Classical theory of non-degenerate sum-frequency generation by incoherent nonlinear optical mixing of coherent and chaotic radiations II. Coherent and chaotic input radiations — Efficiency and spectral distribution

Sum-frequency generation by incoherent nonlinear optical mixing of one coherent and one chaotic, mutually uncorrelated input radiations in a dispersive medium is treated in this paper. The efficiency of the process is calculated in the second approximation of the iterative method. It is shown that for perfect phase matching or small phase mismatch of interacting waves and small spectral width of chaotic input radiation the efficiency of incoherent sum-frequency generation can be enhanced compared with the coherent interaction due to the difference between group velocities of sub-frequency radiations. On the other hand, for greater spectral width the efficiency of the process decreases with increasing spectral width of chaotic input radiation. In the case of considerable phase mismatch the efficiency of sum-frequency generation first decreases, but then increases with increasing spectral width of chaotic input radiation. The spectral distribution of the resulting sum-frequency radiation is calculated in the first approximation of the iterative method. There is a general tendency to narrowing the spectral distribution of generated radiation in the course of the process. Moreover, when there is phase mismatch present, a spectral shift of the maximum of generated radiation towards blue or red region, according to the signs of the phase mismatch and the typical dispersion coefficient, appears in the later phases of the sum-frequency generation.This work was partially supported by Research Project C.P.B.P. 01. 07.     

Statistical and coherence effects in nonlinear optical parametric up conversion. I. Coherent interaction

The distinction between coherent and incoherent nonlinear optical interactions is established at the beginning of the paper. In the first part parametric up conversion (PUC) by coherent nonlinear optical mixing of the strong pumping radiation with weak input radiation is treated with respect to statistical properties of generating radiations. The efficiency of PUC is calculated by means of the conserved statistics method. It is shown that the efficiency of PUC depends upon the photon statistics of the strong pumping radiation only, namely, it decreases with increasing fluctuation level in the pumping radiation. The fourth-order statistics of generated sum-frequency radiation is calculated in the first approximation of the iterative solution. The statistics of both generating radiations are projected into the statistical distribution of the resulting sum-frequency radiation in the same way at the beginning of the process.     

Classical theory of non-degenerate sum-frequency generation by incoherent nonlinear optical mixing of coherent and chaotic radiations

The incoherent nonlinear optical sum-frequency generation with non-monochromatic initially uncorrelated sub-frequency input radiations in a dispersive medium is studied in this paper. The efficiency of the process is calculated in the second approximation, whilst the spectral distribution of generated radiation is merely described in terms of the first approximation of the iterative method. The calculations of the efficiency of nonlinear process and the spectral distribution of sum-frequency radiation are performed for one coherent and the other chaotic input radiations, and for both chaotic input radiations, respectively.This work was partially supported by Research Project C.P.B.P. 01. 07.     

Group velocity difference effect on incoherent sum-frequency generation spectrum

The spectral distribution of optical sum-frequency generation (SFG) by incoherent non-linear mixing of two chaotic beams with identical spectral width is calculated theoretically in the first approximation of the iterative method including dispersion of the non-linear medium and the difference between the group velocity of the input beams. It is shown that for the same group velocities (=0) of the input beams in non-linear medium the resultant field has a spectral width narrower than , and if a phase mismatch is present the spectral maximum of the resultant field is shifted towards lower or higher frequencies according to the sign of the phase mismatch. If the input beams have different group velocities (0) in the non-linear medium, then the spectral distribution of SFG is strongly dependent on . For small the spectral distribution of SFG is the same irrespective of . For large the difference in group velocities broadens the spectrum of SFG and for very large differences in group velocity the SFG has a spectral width identical to that of the input beams.     

Optimum conditions for the generation of the second harmonic of intense laser radiation

A generalized approximation of strong interactions of waves is suggested for the theoretical analysis of second-harmonic generation under conditions of self-action. On the basis of the method suggested, approximate solutions for the efficiency of second-harmonic generation are obtained with regard to the influence of higher nonlinearities, depletion of pumping radiation, and linear phase mismatch. The effects of the phase mismatch and the spatial distribution of the amplitude of the fundamental harmonic on the efficiency of second harmonic generation by intense laser radiation is analyzed. The results obtained with the approximate method developed are shown to be in good agreement with known experimental data and numerical calculations. Optimum conditions for second harmonic generation are determined in a wide range of laser radiation intensity and at different spatial distributions of the fundamental harmonic amplitude.     

采用光栅角色散的宽带二倍频及聚焦特性分析

针对带宽为20 nm左右、中心波长为1 053 nm的线性啁啾宽带激光,分析了采用光栅角色散方式宽带二倍频的原理,讨论了光栅角色散性能及光栅加工误差引入的基频光位相扰动对二倍频光转换效率及聚焦特性的影响.研究结果表明:采用光栅角色散方式的宽带二倍频光的转换效率、脉冲宽度和带宽均明显增大;在0～22 nm基频光带宽范围内,二倍频光均可保持80％左右的转换效率;对于入射基频光带宽为22 nm的情况,光栅角色散率在30～80 μrad/nm范围内变化时,宽带二倍频转换效率均可保持在70％以上;基频光有位相扰动时,二倍频光带宽对二倍频聚焦光斑的主瓣影响不大,但对旁瓣有一定的匀滑作用,采用光栅角色散方式宽带二倍频的聚焦光斑旁瓣的匀滑效果更为明显.     

Effect of coherence of generating radiations on optical parametric up conversion

The effect of the coherence properties of pumping and input radiations on parametric up conversion (PUC) is treated in this paper. It is shown here that the PUC depends essentially upon the coherence properties of the pumping radiation whilst it is hardly affected by the coherence properties of the input radiation. It has been found that for chaotic (Gaussian) pumping radiation with an extremely high degree of coherence the total conversion efficiency is one half of that for coherent (Poisson) pumping radiation, whilst for chaotic pumping radiation with a very low degree of coherence the PUC is much more effective. The influence of the coherence properties of pumping radiation upon the PUC is explained by the intermodal correlation effects in the nonlinear interaction.     

Peculiarities of self-action in second harmonic generation of laser radiation in nonlinear crystals

By using the generalized method of strong interaction of nonlinear waves and computer simulation, an analysis of the influence of self-action effects on second harmonic generation of an intense diverging picosecond pulse is performed. Using the approximation of strong wave interaction, an analytic solution is obtained for frequency conversion of the laser radiation taking into account the pump intensity depletion, the influence of the angular dispersion effect (ADE), and the higher nonlinearities. It is shown that the self-action effects, the ADE, and the linear phase mismatch can compensate for each other, increasing the efficiency of second harmonic generation. Optimum conditions for second harmonic generation in converging and diverging laser beams were found. An asymmetry of the angular dependence of the second harmonic intensity was experimentally observed and theoretically explained. The asymmetry is caused by the reverse energy conversion of the second harmonic into the pump by the influence of the ADE and Kerr nonlinearities.     

阵列波导光栅梳状带通滤波器的传输效率

在光波导模场分布高斯近似条件下,根据星形光波导耦合器的耦合特性,推导出了基于累加运算和卷积运算近似表达的阵列波导光栅梳状带通滤波器光谱响应效率的函数表达式。给出了阵列波导光栅梳状带通滤波器光谱响应效率曲线的半最大值全宽度和阵列波导光栅梳状带通滤波器的通道中心波长的光谱响应度与器件参数的关系。在输入信号光谱分布高斯近似条件下,给出了阵列波导光栅梳状带通滤波器信号通道传输效率的计算表达式和输入信号光谱宽度对阵列波导光栅梳状带通滤波器信号通道输出特性的影响。给出了物理意义明确的函数表达式,它们可为快速分析阵列波导光栅梳状带通滤波器的特性提供理论基础。     

透射型光折变体全息光栅对超短脉冲激光光束衍射的特性

在Kogelnik耦合波理论的基础上,考虑光栅记录介质的色散效应的影响,研究了光折变体全息光栅对不同偏振状态的超短脉冲激光光束衍射的性质,讨论了高斯型入射脉冲激光光束的谱宽与光栅的有效衍射谱宽之比不同时,衍射和透射光束的光谱宽度、时间宽度、波形和衍射效率的变化。结果表明,光栅的有效衍射谱宽受光栅参量及入射条件的影响,对衍射性质的影响很大,且在考虑光栅记录介质的色散效应时减小。当入射脉冲的偏振方向垂直于入射面时,光栅的有效衍射谱宽大于偏振方向平行于入射面的情形,衍射效率在入射脉冲宽度较大时小于偏振方向平行于入射面的情形;谱宽比较大时,衍射光束的时间分布曲线产生展宽和变形,且比偏振方向平行于入射面的情形展宽和变形得更加明显。     

Strong-interaction approximation in the theory of second harmonic generation of intense short laser pulses

The method of strong interaction of nonlinear waves has been developed to analyse the second harmonic generation of intense laser radiation in the transient regime. Analytic solution for frequency conversion efficiency – taking into account the pump radiation depletion, influence of phase mismatch, dispersion of group velocities and higher nonlinearities – has been first obtained. A comparison of theoretically derived results and known experimental data has been conducted, and a general agreement of these results has been obtained. The optimal conditions of the second harmonic generation of neodymium laser radiation into femtosecond pulse duration range have been determined.     

High-efficiency blue generation by frequency doubling of femtosecond pulses in a thick nonlinear crystal

We have demonstrated highly efficient frequency doubling of femtosecond pulses in a thick, noncritically phase-matched KNbO(3) crystal under conditions of large group-velocity mismatch. At low power we observed a slope efficiency of ~300% nJ (-1) for harmonic conversion, and at higher powers we generated 170 mW of second-harmonic blue output for 300 mW of input light. Furthermore, we have shown that the focusing dependence for our conditions of large group-velocity mismatch is considerably different from that obtained for frequency doubling of continuous-wave light. We have also demonstrated that one can tune the spectral width of the generated blue light by varying the focusing conditions.     

Generation of Broadband Near-Infrared (2–2.5 μm) Radiation from an Optical Parametric Amplifier Driven by a Cr:Forsterite Laser Near Dispersion Anomalies of Tuning Curves

Pulses with a spectral width of 450 nm at a wavelength of 2.2 μm are generated in a parametric amplifier based on a type-I BBO crystal pumped by the second harmonic (620 nm) of a Cr:forsterite laser. Such a broadband radiation is obtained in a specific regime of the group velocity matching near the vertical region of the tuning curve. The generated pulses can be compressed to a duration of about 2.5 optical cycles (34 fs) in a medium with positive group-velocity dispersion.     

Efficient second-harmonic generation for a high-intensity femtosecond pulse in the absence of group synchronism of interacting waves

A method is proposed to compensate for the influence of the group velocity mismatch on the frequency conversion efficiency for any ratio between the coefficients of square and cubic nonlinearities. The method allows the limiting efficiency of the frequency doubling to be achieved. This efficiency corresponds to the cases of phase and group synchronisms. For this purpose, it is necessary to apply a low-frequency phase modulation of the input radiation at the frequency of the first harmonic in combination with the optimal selection of the wavenumber mismatch. In practice, under certain conditions, this modulation can be obtained only with the aid of the wavenumber mismatch, whose optimal value is determined by the group velocity mismatch. The generation efficiency can be increased several times by introducing a phase shift in certain cross sections of the medium.     

Phase matching limitation of high-efficiency second-harmonic generation in both phase- and group-velocity-matched structures

In this paper, we studied efficient second-harmonic generation (SHG) of femtosecond pulses in both phase- and group-velocity-matched structures. Obtained results show that phase matching becomes more critical under conditions required for high levels of conversion efficiency. And the imperfect phase mismatch caused by mismatched group-velocity dispersion (GVD) will limit conversion efficiency as well as bandwidth of generated second-harmonic (SH) pulses. The spectral characteristics of the generated SH pulses and its conversion efficiency in the strong pump regime are investigated in detail. The acceptance bandwidth of nonlinear crystal in the high-efficiency SHG is redefined in the paper, and the definition is much closer to the practical application of design.     

Generation of high average power, 7.5-fs blue pulses at 5 kHz by adaptive phase control

The spectral width of a 5-kHz Ti:sapphire laser system was broadened by spectral control in a regenerative amplifier consisting of broadband chirped mirrors. The dispersion over the wide spectral range was compensated by a deformable mirror along with a genetic algorithm, resulting in a pulse width of 15 fs. The pulse width is the shortest, to our knowledge, in chirped pulse amplification systems with a regenerative amplifier. The phase distortion of broadband frequency doubling in addition to the Ti:sapphire laser was compensated by using the self-diffraction intensity in sapphire as the feedback signal into the genetic algorithm, resulting in a pulse width of 7.5 fs. The average power of the second harmonic was 1 W with a fundamental input of 7 W.     

Generalized Approximation of Strong Interaction of Waves in the Theory of High-Power Radiation Frequency Doubling

The approximation of strong interaction of waves is developed to analyze the generation of the second harmonic under the conditions of self-action. Based on this method, an approximate expression is obtained for the generation efficiency of the second harmonic with allowance for the effect of higher nonlinearities, depletion of pumping radiation, and linear phase detuning. The effect of phase detuning and change in the spatial distribution of the amplitude of the fundamental radiation on the efficiency of second-harmonic generation has been analyzed. Good agreement of the results of the developed approximate method with experimental data and numerical calculations is shown. The optimum conditions of the second-harmonic generation in a wide range of the laser system radiation intensities are determined.     

Frequency doubling of phase-modulated femtosecond laser pulses in periodically poled and chirped nonlinear crystals

The second harmonic generation (SHG) at a wavelength of 0.8 μm by 50-and 10-fs pulses with and without phase modulation (PM) was systematically studied in LiNbO₃ crystals with regular domain structure and linearly varied domain thickness. The main results were obtained by numerical method, taking into account the difference between group velocities of interacting pulses and the group-velocity dispersion. In the approximation of the given field of the fundamental radiation, an analytical expression was derived for the spectral density of the second harmonic in the periodically poled nonlinear crystal (PPNC) under nonstationary excitation conditions. It was numerically found that the conversion efficiency of about 90% can be achieved by doubling the frequency of 50-fs laser pulses without PM in the LiNbO₃ PPNC. The maximum conversion efficiency for the SHG by PM pulses is achieved at a certain optimum chirp step in the crystal domain length, which depends on both the value and sign of frequency modulation.     

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the case of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.     

Generation of a sub-20-fs single optical pulse by four-wave Raman mixing using two Raman cells filled with molecular hydrogen

To attempt to expand the spectral domain for pulse shortening, we generated several emission lines by stimulated Raman scattering and subsequent four-wave Raman mixing. The efficiency of generation of the Raman emission was improved by passing the beam through two Raman cells that were connected in series. The group-velocity dispersion induced by a Raman cell window and hydrogen was compensated for by means of a pair of chirped mirrors for pulse compression. By a phase lock of the emission lines in the process of four-wave Raman mixing, the pulse width was reduced from 114 to 17 fs in the second Raman cell.