Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

TL;DR

This paper investigates theoretically how frequency conversion in second-order nonlinear optical waveguides can be used to selectively multiplex orthogonal waveforms, enabling advanced optical communication and quantum information processing.

Contribution

It provides a comprehensive theoretical model and analytical solutions for optimizing selectivity in frequency conversion-based waveform discrimination.

Findings

Identifies the most favorable parameter regime for high selectivity.

Derives an analytical solution for the optimal regime.

Shows pump chirp does not improve selectivity in the optimal regime.

Abstract

We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three- wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second- order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, and employ Schmidt (singular- value) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical computations. We identify the most favorable regime (at least in the case of no pump chirp) and derive the complete analytical solution for the same. We bound the maximum achievable selectivity in this parameter space. We show that including a frequency chirp in the pump does not improve selectivity in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion.