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Conference on Lasers and Electro-Optics

Photon-pair Generation by Spontaneous Four-wave Mixing in Integrated Optical Waveguides: a Nonlinear Time-domain Model

Gary F. Sinclair, Mark G. Thompson

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We model photon-pair generation in the presence of parasitic nonlinearities such as self- and cross-phase modulation. The effect of these nonlinearities on the pair production rate and heralded photon purity is explored.
DOI
10.1364/cleo_at.2017.jw2a.20

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A time-domain approach using the momentum operator is used to model spontaneous four-wave mixing in a lossless nonlinear waveguide. The effects of self- and cross-phase modulation on the photon-pair production rate and heralded photon purity are investigated. We show that in the special case where only one half of the photon-pair state is filtered the generation rate and purity of the heralded photons are unmodified by the presence of self- and cross-phase modulation. The significance of this special case arises when we consider heralded single-photon sources, where future schemes are likely to only filter the herald photon to ensure a high heralding efficiency is maintained.
We consider integrated photon pair sources based on spontaneous four-wave mixing and derive expressions for the pump powers at which various nonlinear processes become relevant for a variety of source materials and structures. These expressions serve as rules of thumb in identifying reasonable parameter regimes for the design of such sources. We demonstrate that if pump powers are kept low enough to suppress cross-phase modulation, multi-pair events as well as many other nonlinear effects are often also constrained to negligible levels.
As four-wave-mixing-based photon-pair sources mature, accurate modeling of the photon-pair properties becomes important. Unlike spontaneous parametric down-conversion, four-wave mixing is accompanied by a number of parasitic effects such as nonlinear self- and cross-phase modulation. Currently, most modelings of photon-pair states are analytic in nature, which limits the number and type of effects that can be taken into account. In this work, we derive a complete, dual-pump evolution equation for the joint amplitude of photon pairs, wherein any desired effects can be included. We describe how to efficiently obtain numerical solution to this equation using a split-step approach. Lastly, we cover a few analytical solutions and compare two schemes for pure-photon generation under three different parasitic effects. We show how one scheme is highly sensitive to parasitic effects, while the other is very robust.
Enhancing nonlinear optical effects is critical to improving the performance of many functional devices for nonlinear and quantum optical applications. Here, we study the possibility of bending a waveguide to enhance the photon pair generation rate in a spontaneous four-wave mixing process. Whereas intuition might suggest that bending makes the process less efficient because the waveguides are more lossy when bent, we show that the increase in the effective nonlinearity outperforms the loss disadvantage for moderate bending radii. That can be explained by a better localization of the guided eigenmodes, leading to a reduced mode area. By studying selected waveguide devices with a fixed length, we demonstrate an improvement in the photon pair generation rate between 5% and 210% for an optimal bending radius. These findings have implications for the future design of integrated photonic devices for quantum optical applications, especially in cases where the chip estate tends to be a limiting factor.
Enhancing nonlinear optical effects is critical to improving the performance of many functional devices for nonlinear and quantum optical applications. Here we study the possibility of bending a waveguide to enhance the photon pair generation rate in a spontaneous four-wave mixing process. Whereas intuition might suggest that bending makes the process less efficient, because the waveguides are more lossy when bent, we show that the increase in the effective nonlinearity outperforms the disadvantage for moderate bending radii. That can be explained by a better localization of the guided eigenmodes, leading to a reduced mode area. By studying selected waveguide devices with a fixed length, we demonstrate an optimal improvement between 5 % and 270 % in the photon pair generation rate for an optimal bending radius. These findings have implications for the future design of integrated photonic devices for quantum optical applications, especially in cases where the chip estate tends to be a limiting factor.