Idler Phase-shift Study In The Mid-infrared Femtosecond Optical Parametric Amplification Process

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.