An Endless Optical Phase Delay for Harmonic-Free Phase/Frequency Shifting in Coherent-Lite DCIs and Microwave Photonics

An optical IQ modulator (IQM), when driven by quadrature-phase sinusoidal electrical signals, adds a phase/frequency offset to the optical input. However, harmonics of the applied electrical signals are also generated in the optical domain. In this work, we analytically derive the waveform shapes that achieve a harmonic-free phase/frequency shift with high spectral purity using the IQM. Using these waveforms, an endless optical phase delay (EOPD), wherein the phase delay can be increased or decreased continuously and arbitrarily in a reset-free manner, has been presented. The EOPD can be used in coherent-lite or analog coherent receiver based DCIs, phased array LiDAR, and many other applications. In order to adjust for the bias voltages and control signal gains in the EOPD, some of which may be time varying, a multivariate gradient descent algorithm is presented. Use of the EOPD for phase synchronization in a self-homodyne coherent-lite optical link has been demonstrated, making it a promising solution for low-power high-capacity coherent data center interconnects (DCIs).

I. Introduction

Electro-optic phase modulation, which involves altering the instantaneous phase of continuous wave (CW) optical signal in proportion to the applied electric field, is a crucial operation in optical and microwave signal processing and communication systems [1], [2]. The instantaneous phase of the optical signal can be modulated by altering the refractive index of the material guiding the optical signal, which generally uses the Pockels electro-optic effect [3]. The Pockels effect based phase modulation, which inherently has a direct relation between the induced phase shift and the applied electric field is given by , where , , , , , and denote phase shift, refractive index, electro-optic Pockels coefficient, applied electric field, interaction length, and wavelength, respectively [4]. From the aforementioned Pockels effect relation, it is evident that the maximum phase shift that can be attained using a Pockels cell is constrained by the limitation on the maximum electric field that can be applied without resulting in breakdown, heating, and reliability issues of the material. Similarly, in tunable phase modulators in photonic integrated circuits rely on the electro-optic or thermo-optic effects, and can achieve only a limited amount of phase shift tunability [5], [6]. In addition, thermo-optic phase shifters are slow and electro-optic phase shifters are highly lossy.