We present a method using spectral interferometry (SI) to characterize a pulse in the presence of an incoherent background such as amplified spontaneous emission (ASE). The output of a regenerative amplifier is interfered with a copy of the pulse that has been converted using third-order cross-polarized wave generation (XPW). The ASE shows as a pedestal background in the interference pattern. The energy contrast between the short-pulse component and the ASE is retrieved. The spectra of the interacting beams are obtained through an improvement to the self-referenced spectral interferometry (SRSI) analysis.
© 2014 Optical Society of America
In chirped-pulse amplification (CPA), a technique in common use for modern amplifiers for ultrafast pulses, short laser pulses are stretched, amplified and then re-compressed in order to achieve ultra-high peak intensities [1–4]. In addition to the amplified injected pulses, undesirable amplified spontaneous emission (ASE) and low-energy satellite pulses emerge at the output. ASE is present in all laser amplifiers, since the gain medium integrates and stores the pump energy before it is extracted, but it is particularly an issue in certain architectures such as high repetition rate regenerative amplifiers and fiber laser amplifiers, where the ASE propagates in a common spatial mode with the injected pulse and the gain medium is pumped over a time much longer than the extraction time. Many discussions of ASE are concerned with the intensity contrast between the compressed short-pulse and the background pedestal. In many high-intensity applications, especially with solid-density targets, the ASE and satellite pulses that arrive before the main pulse (pre-pulse) can induce nonlinear changes in the target . For example, the expanded plasma created by pre-pulse has been found to dramatically enhance resonance absorption by the main pulse, which can enhance x-ray emission  or prevent interaction of relativistic intensity pulses with solid density . There are also many situations where the energy contrast is the important parameter. If the target linearly absorbs the incident light, the integrated energy in the background can affect the target medium, for example, through heating in metal or semiconductor targets. Even in a simple measurement of a self-phase modulated spectrum, there is a linear sum of the broadened short pulse spectrum and the spectrum of the long pulse. A final example that is relevant to the technique presented in this paper is our recent interferometric measurement of the nonlinear response of a material . In that experiment, the laser beam was split into low and high power arms, with the latter arm undergoing a nonlinear interaction with a test material. The beams were then recombined with a relative delay, so that spatially resolved spectral interferometry showed fringes in the spectral direction. Fourier analysis of the fringes led to a spatially-resolved measurement of the nonlinear spectral phase. In the case of a low energy pedestal, the observed spectral fringes become a superposition of two interferograms: 1) the ASE interfering with itself, and 2) the desired short reference pulse interfering with the nonlinear test beam. The superposed interferograms cannot be separated, and the resulting characterization of the nonlinear phase is compromised.
Even when the intensity contrast is reasonably good (for example 106), the energy contrast may be poor. Consider, for example a regenerative amplifier system that produces a compressed output pulse of 50fs duration. With an output Pockels cell with a 5 ns window to pass the short pulse and reject the majority of ASE, an intensity contrast of 106 still results in a substantial fraction (> 10%) of energy in the ASE. Several techniques of pulse cleaning that have been demonstrated, including fast Pockels cells, saturable absorbers, harmonic conversion, plasma mirrors  and nonlinear ellipse rotation . One approach that has had recent success is cross-polarized wave generation (XPW) [11, 12], which is a degenerate four-wave mixing process, producing orthogonally polarized to the input field polarization, high-fidelity pulses. The XPW output, easily selected with a polarizer, has been used for pulse cleaning in double-CPA systems [13, 14] as well as for hollow fiber pulse compression . Alternatively, optical parametric amplification can be used as a high-gain, high-contrast front-end to avoid ASE altogether .
Intensity contrast of laser systems can be measured with third-order autocorrelation , where the second harmonic of a pulse is cross correlated with the fundamental to produce third harmonic. Because of the wide wavelength separation of the signals, extremely high intensity contrast (up to 1012) can be measured (for example ). The scan range of the cross-correlation is typically in the sub nanosecond range, not sufficiently long to capture the full long pulse pedestal that is at least several ns in duration. A fast photodiode or photoconductive detector can also be used to estimate the energy before the short pulse, but cannot measure the total ASE energy, as it will saturate the moment the main pulse gets detected, or the ASE will be close to background noise. This method also has limited temporal resolution compared to cross-correlation techniques.
In this paper, we demonstrate the use of XPW and spectral interferometry (SI) to measure the energy contrast, as well as improve on the already existing techniques to improve the accuracy of measured spectral shape of a laser system output pulse. In one path of an interferometer, the XPW signal is generated, then interfered in a spectrometer with a copy of the input pulse from the other path. Since the XPW generation process acts as a temporal filter to pass high intensity, the low intensity background is significantly reduced, and the interference primarily takes place between the XPW signal and the short-pulse component of the input pulse. The incoherent ASE shows as a background and results in lower fringe contrast in the interferogram. This allows the determination of the relative energy content of the ASE. The technique makes use of a similar optical arrangement that is found in self-referenced spectral interferometry (SRSI) , in which the XPW signal serves as a reference pulse for the characterization of the spectral phase of the input pulse under test. We extend the SRSI retrieval algorithm to find an improved estimate of the shapes of both the fundamental and the XPW spectra. Finally, the retrieved information is used to measure the ASE background spectrum and energy content.
2. Experimental setup and algorithm for analysis
For our experiments, we used a regenerative amplifier of our own design with 1KHz repetition rate, pumped with 5.8mJ by a frequency-doubled Nd:YLF laser. The amplifier, which has an internal Pockels cell and second external Pockels cell that is used to select the amplified pulse. The amplifier is seeded with approximately 75pJ per pulse, a small energy relative to other systems owing to the low oscillator power and the low efficiency of the double-pass grating-based stretcher. The regenerative amplifier output is capable of producing 400μJ/pulse, 30fs pulses after compression. A schematic of the in-line interferometer used to create spectral interferograms is shown in Fig. 1. Although it was not critical, we used an imaging spectrometer in our experiment. The spectrometer had a nominal resolution of 0.134nm/pixel, collected with a 1024×1024 TE-cooled CCD array with 16bit resolution. The integration time used for the spectrometer was 30ms (thirty shots). First a clean-up polarizer (P1) ensures polarization purity of the input beam, after which a 1mm thick birefringent calcite plate (CP) is used to produce small and large amplitude pulses delayed by τ =600fs. Focused by a lens (L1, focal length 400mm), the large amplitude pulse is intense enough to generate an XPW signal in a BaF2 crystal (1mm thick, ¡110¿-cut). After being collimated by another lens (L2, focal length 400mm), it passes through the second polarizer (P2) oriented to pass the XPW signal and the low amplitude delayed pulse from the calcite window. The interference patterns are collected in the spectrometer. The sampling rate in the slit direction was approximately 30μm per pixel. A low percentage (∼2%) of XPW is generated to avoid any saturation and cross-phase modulation effects.
For our analysis, we require measurements of the spectral interferogram and the individual spectra of XPW and output of the laser, which contains the short-pulse fundamental wave (FW) and the ASE background. P1 and P2 are first aligned for best extinction without the calcite or BaF2 in between the polarizers. The calcite plate (CP) is inserted and oriented to maintain extinction, then the XPW crystal is inserted and rotated for best XPW generation. The input chirp of the pulse is also adjusted for maximum XPW bandwidth. This position allows the collection of the individual spectrum of the XPW ( ). The nonlinear crystal is then rotated to suppress conversion and the calcite plate is rotated at a small angle to recover the FW + ASE spectrum ( ) which is the output of the laser. Finally, the BaF2 crystal is rotated back to the position for maximum XPW generation. CP is adjusted for best fringe contrast to collect the interference pattern ( ). As part of the process to calibrate the resolution of the spectrometer, we also collect an interferogram where the output of the laser is interfered with itself. In this case, the BaF2 is removed and P2 is rotated to maximize fringe contrast. A Mach-Zehnder interferometer could also be used, such as what was used in earlier experiments that measured the spatio-temporal dynamics of XPW . Acquiring reference spectra in the Mach-Zehnder interferometer is more straightforward, but the inline interferometer is more compact and, if the optics are not wedged, the parallelism and overlap of the beams is ensured.
Figure 1 also shows simulated spectra for the signals in the measurement. The contributions to these signals in frequency-space are described by the following expression:
The interferogram IINT gathered by the spectrometer in Fig. 1 is the sum of the ASE background (non-interfering) and the FW-XPW interference. As shown in Eq. (1), it can be understood as a sum of interfering (IAC(ω)) and non-interfering (IDC(ω)) components. The DC (zero-modulation) component is the sum of the intensities all of the beams (first 3 terms in Eq. (1)). The AC component (modulated because of the time delay) has an amplitude that is the product of the interfering terms. The relative spectral phase between the two interfering pulses is also included in the AC term. The AC component is selected with a window in transform (delay) space and re-centered on the grid to place the centroid of the AC peak at zero delay. This removes linear phase terms that are unimportant to the shape of the pulse.
Several approximations and assumptions have been made in writing Eq. (1). First, we assume that the XPW intensity IX and amplitude AX are solely the XPW signal from the coherent FW pulse and do not have any contribution of the ASE to the XPW signal either from direct conversion or mixing with the FW. We also assume perfect contrast for the analyzing polarizer P2 so that there will not be any contribution of FW or ASE leakage to the interference signal. Shot-to-shot variations in the FW pulse and direct interference between the FW and ASE are also neglected. Finally, by using an imaging spectrometer and selecting signal from the central portion of the beam, any relative variation of spatial phase difference between the FW and XPW signals will not significantly contribute to a reduction of fringe contrast. A more complete discussion of these issues will be found in Section 3.
The simulation plots in Fig. 1 illustrate the different spectral terms for an example where the ASE and FW have different spectral shapes. The ASE background results in reduced contrast in the interferogram. Even though the relative pulse energies are adjusted to optimize fringe contrast, there are other contributions to imperfect contrast, such as resolution limits in the spectrometer, scattered light, and local mismatch of the FW and XPW spectral shapes. The analysis described below accounts for these effects.
Our full algorithm, presented in Fig. 2, consists of two loops, one for spectral phase (blue) and the other for spectral amplitude (red). Note that the superscripts M and R denote measured and retrieved (calculated), signals, respectively. Using a third-order polynomial calibration of the spectrometer camera pixels to wavelength, we use third-order interpolation on the measured spectra and interferogram, then resample on a grid with equal spacing in ω. Since our two-pulse delay is sufficiently small to avoid pushing the Nyquist sampling limit, the resampling artifacts described by Albrecht  and Dorrer  are not expected to greatly decrease the dynamic range of our measurement. The alternative method of resampling described in those papers could be employed to avoid interpolation-induced noise. The spectral phase loop generally follows the SRSI algorithm , except in the initial choice of the spectrum of the fundamental. Instead of using the measured spectrum of the laser, , which can be distorted by the presence of ASE, we derive our initial guess for the FW spectrum by the following procedure. We select one of the AC peaks of the Fourier transform of with a tapered window. The spectral window used to select the AC peak extended from halfway between the DC and AC peaks and was symmetric around the DC peak. This excluded any high frequency contributions, but for our measurements, there was no signal observed above the noise level in that frequency range. The AC peak was then shifted to place the centroid at the center of the grid to remove unimportant linear spectral phase terms. The resulting signal was finally transformed back to frequency space. The amplitude of this signal is the product between the actual XPW and FW fields, so we used its square root as the starting amplitude of the FW ( ). The measured spectral phase difference was used as the initial guess for the FW phase. The phase of the AC peak represents the measured spectral phase difference between the short pulse and the XPW, .
The phase-retrieval loop of the original SRSI algorithm is then calculated. Using the initial guess of the time-domain field of the fundamental , the corresponding XPW field is calculated. Since a linear spectral phase on the pulses is not important for the algorithm, we position the centroid of the pulse on the temporal grid as described above. This re-centering is particularly helpful for pulses with odd orders of phase that are asymmetric in time. After transforming back to ω–space, an improved guess for the spectral phase of the fundamental ( ) can be obtained by adding the retrieved XPW spectral phase to the measured spectral phase difference ( ). The updates lead to a new calculated from which we can calculate the error ε by integrating the root-mean-square (RMS) difference from across the laser bandwidth. Since the loop can sometimes stagnate with an error that oscillates with iteration, we monitor the average error of several loops and stop the iteration when this average error stabilizes. The oscillatory behavior was noticed predominantly when using the the square root of as the starting FW spectrum as is conventional for the SRSI algorithm. At the end of the phase portion of the algorithm the retrieved FW ( ) and XPW ( ) are saved and used as input for the spectral part the algorithm.
As described above, the spectral content of the measured FW+ASE may be different from the short-pulse component, for example, if the amplifier is seeded with a pulse that is away from the spectral peak of the gain. One indication that the assumed FW spectrum for the SRSI algorithm is incorrect can be seen by comparing the XPW spectrum calculated from the SRSI algorithm with the measured XPW spectrum. Another check is to compare the shapes of the measured and calculated AC spectrum (AX (ω)AF(ω)). We use the latter spectrum to improve our estimate for the fundamental spectrum since it is less influenced by measurement noise. The estimate for the FW spectrum to be used for the next iteration of the SRSI loop is improved by dividing the retrieved XPW spectrum into the measured AC peak: . This loop continues until the current product of the retrieved XPW and FW spectra is consistent with the measured using a 5% threshold for the RMS-difference value.
As noted in previous work , the accuracy of the SRSI phase retrieval algorithm diminishes with large amounts of even-order phase when the spectrum is smooth and symmetric. For example, an input pulse with strong second-order phase will lead to an XPW spectrum that is narrower than the FW spectrum and with a similar chirp rate. Since the chirp rates of the two signals are comparable, the measured spectral phase difference is small, and the SRSI algorithm will retrieve with a phase with a second order phase that is lower than that of the input pulse. Our algorithm shares this sensitivity to input second order phase: if a phase is retrieved with too little second-order component, the predicted XPW spectrum will be larger than it should be, and the new spectral estimate of the FW obtained by dividing the AC peak by the XPW spectrum will be too narrow. When the FW is retrieved at the end of our algorithm, we check the XPW retrieved spectrum against what was experimentally measured (the two curves are normalized to have the same area). When the input second-order phase is not large, the RMS difference between the measured and retrieved spectra is typically less then 5%. In practice, the constraint on input second-order phase is not a severe limitation, since most amplifier systems include a pulse compressor that can be adjusted for maximum XPW bandwidth as discussed above in our alignment procedure. Figure 3(a) shows a comparison of the measured (solid) and retrieved XPW spectra without (red) and with (green) the spectral loop. In this example, where there was approximately 50% ASE energy, the RMS difference error on the XPW spectrum without the spectral loop was 22%. Application of the full phase and spectral optimization loops retrieved an improved guess for the XPW spectrum (4.9% RMS error). Figure 3(b) illustrates the capability of the spectral loop using the model conditions from Figure 1. The retrieved XPW spectrum (green, dashed) lies on top of the spectrum calculated from the input FW pulse (black, solid).
The recovered spectral shapes for the FW and XPW improve the confidence in characterizing the true short pulse spectrum and pulse shape in the presence of ASE background. It is possible to go further, and estimate the energy content and the spectral shape of the FW and ASE components of the laser output. Our modeling shows that if the spectral shapes and energies of the FW and XPW are known, these signals can be subtracted from the DC peak of the interferogram to obtain the incoherent background. In real measurements, there are two challenges to obtaining quantitative energy information from the interferograms.
The first of these is to determine the relative energy contribution of the XPW to the interferogram. In our measurements, we recorded the spectra of the interferogram, XPW and FW+ASE sequentially. Small fluctuations in the pulse energy and spatial walk off due to pointing variations into the spectrometer can lead to small energy differences of a few percent. In our system, there were no significant changes in spectral shape from shot to shot, so we can correct for these fluctuations. Noting that the DC peak of the measured interferogram should be the same as the sum of the measured spectra for the FW+ASE ( ) and XPW ( ), we can find a better estimate of the energy balance by weighting the two spectra by factors cFA and cX
Since the phase and spectral retrieval procedure described earlier in this paper led to the shape of the unknown FW spectrum, the second challenge is to determine the energy content of the FW spectrum. With perfect spectrometer resolution, the FW spectrum with the correct energy can be found by dividing the square of the AC peak spectrum, i.e. . In practice we must account for the line spread function of the spectrometer that leads to a reduction of fringe contrast that is unrelated to the incoherent background. We determined this with two approaches. The simplest approach was to create a spectral interferogram of the output of the laser with itself, taking care to adjust the energy balance to maximize the fringe contrast. In the Fourier transform of this interferogram, the AC peaks should be one half of the height of the DC peak provided that the energies are balanced and that the paths of the interferometer have equal spectral phase. In this case the test interference pattern probes the spectrometer modulation transfer function (MTF) at one modulation frequency. Any reduction in amplitude of the AC peak we attribute to the MTF of the spectrometer. The influence of any spectral phase difference between the paths can be avoided by cutting one of the AC peaks from delay space, then transforming back to frequency space. The ratio of two times the amplitude of the resulting spectrum to that of the spectrum from the DC peak gives the correction factor for the energy of the AC peak in our data.
We also demonstrate a second procedure that is highly accurate but somewhat more labor intensive. The blurring effects from the spectrometer originate from the impulse response function:22], allows us to remove the effects from a system’s impulse response function. To obtain the impulse response of the spectrometer, we measured the spectrum from a krypton lamp and finely adjusted the grating in the spectrometer. These adjustments sweep the peaks of the spectrum across the pixels on the camera. Observing a single pixel as a peak scans past it gives us a higher resolution measurement of the impulse response function for the spectrometer than the resolution of the camera in the spectrometer. This high-resolution impulse response function gives us the ability to effectively de-blur the measured interferogram using the following relation: 22], though the limits in dynamic range have not been fully analyzed in that work. Our simpler procedure described earlier effectively obtains an estimate of the transfer function at a single delay position. The accuracy of the deconvolution procedure, which is limited by the dynamic range and noise of the detector, sets a limit on the ultimate sensitivity of our technique for measuring the incoherent portion of the beam.
Finally the ASE spectrum can be calculated from the DC peak . Alternatively, it can also be calculated via the separately collected (and energy-corrected) FW + ASE spectrum, . We have found that both methods work comparably well when processing with simulated data. The ability to know the intensities of the spectra helps increase the sensitivity of the measurement of background energy to the sub-percent level.
Figure 4 shows data for measurements of the ASE background in our experiment. A line out of the spectral interferogram is shown in Fig. 4(a). Diminished fringe contrast is seen in the 760–775nm spectral region of the interferogram. This resulted from scattered light within the spectrometer for the broader-band XPW signal that was effectively removed from the ASE calculation by our procedure described above. Figure 4(b) shows the normalized Fourier transform of the interferogram taken of the FW+ASE only (red). The height of the AC peak is seen to be lower than the expected value of 1/2, partly because of imperfections of the spectrometer resolution. Spectral phase difference in the paths leads to broadening of the AC peak in this domain. The upper dashed curve in this figure is the measured transfer function of our spectrometer using the method outlined in Yetzbacher et al  described above. Dividing the transfer function, and selecting the AC peak yields a spectrum that is the same shape as the DC spectrum as expected, and is within a fraction of a percent of one half of its amplitude, confirming the validity of the deconvolution process.
We varied the ASE energy content of our amplifier system by either using or bypassing the Pockels cell that followed our regenerative amplifier. Fig. 4(c) shows the retrieved, normalized fundamental spectrum and the retrieved ASE spectra with the post-regenerative amplifier Pockels cell on (solid) and off (dotted). For low ASE (Pockels cell on) we recover a smooth Gaussian ASE spectral shape centered at laser system wavelength. The ASE energy calculated via integrating the area under curve of the retrieved spectrum was 7.1% and 7.5% relative to the FW energy, using the reference interferogram and deconvolution methods, respectively. For comparison, the ratio of the energy of the amplifier output unseeded vs seeded was 66%. This is much greater than what we measure with our technique because when seeded, much of the energy goes to the injected pulse. When the Pockels cell was turned off and bypassed, the energy content of the ASE was 131% of the fundamental.
In the present experiment, we have demonstrated measuring the incoherent content of the amplifier output at the 7% level, but to extend the measurement sensitivity to levels below the single percent level, it is important to consider other sources of degradation of fringe contrast. First, in Eq. (1), any contribution to the XPW signal from the ASE is neglected. There will be some XPW generated from the ASE, but this contribution will be negligible in most cases owing to the relatively low intensity of this signal. For example, if the FW and ASE signals have equal energy, but with durations of 100fs and 1ns respectively (10−4 intensity ratio), the contribution of the ASE to the XPW signal would be 10−12 of that of the FW. More important would be mixing terms in the nonlinear XPW process between the FW and the ASE. The strongest of these terms will be linear in the ASE and second-order in the FW intensities. The term would have the same phase as the ASE and would therefore produce an interference pattern superposed on that of the FW-XPW interference. The strength of this artifact interference pattern would still be lower than the principal one by the ratio of the intensities. More significant is the assumption that the calcite polarizer P2 has perfect contrast, rejecting all of the unconverted input light (FW and ASE) in that path. In practice, we check to see that the contrast is sufficient by blocking the seed to the amplifier and verifying that the transmission is near the detection limit of our 16-bit camera at the same exposure time as used to collect the data. Imperfect contrast will lead to additional interference terms that would add to the desired modulation term. The order of magnitude of the resulting distortion of the retrieved spectral amplitude and phase would be approximately equal to the fractional energy leakage.
In principle, the ASE and the XPW signals do interfere, but owing to the slow shutter speed of our camera (30ms), the interference pattern would wash out when averaged over this many shots. Moreover, even if the data were taken single shot, the large amplitude phase variations that cause the ASE pulse to extend over several ns would lead to fringes that would not be resolved by our spectrometer. Mechanical vibrations in the interferometer can lead to degraded fringe contrast, but we find that the inline set up quite stable. As pointed out in a recent paper , shot-to-shot variations in the pulses can lead to a reduction of fringe contrast that would be interpreted by our algorithm as incoherent signal. The presence of these variations could be detected by performing a frequency-resolved optical gating experiment on the pulse. Finally, we note that if an imaging spectrometer is not used, the fringe contrast can be degraded if there is a difference in spatial phase between the FW and XPW pulses. In our optical arrangement, the spectral fringes were observed to be straight, indicating that both beams had the same divergence. When using an imaging spectrometer, any spatial variation in the fringes is resolved, and in fact the whole image could be used to improve the dynamic range. In future work we will investigate some of these issues to extend our technique to greater sensitivity.
We have presented a technique for measuring the energy and spectrum of the ASE emerging from a pulse amplifier. We achieve this by carefully calibrating the energy content of the pulses making up the interferogram, and adding an improvement to the self-referenced spectral interferometry (SRSI) algorithm to ensure that the FW and XPW spectra are consistent. The measurements described here can be performed with a simple in-line interferometer and a non-imaging spectrometer. We are currently working on new experiment design that can make these measurements in a single shot, which we anticipate will lead to higher accuracy and sensitivity. The analysis is sufficiently fast in computational power that such a measurement could be performed in real time during the alignment or day-to-day operation of an amplifier system.
We acknowledge funding support from AFOSR ( FA9550-10-1-0394) and from DOE ( DESC0001559). CD and AM acknowledge funding support from AFOSR ( FA9550-10-1-0561).
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