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Optical arbitrary waveform generation using spectro-temporal unitary transforms

Callum Deakin

TL;DR

The paper tackles beating the bandwidth and loss constraints of conventional coherent modulation by introducing spectro-temporal unitary transforms, realized through cascaded phase modulators and dispersive elements. It formulates a universal unitary decomposition $U = \Lambda_1 H \Lambda_2 H \cdots \Lambda_n H$, realized with diagonal phase blocks and a mode-mixing operator $H$ (e.g., a DFT with $DFT_m = \frac{1}{\sqrt{m}}[\exp(2\pi i jk/m)]$), enabling lossless transfer between spectral and temporal modes. Phase instructions are found by minimizing $NSR = \frac{1}{E_{\textnormal{target}}} \sum_{m=0}^M |\Psi_{\textnormal{target}}(mT) - F_N(mT)|^2$ using gradient-based methods, with a detailed complexity analysis indicating high computational load but potential ASIC or CMOS-parallel implementations and applicability to non-continuous tasks. A concrete 5-stage, 1024-symbol demonstration at 200 Gbaud using 100 GHz modulators and 20 ps/nm dispersion per stage, computed via limited-memory BFGS, shows practical on-chip dispersion and provides phase-time series, spectra, and constellation evolutions, underscoring the method’s promise for bandwidth-independent coherent signaling and ultrafast/quantum contexts despite current complexity challenges.

Abstract

We discuss the prospect of using cascaded phase modulators and dispersive elements to achieve arbitrary optical waveform generation. This transform is not limited by the bandwidth of its constituent modulators and is theoretically lossless.

Optical arbitrary waveform generation using spectro-temporal unitary transforms

TL;DR

The paper tackles beating the bandwidth and loss constraints of conventional coherent modulation by introducing spectro-temporal unitary transforms, realized through cascaded phase modulators and dispersive elements. It formulates a universal unitary decomposition , realized with diagonal phase blocks and a mode-mixing operator (e.g., a DFT with ), enabling lossless transfer between spectral and temporal modes. Phase instructions are found by minimizing using gradient-based methods, with a detailed complexity analysis indicating high computational load but potential ASIC or CMOS-parallel implementations and applicability to non-continuous tasks. A concrete 5-stage, 1024-symbol demonstration at 200 Gbaud using 100 GHz modulators and 20 ps/nm dispersion per stage, computed via limited-memory BFGS, shows practical on-chip dispersion and provides phase-time series, spectra, and constellation evolutions, underscoring the method’s promise for bandwidth-independent coherent signaling and ultrafast/quantum contexts despite current complexity challenges.

Abstract

We discuss the prospect of using cascaded phase modulators and dispersive elements to achieve arbitrary optical waveform generation. This transform is not limited by the bandwidth of its constituent modulators and is theoretically lossless.

Paper Structure

This paper contains 4 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Spectro-temporal unitary transformations
  3. Calculation of phase instructions and complexity
  4. Example transformation: RRC shaped 64-QAM

Figures (2)

  • Figure 1: (a) Conventional IQ modulation based on amplitude modulation, $a(t)$. (b) Lossless spectro-temporal unitary transform based arbitrary waveform modulation based on cascaded phase modulators $\phi(t)$ and dispersive elements $H(\omega)$.
  • Figure 2: Example 5 stage transformation for generating a block of 1024 RRC-shaped 200 GBd 64-QAM symbols using 100 GHz phase modulator bandwidth and 20 ps/nm dispersion per stage, sampled at 1600 GSa/s. (a) Phase instructions time series. (b) Phase instruction spectra. (c) Generated constellation. (d)-(h) Optical spectrum after each stage.