Estimation methodology for amplitude of second-order harmonic in nonlinear surface acoustic wave measured by optical diffraction method

An estimation methodology for amplitude from the fundamental to fourth-order harmonic composed of nonlinear surface acoustic waves on a LiNbO₃ substrate with a 128° Y-X propagation axis was demonstrated. First, equations for estimation of amplitudes from diffracted light intensity were shown and then numerical simulations of main factors were carried out. Normalized diffraction light intensities due to components of nonlinear surface acoustic waves were measured and their amplitudes were obtained from measured values. Finally, the amplitude of the second harmonic propagating on a gold thin film of about 50 nm thickness was estimated. It was found that the amplitude of the second harmonic increased continuously from 0.8 to 2.0 Å with propagation distance in the thin film.     

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.     

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.     

Approximate formulae for the overlap integral of two harmonic oscillator wave functions

The use of second-order perturbation theory to derive approximate formulae for the overlap integral of two harmonic oscillator wave functions is discussed, and the results applied to the theory of intensity distributions in vibrational progressions in electronic spectra. For the vibrational progression m←0 an approximate formula is given which, when the vibrational frequencies of the initial and final states differ by less than 10%, reproduces to an accuracy of 1% or less the intensity profile calculated using the exact formulae for the overlap integrals.     

Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator

The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A.     

On the measurement of electronic spin-scattering anisotropy in the presence of magnetic interaction effects,using the dHvA Waveshape Analysis method

We derive an expression for the harmonic content of the oscillatory magnetization (de Haas-van Alphen effect) which is valid in the most general case, when the harmonic amplitudes and the relative harmonic phases of the pure Lifshitz-Kosevitch (LK) theory are modified by an arbitrary combination of magnetic interaction (MI), spin-scattering anisotropy (SSA) and exchange shift effects. The calculation produces several conclusions which bear directly upon the possibility of generally being able to determine separately the up-spin and down-spin conduction electron lifetimes in the presence of magnetic impurities, by means of measurements of the amplitudes and relative phase of the fundamental and second harmonic dHvA oscillations. We have shown that not only does SSA shift the first and second LK harmonics in phase, by amountsΔΘ₁ andΔΘ₂, but SSA also shifts the second harmonic magnetic interaction component by an amount 2ΔΘ₁. We find that, in general, the combined effect of both MI and SSA on the observable relative phase angle, (2 Θ₁?Θ₂), can either add or cancel. In the limit in which the second harmonic is dominated by the MI component it can be shown that (2 Θ₁?Θ₂) goes to π, regardless of the amount of SSA, so that no useful information regarding SSA can be obtained from (2 Θ₁?Θ₂) in this case. Measurable quantities and measurement techniques, for the determination of SSA, are discussed briefly.     

Double-resonant second harmonic generation from surface coverages of nile-blue A

Second harmonic emission from a dye covered quartz surface has been observed in total internal reflection. Coverages with the dye nile-blue A yielded an increase in second harmonic output by several orders of magnitude as compared to coverages with rhodamine 6G. In the latter case only the harmonic light is at resonance with the S₀–S₂ transition of the adsorbed dye molecules, whereas for nile-blue A both, the fundamental and the harmonic frequency, are at resonance with the respective singlet transitions.     

Diffraction of light by phase-shifted adjacent ultrasound beams; ρ ⪢ 1

The system of difference-differential equations for the amplitudes of a diffracted light-wave caused by two adjacent ultrasonic beams, a fundamental followed by its nth harmonic, is solved for values of ρ outside the Raman-Nath region, and simplified expressions are deduced for the intensities up to order n. Conclusions are drawn concerning the influence of the phase-shift δ on the diffraction spectrum, and the calculation of the factor α_n from the intensities (α_n represents the ratio of the ultrasonic pressures). All results are applied to the case of a fundamental and its third or fourth harmonic.     

Model studies on the systematics and interpolation of Franck-Condon factor arrays

A simple harmonic oscillator approximation is used to derive approximate algebraic expressions for low vibrational quantum number Franck-Condon factors for band systems for which molecular data are sparse. These simple expressions involve a transition parameter u which is characteristic of the electronic transition involved. The expressions provide Franck-Condon factors which agree quite well with RKR values when these are available. The formulae are used to explain quantitatively the dependence on u of the systematic properties of Franck-Condon factor arrays and to provide a method for their interpolation. The formulae are also used to describe quantitatively the dependence on u of the gross appearance of molecular band systems in emission and absorption.     

Investigation on high efficiency temporal phase modulated broadband second harmonic laser

In this paper, it is the first time to experimentally demonstrate the second harmonic generation (SHG) of temporal phase modulated broadband laser. The SHG conversion efficiency and the characteristic of SHG spectrum are investigated in detail and the relation between SHG conversion efficiency and incident fundamental light intensity is obtained. The highest efficiency of nearly 70% is achieved at the fundamental pulse intensity of 1.6 GW/cm². The experimental results show that the SHG spectrum widths under high and low intensity are both half of the incident fundamental lights, and don’t result in the spectrum narrowing. The obtained results are very useful for operation at the second harmonic wavelength in inertial confinement fusion (ICF) laser facility.     

Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n

A study has been made of the influence of the phase-difference of two ultrasonic beams, a fundamental and its nth harmonic, on the intensities or amplitudes of diffracted lightwaves. After showing the similarity between superposed and adjacent ultrasound in the Raman-Nath region ρ ? 1, simplified expressions for the intensities have been set up to draw conclusions concerning the symmetry of the diffracted pattern, the amplitude modulation, and the numerical calculation of the factor α_n, from the intensities in which α_n represents the ratio of the ultrasonic pressures. All results are illustrated in the case of a fundamental and its second or third harmonic.     

Generation of second optical harmonic and magnetooptical Kerr effect in ferromagnet-semiconductor heterostructures CaF2/MnAs/Si(111)

The second optical harmonic generation and magnetooptical Kerr effect are investigated for the light (λ=800 nm) reflected by ferromagnet-semiconductor heterostructures CaF₂/MnAs/Si(111). The observed change in the second-harmonic intensity is odd in magnetization. A phenomenological analysis of possible contributions to the second harmonic is carried out, and the sources of optically nonlinear signals are determined from the experimental azimuthal dependences of the light intensity at double frequency. The difference in the field dependences of the second harmonic and the magnetooptical Kerr effect is observed.     

Perturbative analysis of cross-talk of two pieces of photorefractive phase gratings stored in one point by angle multiplexing

In this paper, we have applied a perturbative expanding method to the hopping model, and studied the cross-talk between two pieces of phase gratings stored in one point of photorefractive material by angle multiplexing. The coupling equations and their steady solution have been derived. It has been found that the fundamental harmonic of the first grating is coupled with the second-order harmonic of the second grating and the second-order harmonic of the first gating is coupled with the fundamental harmonic of the second grating. The positions of maximums of the plots about the normalised fundamental and second-order harmonics of the space-charge field vs. the normalised grating vector (k/k₀) are at k/k₀=1.414 and k/k₀=1.01 for Δk/k₀=0, respectively, which are at k/k₀=1 and for the case of storing single grating in one point. This kind of deviation has been confirmed by our two-wave coupling experiment with Ce:KNSBN crystal. At the same time, we have found the degree of deviation of the second-order harmonic of the space-charge field strongly depends on the difference of normalised grating vector (k/k₀)between the two pieces of gratings, but that of fundamental harmonic weakly depends on it. In addition, it has been found that the degrees of deviation of both harmonics do not depend on the modulation depth.     

Silicon microelement vibration testing using conventional and heterodyned time-average interferometry with automated temporal and spatial phase stepping

This paper focuses on the applicability of the temporal (TPS) and spatial carrier (SCPS) phase-shifting techniques to the time-average interferogram intensity modulation distribution determination. Both techniques use the same mathematical formulae, but in different domains: temporal and spatial ones. They are sensitive to different types of errors. The influence of main experimental errors: phase-step miscalibration, spatial carrier miscalibration, average intensity changes and intensity noise in both the presented techniques on the fringe function determination (|J₀| or J₀² in case of sinusoidal vibrations), is discussed. The techniques are compared to find the most appropriate one. The time-average technique with heterodyning for small vibration–amplitude measurements is also discussed. The application of the SCPS method to this technique is shown for the first time.     

A study on surface symmetry and interfacial enhancement of SrTiO3 by second harmonic generation

The symmetry of the surfaces of SrTiO3and slightly Nb-doped SrTiO3crystals was investigated by the optical reflected second harmonic generation technique.The good agreement between experimental and theoretical results of the second harmonic intensity dependence on the azimuth angle indicates that the SrTiO3(001)surface is with 4mm symmetry and the Nb-doped SrTiO3(111)surface with 3m symmetry.The measurements of the polarization dependent second harmonic intensity confirm that conclusion.The enhancement of the surface polarization in the structure of SrTiO3capped La0.9Sr0.1MnO3films compared with that in the La0.9Sr0.1MnO3films has been obtained.     

Intensity measurements in the 4·54μ fundamental of CH3D at low temperatures

The integrated intensities of the J-multiples R(4) through P(12), including the Q-branch, of the 4·54μ fundamental of CH₃D have been measured at 100°K, 150°K, 200°K, 250°K, and 298°K. Comparison of the measured line strengths with values calculated using symmetric-top formulae suggests strong intensity anamolies.     

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.     

Discussion on Unique Characteristics of Second Order Harmonic in a Nonlinear Surface Acoustic Wave Investigated by Optical Diffraction Method

Unique capability of the second harmonic in a nonlinear surface acoustic wave (NLSAW) generated on 128° Y-X LiNbO₃ substrate was investigated by optical diffraction technique. Amplitudes of the fundamental, the second harmonic, and the third harmonic in it were evaluated from an equation composed as a basis of the Beckmann-Spizzichino model. The experimental findings were as follows: the second harmonic velocity was faster than that of the fundamental; a full width at half maximum in envelope profile of the second harmonic was unchanged as if it experienced the gold thin film; total peak intensity in the envelope profile of the second harmonic during collision at gold thin film area was stronger than the sum of individual peak intensity of two second harmonics before the collision. From our experimental findings we conclude that the second harmonic has a soliton-like characteristic.     

Third harmonic generation of CO2 laser radiation in AgGaSe2 crystal

Generation of third harmonic of CO₂ laser radiation has been obtained in a type-II, ϑ=57° cut 9 mm thick AgGaSe₂ crystal for the first time by sum-frequency-mixing of the fundamental with its second harmonic, the latter being obtained using another type-I, ϑ=55° cut 11 mm thick AgGaSe₂ crystal. The energy conversion efficiencies obtained for second harmonic and third harmonic generations are 6.3% and 2.4% respectively with the input fundamental pump power density of 5.9 MW/cm² only. The wavelength of the fundamental CO₂ laser radiation used for the generation of harmonics is 10.6 μm, P(20) line. A compact TEA CO₂ laser source has been built in the laboratory.     

Theory of second harmonic generation at a metal surface with surface plasmon excitation

Theory of second harmonic generation at a metal surface is developed, when surface plasmon-polaritons are resonantly excited by the incident electromagnetic field. For harmonic generation from small metallic spheres characterized by the dielectric function ?₁(ω) + i?₂(ω), the resonant enhancement of the second harmonic intensity is predicted to be of the order of ($\text{?}{}_1\text{?}{}_2\text{)}{}^4$. The resonant enhancement is much smaller for the case of a metallic grating.