Second harmonic generation using partially coherent light

The second harmonic generation process is considered using partially coherent light formed by the superposition of a coherent field and a chaotic field. The conversion efficiency is derived. Expressions are also presented for the variance and for the probability density function of the second harmonic intensity and of the transmitted intensity at the fundamental wavelength.     

Theory of light fluctuation filtering in the two-photon absorption process by multiple second harmonic generation. II. Quantum description. Possibilities of experimental realization

Two-photon absorption is treated from the point of view of quantum theory in this paper. Both rigorous and approximate solutions are presented. It is shown that the theoretical extreme value of photon antibunching, characterized by the normalized variance of integrated intensity, is ? 1/2, while its practical value in real experiments is about ?1/3 for both coherent and chaotic input radiation. In the case of the chaotic input radiation, fully coherent radiation can be obtained in this process. Possibilities for experimental realization of two-photon absorption by means of multiple second harmonic generation in thin nonlinear plates, with the generated second harmonic radiation filtered out, are discussed and some values of nonlinear plate thickness, number of light transits and mean intensity of input radiation are estimated. From the standpoint of the possibilities of detection of statistical properties of the resulting light, classical light fluctuation filtering seems to be more practical than the quantum counterpart.     

Theory of light fluctuation filtering in two-photon absorption process by multiple second harmonic generation. I. Basic equations. Classical description

Multiple second harmonic generation in which the generated second harmonic radiation is filtered out at each stage is studied in this paper. Both classical and quantum equations describing this process are derived, and it is shown that multiple second harmonic generation in thin nonlinear plates acts in the same way as the two-photon absorption process. A closed classical solution for stochastic photon number is found and, for chaotic input radiation, the mean photon number and the mean quadratic fluctuation (variance) of the integrated intensity in the fundamental radiation are calculated. It is shown that the variance of the intensity systematically decreases in the course of the process and, thus, the statistical distribution of the fundamental radiation approaches the coherent state from the point of view of classical theory.     

Second harmonic generation of light in the Kretschmann attenuated total reflection geometry in the presence of surface roughness

Abstract

Using a computer simulation approach we study the generation of second harmonic light in reflection and in transmission in the Kretschmann attenuated total reflection geometry. In this geometry a thin metal film is deposited on the planar base of a dielectric prism, through which p-polarized light is incident on the film. The back surface of the film, which separates the film from vacuum, is a one-dimensional, randomly rough surface, whose generators are normal to the plane of incidence of the light. The nonlinearity responsible for the second harmonic generation is assumed to arise at the prism-metal and metal–vacuum interfaces, and thus enters the problem only through the boundary conditions at these interfaces at the harmonic frequency. The source terms entering these boundary conditions are obtained from the solutions of the corresponding scattering and transmission problems at the fundamental frequency. It is found that a peak in the angular dependence of the intensity of both the transmitted and reflected second harmonic light occurs in the directions normal to the mean scattering surface, in addition to an enhanced backscattering peak in the retroreflection direction. The enhanced transmission peak occurs in the non-radiative region, and therefore cannot be observed in the far field.     

Dynamics of non-linear optical processes

We study the statistical properties of parametric processes (parametric amplification, frequency conversion, splitting of frequency, etc.) described by the trilinear Hamiltonian and of the second harmonic generation including the lossy mechanism and rotating terms. In a short-time approximation some conservation laws are derived and the existence of the Glauber-Sudarshan weighting function is discussed. It is shown in the second harmonic generation case that good coherence of the incident radiation is lost proportionally to the intensity in interaction while the second harmonic radiation has tendency to be coherent. The effects of the spontaneous emission of the medium and of the physical vacuum are also discussed. In this approximation the statistics is generally described by the superposition of coherent and chaotic fields with correlated components.     

Theory of second harmonic generation in collimated light beams with the Gaussian distribution of light intensity for the interaction of typeo+e→e

The process of second harmonic generation (S.H.G.) in collimated light beams with Gaussian distribution of light intensity at the interaction of typeo+e→e in a uniaxial negative crystal for a case of perpendicular incidence on the boundary plane is studied in this paper. In case of very wide light beams of fundamental frequency with Gaussian distribution of light intensity, the coefficient of mutual energy conversion in the region of small energy conversions is about one half of that following from the model of the interaction of unlimited plane waves. The process of S.H.G. at the interaction o+ e→e is less profitable than that of interaction o+o→e especially for narrow fundamental-frequency light beams as a consequence of the anisotropic mutual divergence of both beams.     

Filtering of light fluctuations by multiple second harmonic generation

It is shown that the level of both quantum and classical light fluctuations can be considerably decreased by multiple second harmonic generation in thin nonlinear plates, when filtering out the generated second harmonic radiation behind each plate. As for the application, a second harmonic plate is proposed to be placed in the laser resonator in order to improve statistical and coherence properties of the lasing mode.     

Theory of second harmonic generation in focused light beam of fundamental frequency with the Gaussian distribution of light intensity under the interaction of type o+o→e

A process of generation of second harmonic frequency (S.H.G.) in focused light beam with the Gaussian distribution of light intensity is studied with the help of generalized diffraction theory in this work. Three methods of focusing are considered, namely, focusing with the spherical lens, focusing with the cylindrical lens in the plane of the principal cut and finally focusing with the cylindrical lens in the plane perpendicular to the plane of the principal cut. Two cases are discussed, namely, the case of S.H.G. in “diffractionless” light beam and the case of S.H.G. in strongly diffracted light beam.     

Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.     

Polar light and symmetry of electro-optical effects

General regularities of the interaction of a polar light wave synthesized from the Fourier harmonics of a fundamental frequency with a transparent centrosymmetric optically nonlinear medium are considered. The notion of light polarity is introduced and transverse electro-optical effects specific for the problem of interaction between polar light and isotropic nonlinear media (optical rectification and the linear electro-optical effect) are analyzed. Estimates of values of the effects in combination with published experimental data on optically encoded second harmonic generation in glasses indicate promising opportunities for practical application of the effects of the interaction of polar light and matter in optical systems of information recording and processing.     

基于混频效应的宽带激光谐波转换理论

提出了一种新的宽带激光谐波转换理论,指出实际宽带激光谐波转换不能简单应用倍频理论,提出同时存在不同波长之间满足和频相位匹配情况,因而宽带谐波转换应该是一个倍频加和频的混合转换过程.在合理设计下,不同波长之间的和频效应可以在整个谐波转换中占主导地位,突破了传统允许波长的限制,这种理论和方法不仅适合二倍频,同时适合三倍频等高次谐波转换 关键词： 宽带激光 谐波转换 混频     

Fluctuations of second harmonic generated light

We calculate the statistical properties of light, arising by second harmonic generation from stationary quasimonochromatic light fields as thermal and single-mode laser light. After a derivation of the correlationfunctions we draw conclusions about spectral densities and the expected results for photon-counting experiments for the converted light.     

Determination of spectral width and chirp of ultrashort light pulses by analysis of second harmonic beam divergence

It is shown that in the noncollinear second harmonic generation scheme used for ultrashort light pulse duration measurements the divergence of the second harmonic beam is determined by the spectral width and chirp of the pulse. This enables one to measure simultaneously the spectral width, pulse duration, spectral-time product, chirp and its sign for a single pulse in the same device.     

Yellow light generation by frequency doubling of a diode-pumped Nd:YAG laser

We demonstrate the generation of TEM₀₀ mode yellow light in critically type II phase-matched KTiOPO₄ (KTP) with intracavity frequency doubling of a diode-pumped Nd:YAG laser at room temperature. After a 150 μm thick etalon have been inserted into the cavity, the stability and beam quality of the second harmonic generation (SHG) is enhanced. A continuous wave (CW) TEM₀₀ mode output power of 1.67 W at 556 nm is obtained at a pump level of 16 W. The total optical to optical conversion efficiency is about 10.44%. To the best of our knowledge, this is the first Watt-level yellow light generation by frequency doubling of Nd:YAG laser.     

三次谐波系统在混沌状态下光场的统计特性

数值分析了三次谐波系统在混沌状态下光场的统计特性。三次谐波混沌状态下光场统计服从超泊松分布,谐波光场涨落皆大于基波光场涨落,这种光场涨落随系统最大李亚普诺夫指数增大而无规律地发生起伏变化。     

Nonlinear second harmonic generation by light wave-plasma interaction in oscillating magnetic field

The nonlinear generation of second harmonic electromagnetic waves in a thin inhomogeneous (dense and rarefied) plasma layer (of lengthd) by obliquely and normally incident light waves is analyzed. We consider the effect of an external time-dependent magnetic field on the generation and amplification of waves. Two cases are considered, when the magnetic field oscillates at a frequency (i) equal to and (ii) double that of the incident wave. For normal incidence, waves are not radiated in case (i), while in case (ii) the second harmonics are radiated equally from the plasma boundaries atx=0 andx=d. For a rarefied plasma, the second harmonics are radiated with equal amplitudes in both cases.     

Extended phase matching of high harmonics driven by mid-infrared light

We demonstrate that phase-matched frequency upconversion of ultrafast laser light can be extended to shorter wavelengths by using longer driving laser wavelengths. Experimentally, we show that the phase-matching cutoff for harmonic generation in argon increases from 45 to 100 eV when the driving laser wavelength is increased from 0.8 to 1.3 microm. Phase matching is also obtained at higher pressures using a longer-wavelength driving laser, mitigating the unfavorable scaling of the single-atom response. Theoretical calculations suggest that phase-matched high harmonic frequency upconversion driven by mid-infrared pulses could be extended to extremely high photon energies.     

Generation of green light in a thermally poled silica fiber by quasi-phase-matched second harmonic generation

Thermal poling is an attractive method to induce a nonlinear coefficient in silica materials. We have investigated potential silica materials with respect to their suitability for thermal poling and analyzed the achievable depletion thickness in the poling process. Based on this investigation, a fiber was designed and prepared for second harmonic generation. The generation of light in the visible range at a wavelength of 532 nm was successfully demonstrated with a poled fiber and with quasi-phase matching using a pump wavelength of 1064 nm.     

Efficiency of second harmonic generation for partially coherent light in anisotropic crystals

This paper analyzes the second harmonic generation (SHG) efficiency of light with partial temporal coherence due to depolarization effects in birefringent media. It discusses relations between SHG efficiency fading, light source spectrum, crystal birefringence, and phase matching conditions. The efficiency of SHG pumped by the partially coherent light beam that may depolarize light in nonlinear birefringent crystal is also analyzed. The basic theory of SHG with its modification for partially coherent light with depolarization and some numerical calculations of the SHG process are described. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 207, May 17–20, 2007, Świnoujście, Poland