Third-harmonic generation in regular domain structures

The process of frequency conversion in regular domain structures is studied using the constant-intensity approximation. The investigations are carried out at values of complex amplitudes of the fundamental radiation and third harmonic at the output of each domain equal to the values of the corresponding complex amplitudes at the input of the subsequent domain. We show that the optimum length of each domain depends on the input pump intensity in the given domain. Thus, it is possible by choosing the optimum lengths of domains, phase mismatch, and pump intensity even at a low number of periods of nonlinear susceptibility modulation of the lattice to reach considerable values of conversion efficiency at the structure output in comparison with the traditional case of homogeneous nonlinear media.     

Efficiency of sum frequency generation by regular domain structures

We theoretically examine generation of sum-frequency radiation in a regular domain structure, taking into account phase changes for all the interacting waves in a dissipative medium. We show that in contrast to the constant-field approximation, in the constant-intensity approximation there is an optimal value for the longitudinal dimension (length) of the domains at which maximum conversion of the signal wave energy to the sum-frequency wave energy occurs. As the pump intensity increases, the optimal domain length decreases. As the losses of the interacting waves increase, both the conversion efficiency and the optimal domain dimensions decrease.     

Phase effects during parametric conversion in layer structures

Coupled-wave equations that describe the parametric amplification and generation of a sum frequency in a three-layer structure are studied theoretically in the constant-intensity approximation taking into account the inverse effect of the excited wave on the phase of the pumping wave. For this purpose, the approximation of constant intensity of the fundamental radiation is applied not to the layer structure as a whole but to each separately taken layer. In this case, the complex amplitudes of the interacting waves at the output of each layer are the input values of the corresponding complex amplitudes for the next layer. Analytical expressions obtained in the constant-intensity approximation for the efficiency of conversion to the sum frequency were analyzed numerically for different parameters of the problem. The efficiency of parametric amplification at a high frequency was found to depend on the intensity of the signal wave at a low frequency.     

Quasi-phase-matched sum-frequency generation in layered structures

A theory has been developed for quasi-phase-matched generation of a wave at a sum-frequency within a constant-intensity approximation. In contrast to a constant-field approximation, the constant-intensity approach has been found to give an optimum pump intensity value at which the conversion efficiency reaches its maximum. Analytical expressions have been derived for optimal values of the problem’s parameters. Ways to enhance the power of the coherent optical radiation are shown and analyzed. This will make it possible, in particular, to increase the power in an RGB-source color for which the sum-frequency generation is responsible.     

Phase effects at second harmonic generation of powerful laser radiation in noncentrosymmetrical media

There has been developed the theory of second harmonic generation of the intensive laser fields in the existence of both quadratic and cubic polarization in medium in the constant-intensity approximation accounting for the reverse effect of the excited wave on the exciting one and simultaneously allowing us to take into account phase mismatch and the damping of all the interacting waves. It is shown that the changes of pump intensity through self-phase and cross-phase modulation processes effect optimum phase relationship between interacting waves, the change of the spatial beating period. The conditions of compensating undesirable phase shifts between interacting waves have been determined, the analytical expressions for calculation of optimum values of phase mismatch, length of noncentrosymmetrical medium and the spatial beating period are offered. It is shown that in the absence of linear phase mismatch with an increase of basic radiation intensity the spatial beating period is being reduced. The numerous analysis has been made of frequency doubling process efficiency for KDP and LiNbO₃ crystals.     

Cascade parametric light amplification with low-frequency pumping

Cascade parametric amplification in a regular domain structure is examined theoretically taking the variations in phase of all the interacting waves in a dissipative medium into account. Analytic expressions are obtained for the conversion efficiency of the laser energy with low-frequency pumping. The dependence of the parametric amplification efficiency on the number of layers is given. Ways of increasing the frequency conversion efficiency are discussed. The presence of a nonzero input intensity at the sum frequency is found to cause a nonlinear increase in the high-frequency signal at the output of the structure. As the losses of the interacting waves increase, both the frequency conversion efficiency and the optimum domain length decrease.     

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.     

Phase effects at second-harmonic generation in metamaterials

We develop the theory of second-harmonic generation in metamaterials where fundamental radiation is considered in the constant-intensity approximation taking into account the phase changes of interacting waves. We investigate the second-harmonic wave intensity in metamaterials at different parameters of the problem under consideration. We consider a self-action effect of the light wave in metamaterials in view of the phase changes of all the interacting waves and compare this effect with an analogous effect in usual homogeneous quadratic media. We show that it is possible to change the phase velocity of the pump wave by varying such parameters as the pump intensity, nonlinear medium length, and phase mismatch between the interacting waves. The metamaterials under consideration provide a possibility to change the phase of the fundamental radiation of order of magnitude higher than those in the usual homogeneous quadratic media.     

Phase Effects of the Parametric Interaction in Metamaterials

We study the phase effects of the three-wave parametric interaction in metamaterials considering the negative refraction at the frequency of a signal wave. We analyze the efficiency of energy conversions between two direct waves with respect to the energy of the backward signal wave along with the dynamics of the signal-wave amplification in metamaterials. We show that there exist optimum values of the fundamental-wave intensity and the phase mismatch at which the efficiency of conversion is maximum. We obtain an analytic expression for the optimum value of the relative length of the metamaterial and present a numerical evaluation of the expected value for efficiency of the frequency parametric conversion in dielectric waveguides. A sufficient enhancement in the signal-wave amplification, which is possible at optimum values of the pump intensity and the metamaterial total length, leads to the parametric generation of the signal wave. Changing the frequency and power of the pump wave, one can realize a regular tuning of the frequencies of parametric converters.     

On the theory of the second optical harmonic in nonlinear crystals with a regular domain structure

The theory of the second-harmonic generation in crystals with a regular domain structure (RDS) is developed in the approximation of the fixed intensity of the fundamental radiation. An analytical expression for the second-harmonic intensity is derived. The results are compared with the data obtained in the fixed-field approximation and the numerical solution. The maximum number of layers n _max at which the theory remains valid is determined. Numerical estimates of n _max are presented for the frequency doubling of an ultrashort light pulse in the LiNbO₃ RDS crystal.     

Nonclassical light generation in quasi-phase-matched parametric self-frequency conversion

We present a quantum theory of the parametric self-conversion of the laser radiation frequency in active nonlinear crystals with a regular domain structure. Such crystals feature simultaneous lasing and quasi-phase-matched parametric conversion of the laser radiation frequency. These processes are described using the Heisenberg-Langevin equations in two regimes of the subharmonic generation: super-and subthreshold. The spectral properties of the quadrature components of the laser frequency and its subharmonic and the photon statistics have been studied as dependent on the pump power, crystal length, and reflectance of the laser cavity output mirror. Using the obtained analytical expressions, these characteristics are calculated for a active nonlinear Nd:Mg:LiNbO₃ crystal with a regular domain structure. In the subthreshold regime, the maximum decrease in the spectral density of fluctuations in the subharmonic quadrature component relative to the standard quantum limit may reach 90%; in the above-threshold regime, these fluctuations are virtually not suppressed. A decrease in the spectral density of fluctuations of the laser frequency quadrature does not exceed 10%. In the subthreshold excitation regime, the subharmonic photons obey a super-Poisson statistics; in the above-threshold regime, the photon statistics is Poisson-like.     

Degenerate parametric frequency conversion of phase-modulated femtosecond laser pulses in crystals with a regular and chirped domain structure

A systematic theoretical analysis of the degenerate parametric frequency conversion in a LiNbO₃ crystal with a regular domain structure and a linearly varying domain thickness (chirped crystal) is presented for the pulses of a titanium-sapphire laser with a wavelength of 0.8 μm and durations of 100 and 50 fs in the presence and in the absence of phase modulation. The results are obtained with regard to the difference in the group velocities of interacting pulses and the group velocity dispersion. For an effective frequency conversion of the phase-modulated (PM) pump pulse, it is expedient to employ chirped crystals in which the domain thickness decreases from the entrance to the exit of the crystal. The pump energy is effectively converted into subharmonic energy when the pump carrier frequency decreases with time. It is demonstrated that the efficiency of the energy conversion to a subharmonic of 80% can be realized for PM pumping with a pulse duration of 100 fs in the chirped LiNbO₃ crystal. The efficiency of the parametric frequency conversion depends on the pump intensity as well as on the phase modulation of the pulse and the chirp of the crystal. Note that a variation in one of these parameters causes variations in the remaining parameters needed for the maximum efficiency of the parametric frequency conversion.     

Theoretical studies on frequency doubling in glass optical fibers in constant-intensity approximation

Theoretical consideration of the second harmonic generation in the constant-intensity approximation with account of the inverse effect of the excited wave on a stimulation wave through account of the phase change of interaction waves is presented. The behavior of harmonic wave intensity in a fiber for different parameters of the problem has been studied, the self-action of the light both in glass optical fiber and inside the homogeneous medium has been analyzed. In this approximation a decrease of conversion efficiency and a change of parameters of the curves of synchronism versus the pump intensity, in particular, the change of positions of intensity minima that does not take place in the constant-field approximation, are observed. The propagation of a plane wave packet in the homogeneous medium with quadratic nonlinearity and in an optical fiber accompanied by the self-phase modulation and leading to the change of the Gaussian pulse spectrum is analyzed with account of the phase changes of all the interacting waves.     

Effect of thermal blooming in second-harmonic generation in nonlinear crystals with a regular domain structure

Analytical expressions are obtained for the power of the second harmonic in nonlinear crystals having a regular domain structure with allowance for thermal blooming for a Gaussian beam of basic radiation in the quasi-stationary plane-wave approximation. Calculations were carried out in both the approximation of an assigned field of basic radiation and a substantially nonlinear regime of exhaustion of basic radiation. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 2, pp,. 257–260, March–April, 2000.     

Numerical optimization of the extracavity Raman laser with barium nitrate crystal

The radiation transfer equations of the extracavity Raman laser including up to the third Stokes beams and backward Raman scattering terms were deduced in detail from the wave equation and material equations of stimulated Raman scattering. The radiation transfer equations were solved numerically to optimize the performance of the extracavity Raman lasers with barium nitrate crystal as the nonlinear medium. The optimum reflectivity of the output coupler at the first Stokes was figured out numerically to achieve the maximum conversion efficiency of the first Stokes, and found to be closely related to the pump pulse duration, peak intensity of the pump pulse, and Raman crystal length. With the resonator mirrors highly reflective at the first Stokes, the highest conversion efficiency of the second Stokes was obtained when the input mirror was highly reflective at second Stokes, whereas the output coupler was highly transmissive at the second Stokes. It was found that too high intracavity intensity of the second Stokes would impede the efficient energy extraction from the pump pulse to the first Stokes, and consequently, limit the conversion efficiency of the second Stokes.     

Beam divergence effects on high power optical parametric oscillation

The beam divergence effects of the input pump laser on a high power nanosecond optical parametric oscillator （OPO） have been numerically simulated. The OPO conversion efficiency is affected due to the angular deviation of real laser beams from ideal phase matching conditions. Our theoretical model is based on the decomposition of the Gaussian beam and assumes each component has a single deviation angle and thus a particular wave vector mismatch. We take into account the variable intensity profile in the spatial and temporal domains of the Gaussian beam, the pump depletion effects for large-signal processes as well as the oscillatory effects of the three waves. Two nonlinear crystals β-BaB2O4 （BBO） and LiB305 （LBO） have been investigated in detail. The results indicate that the degree of beam divergence strongly influences the maximum pump intensity, optimum crystal length and OPO conversion efficiency. The impact of beam divergence is much more severe in the case of critical phase-matching for BBO than in the case of non-critical phase-matching for LBO. The results provide a way to choose the optimum parameters for a high power ns OPO such as the nonlinear material, the crystal length and the pump intensity, etc. Good agreement is obtained with our experimental results.     

Cross-phase-modulation-induced instability and efficient parametric frequency conversion of ultrashort light pulses

We experimentally demonstrate efficient controlled parametric frequency conversion of femtosecond laser pulses through cross-phase-modulation-induced instability in the presence of a copropagating pump field in a fused silica photonic-crystal fiber. The amplitudes and the frequency shifts of sidebands generated in the spectrum of the probe field at the output of the fiber as a result of parametric four-wave mixing are controlled by varying the intensity of the pump field.     

High conversion efficiency of second harmonic generation in a short nonlinear photonic crystal with distributed Bragg reflector mirrors

Second harmonic generation (SHG) in a short nonlinear photonic bandgap (PBG) structure coated with distributed Bragg reflector (DBR) mirrors is theoretically investigated by means of an iteration approach that fully considers pump depletion. A total conversion efficiency of about 96% can be obtained in an optimized structure with a size scale of about 0.2 mm and at the modest pump intensity of about 0.133 MW/cm², which is four orders of magnitude more than that in a quasi-phase-matching (QPM) structure with the same sample length. Such a high conversion efficiency of SHG will greatly facilitate the success of short frequency conversion devices and all-optical integration in nanostructures.     

Cascaded compression of the first and second Stokes pulses during forward transient stimulated Raman amplification

The results of numerical modelling of cascaded compression of the first and second Stokes pulses during regenerative regime of the forward transient stimulated Raman amplification are presented for the case when the walk-off length of the first Stokes pulse due to group velocity mismatch is shorter than the length of the nonlinear medium. The influence of the initial amplitudes of the seed first Stokes pulses, its durations and its time delay with respect to the pump pulse, the Kerr nonlinearity of the medium on the conversion efficiency, duration and propagation factor M² of the first and second Stokes pulse are studied. It is demonstrated that for the pump pulse duration of 1 ps the duration of the compressed second Stokes pulses in a KGW crystal near the beam axis may be approximately 14 times shorter than the pump pulse duration. It is shown that the propagation factor of the compressed pulses increases significantly because of complex spatial-temporal dynamics of compression and the influence of Kerr nonlinearity of Raman medium.     

负折射率材料中二次谐波转换效率的理论分析

研究了二次谐波是负折射率而基频光是正折射率材料中,在考虑吸收系数、走离效应和相位失配的情况下,推导出平面波振幅缓变近似下,二次谐波的耦合波方程.根据该方程在基频光小信号近似下推导出二次谐波转换效率表达式.最后采用数值计算的方法分别研究了相位失配量Δk、走离角ρ和二次谐波的吸收系数α对转换效率的影响.结果表明,由于相位失配量的存在二次谐波的转换效率随负折射率材料长度的变化存在极大值,即负折射率材料长度存在最佳值,并且随着长度的增加,转换效率呈明显的周期性振荡并且极大 关键词： 负折射率材料 二次谐波 转换效率 相位匹配