Abstract:
The aim of the present disclosure is to enable a fast CE phase evaluation of the laser pulses, in particular in real time, including for multi-cycle pulses. Said aim is achieved by providing a polarization gating stage ( 8 ) for changing the laser pulses ( 7 ) to be evaluated in the phase and subsequent phase evaluation stage ( 15 ) for measuring the phase position of the changed laser pulses. The descriptions in the present disclosure can be used for example in laser technology for producing and monitoring single-cycle pulses.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a 35 U.S.C. §371 National Phase conversion of PCT/DE2012/000387, filed Mar. 30, 2012, which claims benefit of German Application No. 10 2011 016 441.3, filed Apr. 6, 2011, the disclosure of which is incorporated herein by reference. The PCT International Application was published in the German language. 
     TECHNICAL FIELD OF THE INVENTION 
     The invention relates to a method and device for the fast phase evaluation, in particular of multi-cycle pulses of a laser radiation. 
     BACKGROUND OF THE INVENTION 
     The absolute phase is defined as the shift between the maximum of the pulse envelope and the nearest maximum of the carrier wave of the electric field of a laser pulse. The absolute phase is frequently also referred to as carrier-envelope phase (CEP). This is, thus, a quantity that is required to describe the exact course of the electric field of laser pulses of any kind. CEP plays a central role, particularly in laser pulses whose pulse envelopes have a FWHM (full widths at half maximum) of only a few optical cycles, so-called few-cycle pulses or single-cycle pulses, since the electric field of these pulses has particularly large CEP-dependent asymmetries. CEP-dependencies are, however, also observed in experiments with multi-cycle pulses. 
     The generation of single-cycle pulses has been possible since 1997 (M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, F. Krausz: A novel high energy pulse compression system: Generation of multigigawatt sub-5-fs pulses, Applied Physics B-Lasers And Optics, 1997, Vol. 65; 189-196). Since then, these laser pulses and their interactions with matter constitute a field of research of central interest and are extensively studied. 
     In 2001, effects of the absolute phase were directly detected in the photoionization of noble gases (G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, S. De Silvestri: Absolute-phase phenomena in photoionization with few-cycle laser pulses, NATURE, 2001, Vol. 414, 182-184). In doing so, the CEP-dependent asymmetries of single-cycle pulses were observed in the form of spatially asymmetrically emitted photoelectrons. To this end, two oppositely arranged time-of-flight spectrometers (stereo time-of-flight spectrometers) were used. 
     Since then, other devices for CEP measurements have also been proposed and partially implemented. In those cases, it was usually necessary to average over effects induced by hundreds or thousands of laser pulses in order to determine the CEP of the laser pulses. Similarly, the majority of those methods would usually only work if the laser pulses are shorter than approximately two optical cycles (half width) (about 6 fs at 800 nm central wavelength of the laser). (T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, J. E. Sipe: Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors, Phys. Rev. Letters, 2004, Vol. 92, No. 14; A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, F. Krausz: Observation of Light-Phase-Sensitive Photoemission from a Metal. Phys. Rev. Letters, 2004, Vol. 92, No. 7; M. Kreβ, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, H. G. Roskos: Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy, Nature Physics Let., 2006, Vol. 2, 327-331; C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, J. W. G. Tisch: Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval, Nature Physics, 2007, Vol. 3, 52-57; G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, F. Krausz: Measurement of the phase of few-cycle laser pulses, Phys. Rev. Let., 2003, Vol. 91, Issue 25). 
     In 2009, it was for the first time possible to determine the CEP of single-cycle pulses with high accuracy using the above-mentioned stereo time-of-flight spectrometer arrangement in the single-shot mode (T. Wittmann, B. Horvath, W. Helml, M. G. Schatzel, X. Gu, A. L. Cavalieri, G. G. Paulus, R. Kienberger: Single-shot carrier-envelope phase measurement of few-cycle laser pulses, Nature Physics, 2009, Vol. 5; 357-362). This set-up, too, is only suitable for measuring the CEP of single-cycle pulses having a half-peak duration of less than 8 fs. 
     In 2010, a further method was demonstrated, which enabled the measurement of the CEP of ultrashort pulses having pulse durations of 38 fs in the single-shot mode (P. Tzallas, E. Skantzakis, and D. Charalambidis: Measuring the absolute carrier-envelope phase of many-cycle laser fields, PHYSICAL REVIEW A 82, 061401(R), 2010). There, a laser pulse with time-dependent polarization is used in interaction with a noble gas for the generation of radiation in the extreme ultraviolet range, so called high harmonics. The CEP of the ultrashort pulse can be determined from the exact measurement of the course of the spectral intensity of the extreme ultraviolet radiation. That method can, however, only be implemented at very high pulse energies (higher than 50 mJ), requiring comparatively expensive equipment. That method, moreover, involves high expenditures in the data transfer and calculation of the CEP such that the pulse repetition rate is limited. That method, thus, enables neither the determination of the CEP nor any influence on the CEP or a correlation of the CEP measurement with the measurement of other physical quantities in real time. In particular the need for very high pulse energies allows the use of that method as a basis for CEP control or a correlation of the CEP measurement with the measurement of other physical quantities in real time (CEP tagging) only for laser systems that provide low pulse repetition rates and pulse energies of several 10 mJ. 
     A device for the fast phase evaluation of single-cycle pulses was also already proposed (DE 10 2010 019 814.5), by which the determination of the CEP could be markedly improved based on the principle of the stereo time-of-flight spectrometer. That device allows for the single-shot determination of the CEP of single-cycle pulses in real time at repetition rates in the KHz range. At the same time, the equipment required for the CEP measurement is considerably reduced, and a high accuracy of the CEP measurement in the range below 200 mrad is achieved, while needing comparatively moderate pulse energies in the order of some 10 μJ. That device can thus serve as a basis for CEP control or a correlation of the CEP measurement (CEP tagging) with the measurement of other physical quantities in real time (A. M. Sayler, Tim Rathje, Walter Müller, Klaus Rühle, R. Kienberger, G. G. Paulus: Precise, real-time, every-single-shot, carrier-envelope phase measurement of ultrashort laser pulses, OPTICS LETTERS, Vol. 36, No. 1, 2011), although it is disadvantageous for the determination of the CEP that the output radius parameter R is reduced at the transition from single-cycle pulses to multi-cycle pulses, while the scatter Δr remains largely constant (A. M. Sayler, Tim Rathje, W. Müller, Ch. Kürbis, Klaus Rale, Gero Stibenz, and G. G. Paulus: Real-time pulse length measurement of few-cycle laser pulses using above-threshold ionization, Optics Express Vol. 19, Iss. 5, 2011, 4464-4471). Since the uncertainty of the CEP measurement ΔΦ approximately behaves like Δr/R (ΔΦ˜Δr/R), this leads to two essential problems for the CEP determination in real time and the single-shot mode:
         1) The uncertainty of the CEP determination increases with the pulse duration, since the radius parameter R decreases at an increasing pulse duration, and ΔΦ˜Δr/R applies.   2) The CEP measurement will no longer be feasible, if Δr reaches the order of dimension of R, because the uncertainty of the CEP determination will become too large. The limit is typically at 8 fs (at a central wavelength of 800 nm).       

     It is also known that laser pulses with time-dependently changing polarization directions are applied in the examination and optimization of the interaction of laser pulses with matter. The generation of laser pulses with time-dependently changing polarization directions takes place in a so-called polarization gating stage, which can be realized in various ways. (O. Tcherbakoff, E. Mével, D. Descamps, J. Plumridge, and E. Constant: Time-gated high-order harmonic generation, PHYSICAL REVIEW A 68, 2003, 043804; G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli: Isolated Single-Cycle Attosecond Pulses, Science 314, 2006, 443; P. Tzallas, E. Skantzakis, C. Kalpouzous, E. P. Benis, G. D. Tsakiris, D. Charalambidis: Generation of intense continuum extreme-ultraviolet radiation by many-cycle laser fields, Nature Physics, Vol. 3, 2007; P. B. Corkum, N. H. Burnett, M. Y. Ivanov: Subfemtosecond pulses, Optics Letters, Vol. 19, No. 22, 1994). 
     A special possibility is the use of different birefringent quartz plates of different thicknesses in combination with one or several Brewster windows (S. Gilbertson, Y. Wu, S. D. Khan, M. Chini, K. Zhao, X. Feng, and Z. Chang: Isolated attosecond pulse generation using multicycle pulses directly from a laser amplifier, PHYSICAL REVIEW A 81, 2010, 043810). So far, these techniques have been used to generate attosecond laser pulses. The use of these techniques for fast CE-phase evaluation is not known. 
     SUMMARY OF THE INVENTION 
     The invention is based on the object to enable the fast CE-phase evaluation of laser pulses, in particular in real time, also for multi-cycle pulses. 
     This object is achieved by a method for the fast phase evaluation, in particular of multi-cycle pulses of a laser radiation, in that laser pulses each comprising at least one region of approximately linear polarization and at least one region of non-linear polarization are generated, wherein the respective phase of the at least one region of approximately linear polarization is measured. 
     In a particular case, in order to generate differently polarized pulse regions, at least a second, time-delayed pulse partially overlapping the original pulse is generated of each linearly polarized laser pulse for the purpose of the phase evaluation of the latter, wherein, of the laser pulse combinations each made up of a first and the respectively associated, at least second, time-delayed pulse, the overlapping pulse area each comprises an approximately linear polarization, whose phase is measured. 
     A device for the fast phase evaluation, in particular of multi-cycle pulses of a laser radiation, comprises a polarization gating stage for changing the laser pulses to be evaluated in the phase, and a phase evaluation stage connected to the polarization gating stage for measuring the phase position of the changed laser pulses. 
     The polarization gating stage and the phase evaluation stage can be realized by different optical and/or electronic or computational arrangements. 
     The currently known options allow for the determination of the CE phase in the single-shot mode in real time only for single-cycle pulses. By contrast, the invention allows for the determination of the CE phase in real time and in the single-shot mode with high precision also of multi-cycle pulses. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following, the invention will be explained in more detail by way of exemplary embodiments illustrated in the drawing. Therein: 
         FIG. 1  depicts a schematically illustrated laser pulse; 
         FIG. 2  depicts a schematically illustrated laser pulse with an overlapping, time-delayed copy thereof; 
         FIG. 3  depicts the polarization of the laser pulse; 
         FIG. 4  depicts a scheme of a possible arrangement for the fast phase evaluation of ultrashort laser pulses. The laser pulses are changed in polarization direction in a time-dependent manner by a polarization gating stage prior to their interaction with a gas. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG. 1  schematically illustrates the intensity course of a known laser pulse  1 . In  FIG. 2 , a second laser pulse  2 , which is time-delayed relative to the first laser pulse  1 , is indicated in broken lines as a copy of the first laser pulse  1  behind the latter, the two laser pulses  1 ,  2  partially overlapping each other. An overlapped laser pulse  3  is formed. 
     This overlapped laser pulse  3  is linearly polarized in its central pulse area  4  and elliptically polarized in its two outer pulse areas  5 ,  6 . 
       FIG. 3  shows the course  16  of the elliptical polarization in the two outer pulse areas  5 ,  6 . In the area  4 , the polarization is linear only for about two optical cycles. 
       FIG. 4  illustrates an optional embodiment of the invention as an arrangement for the fast phase evaluation of ultrashort laser pulses. For the time-dependent change of its polarization, a laser pulse train  7  at first hits a polarization gating stage  8  comprising an aperture  9 , a full-wave plate  10  of quartz glass, one or several Brewster windows  11  and a final, zero-order quarter-wave plate  12 . 
     Within the polarization gating stage  8 , the laser pulse train  7  at first passes the circular aperture  9  of variable diameter, for manual regulation of the pulse energy. The intensity curve of an individual laser pulse is illustrated in  FIG. 1  (cf. laser pulse  1 ). 
     In the optical path of the laser pulse train  7 , the full-wave plate  10  of quartz glass is disposed behind the aperture  9 , which full-wave plate is oriented at an angle α=45° relative to the linear input polarization and generates pulse copies of the same amplitude, which are each perpendicular to each other (cf. laser pulses  1 ,  2  in  FIG. 2 ), yet have pulse centers that are mutually delayed. The produced delay depends on the thickness  1  of the full-wave plate  10 , which is selected such that the produced delay corresponds to an integer multiple of the cycle duration at the central wavelength T 0 , of the ultrashort laser pulse  1 . With a thickness of about l 0 =88.6 μm (at a central wavelength of 800 nm), a delay of exactly one cycle duration will be achieved. From this, the thickness of the full-wave plate  10  for higher orders of the delay &lt;l=n l 0 &gt; can be calculated via &lt; &gt;, n denoting the order of the full-wave plate  10 . The resulting delay between the pulse centers of the laser pulses  1 ,  2  results from δ=n T 0 . Other angles α will change the ratio between the amplitudes of the pulse copies and their polarization directions relative to the axes of the lab coordinate system x and y. Thus, α can be used to optimize the polarization direction onto the axis of the device proposed in DE 10 2010 019 814.5. 
     After this, the mutually delayed pulse copies pass the ultra-thin Brewster window(s)  11 , which reflect a portion of the horizontal field components as a function of their orientation relative to the vertical axis of the lab coordinate system, indicated by the angle γ, and hence change the ratio between the horizontal and vertical field components. This causes a change of the ellipticity in the pulse areas  5 ,  6  of the overlapped laser pulse  3  outside the overlap area of the laser pulses  1 ,  2 . 
     The optical axis of the zero-order quarter-wave plate  12  consecutively arranged in the optical path of the laser pulse train  7  encloses an angle β=0° with the horizontal axis of the lab coordinate system. This generates a delay of T 0 /4 between the horizontal field components relative to the vertical field components, and hence produces a linear polarization in the overlap area (cf. pulse area  4  in  FIG. 2  and  FIG. 3 ). Outside the overlap area, the pulse copies are elliptically polarized (cf. pulse areas  5 ,  6  in  FIG. 2  and  FIG. 3 ). 
     After having passed the polarization gating stage  8 , the then produced, overlapped laser pulses  3  of the laser pulse train  7  are reflected by a plane mirror  13  and directed by a focussing mirror  14  to a phase evaluation stage  15  for measuring the phase position of the changed laser pulses of the laser pulse train  7 . 
     The phase evaluation stage  15 , which is preferably realized by the arrangement proposed in DE 10 2010 019 814.5, outputs angle parameters φ and a radius parameter R (cf.  FIG. 4 ). In particular, an English translation of portions of DE 10 2010 019 814 A1, which published DE 10 2010 019 814.5, provides, with regard to an arrangement realizing the phase evaluation stage  15 , that, 
       FIG. 3  illustrates a block diagram of the apparatus according to the invention for the rapid phase evaluation of the individual cycle pulses of the laser beam  1  (cf.  FIG. 2 ) as a purely analog variant. The photoelectrons  5 ,  6  released on both sides in the gas in the gas channel  2  are recorded in the stereo time-of-flight spectrometer according to  FIG. 2  as time-of-flight spectra (left-hand and right-hand time-of-flight signals) using the detectors  8 ,  9 . Each of these time-of-flight signals is respectively passed to two current integrators  10 ,  11  and  12 ,  13 . For this purpose, the detector  8  is connected, on the output side, to the inputs of both the current integrator  10  with an output signal L S  and the current integrator  11  with an output signal L 1 . The detector  9  is suitably coupled to the current integrator  12  (output signal R S ) and to the current integrator  13  (output signal R 1 ). 
     A photodiode  14  which is set up at the output of the stereo time-of-flight spectrometer is respectively connected to two of the current integrators  10 ,  11 ,  12 ,  13  in pairs via two time-delayed trigger stages  15 ,  16  by virtue of the output of the trigger stage  15  respectively being connected to a control input (gate) of the current integrators  10 ,  12  and the output of the trigger stage  16  respectively being connected to a control input of the current integrators  11 ,  13 . This gate control of the current integrators  10 ,  11 ,  12 ,  13  starts and ends the current integration intervals (slow and fast time of flight) for the photoelectrons of the stereo time-of-flight spectrometer (cf.  FIG. 2 ) which are detected using the detectors  8 ,  9 . The outputs of the current integrators  10 ,  11 ,  12 ,  13  are coupled to an analog evaluation unit  17 . The latter contains two evaluation stages  18 ,  19  with the output signals x and y, respectively, for calculating the asymmetry of the individual cycle pulses of the laser radiation  1  which are to be evaluated (cf.  FIG. 1  and  FIG. 2 ) and an evaluation stage  20  which carries out a coordinate transformation and therefore outputs the absolute phase φ and the radius R. 
     The output of the current integrators  10  and  12  is respectively connected to an input of the evaluation stage  18  for calculating the asymmetry parameters for a fast time of flight (output signal x). The calculation in the evaluation stage  18  follows the general formula (L S −R S )/(L S +R S ). The output of the current integrators  11  and  13  is respectively connected to an input of the evaluation stage  19  for calculating the asymmetry parameters for a slow time of flight (output signal y). The calculation in the evaluation stage  19  follows the general formula (L 1 −R 1 )/(L 1 +R 1 ). Said asymmetry parameters for a fast and a slow time of flight are output as analog output signals x and y in cartesian coordinates. In the optional evaluation stage  20 , the cartesian coordinates x and y are additionally converted into radial coordinates with the radius R (is a measure of the asymmetry) and the angle φ (corresponds to the absolute phase) which are likewise output as an analog signal. 
       FIG. 3  shows four individual current integrators  10 ,  12 ,  11 ,  13  (connected downstream of the detectors  8 ,  9 ). In contrast, it would also be possible (not illustrated in the drawing for reasons of clarity) for the individual current integrators  10 ,  11 ,  12 ,  13  to be implemented, for example, by means of a single integrator unit, this integrator stage respectively carrying out at least two integration functions (different time-of-flight ranges) which are triggered with a time delay for each detector channel. In this case, all integration functions for evaluating the detected photoelectrons of the stereo time-of-flight spectrometer would be combined in only one integrator unit, by way of example, as a component. 
     In contrast to  FIG. 3 ,  FIG. 4  shows an analog/digital block diagram of the apparatus according to the invention for the rapid phase evaluation of said individual cycle pulses. 
     As illustrated in  FIG. 3 , the output signals L S , L 1 , R S , R 1  are generated in an analog manner from the time-of-flight signals from the detectors  8 ,  9  with the aid of the current integrators  10 ,  11 ,  12 ,  13  controlled, in terms of the time of flight, via the photodiode  14  and the trigger stages  14 ,  15 , but pass to a digital evaluation unit  22  via an A/D converter  21 . This evaluation unit contains digital evaluation stages  23 ,  24 ,  25 , the functions of which each correspond, in terms of the principle, to the corresponding calculation functions of the analog evaluation stages  18 ,  19 ,  20  described with respect to  FIG. 3 , with the difference of the digital calculation. 
     The digital evaluation stages  23 ,  24 ,  25  are preferably implemented by means of a processor (not explicitly illustrated) which calculates said asymmetries and provides them in radial and cartesian coordinates. In this case, it is possible to output the calculated values in the form of signal amplitudes and/or to convert the values into times so that they can be output in the form of delayed pulses. 
     The outputs of the digital evaluation unit  21  with said functional digital evaluation stages  23 ,  24 ,  25  are connected to a D/A converter  26  which is in turn used to output the output signals x, y, R, φ described with respect to  FIG. 3  in an analog manner. 
       FIG. 5  shows a block diagram of the apparatus according to the invention for the rapid and purely digital phase evaluation of the individual cycle pulses. 
     The time-of-flight signals (time-of-flight spectra) from the detectors  8 ,  9  and the signal from the photodiode  14  are digitized by an A/D converter  27  in this exemplary embodiment and are supplied to a digital evaluation unit  28 . This digital evaluation unit  28  contains, as functional groups, two integrator stages  29 ,  30  for the digitized time-of-flight signals from the detectors  8 ,  9 , two evaluation stages  31 ,  32  for said asymmetrical calculation according to the function (L S −R S )/(L S +R S ) and according to the function (L 1 −R 1 )/(L 1 +R 1 ) which correspond, in terms of the calculation function, to the evaluation stages  18 ,  19  from  FIGS. 3 and 23 ,  24  from  FIG. 4  as well as two digital evaluation stages  33 ,  34  for digitally calculating data both in cartesian and in radial coordinates, the signals from which are digitally output via an output stage  35 ,” (English translation of paragraphs [0030]-[0039] of DE 10 2010 019 814 A1). 
     The interaction of the overlapped laser pulse  3 , which thus comprises a time-dependent polarization direction, with a gas during the ionization differs from the interaction of laser pulses with time-independent polarization direction. High-kinetic energy electrons are efficiently produced only with sufficiently constant polarization directions. At the same time, the production rate of these high energetic electrons has the highest CEP dependency. Consequently, these particularly CEP-sensitive electrons are exclusively produced during the time period of near-constant polarization directions, i.e. in the center of the overlap area of the two pulse copies. 
     Hence a situation results that exhibits a similar CEP sensitivity as a single-cycle pulse. Correspondingly, the photoelectron distributions produced by laser pulses with time-dependent polarization directions have asymmetries that can be compared to those generated by single-cycle pulses. The radius parameter R, which is output by the already proposed device according to DE 10 2010 019 814.5 would thus be increased. 
     Due to this increase of the radius parameter R at a near-constant scatter Δr, the accuracy of the device is increased. The usable application range is thus expanded to laser pulses of a duration up to about 12 fs (at 800 nm central wavelength). 
     Alternatively to the polarization gating stage  8  illustrated in  FIG. 3 , the function of the same could also be realized by an interferometric set-up (not illustrated in the drawing) (e.g., P. Tzallas, E. Skantzakis, C. Kalpouzous, E. P. Benis, G. D. Tsakiris, D. Charalambidis: Generation of intense continuum extreme-ultraviolet radiation by many-cycle laser fields, Nature Physics, Vol. 3, 2007), or also by a set-up (not illustrated in the drawing, either) that uses the beat of mutually perpendicular, linearly polarized laser pulses with slightly different mean frequencies (e.g. P. B. Corkum, N. H. Burnett, M. Y. Ivanov: Subfemtosecond pulses, Optics Letters, Vol. 19, No. 22, 1994). 
     LIST OF REFERENCE NUMERALS USED 
     
         
           1 —laser pulse 
           2 —laser pulse (timely offset copy of laser pulse  1 ) 
           3 —overlapped laser pulse 
           4 —central pulse area (of the overlapped laser pulse  3 ) 
           5 , 6 —outer pulse areas (of the overlapped laser pulse  3 ) 
           7 —laser pulse train 
           8 —polarization gating stage 
           9 —aperture 
           10 —full-wave plate 
           11 —Brewster window 
           12 —zero-order quarter-wave plate 
           13 —plane mirror 
           14 —focussing mirror 
           15 —phase evaluation stage 
           16 —curve of the elliptical polarization in the outer pulse areas  5 , 6   
         r—radius parameter output by phase evaluation stage  15   
         θ—angle parameter output by phase evaluation stage  15