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

Physical Review A

Cascading of quadratic nonlinearities: An analytical study

Andrey E. Kobyakov, F. Lederer

Published Oct 1, 1996• 82 citations
Publisher

Abstract

A comprehensive analytical approach to scalar and vectorial interaction in cascaded quadratic nonlinearities is presented. Exact formulas for the intensity as well as the phase modulation in dependence on all conceivable control parameters are derived, provided that group-velocity dispersion, diffraction, and pulse walk off can be neglected. The first two constraints are uncritical as far as channel waveguides and thin bulk crystals are concerned. Particular emphasis is paid to a detailed study of the phase evolution in order to identify optimum conditions for an almost homogeneous phase shift across an entire pulse which is in contrast to the generation of a large chirp in cubic nonlinear materials. Moreover, the general results are simplified to relevant limiting cases where simple analytical formulas emerge for the amplitude and phase modulation. The analytical results are used for a classification of all-optical effects based on cascading. Optimum conditions for picosecond modulation processes are discussed. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3455

Related papers

Generation of a pure phase-modulated pulse by cascading effect: a theoretical approach

L. Videau, Claude Rouyer, Josselin C. Garnier +1 more

We propose new smoothing techniques involving nonlinear cascaded processes. The scheme is based on the transfer of incoherent amplitude modulations of a pump beam to the phase of a monochromatic plane wave signal. For that, we can use nonlinear cascaded processes which create crossed phase modulation without efficient energy transfer. With this technique, we should be able to produce a temporal or/and spatial incoherent phase modulation without using electro- optic devices. We describe the mechanisms and the different schemes we propose such as a random temporal phase modulator or a temporally varying random phase plate. We present theoretical results by developing analytical calculations of the nonlinear phase. Then, we analyze the incoherent phase modulation with the correlation functions formalism. We present results which take into account temporal limitations such as the Group Velocity Dispersion (GVD) or the Group Velocity Walk-off (GVW) and spatial limitations such as the Diffraction and the Spatial Walk-off. Finally, we present an all-optical sinusoidal phase modulator setup.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 2001•0 citations

Using system-reservoir methods to derive effective field theories for broadband nonlinear quantum optics: a case study on cascaded quadratic nonlinearities

Chris Gustin, Ryotatsu Yanagimoto, Edwin Ng +2 more

In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model (effective field theory) for the remaining system. Our approach combines approximate diagonalization of judiciously partitioned subsystems with master equation techniques. We consider cascaded optical $χ^{(2)}$ (quadratic) nonlinearities as an example and show that the dynamics can be construed (to leading order) as self-phase modulations of dressed fundamental modes plus cross-phase modulations of dressed fundamental and second-harmonic modes. We then formally eliminate the second-harmonic degrees of freedom and identify emergent features of the fundamental wave dynamics, such as two-photon loss channels, and examine conditions for accuracy of the reduced model in dispersive and dissipative parameter regimes. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models for complex dynamics in broadband nonlinear quantum photonics.

arXiv:2311.03597•Nov 6, 2023•1 citation

Effective field theories in broadband quantum optics: modeling phase modulation and two-photon loss from cascaded quadratic nonlinearities

Chris Gustin, Ryotatsu Yanagimoto, Edwin Ng +2 more

Abstract In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model (effective field theory) for the remaining system. Our approach combines approximate diagonalization of judiciously partitioned subsystems with master equation techniques. We consider cascaded optical χ ( 2 ) (quadratic) nonlinearities as an example and show that the dynamics can be construed (to leading order) as self-phase modulations of dressed fundamental modes plus cross-phase modulations of dressed fundamental and second-harmonic modes. We then formally eliminate the second-harmonic degrees of freedom and identify emergent features of the fundamental wave dynamics, such as two-photon loss channels, and examine conditions for accuracy of the reduced model in dispersive and dissipative parameter regimes. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models for complex dynamics in broadband nonlinear quantum photonics, and may help guide quantum technological proposals in emerging systems where quantum effects become significant at the single-photon level.

Quantum Science and Technology•Jan 27, 2025•0 citations

Ultrafast group-velocity control via cascaded quadratic nonlinearities in optical parametric amplification

Bingjie Zhou, Jingui Ma, Jing Wang +3 more

Slow and fast light are ubiquitous in optical amplifiers. In this Letter, we show for the first time, to the best of our knowledge, that optical parametric amplification (OPA) in chirped quasi-phase-matching structures can act as a platform for group-velocity control in the femtosecond regime. The resonant cascaded nonlinear phase underlies the group-velocity control, which manifests an unusual effect that both slow and fast light can be achieved under the normal condition of signal amplification. As numerically demonstrated in the OPA based on the lithium niobate crystal, the signal and idler pulse can be significantly delayed in time comparable to the signal duration and can also keep high fidelity for durations down to 100 fs until the crystal dispersion becomes effective. The broad bandwidth, large group delay, and direct compatibility with integrated optics will make the proposed platform attractive to both fundamental research and applied science.

Optics Letters•Aug 1, 2018•5 citations

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

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
A comprehensive analytical approach to scalar and vectorial interaction in cascaded quadratic nonlinearities is presented. Exact formulas for the intensity as well as the phase modulation in dependence on all conceivable control parameters are derived, provided that group-velocity dispersion, diffraction, and pulse walk off can be neglected. The first two constraints are uncritical as far as channel waveguides and thin bulk crystals are concerned. Particular emphasis is paid to a detailed study of the phase evolution in order to identify optimum conditions for an almost homogeneous phase shift across an entire pulse which is in contrast to the generation of a large chirp in cubic nonlinear materials. Moreover, the general results are simplified to relevant limiting cases where simple analytical formulas emerge for the amplitude and phase modulation. The analytical results are used for a classification of all-optical effects based on cascading. Optimum conditions for picosecond modulation processes are discussed. \textcopyright{} 1996 The American Physical Society.
We propose new smoothing techniques involving nonlinear cascaded processes. The scheme is based on the transfer of incoherent amplitude modulations of a pump beam to the phase of a monochromatic plane wave signal. For that, we can use nonlinear cascaded processes which create crossed phase modulation without efficient energy transfer. With this technique, we should be able to produce a temporal or/and spatial incoherent phase modulation without using electro- optic devices. We describe the mechanisms and the different schemes we propose such as a random temporal phase modulator or a temporally varying random phase plate. We present theoretical results by developing analytical calculations of the nonlinear phase. Then, we analyze the incoherent phase modulation with the correlation functions formalism. We present results which take into account temporal limitations such as the Group Velocity Dispersion (GVD) or the Group Velocity Walk-off (GVW) and spatial limitations such as the Diffraction and the Spatial Walk-off. Finally, we present an all-optical sinusoidal phase modulator setup.
In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model (effective field theory) for the remaining system. Our approach combines approximate diagonalization of judiciously partitioned subsystems with master equation techniques. We consider cascaded optical χ(2)χ^{(2)}χ(2) (quadratic) nonlinearities as an example and show that the dynamics can be construed (to leading order) as self-phase modulations of dressed fundamental modes plus cross-phase modulations of dressed fundamental and second-harmonic modes. We then formally eliminate the second-harmonic degrees of freedom and identify emergent features of the fundamental wave dynamics, such as two-photon loss channels, and examine conditions for accuracy of the reduced model in dispersive and dissipative parameter regimes. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models for complex dynamics in broadband nonlinear quantum photonics.
Abstract In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model (effective field theory) for the remaining system. Our approach combines approximate diagonalization of judiciously partitioned subsystems with master equation techniques. We consider cascaded optical χ ( 2 ) (quadratic) nonlinearities as an example and show that the dynamics can be construed (to leading order) as self-phase modulations of dressed fundamental modes plus cross-phase modulations of dressed fundamental and second-harmonic modes. We then formally eliminate the second-harmonic degrees of freedom and identify emergent features of the fundamental wave dynamics, such as two-photon loss channels, and examine conditions for accuracy of the reduced model in dispersive and dissipative parameter regimes. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models for complex dynamics in broadband nonlinear quantum photonics, and may help guide quantum technological proposals in emerging systems where quantum effects become significant at the single-photon level.
Slow and fast light are ubiquitous in optical amplifiers. In this Letter, we show for the first time, to the best of our knowledge, that optical parametric amplification (OPA) in chirped quasi-phase-matching structures can act as a platform for group-velocity control in the femtosecond regime. The resonant cascaded nonlinear phase underlies the group-velocity control, which manifests an unusual effect that both slow and fast light can be achieved under the normal condition of signal amplification. As numerically demonstrated in the OPA based on the lithium niobate crystal, the signal and idler pulse can be significantly delayed in time comparable to the signal duration and can also keep high fidelity for durations down to 100 fs until the crystal dispersion becomes effective. The broad bandwidth, large group delay, and direct compatibility with integrated optics will make the proposed platform attractive to both fundamental research and applied science.
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.