On certain regularities of the response of a medium upon generation of the triple frequency of a few-period laser pulse in the case of its passage through an optically thin nonlinear layer

Svetlana A. Varentsova, Tatiana M. Lysak, Vyacheslav A. Trofimov

Optics and SpectroscopySep 1, 20080 citations

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Analysis of THG modes for femtosecond laser pulse

Vyacheslav A. Trofimov, Pavel S. Sidorov

Published May 16, 2017• 1 citation

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Abstract

DOI: 10.1117/12.2267499

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Analysis of THG modes for femtosecond laser pulse

Vyacheslav A. Trofimov, Pavel S. Sidorov

THG is used nowadays in many practical applications such as a substance diagnostics, and biological objects imaging, and etс. With developing of new materials and technology (for example, photonic crystal) an attention to THG process analysis grow. Therefore, THG features understanding are a modern problem. Early we have developed new analytical approach based on using the problem invariant for analytical solution construction of the THG process. It should be stressed that we did not use a basic wave non-depletion approximation. Nevertheless, a long pulse duration approximation and plane wave approximation has applied. The analytical solution demonstrates, in particular, an optical bistability property (and may other regimes of frequency tripling) for the third harmonic generation process. But, obviously, this approach does not reflect an influence of a medium dispersion on the frequency tripling. Therefore, in this paper we analyze THG efficiency of a femtosecond laser pulse taking into account a second order dispersion affect as well as self- and crossmodulation of the interacting waves affect on the frequency conversion process. Analysis is made using a computer simulation on the base of Schrodinger equations describing the process under consideration.THG is used nowadays in many practical applications such as a substance diagnostics, and biological objects imaging, and etс. With developing of new materials and technology (for example, photonic crystal) an attention to THG process analysis grow. Therefore, THG features understanding are a modern problem. Early we have developed new analytical approach based on using the problem invariant for analytical solution construction of the THG process. It should be stressed that we did not use a basic wave non-depletion approximation. Nevertheless, a long pulse duration approximation and plane wave approximation has applied. The analytical solution demonstrates, in particular, an optical bistability property (and may other regimes of frequency tripling) for the third harmonic generation process. But, obviously, this approach does not reflect an influence of a medium dispersion on the frequency tripling. Therefore, in this paper we analyze THG efficiency of a femtosecond laser pulse taking into account a second order dispersion affect as well as self- and crossmodulation of the interacting waves affect on the frequency conversion process. Analysis is made using a computer simulation on the base of Schrodinger equations describing the process under consideration.

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Phase-modulation effects on the spectrum of third-harmonic generation

Y. B. Band

We calculate the spectrum of third-harmonic generation (THG) for multimode fundamental input fields. We consider input fields from (1) a laser with gain on several cavity modes, (2) pulses with short temporal duration, and (3) frequency-modulated input fields. The effects of phase modulation in the nonlinear medium on the spectrum of the THG field are considered. Using the estimates by Miles and Harris [IEEE J. Quantum Electron. QE-9, 470 (1973)] for the nonlinear susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) in alkali-metal vapors, we find that phase modulation can profoundly affect the efficiency and the spectrum of the THG. Generally, the self-phase modulation of the fundamental will tend to reduce the phase matching of an intense fundamental field and the third harmonic and thereby lower the conversion efficiency. New frequencies not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{k}}$, where {${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$} are frequencies in the fundamental laser spectrum, are created even at relatively low conversion due to phase modulation. Effects of cross phase modulation are also studied.We calculate the spectrum of third-harmonic generation (THG) for multimode fundamental input fields. We consider input fields from (1) a laser with gain on several cavity modes, (2) pulses with short temporal duration, and (3) frequency-modulated input fields. The effects of phase modulation in the nonlinear medium on the spectrum of the THG field are considered. Using the estimates by Miles and Harris [IEEE J. Quantum Electron. QE-9, 470 (1973)] for the nonlinear susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) in alkali-metal vapors, we find that phase modulation can profoundly affect the efficiency and the spectrum of the THG. Generally, the self-phase modulation of the fundamental will tend to reduce the phase matching of an intense fundamental field and the third harmonic and thereby lower the conversion efficiency. New frequencies not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{k}}$, where {${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$} are frequencies in the fundamental laser spectrum, are created even at relatively low conversion due to phase modulation. Effects of cross phase modulation are also studied.

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A technique of third-harmonic generation (THG) with nonsynchronous pulses is applied to study the dynamics of resonant wave mixing. A circularly polarized laser pulse is focused into a cell containing ${\mathrm{I}}_{2}$ vapor to create the coherent dipole moments. An oppositely circularly polarized pulse is then focused into the same region to generate the third harmonic. Since no THG is produced by any individual pulse, correlated THG can be easily measured without using any fast detection scheme. A theory is presented to explain the measured coherent lifetime of approximately 1 ns. The technique of wave mixing with two linearly polarized pulse is applied to study saturation in resonant THG and to measure the homogeneous relaxation rate of the molecular states. This technique is also applied to study the photon echo generating process.A technique of third-harmonic generation (THG) with nonsynchronous pulses is applied to study the dynamics of resonant wave mixing. A circularly polarized laser pulse is focused into a cell containing ${\mathrm{I}}_{2}$ vapor to create the coherent dipole moments. An oppositely circularly polarized pulse is then focused into the same region to generate the third harmonic. Since no THG is produced by any individual pulse, correlated THG can be easily measured without using any fast detection scheme. A theory is presented to explain the measured coherent lifetime of approximately 1 ns. The technique of wave mixing with two linearly polarized pulse is applied to study saturation in resonant THG and to measure the homogeneous relaxation rate of the molecular states. This technique is also applied to study the photon echo generating process.

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Study of third harmonic generation in quantum wells with a new potential

Guo Kang-xia

The third harmonic generation coefficients( THG) in quantum wells with a new potential are studied theoretically. We obtain eigenfunctions and energy eigenvalues by means of solving Schrodinger equation within the framework of effective mass approximation method. The analytic expressions of the third-harmonic generation coefficients can be got using the compact-density-matrix approach and iterative method. It is found that the THG coefficients are affected by the width of the quantum well d and the parameter U0.The third harmonic generation coefficients( THG) in quantum wells with a new potential are studied theoretically. We obtain eigenfunctions and energy eigenvalues by means of solving Schrodinger equation within the framework of effective mass approximation method. The analytic expressions of the third-harmonic generation coefficients can be got using the compact-density-matrix approach and iterative method. It is found that the THG coefficients are affected by the width of the quantum well d and the parameter U0.

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On certain regularities of the response of a medium upon generation of the triple frequency of a few-period laser pulse in the case of its passage through an optically thin nonlinear layer

Svetlana A. Varentsova, Tatiana M. Lysak, Vyacheslav A. Trofimov

The response of a medium at the triple frequency under the action of few-period laser pulses is considered within the framework of the thin-optical-layer approximation for the case where the triple frequency is close to the natural frequency of the linear oscillator. It is shown that a bistable dependence of the polarization amplitudes on the external action amplitude simultaneously appears at both the natural frequency and the frequency of the external action. This allows one, in particular, to reveal the presence of bistability of the regime of third harmonic generation in a physical experiment by using the transmitted radiation of the acting pulse. A decrease in the duration of the pulse incident on the medium leads to an increase in the hysteresis loops. The effect of the absolute phase of a short pulse on the spectral composition of the response of the medium is studied. For pulses of medium duration, in addition to the resonant response of the medium, the presence of the dynamic response of the medium at the triple frequency was revealed, despite a detuning of the latter from the resonance. The presence of this frequency in the spectrum of the response of the medium results in the dependence of the resonant response of the medium on the absolute phase even for a sufficiently long pulse containing tens oscillations of the electric field strength under the pulse envelope. To obtain the dynamics of the spectral lines from the results of computer simulation, the Fourier-Gabor method is used, the applicability of which is demonstrated by the comparison of the results obtained on its basis with the corresponding analytical dependences.The response of a medium at the triple frequency under the action of few-period laser pulses is considered within the framework of the thin-optical-layer approximation for the case where the triple frequency is close to the natural frequency of the linear oscillator. It is shown that a bistable dependence of the polarization amplitudes on the external action amplitude simultaneously appears at both the natural frequency and the frequency of the external action. This allows one, in particular, to reveal the presence of bistability of the regime of third harmonic generation in a physical experiment by using the transmitted radiation of the acting pulse. A decrease in the duration of the pulse incident on the medium leads to an increase in the hysteresis loops. The effect of the absolute phase of a short pulse on the spectral composition of the response of the medium is studied. For pulses of medium duration, in addition to the resonant response of the medium, the presence of the dynamic response of the medium at the triple frequency was revealed, despite a detuning of the latter from the resonance. The presence of this frequency in the spectrum of the response of the medium results in the dependence of the resonant response of the medium on the absolute phase even for a sufficiently long pulse containing tens oscillations of the electric field strength under the pulse envelope. To obtain the dynamics of the spectral lines from the results of computer simulation, the Fourier-Gabor method is used, the applicability of which is demonstrated by the comparison of the results obtained on its basis with the corresponding analytical dependences.

Optics and SpectroscopySep 1, 20080 citations

{\mathrm{I}}_{2}

vapor to create the coherent dipole moments. An oppositely circularly polarized pulse is then focused into the same region to generate the third harmonic. Since no THG is produced by any individual pulse, correlated THG can be easily measured without using any fast detection scheme. A theory is presented to explain the measured coherent lifetime of approximately 1 ns. The technique of wave mixing with two linearly polarized pulse is applied to study saturation in resonant THG and to measure the homogeneous relaxation rate of the molecular states. This technique is also applied to study the photon echo generating process.