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Laser Resonators, Microresonators, and Beam Control

Correlated combs to perform measurements at the attometer scale

Jean-Claude M. Diels, Xiaobing Zhu, Elaheh Zamani, M. Lenzner, Stephen S. Eikenberry, Eric Van Stryland

Published Mar 16, 2026• 1 citation
Publisher

Abstract

When a linear Optical Parametric Oscillator (OPO) is pumped at twice the round-trip rate of its cavity, it generates an optical comb. This comb is degenerate, made by two intertwined undistinguishable pulse trains at half the repletion rate of the pump. If one pulse experiences a phase shift at each round-trip, the degeneracy is lifted, and each tooth of the comb splits in two. Even though each comb of this unstabilized source has a bandwidth of tens of MHz, interfering them on a detector leads to a beat note with a bandwidth vanishing the closer to degeneracy. At 3 Hz beat note, we measure a bandwidth of 0.003 Hz (FWHM of the beat note spectrum), corresponding to a phase resolution of 50 picoradian, or an optical path difference of 10 attometer. Several applications will be discussed, ranging from inertial navigation to magnetometry to gravitational wave detection.

DOI
10.1117/12.3096594

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When a linear Optical Parametric Oscillator (OPO) is pumped at twice the round-trip rate of its cavity, it generates an optical comb. This comb is degenerate, made by two intertwined undistinguishable pulse trains at half the repletion rate of the pump. If one pulse experiences a phase shift at each round-trip, the degeneracy is lifted, and each tooth of the comb splits in two. Even though each comb of this unstabilized source has a bandwidth of tens of MHz, interfering them on a detector leads to a beat note with a bandwidth vanishing the closer to degeneracy. At 3 Hz beat note, we measure a bandwidth of 0.003 Hz (FWHM of the beat note spectrum), corresponding to a phase resolution of 50 picoradian, or an optical path difference of 10 attometer. Several applications will be discussed, ranging from inertial navigation to magnetometry to gravitational wave detection.
This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields… While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.
Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables [1]. They can be generated either by mixing different squeezed light sources using linear optical operations [2], or directly in a multimode optical device [3, 4]. Synchronously Pumped Optical Parametric Oscillators (SPOPO) — which correspond to an OPO pumped by a train of ultrashort pulses that are synchronized with the cavity round-trip time — have been theoretically shown to be promising devices for the generation of multimode nonclassical frequency combs, since a SPOPO is a sole optical cavity acting as an assembly of independent squeezers in a particular basis called the supermodes basis [5]. The supermodes are optical frequency combs with specific spectrum and phase profiles that are determined by the length of the intracavity nonlinear crystal and the pulse shape of the pump.
Frequency division in the optical regime is a desirable capability for precision measurement applications. We have recently demonstrated a new approach to tunable frequency division based on an optical parametric oscillator (OPO). By phase locking the signal–idler beat frequency to a microwave frequency source, an input pump frequency is halved. This beat frequency measurement precisely determines the signal and idler frequencies. The method is an efficient one-step process, and OPO dividers can be operated in series or in parallel to measure, compare, and synthesize frequencies from optical to microwave. Our initial results from a cw tunable KTP OPO divider indicate good frequency control and tuning capability, with a signal-idler beat-note linewidth at the hertz level. We will discuss the prospects for an OPO-based optical frequency counter that can accurately measure any optical frequency relative to a microwave frequency standard.
In this work, we report on experimental measuring of the coherence length of a single photon, which is generated via a degenerated optical parametric oscillator (OPO) operated far below threshold. Although the bandwidth of the OPO cavity is about 7.8 MHz, the measured coherence length of the single photon is only about 90 µm via a Michelson interferometer, due to the multimode property of the photon generated in the experiment. Therefore, further reducing the bandwidth of the photon is necessary for its application in some fields, such as transferring the information between the photon and an atomic system.