Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Letters

Induced phase modulation of a generated second-harmonic signal

Jamal T. Manassah, Orville R. Cockings

Published Dec 1, 1987• 49 citations
Publisher

Abstract

The weak induced-phase-modulation effects on the shape and the phase of a generated second-harmonic signal, due to the primary signal, are investigated in the regime of weak conversion and with velocity dispersion and absorption present. In the time domain a two-peaks structure appears in the shape of the signal, and in the frequency domain the spectral distribution is broadened compared with that of the second-harmonic signal generated in the absence of induced phase modulation.

DOI
10.1364/ol.12.001005

Related papers

Second-harmonic generation in a quasi-phase-matched structure: Saturable absorption in plane-wave and diffractive regimes

Igor V. Mel’nikov, L.-C. Crasovan, DUMITRU BOGDAN MIHALACHE

The effect of saturable absorption on second-harmonic generation in a quasi-phase-matched structure is studied, including both plane-wave and diffractive coupling of the fields and detuning of the pump field from resonance. In the regime of large Fresnel numbers, the main effect of saturable absorption is to suppress the parametric instability, which limits the efficiency of the second-harmonic generation and places a bound on the device length in order to fit sufficient harmonic power. The optical limiting nature of resonance absorption places an upper bound on the gain that quasi-phase-matching can achieve. In the diffractive regime, a variety of output transverse structures may be initiated by modulation of the relative phase and mutual displacement between the input beams of the pump and seeding harmonic signal. In particular, second-harmonic dragging, i.e., the asymmetric interaction between initially overlapping pump and second-harmonic beams propagating at different angles, is observed such that a pump beam can drag a second-harmonic one out a spatial aperture, thereby implementing a colored logical switch with gain.

Physical Review A•Sep 1, 1998•0 citations

Spectral compression and modulation of second harmonic generation by Fresnel-inspired binary phase shaping

Baihong Li, Yonggang Xu, Haifei Zhu +4 more

The second harmonic generation (SHG) process is investigated theoretically using the quantum mechanics method of coherent control. Based on the extremum conditions for the SHG intensity at the center frequency, a Fresnel-inspired binary phase shaping scheme is proposed for tailoring the fundamental pulse. The SHG spectrum can be compressed into a narrowband signal with lower background by modulating the relative phases between the frequency components within the fundamental pulse, inducing constructive interference at the center frequency and destructive interference elsewhere. Multipeak second harmonic signals can also be obtained by properly modulating various interference pathways. These results have potential applications in high resolution nonlinear spectroscopy, microscopy, and information coding.

Journal of the Optical Society of America B•Oct 1, 2014•5 citations

Frequency-modulated spectra of coherently driven systems

G. S. Agarwal

Frequency-modulated spectra of coherently driven quantum systems are calculated using the density-matrix formulation. The modulated spectra are shown to be related to the two-time correlation functions of the polarization operators of the system. In the limit of modulation frequencies small compared to the width of the spectral features under study, the in-phase signal (quadrature signal) is shown to be related to the derivative of absorption (second derivative of dispersion) in the absence of any modulation. Modulation spectra in strong fields are calculated explicitly for two-level systems; such spectra are shown to yield useful information concerning light shifts and Rabi splittings. The influence of laser temporal fluctuations on such modulation spectra is also discussed.

Physical Review A•Mar 1, 1981•10 citations

Grating-induced slow-light enhancement of second-harmonic generation in periodically poled crystals

Thomas E. Maybour, Devin H. Smith, Péter Horák

The effect of slow light on second-harmonic generation in a periodically poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium is investigated theoretically. A linear $\ensuremath{\pi}$ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.

arXiv:2109.11368•Physical Review A•Jan 18, 2022•2 citations

Spectrum of second-harmonic generation for multimode fields

Y. B. Band, Donald F. Heller, Jay R. Ackerhalt +1 more

We calculate the spectrum of second-harmonic generation (SHG) for multimode input fields. We show that SHG cannot be described as the degenerate limit of sum-frequency generation (SFG) for multimode fields, because the dynamical equations describing SFG do not properly account for this degeneracy. We consider SHG for amplitude-modulated as well as frequency-modulated fundamental fields. The bandwidth of the second harmonic generated from an amplitude-modulated fundamental field depends on the fundamental input intensity and the conversion strength of the nonlinear medium. Additional frequencies that are not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$ will be created at intermediate conversion strengths. However, the growth of the spectral bandwidth is much less pronounced than in SFG. For very high conversion, the spectrum of the second harmonic narrows with increased conversion strength. For frequency-modulated input fields, the second-harmonic spectrum is independent of both the fundamental input intensity and the conversion strength.

Physical Review A•Aug 1, 1990•10 citations

Quasi-phase-matched second-harmonic generation by backward propagating interaction

M. Matsumoto, Kazuo Tanaka

Both static and dynamical analyses of quasi-phase-matched second-harmonic generation by backward propagating interaction, where the second-harmonic wave is generated in reflection, are presented. It is shown that bistability appears in the generated second-harmonic power if the amount of phase mismatch is suitably chosen. The bistability also appears in the output fundamental wave, since the cascaded second-order nonlinear process gives rise to the effective self-modulation of the fundamental wave, which can be applied to all-optical signal processing. The output second-harmonic and fundamental powers can be switched between two bistable states by controlling the intensity or phase of the input fundamental wave.>

IEEE Journal of Quantum Electronics•Apr 1, 1995•41 citations
The weak induced-phase-modulation effects on the shape and the phase of a generated second-harmonic signal, due to the primary signal, are investigated in the regime of weak conversion and with velocity dispersion and absorption present. In the time domain a two-peaks structure appears in the shape of the signal, and in the frequency domain the spectral distribution is broadened compared with that of the second-harmonic signal generated in the absence of induced phase modulation.
The effect of saturable absorption on second-harmonic generation in a quasi-phase-matched structure is studied, including both plane-wave and diffractive coupling of the fields and detuning of the pump field from resonance. In the regime of large Fresnel numbers, the main effect of saturable absorption is to suppress the parametric instability, which limits the efficiency of the second-harmonic generation and places a bound on the device length in order to fit sufficient harmonic power. The optical limiting nature of resonance absorption places an upper bound on the gain that quasi-phase-matching can achieve. In the diffractive regime, a variety of output transverse structures may be initiated by modulation of the relative phase and mutual displacement between the input beams of the pump and seeding harmonic signal. In particular, second-harmonic dragging, i.e., the asymmetric interaction between initially overlapping pump and second-harmonic beams propagating at different angles, is observed such that a pump beam can drag a second-harmonic one out a spatial aperture, thereby implementing a colored logical switch with gain.
The second harmonic generation (SHG) process is investigated theoretically using the quantum mechanics method of coherent control. Based on the extremum conditions for the SHG intensity at the center frequency, a Fresnel-inspired binary phase shaping scheme is proposed for tailoring the fundamental pulse. The SHG spectrum can be compressed into a narrowband signal with lower background by modulating the relative phases between the frequency components within the fundamental pulse, inducing constructive interference at the center frequency and destructive interference elsewhere. Multipeak second harmonic signals can also be obtained by properly modulating various interference pathways. These results have potential applications in high resolution nonlinear spectroscopy, microscopy, and information coding.
Frequency-modulated spectra of coherently driven quantum systems are calculated using the density-matrix formulation. The modulated spectra are shown to be related to the two-time correlation functions of the polarization operators of the system. In the limit of modulation frequencies small compared to the width of the spectral features under study, the in-phase signal (quadrature signal) is shown to be related to the derivative of absorption (second derivative of dispersion) in the absence of any modulation. Modulation spectra in strong fields are calculated explicitly for two-level systems; such spectra are shown to yield useful information concerning light shifts and Rabi splittings. The influence of laser temporal fluctuations on such modulation spectra is also discussed.
The effect of slow light on second-harmonic generation in a periodically poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium is investigated theoretically. A linear $\ensuremath{\pi}$ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.
We calculate the spectrum of second-harmonic generation (SHG) for multimode input fields. We show that SHG cannot be described as the degenerate limit of sum-frequency generation (SFG) for multimode fields, because the dynamical equations describing SFG do not properly account for this degeneracy. We consider SHG for amplitude-modulated as well as frequency-modulated fundamental fields. The bandwidth of the second harmonic generated from an amplitude-modulated fundamental field depends on the fundamental input intensity and the conversion strength of the nonlinear medium. Additional frequencies that are not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$ will be created at intermediate conversion strengths. However, the growth of the spectral bandwidth is much less pronounced than in SFG. For very high conversion, the spectrum of the second harmonic narrows with increased conversion strength. For frequency-modulated input fields, the second-harmonic spectrum is independent of both the fundamental input intensity and the conversion strength.
Both static and dynamical analyses of quasi-phase-matched second-harmonic generation by backward propagating interaction, where the second-harmonic wave is generated in reflection, are presented. It is shown that bistability appears in the generated second-harmonic power if the amount of phase mismatch is suitably chosen. The bistability also appears in the output fundamental wave, since the cascaded second-order nonlinear process gives rise to the effective self-modulation of the fundamental wave, which can be applied to all-optical signal processing. The output second-harmonic and fundamental powers can be switched between two bistable states by controlling the intensity or phase of the input fundamental wave.>