNbO3 79 receives the cavity output from the polarization beam splitter 29 through an optical isolator 81. In this case, due to the high power capabilities of multi-mode fiber oscillators, higher frequency-doubling conversion efficiencies occur compared to those experienced with single-mode fiber oscillators. Alternatively, bulk-optics dispersion compensating elements may be used in place of the chirped periodically poled LiNbO3 79 for compressing the chirped pulses down to the bandwidth limit.
Generally, any nonlinear optical mixing technique such as frequency doubling, Raman generation, four-wave mixing, etc. may be used in place of the chirped periodically poled LiNbO3 79 to frequency convert the output of the multi-mode oscillator fiber 13 to a different wavelength. Moreover, the conversion efficiency of these nonlinear optical mixing processes is generally proportional to the light intensity or light intensity squared. Thus, the small residual pedestal present in a multi-mode oscillator would be converted with greatly reduced efficiency compared to the central main pulse and hence much higher quality pulses may be obtained.
As shown in the alternate embodiment of
In each of the embodiments of this invention, it is advantageous to minimize saturation of the multi-mode fiber amplifier 13 by amplified spontaneous emission generated in higher-order modes. This may be accomplished by confining the rare-earth doping centrally within a fraction of the core diameter.
Polarization-maintaining multi-mode optical fiber may be constructed by using an elliptical fiber core or by attaching stress-producing regions to the multi-mode fiber cladding. Examples of such fiber cross-sections are shown in
To ensure optimum matching of the fundamental mode of the multi-mode fiber 13 to the mode of the single-mode mode-filter fiber 15 in each of the embodiments of this invention, either a bulk optic imaging system, a splice between the multi-mode fiber 13 and the single-mode fiber 15, or a tapered section of the multi-mode fiber 13 may be used. For example, the multi-mode fiber 13, either in the form shown in one for
Finally, instead of passive mode-locking, active mode-locking or active-passive mode-locking techniques may be used to mode-lock multi-mode fibers. For example, an active-passive mode-locked system could comprise an optical frequency or amplitude modulator (as the active mode-locking mechanism) in conjunction with nonlinear polarization evolution (as the passive mode-locking mechanism) to produce short optical pulses at a fixed repetition rate without a saturable absorber. A diagram of a mode-locked multi-mode fiber 13 with a optical mode-locking mechanism 101 is shown in
Generally, the cavity designs described herein are exemplary of the preferred embodiments of this invention. Other variations are obvious from the previous discussions. In particular, optical modulators, optical filters, saturable absorbers and a polarization control elements are conveniently inserted at either cavity end. Equally, output coupling can be extracted at an optical mirror, a polarization beam splitter or also from an optical fiber coupler attached to the single-mode fiber filter 15. The pump power may also be coupled into the multi-mode fiber 13 from either end of the multi-mode fiber 13 or through the side of the multi-mode fiber 13 in any of the cavity configurations discussed. Equally, all the discussed cavities may be operated with any amount of dispersion. Chirped and unchirped gratings may be implemented at either cavity end to act as optical filters and also to modify the dispersion characteristics of the cavity.
A two-lens telescope 14 (L1 and L2) is used to match the mode from the oscillator 1010 to the fundamental mode of the MM amplifier 1012. In addition, the output of the pumped MM fiber 1012 is imaged into a second SM fiber (mode-filter (MF) fiber 1016 in
In one example of the system arranged according to
The amplifier fiber 12 can be, for example, a double-clad MM erbium/ytterbium amplifier with a core diameter of ≈28 μm and a core numerical aperture of NA=0.19. The inner cladding in this example has a diameter of ≈220 μm and a numerical aperture of NA=0.24. The core is located in the center of the inner cladding. The length of the amplifier is 1.10 m.
To increase the number of propagating modes in the MM amplifier 1012 and for testing purposes, shorter wavelengths such as 780 and 633 nm were also used. In this, a femto-second laser source operating at 780 nm and a cw laser source at 633 nm can be launched into the MM amplifier fiber 1012. The MF fiber 1016 can then be replaced with a fiber with a core diameter of 4 μm to ensure SM operation at these two wavelengths.
The approximate number of modes in the MM amplifier is calculated from its V-value.
For equal excitation of N modes of a MM fiber supporting N modes the maximum coupling efficiency into a SM fiber is given approximately by
Mode-coupling was measured in a 1.1 m length of unpumped amplifier fiber for the above-described erbium/ytterbium fiber (fiber 1), and three commercially available MM-fibers (fiber 2, 3 and 4). The fiber parameters and the mode-coupling coefficient D (in m−1) of these fibers are shown in Table 1. Fibers 1, 3 and 4 are made by the MCVD process; fiber 2 is made by a rod-in-tube technique.
The coupling coefficients allow, in turn, the calculation of the expected M2 value. In this example, the calculated M2-values were produced after propagation through 1 m of MM fiber 1012. For fiber 1, a good agreement between the calculated and separately measured M2-values was obtained.
The beat length Lb between the fundamental LP01 and the next higher-order LP11 mode is also given in Table 1. The beat length Lb is defined as the length it takes for the two modes to accumulate a differential phase-shift of 2π along the propagation direction. Assuming a constant scattering power spectrum, for a fixed wavelength, D can be shown to be proportional to Lb 4.
See: D. Marcuse, “The Theory of Dielectric Optical Waveguides”, p. 238, Academic Press (1974); Gloge. The longer the beat length, the closer the modes are to being phase-matched and the more power will couple as a function of length. Since, as disclosed by Gloge, mode-coupling is expected to be largest between adjacent modes, it is desirable to use LP01/LP11 beat lengths as short as possible to avoid mode-coupling.
In general, high levels of mode-coupling can be expected from fibers with high scattering loss. This suggests the possibility of low mode-coupling coefficients at long wavelengths in fibers with low scattering loss. As can be seen from Table 1, a dramatic reduction of mode-coupling occurs with increased wavelength in fiber 1. An acceptable level of mode-coupling is achieved in fiber 1 down to wavelengths as short as 790 nm. Since the number of modes of an optical fiber depends only on the ratio a/λ, a fiber similar to fiber 1 with a core diameter as large as 56 μm can produce acceptable levels of mode-coupling in a 1 m length. Due to the reduction of scattering at longer wavelengths, even larger core diameters are acceptable at longer wavelengths. For example, a MM fiber with a core diameter of 60 μm can amplify pulses with a peak power 16 times larger than possible with SM amplifiers described by Taverner et al. Indeed, acceptable levels of mode coupling were obtained for a specifically designed fiber with a 50 μm core diameter as evident from Table 1 and explained in the following.
Further, it is clear that, to minimize mode-coupling, step-index MM fibers are more useful than graded-index MM fibers, since the propagation constants in graded-index fibers are very similar, which greatly increases their sensitivity to mode coupling. To minimize mode-coupling, the difference in the propagation constants between fiber modes is preferably maximized.
Fiber 2 was manufactured by a rod-in-tube technique with intrinsic high scattering losses leading to much larger mode-coupling coefficients compared to the MCVD-grown fibers 1, 3 and 4. Also, the mode-coupling coefficients measured in fiber 2 are similar to results obtained by Gambling et al. and Griebner et al., who also used step-index solid-core fibers manufactured by rod-in-tube techniques. As a consequence, reduced mode-coupling can be expected from directly grown MM fibers employing, for example, MCVD, OVD, PCVD or VAD fiber fabrication techniques.
As shown in Table 1, the mode-coupling coefficients obtained in fiber 4 at 1.55 μm are about a factor of 11 smaller than in fiber 3. This difference is explained by the fact that the outside diameter of fiber 4 is 250 μm, whereas the outside diameter of fiber 3 is 125 μm. In general, a thicker fiber is stiffer and less sensitive to bend and micro-bend induced mode-coupling, as evident from Table 1.
In experiments conducted by the inventors, the lowest mode-coupling coefficients were obtained by longitudinally stretching the optical fibers. For example, the mode-scattering coefficients of fiber 2 and 3 were measured while keeping the fiber under tension and while keeping the fiber straight. The application of tension in short lengths of fibers can be useful in obtaining the best possible mode-quality.
Mode-coupling was also measured in a configuration where the amplifier fiber (fiber 1) was pumped, as shown in
The coupling efficiency of the MM amplifier fiber 1012 into the MF fiber 1016 as a function of bend-radius of the MM amplifier fiber 1012 is shown in
Since the measured coupling efficiencies from the MM amplifier 1012 to a SM fiber are nearly the same under unpumped and pumped conditions, it is evident that gain-guiding is relatively weak in this particular amplifier fiber. This observation was also verified by a simple computer model (see below). However, clearly any dopant confinement in the center of the MM amplifier core will predominantly lead to amplification of the fundamental mode. Any light scattered into higher-order modes will experience less gain and, due to the reduced intensity overlap of the higher-order modes with the fundamental mode, low levels of scattered light in higher-order modes will also not saturate the gain of the fundamental mode. Thus, while in the above-described experimental example, the mode-scattering coefficients were so low that any effects due to gain-guiding were not readily observable, in general, gain-guiding plays a role in a MM amplifier system according to the present invention. In addition, the above-mentioned computer model predicts the onset of gain-guiding of the fundamental mode in MM fibers with larger core diameter and/or reduced refractive index differences between the core and cladding.
As the mode diameter increases, the size of the SM can be determined by the gain profile under small signal conditions, i.e. in the absence of gain saturation. This allows a length-dependent mode size. Initially, under small signal conditions, the mode is confined by gain-guiding. As the gain saturates, gain guiding becomes less relevant and the mode size can increase, limited eventually by the core of the MM fiber. A length-dependent mode size can also be achieved by employing a core size which tapers along the fiber length. This can, for example, be achieved by tapering the outside fiber diameter along the fiber length.
In the presence of gain-guiding, amplified spontaneous emission (ASE) is reduced, as the MM fiber essentially becomes SM. In the presence of gain-guiding, ASE is also guided predominantly in the fundamental mode, rather than in all possible modes of the MM fiber, leading to an improvement in the noise properties of the MM fiber.
Equally, in the experimental example, dopant-confinement was observed to lead to a significant reduction in the amplified spontaneous emission (ASE) levels in the fiber. This was verified by measuring the coupling efficiency of the ASE from the MM amplifier 1012 into the MF fiber 1016. In this case, no signal light was coupled into the MM amplifier fiber 1012. For an ASE power level of 1 mW, a coupling efficiency as high as 15% was measured. A comparison with equation (2) indicates that ASE is generated mainly in about 13 low-order modes (here a factor of two from polarization degeneracy is accounted for), i.e., ASE is generated in only about 20% of the total mode-volume of the amplifier fiber. The large reduction in ASE which was observed not only reduces the noise level in the amplifier; low levels of ASE also allow a reduction of the signal power that is required to saturate the amplifier. To extract the highest energy from an oscillator-amplifier signal pulse source, an operation of the amplifier in saturation is generally preferred.
The coupling efficiency at 1.55 μμm and at 780 nm from the MM amplifier fiber 1012 to the MF fiber 1016 was not found to vary when applying small mechanical perturbations to the optical fiber. In a practical optical system, the applied mechanical perturbations are small compared to the perturbations inflicted by a 5 cm bend radius, which indicates that long-term stability of the mode-propagation pattern in such fibers can be achieved.
The MM amplifier 1012 is polarization preserving for bend-radii as small as 10 cm. To obtain a high-degree of polarization holding, elliptical fiber cores or thermal stresses can be used in such fibers.
The autocorrelation of the amplified pulses from the MM amplifier fiber 1012 (bend radius=10 cm) measured under the condition of optimum mode-match and a condition of non-optimum mode-match are respectively shown in
In general, the spectrum of the pulses measured at the output of the MM amplifier fiber 1012 is more critically dependent on the coupling conditions than the autocorrelation. The reason for this is that the spectral measurement is sensitive to the phase between the fundamental mode and the higher-order modes, i.e., an energy content of higher-order modes of only 1% in the output of the MM fiber leads to a perturbation of the shape of the spectrum by 10%.
In the case of co-directional pumping, the pump light and the signal light are launched via a dichroic beamsplitter (not shown). The coupling optics are then optimized to simultaneously optimize the coupling of the pump beam and the signal beam.
A single or a double pass of the signal through the MM fiber 1052 is most convenient. In the case of a double-pass configuration, a Faraday rotator mirror can be employed to eliminate polarization drifts in the system. Of course, in a double-pass configuration, after the first pass through the amplifier the coupling of the signal into higher-order modes must be avoided to ensure a near-diffraction limited output.
Optionally, linear or nonlinear optical elements can be used at the output of the system. Such a system is compatible with any application that has been used in conjunction with conventional laser systems.
Many nonlinear applications indeed require high peak pulse powers for their efficient operation, which are very difficult to achieve in cladding-pumping SM amplifiers due to the 10s of meters of fiber length that are typically employed in such systems. Even in standard SM optical amplifiers, peak powers greater than 1 kW/amplifier length can rarely be achieved. In contrast, peak powers of ≈15 kW are achievable in a 1.5 m length of double-clad Er/Yb fiber (fiber 1 from Table 1) without appreciable non-linear effects, i.e., peak powers greater than 20 kW/amplifier length can be achieved.
According to the present invention, the use of a MM amplifier is beneficial not only by way of allowing the use of a large core diameter; the use of a MM amplifier also allows a reduction of the ratio cladding/doped core diameter, which minimizes the amplifier length and thus the amplifier non-linearity. However, this leads to the generation of more ASE noise.
When the MM fiber 1060 is soliton supporting, higher-order soliton compression may be used to produce short pulses from the MM fiber 1060 directly. In general, in the case of positive dispersion (non-soliton supporting) fiber, additional linear or nonlinear pulse-compression components must be used to compress the spectrally broadened optical pulses. In this case, a conventional linear pulse compressor 1062 (such as a prism, grating, grism or SM chirped fiber Bragg grating) may be used at the output of the system. Also, chirped periodically poled doubling crystals may be used to obtain a compressed, frequency-doubled pulse. Equally, chirped fiber Bragg gratings may be written into the MM optical fiber 1060 with reduced mode-coupling to reduce the nonlinearities of such structures when applied to linear pulse compressor 1062. The Bragg grating should not be blazed to eliminate the excitation of higher-order modes in reflection.
According to a fifth embodiment, the use of MM fiber allows the design of double-clad fibers with low absorption cross sections. For example, a double-clad Er-doped amplifier fiber may be constructed from MM fibers. Typically Er-doped double-clad fibers are relatively inefficient, since large cladding/core ratios have to be employed in order to absorb pump light from broad area diode lasers while still preserving a SM fiber core. Typically, such a design would involve a Φcl=100 μm diameter cladding and a Φco=10 μm diameter core. The effective absorption of such a structure is 100 times (=Φcl/Φco)2 smaller than the absorption in a single-clad Er-doped fiber. Thus, 100 times longer fiber amplifier lengths are required in this case. However, by implementing MM Er-doped fiber, the core size can be greatly increased, producing much smaller cladding/core ratios and shorter amplifier lengths which is very beneficial for the design of high-power lasers. Of course, for the design of high-power Er double-clad lasers, cladding diameters even larger than 100 μm can be implemented. A conceptual drawing of a fiber cross section employing a doped MM fiber core and an undoped fiber cladding is shown in
According to a sixth embodiment of the present invention, as shown n
The seed pulse is selected from the oscillator 1096 by the optical switch 1092 at the desired repetition rate. The Faraday rotator 1098 and the polarization beam splitter 1099 are used to couple the amplified pulse out of the system.
Either cw or pulsed pumping of the amplifier can be employed.
According to a seventh embodiment of the present invention shown in
According to an eighth embodiment of the present invention shown in
More than one preamplifier can be used in the system, where isolators and optical filters and optical switches can be used to minimize the amount of generated ASE in the system. Further, nonlinear processes in the preamplifiers and the final MM amplifier can be used for pulse compression.
According to a ninth embodiment of the present invention shown in
Although several exemplary embodiments have been herein shown and described, those of skill in the art will recognize that many modifications and variations are possible without departing from the spirit and scope of the invention, and it is intended to measure the invention only by the appended claims.