Abstract:
To avoid harmful nonlinear effects in the amplification of short optical pulses, an initial pulse is divided into a sequence of lower-energy temporally spaced pulses that are otherwise identical to the original pulse. The low-intensity pulses are amplified and then recombined to create a final amplified output pulse.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit under 35 USC 119(e) of U.S. Provisional Application No. 60/861,977, filed Dec. 1, 2006. 
    
    
     GOVERNMENT SPONSORSHIP STATEMENT 
     The work on this invention was supported by the National Science Foundation under Grant No. ECS-0500956 and PHY-0131508. The Government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates in general to a short-pulse amplification technique which reduces or avoids nonlinear effects, thus allowing higher pulse energies without pulse distortion. A pulse to be amplified is divided into a selected number of smaller magnitude pulses that are otherwise identical in shape to the original pulse. The pulses are amplified and then recombined coherently to produce a final output pulse that is an amplified version of the original pulse. 
     2. Description of the Background Art 
     Ultrashort light pulses on the order of picoseconds or shorter are now finding application in a wide range of science and technology. Many applications require high-energy pulses, which are obtained by amplifying low-energy pulses generated by a laser. Amplification of the pulses with high fidelity is crucial, but nonlinear phase shifts accumulated by an intense pulse generally distort its spectral and temporal profiles. Dispersion management, exemplified by chirped-pulse amplification, has proved to be an effective way to control nonlinearity. However, the limits of chirped-pulse amplification are reached by many sources of picosecond and femtosecond pulses. 
     If an optical pulse accumulates a nonlinear phase shift 
                 Φ   NL     ⁡     (     t   ,   z     )       =       ω   c     ⁢     ∫       n   2     ⁢     I   ⁡     (     t   ,   z     )       ⁢     ⅆ   z                 
(where I is the intensity and n 2  is the nonlinear refractive index of the medium) that is greater than ˜1, its spectral, temporal, and/or spatial profiles are likely to be distorted. In chirped-pulse amplification (CPA), a pulse is stretched temporally by a dispersive delay line. The stretched (thus frequency-chirped) pulse is amplified, and then the pulse is dechirped to its initial duration in another dispersive delay line. This technique reduces the intensity when the pulse is propagating through the (solid) amplifying medium, and allows the intensity to be a maximum when the pulse is propagating linearly. Self-similar amplification also controls nonlinearity through dispersion.
 
     Short-pulse amplifiers based on CPA have been responsible for a major fraction of the ultrafast science performed to date. There is ongoing interest in the generation of ultrashort pulses with ever-higher energies, for applications such as the generation of attosecond pulses and ultrafast x-rays. Many existing CPA systems are operated close to the limit Φ NL ˜1, owing to limitations on the stretching ratio. In practice, it is difficult to stretch and compress a pulse by more than a factor of 10 4  with high fidelity. As a separate issue, practical devices that provide enough dispersion to stretch and compress high-energy pulses longer than a few picoseconds do not exist. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a short-pulse amplification technique which produces improved performance over known CPA techniques, along with ease of implementation, in some situations. In this technique, referred to as divided-pulse amplification (DPA), a pulse to be amplified is divided into a plurality of smaller copies of itself. The pulses are approximately equally-spaced temporally in a sequence and have the same shape as the original pulse, but are of lower magnitude and energy. The sequence of pulses is amplified and then the pulses in the sequence are recombined coherently to produce a final large energy pulse, which is an amplified version of the original pulse. This arrangement reduces or avoids the nonlinear effects associated with other short-pulse amplification techniques. 
     An essential component of the DPA technique is the process of pulse division and recombination. In the preferred embodiments, birefringent components are employed to divide an incoming pulse and later recombine the amplified pulses into an output pulse. More particularly, in a first preferred embodiment, a sequence of birefringent crystals is employed to split the pulse into a desired number of pulses. The crystals at odd-numbered positions in the sequence have their optic axes oriented at a 45-degree angle relative to the direction of linear polarization of the pulse to be amplified, while those at the even-numbered positions are oriented in the same direction as the polarization. At each crystal, a pulse is split into two equal-intensity pulses, one an ordinary (o) wave and one an extraordinary (e) wave. The “o” and “e” pulses are separated in time because the group velocities of the o- and e-waves are different from one another. In this manner, a sequence of pulses is generated in which the linear polarizations of adjacent pulses alternate. 
     The length of each crystal determines the time spacing Δt of the pulses. The length of the shortest crystal (which is selected to be the first crystal, L 1 ) is chosen so that Δt exceeds the pulse duration. To produce equally-spaced pulses, the length of the m th  crystal in the sequence should be L m =2 m-1 L 1 . A sequence of M crystals thus splits the original pulse into 2 M  pulses, with alternating linear polarizations. 
     After passing through one or more amplification stages, the amplified pulses are preferably recombined in a sequence of crystals similar to the one that divided the pulses. In some cases, the pulses can be recombined by passing them in reverse order through the same sequence of crystals used to divide the input pulse. 
     In each of the embodiments of the invention, amplification of the pulses can be achieved through known techniques. Use of polarization insensitive components, such as optical fiber amplifiers, is preferred in view of the different polarizations of the alternating pulses in the pulse sequence. However, a polarization sensitive amplifier, such as a regenerative amplifier, can also be used in another embodiment of the present invention. In this embodiment, a polarization beam splitter is employed to separate the horizontal and vertical polarization components in the pulse sequence to be amplified. The separated pulses are passed in opposite directions through a polarization sensitive amplifier that amplifies only one of the two polarization components in either direction. A half wave plate is employed to rotate the other polarization component to the correct value before passing through the amplifier. The amplified polarization components of the pulse sequence are then recombined as they go in the reverse direction back through the beam splitter. Finally, each of the pulses in the sequence is combined into a final single amplified output pulse as they pass in the reverse direction through the divider/combiner. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The features and advantages of the present invention will become apparent from the following detailed description of preferred embodiments thereof, taken in conjunction with the accompanying drawings, which are briefly described as follows. 
         FIG. 1  illustrates the basic elements needed to implement any embodiment employing the DPA principle of the present invention. 
         FIG. 2  is a schematic illustration of an embodiment of the invention that was actually constructed and employed in experiments used to verify operation of the invention. 
         FIGS. 3A-3F  are graphs showing results of the experiments with DPA of picosecond pulses.  FIG. 3A  shows the initial pulse spectrum;  FIG. 3B  shows the initial pulse autocorrelation;  FIGS. 3C and 3D  show the amplified spectrum and autocorrelation without DPA, respectively; and,  FIGS. 3E and 3F  show the amplified spectrum and autocorrelation with DPA, respectively. 
         FIGS. 4A-4F  are graphs showing results of the experiments with DPA of femtosecond pulses.  FIG. 4A  shows the initial pulse spectrum;  FIG. 4B  shows the initial pulse autocorrelation;  FIGS. 4C and 4D  show the amplified spectrum and autocorrelation without DPA, respectively; and,  FIGS. 4E and 4F  show the amplified spectrum and autocorrelation with DPA, respectively. 
         FIG. 5  illustrates a second embodiment of the present invention, which allows the DPA technique to be employed with a polarization-sensitive amplifier. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  is a schematic illustration of a pulse amplifier  10  that is designed to operate in accordance with the DPA principle of the present invention. A pulse source  12 , such as a laser oscillator, generates a pulse  14  to be amplified. The pulse  14  is first fed though a pulse divider  15  which divides the original pulse  14  into N smaller copies of itself. N is dependent on the number of divider stages M, where N=2 M . The N pulses form a sequence of pulses  16  which is amplified in one or more amplifier stages  18  having a gain G. Finally, the N amplified pulses  20  are passed through a recombiner  22  which combines the amplified pulses  20  to form one large amplified pulse  24 . The pulse  24  is a version of the original pulse  14  that has been amplified by the factor G. 
     An essential component of DPA is the process of pulse division and recombination. It is known, theoretically that a pulse can be split and then recombined in a birefringent crystal. One embodiment of the present invention can thus consist of first and second sets of crystals for division and recombination, which are suitably chosen (lengths, transverse dimensions) for the given application. However, other birefringent materials could be used in place of the crystals. One obvious material to consider is optical fiber, which is birefringent in general. The divider and recombiner can thus be implemented as segments of fiber, which are ultimately connected together. For high-pulse-energy devices, the fiber can be large-mode-area photonic-crystal fiber or hollow-core photonic-bandgap fiber, to reduce nonlinear effects. In addition, the pulse dividing and recombining functions can be combined into one component by reversing the direction through which incoming and outgoing pulses pass. Other more conventional optical elements could be used for dividing and recombining the pulses, such as beam splitters and delay lines. The use of birefringent crystals is preferred because of the simplicity of the design. 
     In the case where birefringent crystals or other birefringent elements are used, the sequence of pulses  16  shown in  FIG. 1  includes a first group of pulses  26  in which the pulses are each of a first linear polarization and a second group of pulses  28  in which the pulses are of an opposite linear polarization. The pulses  26  and  28  are interleaved with one another so that pulses of the first polarization alternate with those the opposite polarization. The same holds true for the sequence of amplified pulses  20  which includes a first group of pulses  30  of the first polarization and a second group of pulses  32  of the opposite polarization. This will be discussed in greater detail in conjunction with  FIG. 2   
       FIG. 2  is a schematic illustration of an embodiment of the invention that was actually constructed and employed in experiments used to verify the operational principles of the invention. A pulse amplifier  50  is shown which comprises an oscillator  52 , a polarization beam splitter (PBS)  54 , a combination pulse divider/combiner  56 ; a ytterbium (Yb) fiber amplifier  58 ; a 45° Faraday rotator  60 ; and, a mirror  62 . A grating compressor  64  is placed as the last element after the PBS  54  for femtosecond-pulse operation, but is not necessary for picosecond operation. 
     In the pulse amplifier  50 , the pulse divider/combiner  56  is implemented by a stack of three birefringent crystals  66 ,  68  and  70  through which pulses pass in sequence. Regardless of the number of crystals, the crystals at odd-numbered positions (1, 3, 5, etc.) in the sequence have their optic axes oriented at a 45-degree angle relative to the direction of linear polarization of the pulse to be amplified, while the crystals at the even-numbered positions (2, 4, 6, etc.) are oriented in the same direction as the polarization of the input pulse. Thus, the pulses have their two perpendicular polarizations interleaved. The optic axes of neighbor crystals are rotated 45° about the direction of propagation. The output pulse polarization is perpendicular to that of the input pulse. 
     At each of the crystals  66 ,  68  and  70 , a pulse is split into two equal-intensity pulses, one an ordinary (o) wave and the other an extraordinary (e) wave. The “o” and “c” pulses are separated in time by Δt=|1/ν e −1/ν o |L, where ν o  and ν e  are the group velocities of the o- and e-waves and L is the crystal length. The length of the shortest crystal (which is the first crystal  66 , with length L 1 ) is chosen so that Δt exceeds the pulse duration. To produce equally-spaced pulses, the length of the m th  crystal in the sequence should be L m =2 m-1 L 1 . A sequence of crystals splits the original pulse into 2″ pulses, with alternating linear polarizations. In the embodiment shown in  FIG. 2 , for convenience, the amplified pulses are recombined by being passed in the reverse direction through the same sequence of crystals  70 ,  68  and  66 . Alternatively, a separate stack of crystals could be employed for this purpose as in  FIG. 1 . 
     The final amplified input pulse  72  is passed out of the PBS  54  at a 90 degree angle relative to the input received from the oscillator  52 . In the case of femtosecond operation, the output pulse is fed through the grating compressor  64 , which is implemented by a pair of gratings as is conventional. 
     In the experiment, a Yb fiber soliton laser  12  generates seed pulses of either 2.6 ps or 300 fs duration at 1038 nm. The repetition rate is 47 MHz and the pulse energy is ˜0.2 nJ. The amplifier  58  was implemented by a polarization-insensitive Yb-doped fiber 1.5 m long that provides (intensity) gain of ˜12. Yttrium vanadate (YVO 4 ) was chosen as the birefringent material for the crystals  66 ,  68  and  70  for its large polarization mode delay (˜1 ps/mm) and excellent transparency in the range of 500-2000 nm. The crystals  66 ,  68  and  70  are a-cut crystals with lengths of 6.5 mm, 10 mm, and 22, respectively, which therefore divide the initial pulse into 8 sub-pulses. In the pulse amplifier  50  used in the experiment, the same sequence of crystals, but in reverser order ( 70 ,  68  and  66 ) was used to recombine the pulses after amplification. The Faraday rotator mirror  60  rotates the polarization of the divided pulses by 90 degrees. Pulses that were e-waves during pulse division become o-waves during pulse recombination, and vice-versa, so all pulses experience the same total delay and recombine into the final amplified pulse  72 . 
     To demonstrate division and faithful recombination of picosecond pulses during experiments on the pulse amplifier  50 , the amplifier  58  was first bypassed. The fiber oscillator  52  produced 2.6-ps pulses with 0.8-nm bandwidth. The spectrum and pulse autocorrelation after division and recombination are essentially identical to those of the initial pulse, which are shown in  FIG. 3A  and  FIG. 3B , respectively. The insertion loss of the divider crystals  66 ,  68  and  70  is about 10%, and this could easily be reduced to &lt;1% with anti-reflection coatings. 
     As a control experiment, the 2.6-ps pulses were amplified without DPA. The group-velocity dispersion (GVD) of all components is negligible for the 2.6-ps pulse duration. The pulse was amplified to 2 nJ. The nonlinear phase shift accumulated by the pulse is estimated as Φ NL ≈π. The spectrum ( FIG. 3C ) and autocorrelation ( FIG. 3D ) exhibit substantial distortions, as expected owing to the nonlinear phase shift. With the three-crystal divider/recombiner, the nonlinear phase shift is reduced to Φ NL &lt;1, and the spectrum ( FIG. 3E ) and pulse autocorrelation ( FIG. 3F ) become nearly identical to those of the initial pulse. The fringes observed in the autocorrelations ( FIG. 3F ) confirm that the pulses are coherently recombined. For comparison, a chirped-pulse amplifier (CPA) system designed to stretch 2.6-ps pulses by a factor of 8 would require the dispersion of ˜10 km of fiber, and compression after amplification would be impractical. There are therefore a number of picosecond based systems that could benefit from the DPA technique. 
     For the amplification of shorter pulses, the GVD of the divider crystals and the amplifier  58  will become significant. The total of ˜40 mm of YVO 4  employed in these experiments presents negligible GVD for pulses longer than ˜200 fs. The fiber oscillator  52  was adjusted to generate ˜300-fs pulses ( FIGS. 4A and 4B ). After traversing the divider/combiner  56 . Faraday rotator  60  and divider/recombiner  56  in reverse, the spectrum and autocorrelation were unchanged (data not shown), which verifies the division/recombination process. The pair of diffraction gratings (600 lines/min)  64  was employed to compensate the GVD of the amplifier  58 . It should be noted that the apparatus is not designed to be a chirped-pulse amplifier, nor a self-similar amplifier; the gratings  64  are adjusted to simply compensate the GVD of the gain fiber  58  in linear propagation. 
     As the control measurement, the divider crystals  66 ,  68  and  70  were removed and the pulses were amplified to 1 nJ, which corresponds to a nonlinear phase shift Φ NL ≈2π. As a result, the spectrum ( FIG. 4C ) and autocorrelation ( FIG. 4D ) are distorted significantly. The accumulation of the nonlinear phase shift in the presence of normal GVD allows for some pulse compression in this case, but that is incidental. The key point is that the amplified pulse is not a faithful replica of the input pulse. In contrast, amplification to the same pulse energy with the DPA technique of the present invention produces minimal distortion as illustrated in  FIGS. 4E and 4F . 
     Much greater impact will come from scaling DPA to higher performance levels. Larger divisors and hence larger pulse energies will be straightforward. Division of 100-fs pulses by 1000, e.g., will require 10 crystals, with a total length of ˜20 cm. This is comparable to the size of a grating stretcher and is much simpler. For large-enough pulse energies, the amplified beam may be expanded spatially before recombination in large-aperture crystals to avoid excessive nonlinear phase shift in the recombiner itself. In this case separate divider and recombiner sequences may be preferred. It should be noted that it is not necessary to match the lengths of divider and recombiner crystals to sub-wavelength accuracy, because pulses with orthogonal polarizations recombine. Mismatch of the lengths will produce elliptical polarization across the edges of the pulse, but not destructive interference. The pulse duration will increase proportionally to the length mismatch. Incidentally, it was also verified experimentally that recombination in a separate divider produces a faithful replica of the 2.6-ps pulse. 
     Implementation of DPA with 100-fs pulses will require matching of the path lengths in the divider and recombiner to ˜10 microns, which is readily achievable. Some form of dispersion control will also be needed. Faithful recombination of 100-fs pulses has in fact been verified experimentally. With divider crystals of more than one kind of material, it may be possible to construct divider/recombiner sequences with net zero GVD at some wavelengths. Finally, it should be possible to combine CPA and DPA to design hybrid amplifiers that out-perform either technique by itself. 
     DPA offers significant practical features. The sequence of divider/combiner crystals  66 ,  68  and  70  is trivial to align optically. It is not necessary to divide the input pulse into equal-energy pulses, nor need they be equally-separated (as illustrated by the experiments described above, where the crystal lengths are not the nominal values). Because the divided pulses alternate polarization directions. DPA is ideally-suited to polarization-insensitive amplifiers such as the fiber amplifiers of the first and second embodiments. 
     However, DPA can also be adapted to polarization-sensitive amplifiers.  FIG. 5  illustrates an exemplary embodiment of a DPA based pulse amplifier  100  that is compatible with existing regenerative amplifiers. An input pulse  102  is passed through a combination divider/recombiner  104  to form a sequence of smaller pulse replicas  106  with alternating orthogonal polarizations as in the other embodiments of the invention. The different polarization pulses are separated with a polarizing beam splitter (PBS)  108 , and are directed in opposite directions as counter-propagating beams  110  and  112  through a gain medium  114  that requires a specific direction of linear polarization (assumed to be horizontal). A ½ wave plate  116  exchanges the direction of polarization of the counter-propagating beams, ensuring the correct polarizations for the beam entering the gain medium  114 . The ½ wave plate  116  also reverses the two polarization pulse replicas  110  and  112  before they pass through the PBS  108  and form an amplified sequence of pulses  118  that are passed through the divider/recombiner  104  in the reverse direction to form the final amplified pulse. 
     Although the invention has been disclosed in terms of a number of preferred embodiments and variations thereon, it will be understood that numerous additional variations and modifications could be made thereto without departing from the scope of the invention as defined by the following claims.