Nonreciprocal Dissipation Engineering via Strong Coupling with a Continuum of Modes

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Nonreciprocal Dissipation Engineering via Strong Coupling with a Continuum of Modes

Yishu Zhou, Freek Ruesink, Shai Gertler, Haotian Cheng, Margaret Pavlovich, Eric Kittlaus, Andrew L. Starbuck, Andrew J. Leenheer, Andrew T. Pomerene, Douglas C. Trotter, Christina Dallo, Katherine M. Musick, Eduardo Garcia, Robert Reyna, Andrew L. Holterhoff, Michael Gehl, Ashok Kodigala, John Bowers, Matt Eichenfield, Nils T. Otterstrom, Anthony L. Lentine, and Peter Rakich

Phys. Rev. X 14, 021002 – Published 2 April 2024

Abstract

Optical nonreciprocity plays a key role in almost every optical system, directing light flow and protecting optical components from backscattered light. Controllable forms of on-chip nonreciprocity are needed for the robust operation of increasingly sophisticated photonic integrated circuits (PICs) in the context of classical and quantum computation, networking, communications, and sensing. However, it has been challenging to achieve wideband, low-loss optical nonreciprocity on-chip. In this paper, we demonstrate strong coupling and Rabi-like energy exchange between photonic bands, possessing a continuum of modes, to unlock nonreciprocity and frequency translation over wide optical bandwidths in silicon. Using a traveling-wave phonon field to drive indirect interband photonic transitions, we demonstrate band hybridization that enables an intriguing form of nonreciprocal dissipation engineering. Using the converted mode to create a nonreciprocal dissipation channel, we demonstrate a frequency-neutral, low-loss (less than 1 dB) isolator with high nonreciprocal contrast (more than 14 dB) and broad operating bandwidth (more than 59 GHz). Additionally, through the implementation of complete interband conversion, we demonstrate a high extinction (more than 55 dB) optical frequency translation operation with near-unity efficiency.

Received 9 March 2023
Accepted 22 February 2024

DOI:https://doi.org/10.1103/PhysRevX.14.021002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Integrated optics Optomechanics Phonons

Optical isolators

Rabi model

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yishu Zhou ^1,*, Freek Ruesink¹, Shai Gertler ¹, Haotian Cheng¹, Margaret Pavlovich ¹, Eric Kittlaus², Andrew L. Starbuck³, Andrew J. Leenheer³, Andrew T. Pomerene³, Douglas C. Trotter³, Christina Dallo³, Katherine M. Musick³, Eduardo Garcia³, Robert Reyna³, Andrew L. Holterhoff³, Michael Gehl³, Ashok Kodigala³, John Bowers⁴, Matt Eichenfield^3,5, Nils T. Otterstrom³, Anthony L. Lentine³, and Peter Rakich ^1,†

¹Department of Applied Physics, Yale University, New Haven, Connecticut, USA
²Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA
³Microsystems Engineering, Science, and Applications, Sandia National Laboratories, Albuquerque, New Mexico, USA
⁴Department of Electrical and Computer Engineering, University of California, Santa Barbara, California, USA
⁵James C. Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona, USA

^*Corresponding author: yishu.zhou@yale.edu
^†Corresponding author: peter.rakich@yale.edu

Popular Summary

Optical nonreciprocity is a phenomenon in which an optical system allows light to travel in one direction while blocking it in the opposite direction. This is a crucial tool in almost every optical system, as it helps in protecting and stabilizing sensitive optical components from backscattering. Controllable forms of optical nonreciprocity are needed for the robust operation of photonic integrated circuits: Akin to electronic integrated circuits but for light, these circuits integrate multiple photonic functions on a single chip. This enables complex manipulation of optical signals, which is central to applications such as classical and quantum computation, sensing, imaging, and communication. In this Letter, we demonstrate a novel form of dissipation channels that can give high-performance nonreciprocity—suitable for integrated devices—specifically aiming for broad-spectrum coverage and minimal signal loss.

To achieve this, we introduce a nonreciprocal hybridization of two photonic bands through interactions between light and sound. When increasing the sound intensity, the energy can be fully transferred from one photonic band to the other and then converted back. When the light is fully converted, we use the converted light as the nonreciprocal dissipation channel, thereby achieving a low-loss optical isolator ( $< 1 dB$ ) with more than 10 dB of isolation over a 59-GHz range.

Our work marks a milestone in solving the long-standing challenge of building practical on-chip isolators. Moreover, the realization of strong coupling between two photonic bands pushes the photonics field in a new direction, moving the focus from discrete resonant modes to continuous bands. This transition holds the potential to lead to crucial advancements in wideband photonic functionalities.

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Vol. 14, Iss. 2 — April - June 2024

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Figure 1
Strong coupling between two traveling modes. (a) Indirect interband photonic transitions in a multimode, linear waveguide. Two mode multiplexers are fabricated at the ends of the waveguide to selectively couple in and out of each optical mode. A counterpropagating phonon mediates the symmetric (red) to antisymmetric (blue) mode scattering, resulting in a fast energy exchange between the optical modes in the spatial domain. (b),(c) Phase-matching diagram of optomechanical scattering in the static (b) and rotating (c) frames. (b) Phonon with frequency $Ω_{0}$ and wave vector $- q$ participating in the optical interband transition (from open to closed circle) when energy conservation $ω_{2} - ω_{1} = Ω_{0}$ and momentum conservation $k_{1} - k_{2} = q$ are satisfied. (c) Rotated optical bands intersecting at the phase-matching point and subsequently split into two new hybrid modes according to the anticrossing principle, which leads to the formation of synthetic band hybridization. As the system deviates from the phase-matching point, the new hybrid mode converges back into the original modes. The wave-vector splitting $β$ at the phase-matching point is determined by the coupling strength. (d),(e) Nonreciprocal photonic band hybridization in the static (d) and rotating (e) frames. In diagram (d), we show that, at $ω_{a}$ , the Stokes (anti-Stokes) scattering process is (is not) phase matched in the backward (forward) direction, while at frequency $ω_{b}$ , the phase-matching condition is reversed. In diagram (e), the photonic bands are hybridized at $ω_{b}$ ( $ω_{a}$ ) in the forward (backward) direction, resulting in complete mode conversion in the forward (backward) direction in diagram (f).
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Figure 2
Device characterization. (a) A 3D rendering of an active unit of the device. An electromechanical transducer launches acoustic waves towards a silicon optomechanical waveguide. The tri-ridge optomechanical waveguide confines an acoustic wave. Each ridge waveguide supports a symmetric and an antisymmetric optical mode. (b) Optical micrograph of the actual device. (c) Spiral-shaped multipass device that connects eight active units, resulting in 24 electro-optomechanical interaction segments ( $8 units \times 3 passes$ ). This result reduces the phonon energy threshold for strong coupling by a factor of $24^{2}$ . (d) rf power reflection ( $S_{11}$ , measured with a VNA) of a spiral-shaped multipass device (blue) and a single-pass reference device that contains only one IDT unit (black). (e) Optical conversion efficiency of the multipass and single-pass devices, measured using a heterodyne setup. (d),(e) Multipass device featuring more efficient transduction in panel (d) and a 20.9-dB conversion efficiency improvement in panel (e). (f),(g) Rabi-like energy exchanges between the symmetric mode (red) and the antisymmetric mode (blue) for symmetric (antisymmetric) input in panel (f) [(g)]. As $P_{rf}$ increases, the optical power is converted from one mode into the other mode (dashed line) and converted back (point C). The different peak amplitudes at points A, B, and C are determined by the spatial decay rates of the optical modes. From the data at $\sqrt{P_{rf}} = 0$ , we retrieve the linear propagation loss for the symmetric (f) and antisymmetric (g) modes.
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Figure 3
Optical frequency translation with high efficiency and high extinction. (a) Measuring the output of the symmetric mode of the frequency shifter as a function of optical wavelength and for fixed rf drive frequency $Ω_{0} / (2 π) = 3.13 GHz$ . Incident light in the antisymmetric mode at frequency $ω_{p}$ is converted into the symmetric mode with Stokes frequency $ω_{s} = ω_{p} - Ω_{0}$ (red) and anti-Stokes frequency $ω_{as} = ω_{p} + Ω_{0}$ (purple). The symmetric mode also contains a residue at the carrier frequency (blue). Inset: overview of the dominant frequency tones and modes in this experiment. (b) The rf sweep at fixed input wavelength ( $λ_{p} = 1539.2 nm$ ). Colors are similar to panel (a). We achieve an insertion loss of 2 dB, a carrier-suppression ratio of 55.3 dB, and a single-sideband selectivity of 32.1 dB.
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Figure 4
Wideband, low-loss nonreciprocity. (a) Optomechanical scattering process, which is not phase matched in the forward direction, such that the pump light in the symmetric mode (blue) travels through the device unaltered. The optomechanical scattering is phase matched in the backward direction, such that the pump light is fully converted into the antisymmetric mode (red) and is filtered out by the mode multiplexers. (b) Optical transmission measurement using an optical power meter, showing isolation with 0.7-dB insertion loss and 59-GHz 10-dB isolation bandwidth. The blue (gray) window corresponds to the 10-dB isolation window at $ω_{a}$ ( $ω_{b}$ ). The practical optical power isolation is measured to be 14.4 dB while the frequency-resolved isolation is more than 40 dB according to the heterodyne detection in Sec. 2 of Supplemental Material [32].
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Figure 5
Further experimental details. (a) Optical micrographs of the fabricated device. (b) Experimental setup to study the optical mode conversion. A rf signal drives two ( $50 / 50$ ) IDT channels, where an external phase shifter is used for phase control. Light is injected into the symmetric (antisymmetric) mode to characterize optical mode conversion. An optical $2 \times 2$ switch is used to perform either an optical power measurement or a frequency-resolved measurement using heterodyne detection. SG, signal generator; Amp, rf amplifier; Splitter, $50 / 50$ power splitter; PS, rf phase shifter; AOM, acousto-optic modulator; PD, photodiode; and RFSA, rf spectral analyzer. (c) Experimental setup to characterize the isolator. A $2 \times 2$ switch allows rapid measurements of the device in forward or backward operation; using a directional coupler, we perform a frequency-resolved measurement (heterodyne detection) and optical power measurement (optical power meter). (d) Device robustness to optical power. When increasing the on-chip optical power to 100 mW, our device only features about 2-dB conversion efficiency deterioration, which we attribute to nonlinear loss mechanisms in silicon. (e) Raw (i) and processed (ii) data of Rabi-like energy exchange measurement. Here, we measure the symmetric-to-symmetric mode conversion efficiency as a function of optical wavelength and rf drive power. We expect a periodic modulation of the conversion efficiency when sweeping the wavelength, given the presence of evanescent coupling between adjacent waveguides. Thus, the skewed modulation in (i) is used to track and correct thermal drift at high rf power. A line cut at $Δ λ = 0$ in (ii) corresponds to the red data points in Fig. 2. Panel (fi) displays the line cut of the raw data, as indicated by the black dashed line in (ei), taken at 1538.8 nm, which corresponds to the phase-matched wavelength at low microwave input. Panel (fii) presents the processed line cut of the Rabi oscillations, as denoted by the white dashed line in (ei) or the white solid line in (eii).
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