Inverse Faraday Effect in an Optomagnonic Waveguide

Na Zhu, Xufeng Zhang, Xu Han, Chang-Ling Zou, and Hong X. Tang

Phys. Rev. Applied 18, 024046 – Published 17 August 2022

Abstract

Single-mode high-index-contrast waveguides have been ubiquitously exploited in optical, microwave, and phononic structures for achieving enhanced wave-matter interactions. Although microscale optomechanical and electro-optical devices have been widely studied, optomagnonic devices remain a grand challenge at the microscale. Here, we introduce a planar optomagnonic waveguide platform based on a ferrimagnetic insulator that simultaneously supports single transverse mode of spin waves (magnons) and highly confined optical modes. The colocalization of spin and light waves gives rise to an enhanced inverse Faraday effect, and as a result, magnons are excited by an effective magnetic field generated by interacting optical photons. Moreover, the strongly enhanced optomagnonic interaction allows us to observe such an effect using low-power (milliwatt level) light signals in the continuous-wave form, as opposed to high-intensity (megawatt peak power) light pulses that are typically required in magnetic bulk materials or thin films. The optically driven magnons are detected electrically with preserved phase coherence, showing the feasibility for launching spin waves with low-power continuous optical fields.

Received 12 March 2022
Accepted 28 June 2022

DOI:https://doi.org/10.1103/PhysRevApplied.18.024046

Physics Subject Headings (PhySH)

Faraday effect Light-matter interaction Photonics Spin optoelectronics Spin waves

Magnetic insulators Magnonic crystals Waveguides

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Na Zhu , Xufeng Zhang, Xu Han, Chang-Ling Zou , and Hong X. Tang^*

Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA

^*hong.tang@yale.edu

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Vol. 18, Iss. 2 — August 2022

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Figure 1
Integrated optomagnonic waveguide. (a) Schematic of the integrated optomagnonic waveguide. The single crystalline YIG ridge waveguides are patterned on the GGG substrate, which simultaneously confine optical photons and magnons. (b) Schematic cross section of YIG-on-GGG ridge waveguide. (c) The simulated normalized electric field distribution of the optical mode. (d) The simulated normalized magnetic field distribution of the magnon mode at the cross-section view, indicating the confinement of magnons in the YIG-on-GGG ridge waveguide.
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Figure 2
Light-magnon interaction in a planar waveguide. (a). Inverse Faraday effect in a bulk magnetic material: a circularly polarized light pulse causes the magnetization to process at a tilt angle. (b). Interacting light and spin waves in an optomagnonic ridge waveguide. Two coherent linearly polarized cw lights (TE and TM) are sent to the device via the cleaved optical fibers, forming the effective circularly polarized light when propagating along the waveguide as a result of the polarization beating, which creates an oscillating fictitious magnetic field along the $z$ axis and excites magnons. The magnon signals are read out electrically by coupling to a rf cavity antenna. (c). Illustration of the spatial distribution of the beat note between two coherent and orthogonally polarized cw lights. Both TE and TM are standing wave modes formed due to the reflection at two waveguide facets (fabricated Fabry-Perot cavity). The top panel represents the electric field distribution along with $z$ axis when TE and TM standing wave lights have the same intensity but slightly different effective refractive indices, and the bottom panel shows the total intensity change as a relation of the propagating length. It is worth noting that beating note is formed as a result of slightly different dispersion between TE and TM in this patterned waveguide, which is different from the conventional beating, which only accounts for the amplitude superposition of two optical modes of the same polarization.
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Figure 3
Characterization of the magnonic waveguide. (a) The cross-section view of the ridge waveguide. (b) The top-view SEM image of the magnonic waveguide (enlarged at the center of the ridge waveguide). (c) Schematic of the coplanar rf circuit for electrical excitation and readout of magnons. The yellow area is the copper layer, which also covers the backside of the circuit, with the rest of the white area being the high-dielectric constant substrate. The microstrip cavity (dashed box) supports a microwave half- $λ$ resonant mode, which can effectively couple with magnon modes. The bottom plot in the dashed box shows the magnetic field distribution of the rf cavity half- $λ$ microwave mode resonates at approximately $2 π \times 8.45$ GHz, showing the maximized rf magnetic field intensity at the center of the rf cavity, overlapping with the magnonic waveguide. (d) The simulated magnon modes spatial magnetization distribution, indicating the spin-wave modes formed along the waveguide length direction. (e) The microwave reflection spectrum when the waveguide is magnetized perpendicularly with approximately $4700$ -Oe static magnetic field. Only the modes with odd mode number are measured because of the effective nonzero coupling with the microwave rf cavity. (f) Dispersion relation of the spin wave in the YIG magnonic waveguide. Blue squares and purple triangles are the experimentally extracted dispersion and magnon linewidth. Solid line is calculated dispersion.
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Figure 4
Experimental characterization of the photonic waveguide. (a) The optical transmission spectra of the waveguide are experimentally measured when the polarization of the input cw lights is aligned at TE, (50% TE $+$ 50% TM), TM, respectively. (b) The simulated electrical field distributions of the TE- and TM-polarized fundamental modes, showing very similar mode profiles ( $n_{TE} = 2.1829$ , $n_{TM} = 2.1827$ , $l_{beat} = 7.6$ mm). (c) The calculated electric field vector of optical mode at the $x$ - $y$ plane when propagating along the waveguide longitudinal direction, showing the pattern of elliptically polarized light due to the polarization spatial beating between TE and TM light. Each plot considers 200- $μ m$ propagation distance.
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Figure 5
Readout of the inverse Faraday effect generated magnons. (a) The experimental setup. (FPC, fiber polarization controller; SSBM, single sideband modulator; WP, waveplate; DUT, device under test; VNA, vector network analyzer.) (b),(c) The magnitude and phase of the measured optically generated magnon signals. (Input local oscillator optical power, 5 mW; VNA output power, 1 mW.) Gray curves are the measurement results without $H$ field applied by removing the magnets under the waveguide device, where no magnon signals are generated. (d) The optical pump power dependence of the optically generated magnon measured via the rf cavity antenna (e). Linear optical power dependence, measured (scatter) and fitted (line).
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Figure 6
(a),(b) Plots of the field distributions for the optical TE and TM modes. (c) Mode profile of the magnon modes at the same cross-section view. (d) Spatial distribution of the magneto-optical coupling strength. $| G (r) |$ is calculated from Eq. (A8) then normalized.
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