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Journal of the Optical Society of America B

Effects of higher-order spatial modes on the squeezing level in optical parametric amplification with waveguides

Yuki Sano, Yoshitaka Taguchi, Kenichi Oguchi, Yasuyuki Ozeki

Published Nov 27, 2023• 3 citations
Publisher

Abstract

We investigate a limiting factor of waveguide optical parametric amplifiers used for generating broadband squeezed light. We found that spatially non-degenerate optical parametric amplification (OPA) between the fundamental modes and the higher-order modes generates noise, and that this effect can be avoided by detecting the squeezed light with the optimal spatial mode. The analysis is conducted assuming the waveguides with different dimensions, offering valuable insight into the waveguide design for squeezing.

DOI
10.1364/josab.502389

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We investigate a limiting factor of waveguide optical parametric amplifiers used for generating broadband squeezed light. We found that spatially non-degenerate optical parametric amplification (OPA) between the fundamental modes and the higher-order modes generates noise, and that this effect can be avoided by detecting the squeezed light with the optimal spatial mode. The analysis is conducted assuming the waveguides with different dimensions, offering valuable insight into the waveguide design for squeezing.
Waveguide-based optical parametric amplification (OPA) is advantageous in generating broadband or pulsed squeezed vacuum. To enhance the squeezing level, it is crucial to clarify its limiting factors. In this study, we develop a numerical method which allows us to derive the squeezing level in waveguide OPA. Based on the developed method, we investigate the effect of the higher-order mode of the pump light, which generates noise due to the OPA between the fundamental mode and the higher-order mode. We also investigate the effect of optical loss in the waveguide. Specifically, we formulated coupled equations that take into account the degenerate OPA between the pump and signal both in the fundamental mode, and the non-degenerate OPA between the pump in the higher-order mode, the signal in the fundamental mode, and the idler in the higher-order mode. By solving the coupled equations, we can express the quantum state as a linear combination of annihilation and creation operators, and the squeezing level can be derived from its coefficients. The analysis allowed us to quantify the effect of OPA on the fundamental and higher-order modes, and the requirement for mode matching of pump light with the fundamental mode. We also analyzed the effect of loss in the waveguide based on the same procedure. The results show the loss in the waveguide to have less effect than the same loss at the output of the waveguide. These results provide important design criteria of waveguide OPA for squeezing.
We demonstrate the generation of 12.1±0.212.1 \pm 0.212.1±0.2 dB squeezed light from a periodically poled lithium niobate (PPLN) waveguide optical parametric amplifier (OPA). While single-pass OPAs offer squeezed light with THz-order bandwidths, loss from spatial mode mismatch between the squeezed light and the local oscillator (LO) previously capped the squeezing level at $\sim$10 dB [K. Hirota et al., Opt. Express 34, 7958 (2026)]. In this work, we minimize this loss by introducing a machine-learning-optimized spatial light modulator (SLM) in the path of the LO. Specifically, we employed a double-reflection configuration to increase the spatial degrees of freedom, and directly used the measured squeezing level as the optimization's objective function.
We demonstrate broadband phase-sensitive amplification (PSA) measurement of squeezed light generated by a waveguide optical parametric amplifier (OPA) with external dispersion compensation. In broadband systems, group velocity dispersion (GVD) induces a frequency-dependent rotation of the squeezing axis, which limits the observable bandwidth in PSA measurements. To overcome this limitation, we introduce external dispersion compensation between two OPAs and suppress the quadrature rotation over a wide frequency range. As a result, we observe a maximum squeezing of 5.9 dB near the carrier frequency and more than 5 dB of squeezing up to a frequency offset of 4.5 THz from the carrier. Furthermore, squeezing below the shot-noise level is confirmed up to a frequency offset of 6 THz from the carrier, corresponding to the accessible phase-matching bandwidth of the waveguide OPA. Our results establish a practical method for broadband characterization of squeezed light and provide a key step toward ultrafast continuous-variable quantum information processing.
Optical parametric amplifiers (OPAs) configured as phase-sensitive amplifiers (PSAs) can be used for noiseless optical image amplification, generation of non-classical states of light, and, in particular, for multimode squeezed light generation. For all these applications and for effective use of the quantum properties of the multimode PSA, we need to know its independently squeezed (or amplified) eigenmodes. First we present the quantum theory of a spatially multimode traveling-wave PSA pumped by a high-power pump beam with arbitrary spatial profile. To quantitatively identify the Green's function of the PSA, we have developed a semi-analytical coupled-mode-theory of the PSA using 2D Hermite-Gaussian mode expansions of the signal- and pump-beam spatial distributions. By using Green's functions of the classical OPA, we calculate the normallyordered quadrature correlators at its output, which provide complete quantum description of the phase-sensitive OPA and enable determination of its independently squeezed eigenmodes. We find the number of the supported eigenmodes and their shapes for a spatially broadband frequency-degenerate optical parametric amplifier with elliptical Gaussian pump. We conclude by discussing our recent extensions of the coupled-mode-theory to study higher-order pump modes, compact representation of the PSA eigenmodes (especially convenient for experiments), and effect of non-zero phase mismatch on the PSA eigenmodes. We expect that the results from our model can be used for optimum mode matching in phase-sensitive image amplification and multimode squeezing generation.
We demonstrate the experimental detection of an optical squeezing covering several higher resonances of the optical parametric amplifier (OPA) by adopting a bichromatic local oscillator (BLO). The BLO is generated from a waveguide electro-optic phase modulator (WGM) and subsequent optical mode cleaner (OMC), without the need of additional power balance and phase control. The WGM is used for generating the frequency-shifted sideband beams with equal power and certain phase difference, and the OMC is used for filtering the unwanted optical modes. Among a measurement frequency range from 0 to 16.64 GHz, the maximum squeezing factors are superior to 10 dB below the shot noise limit for the first three discrete odd-order resonances of the OPA.
We report generation of 10.1\pm0.2-dB squeezed light from a broadband periodically poled lithium niobate (PPLN) waveguide optical parametric amplifier (OPA). Based on our previous report where a similar PPLN waveguide shows 8.3-dB squeezing [T. Kashiwazaki et al., Appl. Phys. Lett. 122, 234003 (2023)], we reduce phase fluctuations and overall optical losses in the measurement system. In particular, we introduce a novel phase detection technique that does not require tapping a part of the squeezed light to get a phase locking signal. We use a phase-detection OPA seeded by a tapped probe and pump light before a squeezer OPA. This configuration breaks the conventional trade-off between generating a phase-locking signal with high-signal-to-noise ratio and suppressing degradation of squeezing level caused by optical tapping. With all these improvements, the phase fluctuation angle is reduced from 14 mrad to 9 mrad, and the total optical loss from 12\% to 8\%. Achieving more than 10 dB of squeezing by the broadband waveguide OPA is a significant step towards realization of fault-tolerant ultra-fast universal optical quantum computation.