Abstract:
A laser and amplifier combination delivers a sequence of optical pulses. Pulses from the laser are temporally stretched by a pulse stretcher before amplification and temporally compressed by a pulse compressed after amplification. The pulse stretcher includes a diffraction grating on which pulses being compressed are incident. An arrangement is provided for measuring the carrier-envelope phase of the pulses and adjusting the incidence angle of pulses on the grating cooperative with the measurement such that the carrier envelope phase of the pulses in the sequence is about constant.

Description:
PRIORITY CLAIM 
       [0001]    This application claims priority of U.S. Provisional Application No. 61/228,461, filed Jul. 24, 2009, assigned to the assignee of the present invention and the complete disclosure of which is hereby incorporated by reference. 
     
    
     TECHNICAL FIELD OF THE INVENTION 
       [0002]    The present invention relates in general to laser oscillator amplifier arrangements for delivering femtosecond pulses. The invention relates in general to such arrangements wherein a laser pulse is temporally stretched prior to amplification and the amplified pulse is temporally compressed before delivery. 
       DISCUSSION OF BACKGROUND ART 
       [0003]    Optical pulses having a duration of a few femtoseconds or less may include only a few optical cycles at a fundamental carrier frequency of the pulse within an envelope of the pulse. A pulse-envelope typically has a Gaussian or Sech-squared form. The peak power within the envelope will depend on the phase of the carrier cycles relative to the envelope. This is referred to by practitioners of the art as the carrier envelope phase (CEP).  FIG. 1A  is a graph schematically illustrating a condition where the carrier is retarded in phase by an amount φ CE  with respect to the pulse envelope. The highest peak power will occur when a peak of one of the carrier cycles is exactly in phase φ CE =0.0) with the peak of the envelope. This is schematically illustrated in  FIG. 1B . The less the number of cycles within the envelope, i.e., the shorter the pulse, the greater is this phase dependence of peak power in the pulse. 
         [0004]    Techniques for stabilizing the CEP of a laser oscillator have long been known in the art. One such technique involves a closed loop feedback arrangement wherein the CEP is measured and compared with a desired value. Any difference between the measured and actual value is used to vary optical-pump power to a gain medium of the oscillator to drive the measured value back to the desired value. It has been found, however, that if a pulse from a CEP-stabilized oscillator is amplified in a chirped pulse amplification arrangement, wherein the input pulses from the oscillator are temporally stretched from an original duration before amplification and temporally compressed back to about the original pulse duration, the CEP of the amplified pulses will usually not be stable. 
         [0005]    Temporal stretching and compression are typically effected using a separated parallel pair of gratings. One means of stabilizing output pulses from a chirped pulse amplification arrangement is disclosed in PCT publication WO 2007149956. Stabilization is effected by a closed loop arrangement in which the CEP is again measured and compared with a desired value. Any difference between the measured and actual value is used to vary the separation of gratings in the pulse stretcher or compressor of the amplifier to drive the measured value back to the desired value. Piezoelectric transducer (PZT) actuators are used to change the grating separation. It has been found practically that a grating mount with three PZTs is required to translate a grating and maintain parallelism. The PZTs must be identical such that each provides the same displacement for an applied electrical potential. As the CEP is relatively insensitive to change in separation this method stretches the limits of displacement that can be provided by PZTs. There is a need for a more sensitive CEP stabilization method for chirped pulse amplifiers that does not require a plurality of matched PZTs. 
       SUMMARY OF THE INVENTION 
       [0006]    In one aspect of the invention, optical apparatus comprises an arrangement for generating a sequence of optical pulses. A pulse stretcher is provided for temporally stretching the optical pulses. The pulse-stretcher includes a first diffraction grating. The pulses are incident on the diffraction grating at a first incidence angle. An optical amplifier is arranged to amplify the temporally stretched optical pulses. A pulse compressor is provided for temporally compressing the amplified temporally stretched pulses. The pulse compressor includes a second diffraction grating. The amplified temporally stretched pulses are incident on the second diffraction grating at a second incidence angle. An arrangement is provided for periodically measuring a CEP of the temporally compressed amplified pulses and adjusting one of the first and second incidence angles cooperative with the CEP measurement such that the CEP of the temporally compressed amplified pulses is about constant. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1A  is a graph schematically illustrating a carrier wave lagging a pulse envelope in phase by an amount φ CE . 
           [0008]      FIG. 1B  is a graph schematically illustrating a carrier wave exactly in phase with a pulse envelope. 
           [0009]      FIG. 2  schematically illustrates a preferred embodiment of apparatus in accordance with the present invention, including a CEP stabilized oscillator delivering pulses to be amplified, a pulse stretcher for temporally stretching pulses prior to amplification, a regenerative amplifier for amplifying the temporally stretched pulses, and a pulse compressor in accordance with the present invention for temporally compressing the amplified stretched pulses, and an interferometer for measuring the CEP of the compressed amplified pulses, the pulse compressor including a diffraction grating having a selectively variable angle of incidence for varying the CEP responsive to the measurement thereof by the interferometer such that the CEP can be maintained constant. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0010]      FIG. 2  schematically illustrates a preferred embodiment  10  of laser apparatus in accordance with the present invention. Apparatus  10  includes a CEP stabilized master oscillator (laser)  12  for providing seed-pulses for further amplification. One laser suitable for laser  12  is a model Micra-CEPS™ available from Coherent, Inc., of Santa Clara, Calif. 
         [0011]    Laser  12  delivers a seed pulse P to be amplified via a turning mirror  14  into a pulse stretcher  16  for temporal pulse stretching. Stretcher  16  includes a retro-reflecting mirror pair  17  (only one mirror of the pair is visible in  FIG. 2 ). Pulse stretcher  16  also includes a diffraction grating  18 , a concave mirror  20 , and plane mirrors  22  and  24 . 
         [0012]    Seed pulse P enters the stretcher through a space between the mirrors of the retro-reflecting mirror-pair  17  and is diffracted by grating  18 . The pulse then follows a path from grating  18  to mirror  20 ; from mirror  20  to mirror  22 ; from mirror  22  back to mirror  20 ; from mirror  20  to grating  18 ; from grating  18  to mirror pair  17 ; from mirror pair  17  back to grating  18 ; from grating  18  to mirror  20 ; from mirror  20  to mirror  22 ; from mirror  22  to mirror  20 ; from mirror  20  to grating  18 ; and from grating  18  to mirror  24 , which reflects the pulse, now a temporally stretched pulse P S , out of pulse-stretcher  16 . The pulse is incident on grating  18  at a nominal incidence angle β in a plane of incidence corresponding to the plane of the drawing. Minor  20  is tilted slightly in a plane perpendicular to the plane of the drawing which causes separation of beam paths perpendicular to the plane of the drawing. The paths converge from grating  18  to mirror  20  and converge from mirror  20  onto mirror  22 . The converging paths pass over grating  18  in  FIG. 2 . This arrangement provides that grating  18  is imaged back onto itself by mirrors  20  and  22  to provide the effect of a grating pair having a separation therebetween equal to twice the distance between mirrors  20  and  22  plus twice the distance between grating  18  and mirror  20 . The effective grating pair separation for stretching is equal to twice the distance between grating  18  and mirror  22 . 
         [0013]    The temporally stretched pulse PS is delivered from mirror  24  of stretcher  16  to a regenerative amplifier  30  for amplification. One amplifier suitable for use as amplifier  30  is a Legend-Elite™ regenerative amplifier, also available from Coherent, Inc. 
         [0014]    Regenerative amplifier  30  delivers the amplified stretched pulse P SA  via a turning mirror  32  to a pulse compressor  34  in accordance with the present invention. Within pulse compressor  34 , a turning mirror  36  directs the pulse onto a diffraction grating  38  at a nominal incidence angle α to the grating. The pulse is diffracted from the grating and is translated by a pair of mirrors  44  and  46  arranged in the manner of a roof-prism or retro-reflector and returned to grating  38 . 
         [0015]    The pulse is then diffracted again onto another retro-reflecting mirror pair  48  (only one-of the pair visible in  FIG. 2 ). Retro-Minor pair  48  vertically levels up and returns the pulse parallel to the original path to the grating which diffracts the pulse parallel to its originally incident path. Then the diffracted laser beam passes over mirror  36 , and the pulse P SAC  (now temporally compressed by the multiple diffractions from the gratings) is delivered from the pulse compressor as an output pulse. The pulses are incident on grating  38  at a nominal incidence angle α in an incidence plane corresponding to the plane of the drawing. 
         [0016]    A beamsplitter  50  directs a sample, for example, about 2% of the output pulse, via a turning mirror  52  to an f-2f interferometer and processor. One commercially available interferometer for measuring CEP with signal processing for CEP stabilization is a Model APS800, available from MenloSystems GmbH of Munich, Germany. The interferometer measures the CEP of the pulse. The measured phase used by the processor to generate a feedback (error) signal to control the dispersion provided by the pulse compressor as follows. 
         [0017]    Diffraction grating  38  is mounted on optical element mount  42  which can selectively tilt the diffraction grating about an axis  40  as indicated in  FIG. 2  by double-headed arrow A, for controlling dispersion and accordingly CEP. One suitable such mirror mount is a model KC-PZ, available from Thorlabs, Inc., of Newton, N.J. The selective tilting of this mount is accomplished by a single PZT which is driven by the error signal generated by the interferometer and processor. This measurement and tilt (adjustment) process is carried out periodically for pulses in a train of pulses temporally stretched pulses to keep the CEP of pulses in the train constant, and preferably, but not necessarily, in an in-phase condition. 
         [0018]    In the arrangement of  FIG. 2  the incremental change in CEP δφ for a an incremental tilt angle δα (see  FIG. 2 ) is given by an equation: 
         [0000]    
       
         
           
             
               
                 
                   δϕ 
                   = 
                   
                     2 
                     * 
                     
                       
                         4 
                          
                         π 
                          
                         
                             
                         
                          
                         d 
                          
                         
                             
                         
                          
                         G 
                          
                         
                             
                         
                          
                         cos 
                          
                         
                             
                         
                          
                         α 
                       
                       
                         
                           1 
                           - 
                           
                             
                               ( 
                               
                                 
                                   d 
                                    
                                   
                                       
                                   
                                    
                                   λ 
                                 
                                 - 
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   α 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                      
                     δα 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where d is the groove density of the grating in lines/mm, α is the nominal incidence angle on the grating as depicted in  FIG. 2 , λ is the central wavelength of the pulse spectrum and G is the (constant) path length between successive incidences of the pulse on grating  38 . It should be noted here that equation (1) is derived for a similar equation for a grating pair compressor with one of the pair being tiltable, and wherein G is the separation of the gratings in the pair. The factor of 2 in equation 1 reflects the fact that the arrangement of  FIG. 2  is the equivalent of a grating pair in which both gratings are tilted. For a true grating pair with only one grating tiltable, the factor 2 in equation (1) would be dropped and G would be the optical separation of the gratings. 
         [0019]    In an example wherein G=60 centimeters (cm), α=45°, and d=1200/mm, δφ/δα=13.2 radians/microradian (rad/μrad). This means that at α=45°, a 1 μrad incident angle shift provides a 13.2 rad CEP shift. This same analysis can be used for grating stretcher, except that the separation G would be considered a negative value. 
         [0020]    In an experiment to test the analysis using values discussed above for the grating line density, incidence angle and G, and with the grating mounted on the above-recommended PZT mirror mount, the CEP was recorded while the grating was reciprocally drive as indicated by double arrowheads A by a sinusoidal signal applied to the PZT mount at 0.5 Hz. The angular displacement of the PZT mount is about 1 μrad/V. The recorded phase data indicated δφ/δα=11.4 rad/μrad, which agrees relatively closely with the analytical result. 
         [0021]    By way of comparison with the prior-art technique, wherein in CEP is controlled by varying separation G with incidence angle α held constant, the phase drift was measured when the grating was reciprocally horizontally translated by the PZT mirror mount. The result indicated that a 1 volt signal gave rise to only 0.25 rad CEP shift (or 4 rad/micrometer (μm) change in G). This agrees relatively well with a theoretical value of 3.4 rad μm, considering hysteresis of the PZT actuator. This indicates the inventive method of CEP control is about 40 times more sensitive than the prior-art method. 
         [0022]    In an experiment to test stability of the inventive CEP control method, the CEP was locked for over 66 minutes with a RMS error of 169 mrad. Even with this low phase-noise level, however, the CE phase effect in many few-cycle, laser-atom interaction experiments may be detectable to some extent. Certain prior-art CEP stabilized systems reported in the literature use cryogenic cooling of a Ti:sapphire amplifier to minimize temperature-induced CEP drift or noise. In this example, however, the Ti:sapphire rod of the amplifier was only water cooled at the room temperature. Improved CEP stability results may be expected with a cryogenically cooled rod. 
         [0023]    As noted above, while the method of the present invention is described with reference to change the indigence angle of a grating in a grating pulse compressor, the method may also be practiced by changing the incidence angle in a pulse stretcher. By way of example, in stretcher  16  this could be effected by tilting grating  18  about an axis  21 , by an amount δβ (from a nominal incidence angle β as indicated in  FIG. 2 . This would be effected via an actuator (not shown) in a feed-back loop (not shown) with f-2f interferometer and processor similar to actuator  42  of pulse-compressor  34 . The CEP measurement would still be made from the pulse P SAC . 
         [0024]    Also, while changing the incidence angle on the grating is described in terms of tilting the grating, the grating can be held fixed and the incidence angle can be changed by tilting one of the mirrors that are used to steer a pulse onto the grating. Further while the above described pulse compressor uses only a single grating imaged back on itself to create the effect of a grating pair, the inventive method may be implemented in a pulse stretcher or a pulse compressor which includes an actual grating pair by varying the incidence angle of only one of the gratings in the pair. These and other variations of the present invention may be practiced without departing from the spirit and scope of the present invention. 
         [0025]    In summary, the present invention is described above with reference to a preferred and other embodiments. The invention is not limited, however, to the embodiments described and depicted, rather the invention is limited only by the claims appended hereto.