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Study of dispersion compensation effect of femtosecond laser amplifier using home-made third-order autocorrelator
Optics & Laser Technology 54 (2013) 242–248
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Study of dispersion compensation effect of femtosecond laser amplifier using home-made third-order autocorrelator Wenxia Bao, Nan Zhang, Xiaonong Zhu n Institute of Modern Optics, Nankai University, Key Laboratory of Optical Information Science and Technology, Ministry of Education, Tianjin 300071, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 November 2012 Received in revised form 10 March 2013 Accepted 20 May 2013 Available online 26 June 2013
Detailed experimental and theoretical analyses of the dispersion compensation effect in a femtosecond laser amplifier are presented. It is confirmed that the temporal structures in the vicinity of the central peak of the amplified laser pulse are primarily caused by the uncompensated third- and/or fourth-order dispersion. The specific detrimental roles played by the third- and fourth-order dispersions such as resulting in the formation of asymmetrical pulse shapes and satellite pulses are revealed and experimentally verified with third-order autocorrelation measurements. With the help of a third-order autocorrelator, it is more efficient and accurate to optimize the third- and fourth-order dispersion compensation when the roundtrip times of a laser pulse inside the regenerative amplifier changes. For practical applications, in order to achieve laser pulses with highest quality, namely with minimum pulse energy in their wings, it is imperative to optimize the dispersion-control parameters while monitoring the laser pulses with a third-order autocorrelator. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Dispersion compensation Femtosecond laser amplifier system Third-order autocorrelation
1. Introduction Femtosecond laser technologies have been rapidly developed and applied in many research fields since the invention of Ti: sapphire laser and Kerr lensing mode locking around 1990s [1–3]. Along with the development of more and more femtosecond laser amplifiers with ever increasing pulse energy and shorter pulse durations all based on the chirped pulse amplification (CPA) technique [4–7], optimization of dispersion compensation has been extensively studied [8–11]. While for most of the ordinary femtosecond laser amplifiers, the second- and third-order dispersion compensation appears rather straightforward, which at least in theory can be achieved through adjusting both the grating separation and the incident angle of the laser beam at the pulse compressor [12–14], simultaneous fourth and even higher-order dispersion compensation remains as a technical challenge in practice. Moreover, how to detect and clearly identify the effect of the high order dispersion compensation in a femtosecond laser amplifier system is in fact a non trivial problem. For applications where the details of temporal pulse shape matter greatly, it is critical to resolve such a problem especially for pulses near or shorter than 50 fs.
n
Corresponding author. Tel.: +86 222350 3121. E-mail address: [email protected] (X. Zhu).
0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2013.05.026
In the measurements of ultrashort laser pulses, the commonly used second-order autocorrelation method fails in distinguishing pulse asymmetry and any small temporal structures within the leading or trailing edges of a pulse also cannot be resolved. This has led to the on-going exploration of the third-order autocorrelation technique [15–19]. In particular, a design of a single-shot third-order autocorrelator that is able to measure a pulse on a single-shot basis has been presented by Collier et al. [16], and also recently a novel technique for measuring third-order autocorrelation by making use of the nonlinear response of GaAsP PMT and the spectral filtering technique to retract the third harmonic signal has been reported [17]. Besides all the on-going research progresses made on making use of third-order autocorrelation in ultrashort laser pulse characterization, commercial product of third-order autocorrelators also become available[20]. It is clear that the third-order autocorrelation method is not only capable to detect pulse asymmetry, satellite pulses, but also sufficiently sensitive to the height of pulse shoulder, being associated with a larger dynamic range. In this paper, we investigate the effect of the third- and fourth-order dispersions in a femtosecond laser amplifier system with the use of a home-made third-order autocorrelator. With this autocorrelator that has a high dynamic range and is thus sensitive enough to the pulse contrast, the asymmetric features of the laser pulses from a non-optimized commercial femtosecond laser amplifier system are routinely recorded. The observed experimental results are consistent with theoretical predictions. The third-order autocorrelation measurement
W. Bao et al. / Optics & Laser Technology 54 (2013) 242–248
indicates clearly the effect of the third- and fourth-order dispersion that cannot be revealed by the ordinary or standard secondorder intensity autocorrelation. An improved understanding of optimization of dispersion compensation in femtosecond laser amplifier systems is thus obtained. This further helps to form a practical guideline on how to optimize femtosecond laser amplifiers during various femtosecond laser application experiments so that routine generation of shorter and smoother laser pulses can be achieved.
respectively by [21] φ″ðωÞ ¼
−4π 2 cB 2 ω3 d ½1−ð2πc=ωd− sin γÞ2 3=2
" # 2 −3φ″ðωÞ 1 þ ð2πc=ωdÞ sin γ− sin γ φ‴ðωÞ ¼ ω 1−ð2πc=ωd− sin γÞ2 φð4Þ ðωÞ ¼
2. Basic principles of dispersion compensation and the thirdorder autocorrelation measurement Assuming that the complex optical field of an initial laser pulse before entering a dispersion system is given by V i ðtÞ ¼ AðtÞexpf−i½ω0 t þ ϕðtÞg
V o ðtÞ ¼ F −1 fFfV i ðtÞgeiΦðωÞ g
ð2Þ
where ΦðωÞ is the total spectral phase modulation imposed by the dispersion system. In general, ΦðωÞ can be expanded into a Taylor series: ΦðωÞ ¼ Φðω0 Þ þ φ1 ðω−ω0 Þ þ þ
1 φ ðω−ω0 Þ2 2! 2
1 1 φ ðω−ω0 Þ3 þ φ4 ðω−ω0 Þ4 ⋯ 3! 3 4!
ð3Þ
ð4Þ where Φ0 is the total of the frequency-independent phase shift, and Bj (j¼ 1,2,3…) are given by 3
Bj ¼ ∑ φ′i ¼ φ′stretcher þ φ′amplif ier þ φ′compressor
ð5Þ
i
The derivative of ΦðωÞ with respect to frequency ω represents the group delay B3 B4 ðω−ω0 Þ2 þ ðω−ω0 Þ3 þ ⋯ 2! 3!
ð6Þ
It is clear that the optimal dispersion compensation is essentially to have a frequency-independent group delay, or to put it in a more realistic way, to have a minimum group delay variation within a given or interested spectral range. That is, all orders of dispersion are zero, namely, n
Bj ¼ ∑φi ðjÞ ¼ φðjÞ þ φðjÞ þ φðjÞ compressor ¼ 0 stretcher amplifier i
ð9Þ
3 ð2πcÞ φ″ðωÞ 1 þ ð2πc=ωd− sin γÞ2 −2πc=ðω2 dÞ d ω2 ½1−ð2πc=ωd− sin γÞ2 3=2 ½1−ð2πc=ωd− sin γÞ2 1=2
ð10Þ where B is the perpendicular distance between gratings, γ is the incidence angle and d is the grating period. In practice, for pulse stretchers and compressors a single grating with help of roof mirrors is often used such that the laser beam hits the grating four times. Hence in this case, Eq. (8) for GDD should be multiplied by a factor of 2. In order to provide positive GDD, the stretcher is composed of gratings and focusing elements such as spherical or cylindrical mirrors. Here B becomes the equivalent grating distance which is negative in Eq. (8). The material dispersion of various orders in the laser amplifier is given by ð11Þ
i
B2 B3 B4 ðω−ω0 Þ2 þ ðω−ω0 Þ3 þ ðω−ω0 Þ4 ⋯ 2! 3! 4!
τðωÞ ¼ dΦ=dt ¼ B1 þ B2 ðω−ω0 Þ þ
−
ðjÞ φðjÞ a ðωÞ ¼ ∑ ni βi li
in which φ1 , φ2 , φ3 and φ4 are the respective first, second, third and fourth derivatives of ΦðωÞ at the reference frequency ω0 , and they are also named as group delay (GD), group delay dispersion (GDD), third order dispersion (TOD), and fourth order dispersion (FOD) respectively. For a femtosecond laser amplifier system, the total dispersion is contributed by the pulse stretcher, optical materials in the amplifier and the pulse compressor, so the total phase modulation can be expressed as ΦðωÞ ¼ Φ0 þ B1 ðω−ω0 Þ þ
ð8Þ
−3φ‴ðωÞ 3φ″ðωÞ þ ω ω2 3 ð2πcÞ φ‴ðωÞω2 −2ωφ″ðωÞ 2πc=ωd− sin γ − d ω4 1−ð2πc=ωd− sin γÞ2
ð1Þ
where AðtÞ is the amplitude envelope, ω0 is the central circular frequency of the carrier, and ϕðtÞ is the temporal phase term. After passing through the dispersion system, the corresponding output optical field can be obtained through the forward and inversed Fourier transforms:
243
ð7Þ
for j ¼ 2; 3; 4; :::
It is known that due to their large amount of dispersion, grating pairs are most commonly used to construct optical stretchers and compressors. The GDD, TOD and FOD of a grating pair are given
where ni is the number of passes for the pulse to travel through the ith element inside the amplifier, βðjÞ i is the corresponding jth order material dispersion and li is the geometrical length. The issue of dispersion compensation for a femtosecond laser amplifier up to the fourth order is thus equivalent to solving a following group of three equations within a given spectral range: φ″s þ φ″a þ φ″c ¼ 0
ð12Þ
φ‴s þ φ‴a þ φ‴c ¼ 0
ð13Þ
ð4Þ φsð4Þ þ φð4Þ a þ φc ¼ 0
ð14Þ
For the compensation of GDD and TOD only, Eqs. (12) and (13) need to be solved. It is easily to know that by properly adjusting γ c and Bc of the compressor, the complete compensation of the GDD and TOD can be achieved. However, it should be noted that the material dispersion in a regenerative amplifier is related to the pulse roundtrip number n which is half of the pass number of the pulse, and thus the total GDD and TOD of the amplifier system are also the functions of n. If the roundtrip number changes, the incident angle γ c and grating separation Bc should be modified correspondingly. In laser amplifier systems of relatively large material dispersion, the remaining high-order dispersion is likely large. In such cases, compensation for GDD and TOD only does not guarantee a good result since the dispersion above the third order will also largely affect the quality of output pulses. Therefore, dispersion compensation of even higher orders such as the fourth order becomes very important too, especially for the pulses near or shorter than 50 fs. For the FOD compensation, it needs three controllable variables to find solutions of Eqs. (12)–(14). One may thus think that the distance between gratings Bs or the incidence angle γ s of the stretcher can be adjusted for this purpose. However, in the next section our numerical analyses show that complete elimination of the FOD by this approach cannot be achieved within the meaningful and/or practical range of controllable parameters.
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Besides analyzing the effectiveness of methods for high-order dispersion compensation in theories, how to detect and verify the compensation results in practice is always another considerable problem. The effect of the TOD or FOD cannot be clearly revealed from the intensity autocorrelation curves. This is not only because of its limited contrast but also its intrinsically being always symmetrical. Thus, measurement of the third-order autocorrelation of laser pulses comes into the picture. For high energy low repetition rate laser pulses, it is suitable to use a non-collinearly phase matched single-shot third-order autocorrelator [16] although it normally has limited temporal resolution and restricted time window. Contrarily, a time-scanning third-order autocorrelation measurement associated with a larger time scanning range and higher dynamic range is often used for ultrashort laser pulses of relatively high repetition rate. Because of the concern on practical issues such as frequency conversion efficiency and ease of detection, in many applications the third-order autocorrelation is achieved through the interaction of the fundamental and its second-harmonic waves rather than one-step frequency tripling based on the third-order nonlinearity [15]. The third-order autocorrelation function can be expressed in a simplified form as Z ∞ I tc ðτÞ ¼ Iðt−τÞ I 2 ðtÞ dt ð15Þ −∞
The experimental setup of our home-made third-order autocorrelator is shown in Fig. 1. The incident 800 nm laser pulses were first frequency doubled using a 0.25 mm-thick BBO crystal with Type I phase matching to produce second-harmonic pulses. The fundamental and second-harmonic pulses were separated by a dichroic mirror. A delay line was introduced in the 800 nm beam so that the two pulses have an adjustable time delay τ; A half waveplate was placed in the 400 nm beam to change the vertical polarization into horizontal polarization of the laser pulses. Then the two beams were combined at another dichroic mirror and became coincided with each other. The two collinearly propagating pulses were directed onto a 0.1 mm-thick Type I BBO crystal to produce 266 nm signals. Note that, the thickness of the nonlinear crystal is a key parameter that will impact on the measured pulse shape and intensity contrast. In selecting the proper thickness of the nonlinear crystal, the phase matching bandwidth, group-velocity dispersion and walk-off effect should be all taken into account in addition to the conversion efficiency. In addition, another important factor to consider in building a time-scanning third-order autocorrelator is whether the phase matching is achieved with collinear or non-collinear incident beams. For collinear phase matching, it is often easier to align and also it does not have the issue of possible pulse front distortion caused by beam tilt. However, its drawback is that it may lead to lower dynamic range if the residual incident beams cannot be effectively filtered out from the detected third-harmonic signal. In our case, in
Delay line BBO1
BS2
BS1
BBO2
Prism Filter
400nm pulses ND HW
3. Numerical and experimental results The estimated values of β″, β‴, βð4Þ at 800 nm and the geometrical length li for all materials inside the femtosecond laser amplifier (Integra-HE, Quantronix Inc.) of our laboratory are listed in Table 1. The amplifier consists of two parts: a regenerative amplifier and a two-pass amplifier. In the regenerative amplifier, the roundtrip number n is determined by the difference between the time the amplified pulse being switched out and the time of the seed pulse being injected in, divided by the regen. cavity roundtrip time. For the two-pass amplifier, however, the pulse passes through the amplifier only twice and thus the roundtrip number is one. The final lump summed dispersion values of φ″a , φ‴a and φð4Þ a may be obtained according to Eq. (11). Then, by solving Eqs. (12) and (13) with the method described above, we can get the optimized parameters of the pulse compressor, with which both GDD and TOD are compensated. As mentioned above, for different roundtrip numbers the pulse travels inside a regenerative amplifier, the optimization parameters for setting the pulse compressor are also different. Table 2 gives the optimized incident angle γ c , grating separation Bc and remaining FOD under different roundtrip numbers n. Other parameters we used for these calculations are γ s ¼ 45:381 , Bs ¼ −40 cm, and ds ¼ dc ¼ 1=1400 mm. It should be noted that for any real-life femtosecond laser amplifier system, the parameters for pulse stretcher and compressor are chosen in design for a specific roundtrip times, which means the whole CPA system is essentially not optimized for all the other roundtrip times. If in practical uses, the roundtrip number needs to be changed away from the pre-set value for whatever purposes, it is often convenient and thus recommended
Table 1 Dispersion coefficients of optical material at 800 nm in our femtosecond laser amplifier.
Slit 800nm pulses
considering that the laser pulses are only 50 fs in width, being rather short, the collinear phase matching has been chosen. By using a quartz prism, a slit, and an interference filter, the third-harmonic signals were separated from the fundamental and second-harmonic pulses and recorded by a photodetector (Thorlabs: DET210). A computer-controlled stepping-motor was used to vary the delay between the two color pulses, and simultaneously the computer collected the data from the oscilloscope to which the photodetector's output is connected. Thus the third-order autocorrelation curve was obtained. Additional calibrated neutral density filters were used during the measurements to detect the intensity of the third-harmonic signals at a different attenuation level. Obviously, a third-order high dynamic range correlation between the fundamental and second-harmonic pulses can distinguish the pre-pulse from post-pulse. Useful information about the effect of higher-dispersion on the laser pulses output from a femtosecond laser amplifier can be thus obtained from the thirdorder autocorrelation curve. This can be further demonstrated by the following calculations and experiments.
PD
Fig. 1. Experimental setup of a third-order autocorrelator. BS1, BS2: dichroic beam splitters; HW: half waveplate; ND: neutral density filter; and PD: photodetector.
Material
β″ (fs2/cm)
β‴ (fs3/cm)
βð4Þ (fs4/cm)
l (cm)
ni
Ti:sapphirea KDP BK7 Ti:sapphireb Faraday isolator
566 275 446 566 1838
414 482 321 414 900
−155 −405 −106 −155 153
2 2.54 0.3 2 5
2n 2n 2n 2 2
a b
In the regenerative amplifier. In the two-pass amplifier.
W. Bao et al. / Optics & Laser Technology 54 (2013) 242–248
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Table 2 Optimum incident angle γ c , grating separation Bc , and corresponding remaining FOD for different cavity roundtrip number n to achieve completely compensation of both GDD and TOD. γ c (deg)
n 25 26 27 28 29
52.68 52.96 53.23 53.51 53.79
Bc (cm) 47.3702 47.6127 47.8548 48.0966 48.3381
φð4Þ ( 106 fs4) 1.248256 1.286506 1.324520 1.362298 1.399841
Table 3 The remaining TOD and FOD for different roundtrip number n while the second order dispersion is compensated in each case by adjusting grating separation in pulse compressor, the incident angle γ c ¼ 53:23∘ remains unchanged. n
Bc (cm)
φ2 (fs2)
φ3 ( 104 fs3)
φ4 ( 106 fs4)
Δt(fs)
25 26 27 28 29
47.6666 47.7607 47.8548 47.9489 48.0430
0 0 0 0 0
−2.2586 −1.1293 0 1.1293 2.2586
1.369833 1.347176 1.324520 1.301863 1.279207
49.76 51.94 52.63 51.47 48.77
Fig. 2. The simulated electric field and the corresponding intensity profile (left column), intensity autocorrelation (middle column) and third-order autocorrelation (right column) of the laser pulses output from the femtosecond laser amplifier we have for the regenerative cavity roundtrip times of (a) n ¼ 26, (b) n¼ 27, and (c) n¼ 28 respectively. For each roundtrip number the grating separation is adjusted so that the shortest pulse duration is obtained. Note that only for (b) both GDD and TOD are completely compensated.
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to adjust the grating separation Bc in compressor to recompensate the GDD and make the pulse appear to be the shortest. However, in so doing there will be residual TOD. Table 3 presents the remaining TOD, FOD and corresponding output pulse width after compensation for GDD when n changes near a selected optimal value. Here, we assume an initial pulse width of 35 fs and a preselected roundtrip number n¼ 27, for which both GDD and TOD are compensated. From Table 3, it can be seen that equal amount of change in remaining TOD exists but with opposite signs when the roundtrip number increases or decreases by the same amount, whereas the remaining FOD increases almost linearly with the roundtrip number n with no change in sign across the optimized settings associated with n ¼ 27. The pulse width of the final output is all around 50 fs in these five cases of different roundtrip numbers.
With the dispersion values given in Table 3, the electric field, intensity autocorrelation and third-order autocorrelation of the output laser pulses for n¼ 26, 27, and 28 respectively are shown in Fig. 2. From the middle row trances in Fig. 2 that corresponds to n¼ 27 (Fig. 2(b)), it can be clearly seen that the pulse shape is symmetrical and a small “shoulder” appears on both side of the main pulse as both the GDD and TOD are properly compensated but a relatively large FOD is present. Away from this optimized point, the superposition of TOD and FOD will lead to pulses of asymmetric shape in time domain. In particular, for n ¼26 or 28, a bulge or a noticeable satellite pulse is generated at the pulse leading/trailing edge for negative/positive TOD, as shown in Fig. 2 (a) and (c) respectively. Note that the intensity autocorrelation curves (in the middle column of Fig. 2) all look the same for the three different cases owing to the intrinsic symmetrical property of the second-order autocorrelation function. Therefore, it is
Fig. 3. The measured autocorrelation curves by second-order autocorrelator (left) and third-order autocorrelator (right) for roundtrip number n¼ 26 (a), n¼ 27 (b), and n¼ 28 (c) respectively.
W. Bao et al. / Optics & Laser Technology 54 (2013) 242–248
clearly demonstrated that one cannot determine whether there is residual TOD by using an ordinary intensity autocorrelator. Whereas the asymmetry of the pulses can be properly revealed by the third-order autocorrelation curves, and the asymmetry of third-order autocorrelation traces coincide with the real pulse shape. In the case of n ¼27, the third-order autocorrelation curve is symmetrical, which means that no TOD is present. Finally it should be noted that FOD's effect cannot be clearly seen unless GDD and TOD are both compensated perfectly such as the case in Fig. 2(b). The shoulders locate at both sides of the autocorrelation curves in Fig. 2(b) can be partially attributed to FOD. To verify the correctness of the numerical results given above, we have also performed some experiments of measuring the second- and third-order autocorrelation. The corresponding experimental data are reproduced in Fig. 3. In the left column are the autocorrelation curves obtained with a single-shot secondorder autocorrelator (SSA, Positive Light Inc.), and in the right are the associated third-order autocorrelation curves measured by the home-made scanning third-order autocorrelator. During our experiments, the single-shot second-order autocorrelator acts as a real-time monitor of the output pulses from our amplifier system, and the roundtrip number of the pulse circulating inside the regenerative amplifier is altered by changing the time the amplified pulse being switched out. The grating separation of compressor is then adjusted to compress the pulse duration until it appears to be shortest in the second-order autocorrelator and then the data of the second-order autocorrelation curve are saved. At the same time, the third-order autocorrelation curves are measured with the home-made scanning third-order autocorrelator. Recording one complete curve takes about 15 min, and during this period the laser system must remain undisturbed and stable. By repeating these steps, we obtain the results for roundtrip numbers 26, 27, and 28, respectively (as shown in Fig. 3 (a)–(c)). It can be seen that the experimental results are in reasonably good agreement with the numerical predictions. The asymmetry of the pulses can be clearly seen from the measured third-order autocorrelation curves. Note that all the measured curves are normalized. In practice, with the help of the third-order autocorrelation, not only the existence of the TOD can be detected, but also the sign of the TOD can be determined. This is very useful to identify the optimal roundtrip times for an amplifier system and achieving complete compensation of both GDD and TOD each time the roundtrip number n changes. To further compensate the TOD, the incident angle γ c must be tuned correspondingly in addition to the adjustment of grating separation of the compressor. Based on the third-order
247
autocorrelation measurement result and the optimized values given in Table 2, if there is positive/negative TOD, the incident angle γ c should be increased/decreased and then the grating separation Bc needs to be readjusted. In such a process, the asymmetry displayed in the third-order autocorrelation curve indicates that the TOD has not been completely compensated. Continuously optimizing the incident angle and the grating separation until the third order autocorrelation curve becomes symmetrical and at the same time the pulse width is also the shortest, the complete compensations of both GDD and TOD are then achieved. In this way, we can obtain the optimal pulse for any selected roundtrip number, and the measurement result of the optimized output pulse in each case will be similar to that given in Fig. 3(b) except that the specific pulse duration and the height of pulse shoulder differ slightly owing to different FODs. The above analysis and the experimental data demonstrate that both GDD and TOD can be completely compensated by simultaneously adjusting γ c and Bc through using a third-order autocorrelator. However, the data in Table 2 also indicate that the overall FOD in each case is not minimized. In fact, FOD of these cases is relatively large and it increases with the roundtrip number n. While ideally we would prefer a smaller n value so that a reduced FOD can be obtained, the roundtrip number n is predominantly determined by the gain or the magnitude of light amplification of the laser amplifier, and thus it normally cannot be reduced much because of consideration of amplified pulse power. Another approach we have tried to reduce FOD is adjusting the incidence angle γ s or the effective distance between gratings Bs for the stretcher. In particular, Fig. 4(a) presents the remaining FOD as a function of γ s with a fixed Bs ¼ −0:40 m, and correspondingly Fig. 4(b) shows FOD as a function ofBs with a fixed γ s ¼ 45:381 . In both cases the roundtrip number is fixed of n ¼ 27. It can be seen from these two figures that the remaining FOD becomes smaller with increasing γ s and decreasing Bs , but the amount of reduction is actually not large enough to have noticeable effect on the output pulse. According to the above analysis, it turns out that although theoretically three variables can make GDD, TOD and FOD being compensated simultaneously, in practice this cannot be achieved due to the constraints of the selectable variables. However, we can adjust the incidence angle γ s , the effective grating separation Bs , and the roundtrip number n together to get a relative large reduction of the FOD so that the height of the shoulder on both side of the output pulse is reduced to a satisfying level. For instance, changing the roundtrip number to n ¼20, and altering the parameters to γ s ¼601, Bs ¼−40 cm, γ c ¼ 74.751 and
Fig. 4. Remaining fourth-order dispersion obtained for various incident angle γ s (a) and grating separationBs (b) for pulse stretcher while both second- and third-order dispersions are optimally compensated.
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completely compensation of the TOD of the actual laser amplifier system. Unveil of asymmetric pulse shape by the third-order autocorrelation measurements helps to guide adjustment of system parameters to achieve amplified 50 fs laser pulses of 5 mJ level with higher pulse quality.
Acknowledgment This work is supported by the National Natural Science Foundation of China under Grant nos. 11004111, 11274185 and 61137001, the Tianjin Natural Science Foundation under Grant no. 10JCZDGX35100.
Fig. 5. Intensity profile of the output laser pulse for the case of n ¼27 in Table 2 (blue or the upper curve) and n¼ 20 with γ s ¼ 601, Bs ¼ −40 cm, γ c ¼ 74.751 and Bc ¼45.37 cm (red or the lower curve).
Bc ¼ 45.37 cm, the GDD and TOD are both compensated and the FOD is reduced to φð4Þ ¼ 7:28236 105 . The contrast of the pulse peak to its background in this case reaches over 100, which is doubled that of n¼ 27 in Table 2. The output pulse for the two cases is presented in Fig. 5. It can be seen that the relative height of FOD-related shoulder reduces to 0.0092 for n ¼20 compared with 0.0198 for n ¼ 27. In practical applications, the contrast of the laser pulse output from the CPA system can be increased to a maximum by adjusting its intrinsic parameters so that the requirement of the specific experiments may be satisfied. The final result of pulse contrast improvement can be also detected by the third-order autocorrelator. Furthermore, it has been verified that the FOD can be accomplished by using gratings of different groove densities in pulse stretcher and compressor [11,22] or using a prism pair made of highly dispersive material in addition to adjusting grating separation and the incident angle [23]. Our numerical calculation shows that use of an SF-16 prism pair with 276 cm tip-to-tip spacing and 0.3 cm extra insertion into the beam while selecting γ s ¼441, Bs ¼−41 cm, γ c ¼511 and Bc ¼ 44.2 cm in the case of n ¼27, the FOD can also completely eliminated in our laser amplifier system. The experiment study will be performed in the future. 4. Conclusions Detailed analyses of optimization of dispersion compensation for a real-life CPA laser system are presented. It is shown that for a femtosecond laser amplifier system with relatively large material dispersion, dispersion compensation up to the fourth-order is in general difficult to achieve with the standard grating-based optical pulse stretcher and compressor. Each time when the pumping current changes, the cavity roundtrip times will be changed, optimization of the grating separation of the compressor only leads to the compensation of the GDD. To compensate both GDD and TOD, another system parameter such as the incident angle at the pulse compressor or stretcher must be adjusted. Experimentally, while the impact of the remaining TOD and FOD on the output laser pulses can be actually severe, it may be only revealed by third-order autocorrelation measurement. The remaining TOD and FOD normally lead to the asymmetry of pulse shape and the appearance of bulge at the pulse leading or trailing edge, depending on the sign of residual TOD. By using a home-made third-order autocorrelator we are able to find out the parameters for
References [1] Spence DE, Kean PN, Sibbett W. 60 fs pulse generation from a self-modelocked Ti:sapphire laser. Optics Letters 1991;16:42–4. [2] Asaki MT, Huang CP, Garvey D, Zhou J, Kapteyn HC, Murnane MM. Generation of 11 fs pulses from a self-mode-locked Ti:sapphire laser. Optics Letters 1993;18:977–9. [3] Jung ID, Kärtner FX, Matuschek N, Sutter DH, Morier-Genoud F, Zhang G, et al. Self-starting 6.5 fs pulses from a Ti:sapphire laser. Optics Letters 1997;22:1009–11. [4] Strickland D, Mourou G. Compression of amplified chirped optical pulses. Optics Communications 1985;56:219–21. [5] Perry M, Pennington D, Stuart B, Tiebohl G, Britten J, Brown C, et al. Petawatt laser pulses. Optics Letters 1999;24:160–2. [6] Yamakawa K, Aoyama M, Matsuoka S, Kase T, Akahane Y, Takuma H. 100 TW sub-20 fs Ti:sapphire laser system operating at a 10 Hz repetition rate. Optics Letters 1998;23:1468–70. [7] Aoyama M, Yamakawa K, Akahane Y, Ma J, Inoue N, Ueda H, et al. 0.85 PW, 33 fs Ti:sapphire laser. Optics Letters 2003;28:1594–956. [8] Lemoff BE, Barty CPJ. Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses. Optics Letters 1993;181651-1653 1993;18. [9] Cheriaux G, Rousseau P, Salin F, Chambaret JP, Walker B, Dimauro LF. Aberration-free stretcher design for ultrashort-pulse amplification. Optics Letters 1996;21:414–6. [10] Zhu X, Cormier J-F, Piché M. Study of dispersion compensation in femtosecond lasers. Journal of Modern Optics 1996;43:1701–21. [11] Kane S, Squier J. Fourth-order-dispersion limitations of aberration-free chirped-pulse amplification systems. Journal of the Optical Society of America B 1997;14:1237–44. [12] Lenzner M, Spielmann Ch, Wintner E, Krausz F, Schmidt AJ. Sub-20 fs, kilohertz-repetition-rate Ti:sapphire amplifier. Optics Letters 1995;20:1397–9. [13] Joo T, Jia Y, Fleming GR. Ti:sapphire regenerative amplifier for ultrashort highpower multikilohertz pulses without an external stretcher. Optics Letters 1995;20:389–91. [14] Rudd JV, Korn G, Kane S, Squier J, Mourou G, Bado P. Chirped-pulse amplification of 55 fs pulses at a 1 kHz repetition rate in a Ti:A12O3 regenerative amplifier. Optics Letters 1993;18:2044–6. [15] Etchepare J, Grillon G, Orszag A. Third order autocorrelation study of amplified subpicosecond laser pulses. IEEE Journal of Quantum Electron 1983;19:775–8. [16] Collier J, Hernandez-Gomez C, Allott R, Danson C, Hall A. A single-shot thirdorder autocorrelator for pulse contrast and pulse shape measurements. Laser and Particle Beams 2001;19:231–5. [17] Wei Y, Howard S, Straub A, Wang Z, Cheng J, Gao S, et al. High sensitivity third-order autocorrelation measurement by intensity modulation and third harmonic detection. Optics Letters 2011;36:2372–4. [18] Priebe G, Janulewicz KA, Redkorechev VI, Tümmler J, Nickles PV. Pulse shape measurement by a non-collinear third-order correlation technique. Optics Communications 2006;259:848–51. [19] Aoyama M, Sagisaka A, Matsuoka S, Akahane Y, Nakano F, Yamakawa K. Contrast and phase characterization of a high-peak-power 20 fs laser pulse. Applied Physics B 2000;70:149–53. [20] 〈http://www.ultrafast-innovations.com/index.php?option=com_con tent&view=article&id=62&Itemid=74〉2013. [21] Treacy EB. Optical pulse compression with diffraction gratings. IEEE Journal of Quantum Electron 1969;5:454–8. [22] Le Blanc C, Banbeau E, Salin F, Squier JA, Barty C, Spielmann C. Toward a terawatt–kilohertz repetition-rate laser. IEEE Journal of Selected Topics in Quantum Electronics 1998;4:407–13. [23] Durfee III CG, Backus S, Murnane MM, Kapteyn HC. Design and implementation of a TW-class high-average power laser system. IEEE Journal of Selected Topics in Quantum Electronics 1998;4:395–406.
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Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Study of dispersion compensation effect of femtosecond laser amplifier using home-made third-order autocorrelator Wenxia Bao, Nan Zhang, Xiaonong Zhu n Institute of Modern Optics, Nankai University, Key Laboratory of Optical Information Science and Technology, Ministry of Education, Tianjin 300071, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 November 2012 Received in revised form 10 March 2013 Accepted 20 May 2013 Available online 26 June 2013
Detailed experimental and theoretical analyses of the dispersion compensation effect in a femtosecond laser amplifier are presented. It is confirmed that the temporal structures in the vicinity of the central peak of the amplified laser pulse are primarily caused by the uncompensated third- and/or fourth-order dispersion. The specific detrimental roles played by the third- and fourth-order dispersions such as resulting in the formation of asymmetrical pulse shapes and satellite pulses are revealed and experimentally verified with third-order autocorrelation measurements. With the help of a third-order autocorrelator, it is more efficient and accurate to optimize the third- and fourth-order dispersion compensation when the roundtrip times of a laser pulse inside the regenerative amplifier changes. For practical applications, in order to achieve laser pulses with highest quality, namely with minimum pulse energy in their wings, it is imperative to optimize the dispersion-control parameters while monitoring the laser pulses with a third-order autocorrelator. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Dispersion compensation Femtosecond laser amplifier system Third-order autocorrelation
1. Introduction Femtosecond laser technologies have been rapidly developed and applied in many research fields since the invention of Ti: sapphire laser and Kerr lensing mode locking around 1990s [1–3]. Along with the development of more and more femtosecond laser amplifiers with ever increasing pulse energy and shorter pulse durations all based on the chirped pulse amplification (CPA) technique [4–7], optimization of dispersion compensation has been extensively studied [8–11]. While for most of the ordinary femtosecond laser amplifiers, the second- and third-order dispersion compensation appears rather straightforward, which at least in theory can be achieved through adjusting both the grating separation and the incident angle of the laser beam at the pulse compressor [12–14], simultaneous fourth and even higher-order dispersion compensation remains as a technical challenge in practice. Moreover, how to detect and clearly identify the effect of the high order dispersion compensation in a femtosecond laser amplifier system is in fact a non trivial problem. For applications where the details of temporal pulse shape matter greatly, it is critical to resolve such a problem especially for pulses near or shorter than 50 fs.
n
Corresponding author. Tel.: +86 222350 3121. E-mail address: [email protected] (X. Zhu).
0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2013.05.026
In the measurements of ultrashort laser pulses, the commonly used second-order autocorrelation method fails in distinguishing pulse asymmetry and any small temporal structures within the leading or trailing edges of a pulse also cannot be resolved. This has led to the on-going exploration of the third-order autocorrelation technique [15–19]. In particular, a design of a single-shot third-order autocorrelator that is able to measure a pulse on a single-shot basis has been presented by Collier et al. [16], and also recently a novel technique for measuring third-order autocorrelation by making use of the nonlinear response of GaAsP PMT and the spectral filtering technique to retract the third harmonic signal has been reported [17]. Besides all the on-going research progresses made on making use of third-order autocorrelation in ultrashort laser pulse characterization, commercial product of third-order autocorrelators also become available[20]. It is clear that the third-order autocorrelation method is not only capable to detect pulse asymmetry, satellite pulses, but also sufficiently sensitive to the height of pulse shoulder, being associated with a larger dynamic range. In this paper, we investigate the effect of the third- and fourth-order dispersions in a femtosecond laser amplifier system with the use of a home-made third-order autocorrelator. With this autocorrelator that has a high dynamic range and is thus sensitive enough to the pulse contrast, the asymmetric features of the laser pulses from a non-optimized commercial femtosecond laser amplifier system are routinely recorded. The observed experimental results are consistent with theoretical predictions. The third-order autocorrelation measurement
W. Bao et al. / Optics & Laser Technology 54 (2013) 242–248
indicates clearly the effect of the third- and fourth-order dispersion that cannot be revealed by the ordinary or standard secondorder intensity autocorrelation. An improved understanding of optimization of dispersion compensation in femtosecond laser amplifier systems is thus obtained. This further helps to form a practical guideline on how to optimize femtosecond laser amplifiers during various femtosecond laser application experiments so that routine generation of shorter and smoother laser pulses can be achieved.
respectively by [21] φ″ðωÞ ¼
−4π 2 cB 2 ω3 d ½1−ð2πc=ωd− sin γÞ2 3=2
" # 2 −3φ″ðωÞ 1 þ ð2πc=ωdÞ sin γ− sin γ φ‴ðωÞ ¼ ω 1−ð2πc=ωd− sin γÞ2 φð4Þ ðωÞ ¼
2. Basic principles of dispersion compensation and the thirdorder autocorrelation measurement Assuming that the complex optical field of an initial laser pulse before entering a dispersion system is given by V i ðtÞ ¼ AðtÞexpf−i½ω0 t þ ϕðtÞg
V o ðtÞ ¼ F −1 fFfV i ðtÞgeiΦðωÞ g
ð2Þ
where ΦðωÞ is the total spectral phase modulation imposed by the dispersion system. In general, ΦðωÞ can be expanded into a Taylor series: ΦðωÞ ¼ Φðω0 Þ þ φ1 ðω−ω0 Þ þ þ
1 φ ðω−ω0 Þ2 2! 2
1 1 φ ðω−ω0 Þ3 þ φ4 ðω−ω0 Þ4 ⋯ 3! 3 4!
ð3Þ
ð4Þ where Φ0 is the total of the frequency-independent phase shift, and Bj (j¼ 1,2,3…) are given by 3
Bj ¼ ∑ φ′i ¼ φ′stretcher þ φ′amplif ier þ φ′compressor
ð5Þ
i
The derivative of ΦðωÞ with respect to frequency ω represents the group delay B3 B4 ðω−ω0 Þ2 þ ðω−ω0 Þ3 þ ⋯ 2! 3!
ð6Þ
It is clear that the optimal dispersion compensation is essentially to have a frequency-independent group delay, or to put it in a more realistic way, to have a minimum group delay variation within a given or interested spectral range. That is, all orders of dispersion are zero, namely, n
Bj ¼ ∑φi ðjÞ ¼ φðjÞ þ φðjÞ þ φðjÞ compressor ¼ 0 stretcher amplifier i
ð9Þ
3 ð2πcÞ φ″ðωÞ 1 þ ð2πc=ωd− sin γÞ2 −2πc=ðω2 dÞ d ω2 ½1−ð2πc=ωd− sin γÞ2 3=2 ½1−ð2πc=ωd− sin γÞ2 1=2
ð10Þ where B is the perpendicular distance between gratings, γ is the incidence angle and d is the grating period. In practice, for pulse stretchers and compressors a single grating with help of roof mirrors is often used such that the laser beam hits the grating four times. Hence in this case, Eq. (8) for GDD should be multiplied by a factor of 2. In order to provide positive GDD, the stretcher is composed of gratings and focusing elements such as spherical or cylindrical mirrors. Here B becomes the equivalent grating distance which is negative in Eq. (8). The material dispersion of various orders in the laser amplifier is given by ð11Þ
i
B2 B3 B4 ðω−ω0 Þ2 þ ðω−ω0 Þ3 þ ðω−ω0 Þ4 ⋯ 2! 3! 4!
τðωÞ ¼ dΦ=dt ¼ B1 þ B2 ðω−ω0 Þ þ
−
ðjÞ φðjÞ a ðωÞ ¼ ∑ ni βi li
in which φ1 , φ2 , φ3 and φ4 are the respective first, second, third and fourth derivatives of ΦðωÞ at the reference frequency ω0 , and they are also named as group delay (GD), group delay dispersion (GDD), third order dispersion (TOD), and fourth order dispersion (FOD) respectively. For a femtosecond laser amplifier system, the total dispersion is contributed by the pulse stretcher, optical materials in the amplifier and the pulse compressor, so the total phase modulation can be expressed as ΦðωÞ ¼ Φ0 þ B1 ðω−ω0 Þ þ
ð8Þ
−3φ‴ðωÞ 3φ″ðωÞ þ ω ω2 3 ð2πcÞ φ‴ðωÞω2 −2ωφ″ðωÞ 2πc=ωd− sin γ − d ω4 1−ð2πc=ωd− sin γÞ2
ð1Þ
where AðtÞ is the amplitude envelope, ω0 is the central circular frequency of the carrier, and ϕðtÞ is the temporal phase term. After passing through the dispersion system, the corresponding output optical field can be obtained through the forward and inversed Fourier transforms:
243
ð7Þ
for j ¼ 2; 3; 4; :::
It is known that due to their large amount of dispersion, grating pairs are most commonly used to construct optical stretchers and compressors. The GDD, TOD and FOD of a grating pair are given
where ni is the number of passes for the pulse to travel through the ith element inside the amplifier, βðjÞ i is the corresponding jth order material dispersion and li is the geometrical length. The issue of dispersion compensation for a femtosecond laser amplifier up to the fourth order is thus equivalent to solving a following group of three equations within a given spectral range: φ″s þ φ″a þ φ″c ¼ 0
ð12Þ
φ‴s þ φ‴a þ φ‴c ¼ 0
ð13Þ
ð4Þ φsð4Þ þ φð4Þ a þ φc ¼ 0
ð14Þ
For the compensation of GDD and TOD only, Eqs. (12) and (13) need to be solved. It is easily to know that by properly adjusting γ c and Bc of the compressor, the complete compensation of the GDD and TOD can be achieved. However, it should be noted that the material dispersion in a regenerative amplifier is related to the pulse roundtrip number n which is half of the pass number of the pulse, and thus the total GDD and TOD of the amplifier system are also the functions of n. If the roundtrip number changes, the incident angle γ c and grating separation Bc should be modified correspondingly. In laser amplifier systems of relatively large material dispersion, the remaining high-order dispersion is likely large. In such cases, compensation for GDD and TOD only does not guarantee a good result since the dispersion above the third order will also largely affect the quality of output pulses. Therefore, dispersion compensation of even higher orders such as the fourth order becomes very important too, especially for the pulses near or shorter than 50 fs. For the FOD compensation, it needs three controllable variables to find solutions of Eqs. (12)–(14). One may thus think that the distance between gratings Bs or the incidence angle γ s of the stretcher can be adjusted for this purpose. However, in the next section our numerical analyses show that complete elimination of the FOD by this approach cannot be achieved within the meaningful and/or practical range of controllable parameters.
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Besides analyzing the effectiveness of methods for high-order dispersion compensation in theories, how to detect and verify the compensation results in practice is always another considerable problem. The effect of the TOD or FOD cannot be clearly revealed from the intensity autocorrelation curves. This is not only because of its limited contrast but also its intrinsically being always symmetrical. Thus, measurement of the third-order autocorrelation of laser pulses comes into the picture. For high energy low repetition rate laser pulses, it is suitable to use a non-collinearly phase matched single-shot third-order autocorrelator [16] although it normally has limited temporal resolution and restricted time window. Contrarily, a time-scanning third-order autocorrelation measurement associated with a larger time scanning range and higher dynamic range is often used for ultrashort laser pulses of relatively high repetition rate. Because of the concern on practical issues such as frequency conversion efficiency and ease of detection, in many applications the third-order autocorrelation is achieved through the interaction of the fundamental and its second-harmonic waves rather than one-step frequency tripling based on the third-order nonlinearity [15]. The third-order autocorrelation function can be expressed in a simplified form as Z ∞ I tc ðτÞ ¼ Iðt−τÞ I 2 ðtÞ dt ð15Þ −∞
The experimental setup of our home-made third-order autocorrelator is shown in Fig. 1. The incident 800 nm laser pulses were first frequency doubled using a 0.25 mm-thick BBO crystal with Type I phase matching to produce second-harmonic pulses. The fundamental and second-harmonic pulses were separated by a dichroic mirror. A delay line was introduced in the 800 nm beam so that the two pulses have an adjustable time delay τ; A half waveplate was placed in the 400 nm beam to change the vertical polarization into horizontal polarization of the laser pulses. Then the two beams were combined at another dichroic mirror and became coincided with each other. The two collinearly propagating pulses were directed onto a 0.1 mm-thick Type I BBO crystal to produce 266 nm signals. Note that, the thickness of the nonlinear crystal is a key parameter that will impact on the measured pulse shape and intensity contrast. In selecting the proper thickness of the nonlinear crystal, the phase matching bandwidth, group-velocity dispersion and walk-off effect should be all taken into account in addition to the conversion efficiency. In addition, another important factor to consider in building a time-scanning third-order autocorrelator is whether the phase matching is achieved with collinear or non-collinear incident beams. For collinear phase matching, it is often easier to align and also it does not have the issue of possible pulse front distortion caused by beam tilt. However, its drawback is that it may lead to lower dynamic range if the residual incident beams cannot be effectively filtered out from the detected third-harmonic signal. In our case, in
Delay line BBO1
BS2
BS1
BBO2
Prism Filter
400nm pulses ND HW
3. Numerical and experimental results The estimated values of β″, β‴, βð4Þ at 800 nm and the geometrical length li for all materials inside the femtosecond laser amplifier (Integra-HE, Quantronix Inc.) of our laboratory are listed in Table 1. The amplifier consists of two parts: a regenerative amplifier and a two-pass amplifier. In the regenerative amplifier, the roundtrip number n is determined by the difference between the time the amplified pulse being switched out and the time of the seed pulse being injected in, divided by the regen. cavity roundtrip time. For the two-pass amplifier, however, the pulse passes through the amplifier only twice and thus the roundtrip number is one. The final lump summed dispersion values of φ″a , φ‴a and φð4Þ a may be obtained according to Eq. (11). Then, by solving Eqs. (12) and (13) with the method described above, we can get the optimized parameters of the pulse compressor, with which both GDD and TOD are compensated. As mentioned above, for different roundtrip numbers the pulse travels inside a regenerative amplifier, the optimization parameters for setting the pulse compressor are also different. Table 2 gives the optimized incident angle γ c , grating separation Bc and remaining FOD under different roundtrip numbers n. Other parameters we used for these calculations are γ s ¼ 45:381 , Bs ¼ −40 cm, and ds ¼ dc ¼ 1=1400 mm. It should be noted that for any real-life femtosecond laser amplifier system, the parameters for pulse stretcher and compressor are chosen in design for a specific roundtrip times, which means the whole CPA system is essentially not optimized for all the other roundtrip times. If in practical uses, the roundtrip number needs to be changed away from the pre-set value for whatever purposes, it is often convenient and thus recommended
Table 1 Dispersion coefficients of optical material at 800 nm in our femtosecond laser amplifier.
Slit 800nm pulses
considering that the laser pulses are only 50 fs in width, being rather short, the collinear phase matching has been chosen. By using a quartz prism, a slit, and an interference filter, the third-harmonic signals were separated from the fundamental and second-harmonic pulses and recorded by a photodetector (Thorlabs: DET210). A computer-controlled stepping-motor was used to vary the delay between the two color pulses, and simultaneously the computer collected the data from the oscilloscope to which the photodetector's output is connected. Thus the third-order autocorrelation curve was obtained. Additional calibrated neutral density filters were used during the measurements to detect the intensity of the third-harmonic signals at a different attenuation level. Obviously, a third-order high dynamic range correlation between the fundamental and second-harmonic pulses can distinguish the pre-pulse from post-pulse. Useful information about the effect of higher-dispersion on the laser pulses output from a femtosecond laser amplifier can be thus obtained from the thirdorder autocorrelation curve. This can be further demonstrated by the following calculations and experiments.
PD
Fig. 1. Experimental setup of a third-order autocorrelator. BS1, BS2: dichroic beam splitters; HW: half waveplate; ND: neutral density filter; and PD: photodetector.
Material
β″ (fs2/cm)
β‴ (fs3/cm)
βð4Þ (fs4/cm)
l (cm)
ni
Ti:sapphirea KDP BK7 Ti:sapphireb Faraday isolator
566 275 446 566 1838
414 482 321 414 900
−155 −405 −106 −155 153
2 2.54 0.3 2 5
2n 2n 2n 2 2
a b
In the regenerative amplifier. In the two-pass amplifier.
W. Bao et al. / Optics & Laser Technology 54 (2013) 242–248
245
Table 2 Optimum incident angle γ c , grating separation Bc , and corresponding remaining FOD for different cavity roundtrip number n to achieve completely compensation of both GDD and TOD. γ c (deg)
n 25 26 27 28 29
52.68 52.96 53.23 53.51 53.79
Bc (cm) 47.3702 47.6127 47.8548 48.0966 48.3381
φð4Þ ( 106 fs4) 1.248256 1.286506 1.324520 1.362298 1.399841
Table 3 The remaining TOD and FOD for different roundtrip number n while the second order dispersion is compensated in each case by adjusting grating separation in pulse compressor, the incident angle γ c ¼ 53:23∘ remains unchanged. n
Bc (cm)
φ2 (fs2)
φ3 ( 104 fs3)
φ4 ( 106 fs4)
Δt(fs)
25 26 27 28 29
47.6666 47.7607 47.8548 47.9489 48.0430
0 0 0 0 0
−2.2586 −1.1293 0 1.1293 2.2586
1.369833 1.347176 1.324520 1.301863 1.279207
49.76 51.94 52.63 51.47 48.77
Fig. 2. The simulated electric field and the corresponding intensity profile (left column), intensity autocorrelation (middle column) and third-order autocorrelation (right column) of the laser pulses output from the femtosecond laser amplifier we have for the regenerative cavity roundtrip times of (a) n ¼ 26, (b) n¼ 27, and (c) n¼ 28 respectively. For each roundtrip number the grating separation is adjusted so that the shortest pulse duration is obtained. Note that only for (b) both GDD and TOD are completely compensated.
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W. Bao et al. / Optics & Laser Technology 54 (2013) 242–248
to adjust the grating separation Bc in compressor to recompensate the GDD and make the pulse appear to be the shortest. However, in so doing there will be residual TOD. Table 3 presents the remaining TOD, FOD and corresponding output pulse width after compensation for GDD when n changes near a selected optimal value. Here, we assume an initial pulse width of 35 fs and a preselected roundtrip number n¼ 27, for which both GDD and TOD are compensated. From Table 3, it can be seen that equal amount of change in remaining TOD exists but with opposite signs when the roundtrip number increases or decreases by the same amount, whereas the remaining FOD increases almost linearly with the roundtrip number n with no change in sign across the optimized settings associated with n ¼ 27. The pulse width of the final output is all around 50 fs in these five cases of different roundtrip numbers.
With the dispersion values given in Table 3, the electric field, intensity autocorrelation and third-order autocorrelation of the output laser pulses for n¼ 26, 27, and 28 respectively are shown in Fig. 2. From the middle row trances in Fig. 2 that corresponds to n¼ 27 (Fig. 2(b)), it can be clearly seen that the pulse shape is symmetrical and a small “shoulder” appears on both side of the main pulse as both the GDD and TOD are properly compensated but a relatively large FOD is present. Away from this optimized point, the superposition of TOD and FOD will lead to pulses of asymmetric shape in time domain. In particular, for n ¼26 or 28, a bulge or a noticeable satellite pulse is generated at the pulse leading/trailing edge for negative/positive TOD, as shown in Fig. 2 (a) and (c) respectively. Note that the intensity autocorrelation curves (in the middle column of Fig. 2) all look the same for the three different cases owing to the intrinsic symmetrical property of the second-order autocorrelation function. Therefore, it is
Fig. 3. The measured autocorrelation curves by second-order autocorrelator (left) and third-order autocorrelator (right) for roundtrip number n¼ 26 (a), n¼ 27 (b), and n¼ 28 (c) respectively.
W. Bao et al. / Optics & Laser Technology 54 (2013) 242–248
clearly demonstrated that one cannot determine whether there is residual TOD by using an ordinary intensity autocorrelator. Whereas the asymmetry of the pulses can be properly revealed by the third-order autocorrelation curves, and the asymmetry of third-order autocorrelation traces coincide with the real pulse shape. In the case of n ¼27, the third-order autocorrelation curve is symmetrical, which means that no TOD is present. Finally it should be noted that FOD's effect cannot be clearly seen unless GDD and TOD are both compensated perfectly such as the case in Fig. 2(b). The shoulders locate at both sides of the autocorrelation curves in Fig. 2(b) can be partially attributed to FOD. To verify the correctness of the numerical results given above, we have also performed some experiments of measuring the second- and third-order autocorrelation. The corresponding experimental data are reproduced in Fig. 3. In the left column are the autocorrelation curves obtained with a single-shot secondorder autocorrelator (SSA, Positive Light Inc.), and in the right are the associated third-order autocorrelation curves measured by the home-made scanning third-order autocorrelator. During our experiments, the single-shot second-order autocorrelator acts as a real-time monitor of the output pulses from our amplifier system, and the roundtrip number of the pulse circulating inside the regenerative amplifier is altered by changing the time the amplified pulse being switched out. The grating separation of compressor is then adjusted to compress the pulse duration until it appears to be shortest in the second-order autocorrelator and then the data of the second-order autocorrelation curve are saved. At the same time, the third-order autocorrelation curves are measured with the home-made scanning third-order autocorrelator. Recording one complete curve takes about 15 min, and during this period the laser system must remain undisturbed and stable. By repeating these steps, we obtain the results for roundtrip numbers 26, 27, and 28, respectively (as shown in Fig. 3 (a)–(c)). It can be seen that the experimental results are in reasonably good agreement with the numerical predictions. The asymmetry of the pulses can be clearly seen from the measured third-order autocorrelation curves. Note that all the measured curves are normalized. In practice, with the help of the third-order autocorrelation, not only the existence of the TOD can be detected, but also the sign of the TOD can be determined. This is very useful to identify the optimal roundtrip times for an amplifier system and achieving complete compensation of both GDD and TOD each time the roundtrip number n changes. To further compensate the TOD, the incident angle γ c must be tuned correspondingly in addition to the adjustment of grating separation of the compressor. Based on the third-order
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autocorrelation measurement result and the optimized values given in Table 2, if there is positive/negative TOD, the incident angle γ c should be increased/decreased and then the grating separation Bc needs to be readjusted. In such a process, the asymmetry displayed in the third-order autocorrelation curve indicates that the TOD has not been completely compensated. Continuously optimizing the incident angle and the grating separation until the third order autocorrelation curve becomes symmetrical and at the same time the pulse width is also the shortest, the complete compensations of both GDD and TOD are then achieved. In this way, we can obtain the optimal pulse for any selected roundtrip number, and the measurement result of the optimized output pulse in each case will be similar to that given in Fig. 3(b) except that the specific pulse duration and the height of pulse shoulder differ slightly owing to different FODs. The above analysis and the experimental data demonstrate that both GDD and TOD can be completely compensated by simultaneously adjusting γ c and Bc through using a third-order autocorrelator. However, the data in Table 2 also indicate that the overall FOD in each case is not minimized. In fact, FOD of these cases is relatively large and it increases with the roundtrip number n. While ideally we would prefer a smaller n value so that a reduced FOD can be obtained, the roundtrip number n is predominantly determined by the gain or the magnitude of light amplification of the laser amplifier, and thus it normally cannot be reduced much because of consideration of amplified pulse power. Another approach we have tried to reduce FOD is adjusting the incidence angle γ s or the effective distance between gratings Bs for the stretcher. In particular, Fig. 4(a) presents the remaining FOD as a function of γ s with a fixed Bs ¼ −0:40 m, and correspondingly Fig. 4(b) shows FOD as a function ofBs with a fixed γ s ¼ 45:381 . In both cases the roundtrip number is fixed of n ¼ 27. It can be seen from these two figures that the remaining FOD becomes smaller with increasing γ s and decreasing Bs , but the amount of reduction is actually not large enough to have noticeable effect on the output pulse. According to the above analysis, it turns out that although theoretically three variables can make GDD, TOD and FOD being compensated simultaneously, in practice this cannot be achieved due to the constraints of the selectable variables. However, we can adjust the incidence angle γ s , the effective grating separation Bs , and the roundtrip number n together to get a relative large reduction of the FOD so that the height of the shoulder on both side of the output pulse is reduced to a satisfying level. For instance, changing the roundtrip number to n ¼20, and altering the parameters to γ s ¼601, Bs ¼−40 cm, γ c ¼ 74.751 and
Fig. 4. Remaining fourth-order dispersion obtained for various incident angle γ s (a) and grating separationBs (b) for pulse stretcher while both second- and third-order dispersions are optimally compensated.
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completely compensation of the TOD of the actual laser amplifier system. Unveil of asymmetric pulse shape by the third-order autocorrelation measurements helps to guide adjustment of system parameters to achieve amplified 50 fs laser pulses of 5 mJ level with higher pulse quality.
Acknowledgment This work is supported by the National Natural Science Foundation of China under Grant nos. 11004111, 11274185 and 61137001, the Tianjin Natural Science Foundation under Grant no. 10JCZDGX35100.
Fig. 5. Intensity profile of the output laser pulse for the case of n ¼27 in Table 2 (blue or the upper curve) and n¼ 20 with γ s ¼ 601, Bs ¼ −40 cm, γ c ¼ 74.751 and Bc ¼45.37 cm (red or the lower curve).
Bc ¼ 45.37 cm, the GDD and TOD are both compensated and the FOD is reduced to φð4Þ ¼ 7:28236 105 . The contrast of the pulse peak to its background in this case reaches over 100, which is doubled that of n¼ 27 in Table 2. The output pulse for the two cases is presented in Fig. 5. It can be seen that the relative height of FOD-related shoulder reduces to 0.0092 for n ¼20 compared with 0.0198 for n ¼ 27. In practical applications, the contrast of the laser pulse output from the CPA system can be increased to a maximum by adjusting its intrinsic parameters so that the requirement of the specific experiments may be satisfied. The final result of pulse contrast improvement can be also detected by the third-order autocorrelator. Furthermore, it has been verified that the FOD can be accomplished by using gratings of different groove densities in pulse stretcher and compressor [11,22] or using a prism pair made of highly dispersive material in addition to adjusting grating separation and the incident angle [23]. Our numerical calculation shows that use of an SF-16 prism pair with 276 cm tip-to-tip spacing and 0.3 cm extra insertion into the beam while selecting γ s ¼441, Bs ¼−41 cm, γ c ¼511 and Bc ¼ 44.2 cm in the case of n ¼27, the FOD can also completely eliminated in our laser amplifier system. The experiment study will be performed in the future. 4. Conclusions Detailed analyses of optimization of dispersion compensation for a real-life CPA laser system are presented. It is shown that for a femtosecond laser amplifier system with relatively large material dispersion, dispersion compensation up to the fourth-order is in general difficult to achieve with the standard grating-based optical pulse stretcher and compressor. Each time when the pumping current changes, the cavity roundtrip times will be changed, optimization of the grating separation of the compressor only leads to the compensation of the GDD. To compensate both GDD and TOD, another system parameter such as the incident angle at the pulse compressor or stretcher must be adjusted. Experimentally, while the impact of the remaining TOD and FOD on the output laser pulses can be actually severe, it may be only revealed by third-order autocorrelation measurement. The remaining TOD and FOD normally lead to the asymmetry of pulse shape and the appearance of bulge at the pulse leading or trailing edge, depending on the sign of residual TOD. By using a home-made third-order autocorrelator we are able to find out the parameters for
References [1] Spence DE, Kean PN, Sibbett W. 60 fs pulse generation from a self-modelocked Ti:sapphire laser. Optics Letters 1991;16:42–4. [2] Asaki MT, Huang CP, Garvey D, Zhou J, Kapteyn HC, Murnane MM. Generation of 11 fs pulses from a self-mode-locked Ti:sapphire laser. Optics Letters 1993;18:977–9. [3] Jung ID, Kärtner FX, Matuschek N, Sutter DH, Morier-Genoud F, Zhang G, et al. Self-starting 6.5 fs pulses from a Ti:sapphire laser. Optics Letters 1997;22:1009–11. [4] Strickland D, Mourou G. Compression of amplified chirped optical pulses. Optics Communications 1985;56:219–21. [5] Perry M, Pennington D, Stuart B, Tiebohl G, Britten J, Brown C, et al. Petawatt laser pulses. Optics Letters 1999;24:160–2. [6] Yamakawa K, Aoyama M, Matsuoka S, Kase T, Akahane Y, Takuma H. 100 TW sub-20 fs Ti:sapphire laser system operating at a 10 Hz repetition rate. Optics Letters 1998;23:1468–70. [7] Aoyama M, Yamakawa K, Akahane Y, Ma J, Inoue N, Ueda H, et al. 0.85 PW, 33 fs Ti:sapphire laser. Optics Letters 2003;28:1594–956. [8] Lemoff BE, Barty CPJ. Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses. Optics Letters 1993;181651-1653 1993;18. [9] Cheriaux G, Rousseau P, Salin F, Chambaret JP, Walker B, Dimauro LF. Aberration-free stretcher design for ultrashort-pulse amplification. Optics Letters 1996;21:414–6. [10] Zhu X, Cormier J-F, Piché M. Study of dispersion compensation in femtosecond lasers. Journal of Modern Optics 1996;43:1701–21. [11] Kane S, Squier J. Fourth-order-dispersion limitations of aberration-free chirped-pulse amplification systems. Journal of the Optical Society of America B 1997;14:1237–44. [12] Lenzner M, Spielmann Ch, Wintner E, Krausz F, Schmidt AJ. Sub-20 fs, kilohertz-repetition-rate Ti:sapphire amplifier. Optics Letters 1995;20:1397–9. [13] Joo T, Jia Y, Fleming GR. Ti:sapphire regenerative amplifier for ultrashort highpower multikilohertz pulses without an external stretcher. Optics Letters 1995;20:389–91. [14] Rudd JV, Korn G, Kane S, Squier J, Mourou G, Bado P. Chirped-pulse amplification of 55 fs pulses at a 1 kHz repetition rate in a Ti:A12O3 regenerative amplifier. Optics Letters 1993;18:2044–6. [15] Etchepare J, Grillon G, Orszag A. Third order autocorrelation study of amplified subpicosecond laser pulses. IEEE Journal of Quantum Electron 1983;19:775–8. [16] Collier J, Hernandez-Gomez C, Allott R, Danson C, Hall A. A single-shot thirdorder autocorrelator for pulse contrast and pulse shape measurements. Laser and Particle Beams 2001;19:231–5. [17] Wei Y, Howard S, Straub A, Wang Z, Cheng J, Gao S, et al. High sensitivity third-order autocorrelation measurement by intensity modulation and third harmonic detection. Optics Letters 2011;36:2372–4. [18] Priebe G, Janulewicz KA, Redkorechev VI, Tümmler J, Nickles PV. Pulse shape measurement by a non-collinear third-order correlation technique. Optics Communications 2006;259:848–51. [19] Aoyama M, Sagisaka A, Matsuoka S, Akahane Y, Nakano F, Yamakawa K. Contrast and phase characterization of a high-peak-power 20 fs laser pulse. Applied Physics B 2000;70:149–53. [20] 〈http://www.ultrafast-innovations.com/index.php?option=com_con tent&view=article&id=62&Itemid=74〉2013. [21] Treacy EB. Optical pulse compression with diffraction gratings. IEEE Journal of Quantum Electron 1969;5:454–8. [22] Le Blanc C, Banbeau E, Salin F, Squier JA, Barty C, Spielmann C. Toward a terawatt–kilohertz repetition-rate laser. IEEE Journal of Selected Topics in Quantum Electronics 1998;4:407–13. [23] Durfee III CG, Backus S, Murnane MM, Kapteyn HC. Design and implementation of a TW-class high-average power laser system. IEEE Journal of Selected Topics in Quantum Electronics 1998;4:395–406.