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

Journal of Modern Optics

Field phase modulation and input phase and intensity dependence in a nonlinear second-order interaction

Giuseppe D’Aguanno, C. Sibilia, E. Fazio, Ettore Ferrari Júnior, M. Bertolotti

Published May 1, 1998• 9 citations
Publisher

Abstract

We present a unified treatment of three wave interactions in a second-order nonlinear medium under plane wave approximation which analytically clarifies the various processes on amplitude and phase of the fields both in the phase matching and out of phase matching conditions. A classical mechanical analogy is shown to be useful for the study.

DOI
10.1080/09500349808230897

Related papers

Phase modulation in second-order nonlinear-optical processes

Huib J. Bakker, Paul C. M. Planken, L. Kuipers +1 more

If three light pulses interact in a second-order nonlinear-optical process with a phase mismatch, the pulses may acquire a significant phase modulation. This phase modulation leads to a modification of the spectrum of the pulses and may offer the possibility of compressing the pulses. In this paper we discuss the effects of the ratio of intensities of the interacting pulses and the amount of phase mismatch on the phase modulation using analytical and numerical results. When the phase mismatch is small, it turns out that the modulation is also strongly influenced by the initial phase difference between the fields. Finally, we study the combined effects of a phase mismatch and a difference in group velocity on the spectrum and intensity profile of the interacting pulses.

Physical Review A•Oct 1, 1990•99 citations

Spectrum of three-wave mixing for multimode fields

Y. B. Band, Donald F. Heller, Jerzy S. Krasiński

Analytic solutions are developed for the time-dependent intensity that results from the three-wave mixing of multimode fields. These differ dramatically from the solutions for single-mode (time-independent) fields. New frequencies in the output spectrum are created as input intensities increase. Under conditions of strong nonlinear coupling the output spectrum broadens, ultimately reaching the phase-match bandwidth limit, and the dynamics can become chaotic. A new technique for enhancing mixing efficiencies is presented.

Physical Review A•Oct 1, 1989•15 citations

Novel Analytic Solutions to General Four-Wave-Mixing Problems in a Raman Medium

Jay R. Ackerhalt

A new approach to the problem of steady-state plane-wave propagation in a Raman-active medium has lead to general analytical solutions. Any arbitrary number of fields can interact via both Raman and four-wave processes, but all fields must satisfy the phase-matching condition. The solutions will be illustrated with a problem of current interest; multiple first Stokes generation from a multiple-mode pump field.

Physical Review Letters•Apr 6, 1981•33 citations

Spectra of second harmonic generation and sum frequency generation for multimode fields

Jerzy S. Krasiński, Donald F. Heller, Jay R. Ackerhalt +1 more

The theory of three wave mixing was formulated in a classic paper by Armstrong, Bloembergen, Ducuing, and Pershan over 25 years ago.1 A theoretical description of three wave mixing for multimode time-dependent input fields (as opposed to cw single frequency time independent input fields) has recently been presented.2 Analytic solutions were developed for die time-dependent intensities of the output fields. These solutions differ dramatically from those for single-mode fields. New frequencies in the sum-frequency output spectrum and in the input-field output spectrum are created and grow in magnitude as the input intensities are increased. The output spectrum broadens under conditions of strong nonlinear coupling, ultimately reaching the phasematched bandwidth limit. Here, we review the results presented in Ref. 2 for sum frequency generation (SFG) and explicidy compare these results with those for second harmonic generation (SHG). We show that SHG cannot be described as a limit of the SFG formalism for multimode fields. The SFG formulation for the interaction of photons close to frequency ω1 with photons close to frequency ω2 producing photons close to frequency ω 3= ω 1+ ω 2 does not allow ω1(ω2) photons to interact with each other to produce photons close to frequency 2ω1(2ω2). This self interaction is crucial for SHG and must be incorporated. Therefore, a separate formulation is used to describe SHG with multimode input fields.

Nonlinear Dynamics in Optical Systems•Jan 1, 1990•0 citations

Electromagnetic resonances and phase matching in guided-wave nonlinear optics

R. Reinisch, Gerd Blau, Guy Vitrant +2 more

This paper is concerned with the interplay between electromagnetic resonances and the phase-matching condition in guided-wave nonlinear optics. Several examples are given: quasi phase-matched second-harmonic generation using a grating with a subwavelength periodicity, cascaded optical bistability, Kerr-type distributed couplers under pulse illumination with duration of the order of the cavity build-up time or shorter, surface plasmon-enhanced stimulated Raman scattering at a grating overcoated by a few monolayers of a Raman active medium.

Pure and Applied Optics Journal of the European Optical Society Part A•Sep 1, 1996•1 citation

Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media

Andrey E. Kobyakov, F. Lederer, Ole Bang +1 more

Recently it was shown that in quasi-phase-matched quadratic media the average intensities are subject to an induced Kerr effect. We analytically study the influence of this induced cubic nonlinearity on the amplitude and phase modulation of the fundamental wave and predict efficient all-optical switching.

Optics Letters•Apr 1, 1998•47 citations
We present a unified treatment of three wave interactions in a second-order nonlinear medium under plane wave approximation which analytically clarifies the various processes on amplitude and phase of the fields both in the phase matching and out of phase matching conditions. A classical mechanical analogy is shown to be useful for the study.
If three light pulses interact in a second-order nonlinear-optical process with a phase mismatch, the pulses may acquire a significant phase modulation. This phase modulation leads to a modification of the spectrum of the pulses and may offer the possibility of compressing the pulses. In this paper we discuss the effects of the ratio of intensities of the interacting pulses and the amount of phase mismatch on the phase modulation using analytical and numerical results. When the phase mismatch is small, it turns out that the modulation is also strongly influenced by the initial phase difference between the fields. Finally, we study the combined effects of a phase mismatch and a difference in group velocity on the spectrum and intensity profile of the interacting pulses.
Analytic solutions are developed for the time-dependent intensity that results from the three-wave mixing of multimode fields. These differ dramatically from the solutions for single-mode (time-independent) fields. New frequencies in the output spectrum are created as input intensities increase. Under conditions of strong nonlinear coupling the output spectrum broadens, ultimately reaching the phase-match bandwidth limit, and the dynamics can become chaotic. A new technique for enhancing mixing efficiencies is presented.
The theory of three wave mixing was formulated in a classic paper by Armstrong, Bloembergen, Ducuing, and Pershan over 25 years ago.1 A theoretical description of three wave mixing for multimode time-dependent input fields (as opposed to cw single frequency time independent input fields) has recently been presented.2 Analytic solutions were developed for die time-dependent intensities of the output fields. These solutions differ dramatically from those for single-mode fields. New frequencies in the sum-frequency output spectrum and in the input-field output spectrum are created and grow in magnitude as the input intensities are increased. The output spectrum broadens under conditions of strong nonlinear coupling, ultimately reaching the phasematched bandwidth limit. Here, we review the results presented in Ref. 2 for sum frequency generation (SFG) and explicidy compare these results with those for second harmonic generation (SHG). We show that SHG cannot be described as a limit of the SFG formalism for multimode fields. The SFG formulation for the interaction of photons close to frequency ω1 with photons close to frequency ω2 producing photons close to frequency ω 3= ω 1+ ω 2 does not allow ω1(ω2) photons to interact with each other to produce photons close to frequency 2ω1(2ω2). This self interaction is crucial for SHG and must be incorporated. Therefore, a separate formulation is used to describe SHG with multimode input fields.
This paper is concerned with the interplay between electromagnetic resonances and the phase-matching condition in guided-wave nonlinear optics. Several examples are given: quasi phase-matched second-harmonic generation using a grating with a subwavelength periodicity, cascaded optical bistability, Kerr-type distributed couplers under pulse illumination with duration of the order of the cavity build-up time or shorter, surface plasmon-enhanced stimulated Raman scattering at a grating overcoated by a few monolayers of a Raman active medium.