中红外飞秒光参量放大过程中闲频光相移研究
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摘要
本文总结了现阶段飞秒中红外光参量放大过程中,新产生的中红外飞秒脉冲频域相位及载波-包络相位的研究成果。光参量产生及光参量放大属于二阶非线性光学范畴,可以在非中心对称的二阶非线性晶体中产生,它可以拓展飞秒脉冲的波长覆盖范围。通常,将两束高频光(称为泵浦光及信号光)注入到二阶非线性晶体,选择恰当的相位匹配角以满足动量守恒条件,首先会发生差频过程产生中红外闲频光,然后通过参量放大的方式对信号光及闲频光进行放大。目前,工作在中红外波段的宽带激光增益介质数量有限,并且调谐能力受限于增益带宽,因此光参量放大是产生宽带可调谐中红外飞秒脉冲的主要手段。鉴于中红外飞秒脉冲在光谱学方面的重要应用,以及在产生孤立阿秒脉冲方面的潜在应用,通过光参量放大产生中红外飞秒脉冲引起了人们的广泛关注。研究方向主要集中于产生脉宽更短、能量更高的中红外飞秒脉冲。
通过光参量放大产生可调谐中红外飞秒脉冲的问题在于：中红外波段的二阶非线性晶体通常具有较大的反常色散值,因此通过光参量放大过程产生的中红外飞秒脉冲通常具有负啁啾,脉宽偏离傅氏变换极限。为了获得最短脉宽以提高泵浦-探测等实验中的时间分辨率,需要对色散进行补偿以获得最短的飞秒脉冲。鉴于中红外波段反常材料色散及脉冲负啁啾的性质,目前主要采用两种方式对色散进行补偿：(1)让脉冲通过在中红外波段具有正常色散的介质,例如硅、锗等；(2)利用提供正常色散的光栅展宽器对色散进行补偿。然而,要想进行色散补偿,前提是确切知道脉冲的频域相位,特别是二次相位。该值决定了补偿用色散量的大小(在实际中体现为正常色散介质的长度或者光栅间距)。目前,人们对该频域相位的研究较为匮乏,并不清楚它受何种因素影响、影响程度多大等问题。由于该相移对于后续的脉冲压缩过程起决定影响,因此有必要进行深入的理论研究及分析,以期为实验提供理论指导。
光参量放大过程的另一优点在于可以产生载波-包络相位稳定的中红外飞秒脉冲序列。众所周知,光脉冲由脉冲包络以及光载波描述。当(包络)脉宽很短以至于仅包含几个光载波周期时,对应的光脉冲称为周期量级脉冲。此时,对脉冲的完备描述需要第三个物理量,即包络最大值与载波最大值之间的相对相差,称之为载波-包络相位(CEP)。如果该值为0,对应余弦脉冲,该值为π／2对应正弦脉冲。周期量级脉冲的一个重要应用在于阿秒脉冲产生。理论及实验表明：余弦周期量级脉冲可以导致单个孤立阿秒脉冲产生,而正弦脉冲将导致多阿秒脉冲产生。后者对于研究阿秒时间尺度的超快过程(例如电子的迟豫过程)不利,因为它导致时间分辨率下降。因此人们的研究主要集中于产生波形可重复、不存在脉冲间载波-包络相位起伏的周期量级脉冲序列。光参量放大过程中,泵浦光脉冲序列存在脉冲间的载波-包络相位起伏的条件下,如果采用泵浦光在三阶非线性介质中通过空时自聚焦、自相位调制、四波混频以及更高阶非线性效应产生超连续白光作为信号光脉冲序列,则信号光脉冲序列的载波-包络相位起伏与泵浦光完全一致。通过差频及参量放大过程产生的飞秒中红外脉冲正比于泵浦光与信号光共轭的乘积,因此相位相减导致产生的中红外脉冲不存在载波-包络相位起伏。这是一种被动的载波-包络相位稳定方式,仅通过单块二阶非线性晶体就可以实现,因此成为人们研究的热点。然而,该方法的问题在于：闲频光的载波-包络相位与增益有关。已有研究表明泵浦光10%的能量起伏将导致闲频光载波-包络相位的起伏可以达到0.6rad。目前商品化的激光器输出脉冲能量稳定性小于1%。因此由激光器能量起伏造成的载波-包络相位起伏可以忽略。然而,以上分析基于平面波假定,即假设泵浦光、信号光及闲频光均为平面波。而在实际工作中,泵浦光和信号光通常为聚焦高斯光束,因此传输轴上点与轴外点的光强差别可以轻易达到50%。这种横向增益差别必将导致闲频光的载波-包络相位存在横向分布。目前对此问题还没有研究报道。
本文分以下部分进行论述：
第一章,综述飞秒光学的发展,超短脉冲的线性传输性质,并介绍周期量级脉冲及载波-包络相位。自1960年激光发明以来,超快光学发展中的关键技术包括：(1)以Ti:sapphire为代表的高性能宽带固体激光工作介质的应用,以及克尔透镜锁模作为快速可饱和吸收体的应用,最终促成目前应用最广的商品化Ti:sapphire振荡器的出现；(2)最初应用于微波放大的啁啾脉冲放大技术的引入,其中包括能够提供正常色散的Martinez型光栅对的引入,显著提升了超短脉冲的能量并且避免了材料及光学元件的损伤问题；(3)非线性光学、特别是频率转换技术(例如倍频,和频,差频产生及光参量放大等)在超快光学领域的应用,拓展了能够获得的超短脉冲激光波长范围,并能提供显著的波长调谐能力,代表之一是超连续白光作为种子光的光参量放大器。此外,光参量放大与啁啾脉冲相结合的产物——光参量啁啾脉冲放大是超短脉冲产生／放大技术发展中十分重要的进步,它能提供高能超短脉冲并且不受常规激光器／放大器量子缺陷导致的热效应的影响。(4)载波-包络相位稳定的周期量级脉冲与惰性气体相互作用能够获得阿秒脉冲,从而开拓了阿秒科学这一新兴研究领域。
第二章,介绍二阶非线性光学,特别是超短脉冲二阶非线性光学。由于材料色散的作用,介质中互作用的超短脉中之间存在群速度失配。随着传输距离的增大,脉冲之间在时间上发生相互走离,这将导致转换效率下降。此外,在群速度色散的作用下,单个脉冲也会发生脉冲展宽,因此峰值光强下降并且导致转换效率下降,并且脉冲发生啁啾,偏离傅氏变换极限。这是与单色波非线性相互作用的主要差别所在。
第三章,介绍飞秒参量下转换过程中材料色散导致的频域相移研究。在理论上研究了色散介质中,中红外飞秒光参量下转换过程中的频域相移.主要研究材料群速度色散(GVD)对频域相移的影响,目的对中红外飞秒脉冲的压缩给出理论指导。研究结果表明：通过参量下转化产生的中红外飞秒脉冲的频域相移与线性传输得到的结果有显著差别。主要研究两种产生中红外飞秒脉冲的方式：光参量放大以及差频过程。频域相移由初始注入条件、以及高频场累积的相移决定。研究结果表明：差频过程中,泵浦光消耗对中红外飞秒脉冲频域相移几乎没有影响,而在光参量放大过程中,线性GVD以及高的参量增益使中红外飞秒脉冲的频域相移显著区别于线形传输结果：增益越大,频域相移越小。定量来讲：在差频过程中,中红外飞秒脉冲的频域相移接近线性传输值的一半,而在光参量放大过程中,相移更小。为了获得最短的中红外飞秒脉冲,研究结果决定了色散补偿所需要的色散量。
第四章,介绍了差频及参量放大过程中,考虑泵浦光和信号光为实际应用中高斯光束的条件下,闲频光横向载波-包络相位的非均匀分布。在实际的载波-包络相位稳定的差频装置中,泵浦光和闲频光通常是光强分布不均匀的高斯光束。由于载波-包络相位依赖于增益,因此非均匀的光强分布导致了闲频光横向的增益分布不均匀,从而导致了闲频光横向载波-包络相位分布不均匀。研究结果表明,在实际的装置中,在高增益的阶段,载波-包络相位的横向非均匀性要远小于π／2。然而,当增益在传播轴上达到饱和时,载波-包络相位的横向差别将大于π／2。
第五章,总结与展望。
This thesis summarizes our recent research on spectral phase and carrier-envelope phase of the mid-infrared femtosecond pulses generated through optical parametric amplification.Optical parametric generation and amplification are second order nonlinear optical phenomena, which occur in quadratic nonlinear crystals. They can extend the wavelength coverage of femtosecond pulses. If two higher frequency pulses are simultaneously injected into a quadratic nonlinear crystal, under proper conditions of phase matching which guarantee momentum conservation, first new frequency pulses, termed idler, will be generated through difference frequency generation, and then both the signal and the idler will be amplified through optical parametric amplification, at the cost of pump consumption. Nowadays, abailable broadband laser gain media at mid-infrared are quite limited, and tuning capability is further restricted by gain bandwidth. As a result, optical parametric amplification is a necessary way of generating broadband tunable femtosecond mid-infrared pulses. Due to the important applications of mid-infrared femtosecond pulses in spectroscopy and potential use in generating isolated attosecond pulses. Generating mid-infrared femtosecond pulses through optical parametric amplification has aroused widespread interest. Currently, most research is focused on generating shorter and more energetic mid-infrared femtosecond pulses.
It is well known that in the case of linear propagation of ultrashort pulses in dispersive media, transform-limited (TL) pulses will broaden in duration due to the effect of group velocity dispersion (GVD), which in the spectral domain adds a spectral phase proportional to the propagation distance and quadratic in frequency. The effect of GVD will be much more pronounced in generating MIR femtosecond pulses. In the midinfrared region, commonly used nonlinear optical crystals, such as lithium niobate, potassium niobate PPLN, etc., possess anomalous dispersion. So it is quite natural to envisage that MIR femtosecond pulses generated through the aforementioned parametric processes accumulate negative spectral phase shifts corresponding tothis anomalous dispersion. To compensate for this, two methods have been proposed:(ⅰ), use of a grating-based stretcher and (ⅱ) use of materials that can provide normal dispersion at MIR, such as silicon (Si) or germanium (Ge). However, for dispersion compensation, the prerequisite is to know the amount of the spectral phase induced by both material dispersion and the nonlinear interaction process. The center issue can be presented as follows:for a given parametric process, howmuch phase shift is exerted on theMIR femtosecond pulse? Is it merely the same as that accumulated through linear propagation in the nonlinear optical crystal? Thus far, little theoretical investigation has been devoted to this subject. So a though theoretical investigation into this subject is imperative.
Another key advantage of optical parametric amplification is the generation of pulse-to-pulse carrier-envelope-phase stabilized mid-infrared femtosecond pulse train. It is well-known that mathematically, pulse is characterized by envelope and carrier. When the pulse width is so short that there are only few carrier cycles within the envelope, termed few-cycle pulses, the relative position of the envelope maximum and carrier maximum beomes essential to certain applications such as attosecond pulse generation and frequency metrology. This physical quantity is called carrier-enbelope phase. It it is zero, the corresponding pulse is termed cosine wave, whileπ/2 corresponds to sine wave. As for attosecond pulse generation, it is demonstrated both theoretically and experimentally that cosine pulse leads to the generation of isolated attosecond pulses, while sine pulses give rise to attosecond pulse train, which degrades temporal resolution in time-resolved experiments. Thus most research is concentrated on generating pulse-to-pulse carrier-envelope-phase stabilized, reproducible few-cycle pulses. In optical parametric amplification, if the pump pulse train has pulse-to-pulse carrier-envelope-phase fluctuation, however, if the signal pulse train is generated from the pump through white light generation, for example, the same pulse-to-pulse carrier-envelope-phase fluctuation will be automatically impinged on the signal pulse train. As a result, the generated idler mid-infrared pulse train, which is proportional to the product of the pump and the conjugate of the signal, will be exempted from pulse-to-pulse carrier-envelope-phase fluctuation due to phase cancellation. This is a passive way of carrier-envelope-phase stabilization and only needs a single nonlinear crystal, so it is quite easy to implement and hence becomes a hot research topic. A concomitant benefit of this method is the capability of generating tunable infrared few-cycle pulses, and it is known that a shift into the longer wavelength can extend the HHG cutoff. Although it has been demonstrated, both theoretically and experimentally, that CEP stabilized ultrashort pulses can be obtained through DFG, however, as G. Cirmi et al pointed out theoretically, a fluctuation of 10% in the pump intensity may induce non-negligible CEP fluctuation of the idler. For commercial laser systems nowadays, output energy fluctuation below 1% can be realized and hence the above issue may not be a serious problem. However, their analysis is based on the plane-wave approximation. In practical experimental settings, the pump is usually Gaussian beam with non-uniform transverse intensity distribution, with 50% decrease from the propagation axis to its full-width-at-half-maximum (FWHM) waist. As a result, it can be naturally expected that the idler, although CEP stabilized from pulse to pulse, the transverse CEP distribution is not uniform.
In this thesis we presented the following research work carried out during my Ph. D. stage:
1, we theoretically study spectral phase shift of MIR femtosecond pulses generated through parametric down-conversion in dispersive media, in the aim of obtaining guidelines for dispersion compensation in practical parametric femtosecond laser systems. Specifically, we identify the following factors that influence the phase: (i) the initial injection condition, i.e., whether the signal or the idler is injected at the crystal boundary; (ii) transfer of the phase accumulated by the higher-frequency fields due to GVD. Phase transfer has been studied in second-harmonic generation (SHG), in the assumption of large-mismatch which leads to rather poor conversion efficiency, or in OPA in the spatial domain, at degeneracy under the assumption of undepleted plane wave pumping. Through analytic expression derived, we demonstrate that in DFG with signal injection, under the assumption of negligible pump depletion, the phase shift induced by GVD at the MIR wavelength is only half of that experienced in linear propagation. Phase transfer from the pump and the signal to the idler is also analytically investigated, under certain limiting conditions. When pump depletion in DFG, and idler generation through OPA are considered, analytical solutions may not be derived. Through numerical simulation we show that, pump depletion in DFG has little effect on idler phase. On the contrary, in OPA, the resultant phase shift at idler will be significantly affected by the involved high parametric gain. Due to the combined effect of GVD at the idler wavelength and the high gain, the idler phase will decrease with increasing gain. Other factors, such as GVDs at higher-frequency fields, GVMs among the interacting waves are also considered through numerical simulation.
2, we theoretically study transverse inhomogeneous carrier-envelope phase distribution of idler generated through difference-frequency-generation in quadratic nonlinear crystals is. In practical carrier-envelope phase stabilized difference-frequency-generation setups, the pump and the signal are usually Gaussian beams with non-uniform intensity distribution. Since the idler carrier-envelope phase is dependent on gain, this non-uniform intensity distribution leads to inhomogeneous gain across the aperture of the idler beam, resulting in varying transverse idler carrier-envelope phase. Simulation results show that in practical settings, in the high-gain regime, transverse inhomogeneous CEP can be much smaller compared withπ/2; however, when gain on the propagation axis reaches saturation, CEP difference can well exceedπ/2. So although difference frequency generation and subsequent optical parametric amplification can lead to generation of pulse-to-pulse carrier-envelope phase stabilized mid-infrared few-cycle pulse train, the transverse inhomogeneous carrier-envelope phase distribution cannot be eliminated and may hamper the practical applications.
通过光参量放大产生可调谐中红外飞秒脉冲的问题在于：中红外波段的二阶非线性晶体通常具有较大的反常色散值,因此通过光参量放大过程产生的中红外飞秒脉冲通常具有负啁啾,脉宽偏离傅氏变换极限。为了获得最短脉宽以提高泵浦-探测等实验中的时间分辨率,需要对色散进行补偿以获得最短的飞秒脉冲。鉴于中红外波段反常材料色散及脉冲负啁啾的性质,目前主要采用两种方式对色散进行补偿：(1)让脉冲通过在中红外波段具有正常色散的介质,例如硅、锗等；(2)利用提供正常色散的光栅展宽器对色散进行补偿。然而,要想进行色散补偿,前提是确切知道脉冲的频域相位,特别是二次相位。该值决定了补偿用色散量的大小(在实际中体现为正常色散介质的长度或者光栅间距)。目前,人们对该频域相位的研究较为匮乏,并不清楚它受何种因素影响、影响程度多大等问题。由于该相移对于后续的脉冲压缩过程起决定影响,因此有必要进行深入的理论研究及分析,以期为实验提供理论指导。
光参量放大过程的另一优点在于可以产生载波-包络相位稳定的中红外飞秒脉冲序列。众所周知,光脉冲由脉冲包络以及光载波描述。当(包络)脉宽很短以至于仅包含几个光载波周期时,对应的光脉冲称为周期量级脉冲。此时,对脉冲的完备描述需要第三个物理量,即包络最大值与载波最大值之间的相对相差,称之为载波-包络相位(CEP)。如果该值为0,对应余弦脉冲,该值为π／2对应正弦脉冲。周期量级脉冲的一个重要应用在于阿秒脉冲产生。理论及实验表明：余弦周期量级脉冲可以导致单个孤立阿秒脉冲产生,而正弦脉冲将导致多阿秒脉冲产生。后者对于研究阿秒时间尺度的超快过程(例如电子的迟豫过程)不利,因为它导致时间分辨率下降。因此人们的研究主要集中于产生波形可重复、不存在脉冲间载波-包络相位起伏的周期量级脉冲序列。光参量放大过程中,泵浦光脉冲序列存在脉冲间的载波-包络相位起伏的条件下,如果采用泵浦光在三阶非线性介质中通过空时自聚焦、自相位调制、四波混频以及更高阶非线性效应产生超连续白光作为信号光脉冲序列,则信号光脉冲序列的载波-包络相位起伏与泵浦光完全一致。通过差频及参量放大过程产生的飞秒中红外脉冲正比于泵浦光与信号光共轭的乘积,因此相位相减导致产生的中红外脉冲不存在载波-包络相位起伏。这是一种被动的载波-包络相位稳定方式,仅通过单块二阶非线性晶体就可以实现,因此成为人们研究的热点。然而,该方法的问题在于：闲频光的载波-包络相位与增益有关。已有研究表明泵浦光10%的能量起伏将导致闲频光载波-包络相位的起伏可以达到0.6rad。目前商品化的激光器输出脉冲能量稳定性小于1%。因此由激光器能量起伏造成的载波-包络相位起伏可以忽略。然而,以上分析基于平面波假定,即假设泵浦光、信号光及闲频光均为平面波。而在实际工作中,泵浦光和信号光通常为聚焦高斯光束,因此传输轴上点与轴外点的光强差别可以轻易达到50%。这种横向增益差别必将导致闲频光的载波-包络相位存在横向分布。目前对此问题还没有研究报道。
本文分以下部分进行论述：
第一章,综述飞秒光学的发展,超短脉冲的线性传输性质,并介绍周期量级脉冲及载波-包络相位。自1960年激光发明以来,超快光学发展中的关键技术包括：(1)以Ti:sapphire为代表的高性能宽带固体激光工作介质的应用,以及克尔透镜锁模作为快速可饱和吸收体的应用,最终促成目前应用最广的商品化Ti:sapphire振荡器的出现；(2)最初应用于微波放大的啁啾脉冲放大技术的引入,其中包括能够提供正常色散的Martinez型光栅对的引入,显著提升了超短脉冲的能量并且避免了材料及光学元件的损伤问题；(3)非线性光学、特别是频率转换技术(例如倍频,和频,差频产生及光参量放大等)在超快光学领域的应用,拓展了能够获得的超短脉冲激光波长范围,并能提供显著的波长调谐能力,代表之一是超连续白光作为种子光的光参量放大器。此外,光参量放大与啁啾脉冲相结合的产物——光参量啁啾脉冲放大是超短脉冲产生／放大技术发展中十分重要的进步,它能提供高能超短脉冲并且不受常规激光器／放大器量子缺陷导致的热效应的影响。(4)载波-包络相位稳定的周期量级脉冲与惰性气体相互作用能够获得阿秒脉冲,从而开拓了阿秒科学这一新兴研究领域。
第二章,介绍二阶非线性光学,特别是超短脉冲二阶非线性光学。由于材料色散的作用,介质中互作用的超短脉中之间存在群速度失配。随着传输距离的增大,脉冲之间在时间上发生相互走离,这将导致转换效率下降。此外,在群速度色散的作用下,单个脉冲也会发生脉冲展宽,因此峰值光强下降并且导致转换效率下降,并且脉冲发生啁啾,偏离傅氏变换极限。这是与单色波非线性相互作用的主要差别所在。
第三章,介绍飞秒参量下转换过程中材料色散导致的频域相移研究。在理论上研究了色散介质中,中红外飞秒光参量下转换过程中的频域相移.主要研究材料群速度色散(GVD)对频域相移的影响,目的对中红外飞秒脉冲的压缩给出理论指导。研究结果表明：通过参量下转化产生的中红外飞秒脉冲的频域相移与线性传输得到的结果有显著差别。主要研究两种产生中红外飞秒脉冲的方式：光参量放大以及差频过程。频域相移由初始注入条件、以及高频场累积的相移决定。研究结果表明：差频过程中,泵浦光消耗对中红外飞秒脉冲频域相移几乎没有影响,而在光参量放大过程中,线性GVD以及高的参量增益使中红外飞秒脉冲的频域相移显著区别于线形传输结果：增益越大,频域相移越小。定量来讲：在差频过程中,中红外飞秒脉冲的频域相移接近线性传输值的一半,而在光参量放大过程中,相移更小。为了获得最短的中红外飞秒脉冲,研究结果决定了色散补偿所需要的色散量。
第四章,介绍了差频及参量放大过程中,考虑泵浦光和信号光为实际应用中高斯光束的条件下,闲频光横向载波-包络相位的非均匀分布。在实际的载波-包络相位稳定的差频装置中,泵浦光和闲频光通常是光强分布不均匀的高斯光束。由于载波-包络相位依赖于增益,因此非均匀的光强分布导致了闲频光横向的增益分布不均匀,从而导致了闲频光横向载波-包络相位分布不均匀。研究结果表明,在实际的装置中,在高增益的阶段,载波-包络相位的横向非均匀性要远小于π／2。然而,当增益在传播轴上达到饱和时,载波-包络相位的横向差别将大于π／2。
第五章,总结与展望。
This thesis summarizes our recent research on spectral phase and carrier-envelope phase of the mid-infrared femtosecond pulses generated through optical parametric amplification.Optical parametric generation and amplification are second order nonlinear optical phenomena, which occur in quadratic nonlinear crystals. They can extend the wavelength coverage of femtosecond pulses. If two higher frequency pulses are simultaneously injected into a quadratic nonlinear crystal, under proper conditions of phase matching which guarantee momentum conservation, first new frequency pulses, termed idler, will be generated through difference frequency generation, and then both the signal and the idler will be amplified through optical parametric amplification, at the cost of pump consumption. Nowadays, abailable broadband laser gain media at mid-infrared are quite limited, and tuning capability is further restricted by gain bandwidth. As a result, optical parametric amplification is a necessary way of generating broadband tunable femtosecond mid-infrared pulses. Due to the important applications of mid-infrared femtosecond pulses in spectroscopy and potential use in generating isolated attosecond pulses. Generating mid-infrared femtosecond pulses through optical parametric amplification has aroused widespread interest. Currently, most research is focused on generating shorter and more energetic mid-infrared femtosecond pulses.
It is well known that in the case of linear propagation of ultrashort pulses in dispersive media, transform-limited (TL) pulses will broaden in duration due to the effect of group velocity dispersion (GVD), which in the spectral domain adds a spectral phase proportional to the propagation distance and quadratic in frequency. The effect of GVD will be much more pronounced in generating MIR femtosecond pulses. In the midinfrared region, commonly used nonlinear optical crystals, such as lithium niobate, potassium niobate PPLN, etc., possess anomalous dispersion. So it is quite natural to envisage that MIR femtosecond pulses generated through the aforementioned parametric processes accumulate negative spectral phase shifts corresponding tothis anomalous dispersion. To compensate for this, two methods have been proposed:(ⅰ), use of a grating-based stretcher and (ⅱ) use of materials that can provide normal dispersion at MIR, such as silicon (Si) or germanium (Ge). However, for dispersion compensation, the prerequisite is to know the amount of the spectral phase induced by both material dispersion and the nonlinear interaction process. The center issue can be presented as follows:for a given parametric process, howmuch phase shift is exerted on theMIR femtosecond pulse? Is it merely the same as that accumulated through linear propagation in the nonlinear optical crystal? Thus far, little theoretical investigation has been devoted to this subject. So a though theoretical investigation into this subject is imperative.
Another key advantage of optical parametric amplification is the generation of pulse-to-pulse carrier-envelope-phase stabilized mid-infrared femtosecond pulse train. It is well-known that mathematically, pulse is characterized by envelope and carrier. When the pulse width is so short that there are only few carrier cycles within the envelope, termed few-cycle pulses, the relative position of the envelope maximum and carrier maximum beomes essential to certain applications such as attosecond pulse generation and frequency metrology. This physical quantity is called carrier-enbelope phase. It it is zero, the corresponding pulse is termed cosine wave, whileπ/2 corresponds to sine wave. As for attosecond pulse generation, it is demonstrated both theoretically and experimentally that cosine pulse leads to the generation of isolated attosecond pulses, while sine pulses give rise to attosecond pulse train, which degrades temporal resolution in time-resolved experiments. Thus most research is concentrated on generating pulse-to-pulse carrier-envelope-phase stabilized, reproducible few-cycle pulses. In optical parametric amplification, if the pump pulse train has pulse-to-pulse carrier-envelope-phase fluctuation, however, if the signal pulse train is generated from the pump through white light generation, for example, the same pulse-to-pulse carrier-envelope-phase fluctuation will be automatically impinged on the signal pulse train. As a result, the generated idler mid-infrared pulse train, which is proportional to the product of the pump and the conjugate of the signal, will be exempted from pulse-to-pulse carrier-envelope-phase fluctuation due to phase cancellation. This is a passive way of carrier-envelope-phase stabilization and only needs a single nonlinear crystal, so it is quite easy to implement and hence becomes a hot research topic. A concomitant benefit of this method is the capability of generating tunable infrared few-cycle pulses, and it is known that a shift into the longer wavelength can extend the HHG cutoff. Although it has been demonstrated, both theoretically and experimentally, that CEP stabilized ultrashort pulses can be obtained through DFG, however, as G. Cirmi et al pointed out theoretically, a fluctuation of 10% in the pump intensity may induce non-negligible CEP fluctuation of the idler. For commercial laser systems nowadays, output energy fluctuation below 1% can be realized and hence the above issue may not be a serious problem. However, their analysis is based on the plane-wave approximation. In practical experimental settings, the pump is usually Gaussian beam with non-uniform transverse intensity distribution, with 50% decrease from the propagation axis to its full-width-at-half-maximum (FWHM) waist. As a result, it can be naturally expected that the idler, although CEP stabilized from pulse to pulse, the transverse CEP distribution is not uniform.
In this thesis we presented the following research work carried out during my Ph. D. stage:
1, we theoretically study spectral phase shift of MIR femtosecond pulses generated through parametric down-conversion in dispersive media, in the aim of obtaining guidelines for dispersion compensation in practical parametric femtosecond laser systems. Specifically, we identify the following factors that influence the phase: (i) the initial injection condition, i.e., whether the signal or the idler is injected at the crystal boundary; (ii) transfer of the phase accumulated by the higher-frequency fields due to GVD. Phase transfer has been studied in second-harmonic generation (SHG), in the assumption of large-mismatch which leads to rather poor conversion efficiency, or in OPA in the spatial domain, at degeneracy under the assumption of undepleted plane wave pumping. Through analytic expression derived, we demonstrate that in DFG with signal injection, under the assumption of negligible pump depletion, the phase shift induced by GVD at the MIR wavelength is only half of that experienced in linear propagation. Phase transfer from the pump and the signal to the idler is also analytically investigated, under certain limiting conditions. When pump depletion in DFG, and idler generation through OPA are considered, analytical solutions may not be derived. Through numerical simulation we show that, pump depletion in DFG has little effect on idler phase. On the contrary, in OPA, the resultant phase shift at idler will be significantly affected by the involved high parametric gain. Due to the combined effect of GVD at the idler wavelength and the high gain, the idler phase will decrease with increasing gain. Other factors, such as GVDs at higher-frequency fields, GVMs among the interacting waves are also considered through numerical simulation.
2, we theoretically study transverse inhomogeneous carrier-envelope phase distribution of idler generated through difference-frequency-generation in quadratic nonlinear crystals is. In practical carrier-envelope phase stabilized difference-frequency-generation setups, the pump and the signal are usually Gaussian beams with non-uniform intensity distribution. Since the idler carrier-envelope phase is dependent on gain, this non-uniform intensity distribution leads to inhomogeneous gain across the aperture of the idler beam, resulting in varying transverse idler carrier-envelope phase. Simulation results show that in practical settings, in the high-gain regime, transverse inhomogeneous CEP can be much smaller compared withπ/2; however, when gain on the propagation axis reaches saturation, CEP difference can well exceedπ/2. So although difference frequency generation and subsequent optical parametric amplification can lead to generation of pulse-to-pulse carrier-envelope phase stabilized mid-infrared few-cycle pulse train, the transverse inhomogeneous carrier-envelope phase distribution cannot be eliminated and may hamper the practical applications.
引文
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