Triple-Resonant Brillouin Light Scattering in Magneto-Optical Cavities

An enhancement in Brillouin light scattering of optical photons with magnons is demonstrated in magneto-optical whispering gallery mode resonators tuned to a triple-resonance point. This occurs when both the input and output optical modes are resonant with those of the whispering gallery resonator, with a separation given by the ferromagnetic resonance frequency. The identification and excitation of specific optical modes allows us to gain a clear understanding of the mode-matching conditions. A selection rule due to wave vector matching leads to an intrinsic single-sideband excitation. Strong suppression of one sideband is essential for one-to-one frequency mapping in coherent optical-to-microwave conversion.

Figure 1

(a) Top view of experimental setup. The scattered light, with polarization orthogonal to the input beam, emitted at a different angle due to the birefringence of the rutile coupling prism, is spectroscopically analyzed with a scanning Fabry-Pérot etalon. A dc magnetic field $H_{\mathrm{dc}}$ is applied along the $z$ axis. (b) Microwave antenna to drive ferromagnetic resonance in the YIG sphere (side view). The microwave drive is provided by a vector network analyzer (VNA). The FMR modes are identified by measuring the microwave reflection coefficient $|S_{11}|$ as a function of frequency, after which the VNA is configured in the continuous-wave mode to drive the resonance. (c) Coordinate systems used in the analysis.

Figure 2

Optical mode identification for an $r\approx 250\mu \mathrm{m}$ YIG sphere. (a) Schematic of mode families for radial indices $q=1$, 2, and for $h$ and $v$ polarization. The free spectral range ${\lambda }_{\mathrm{FSR}}$ is indicated by the black solid line. The $h\text{−}v$ splitting ${\lambda }_{h\text{−}v}$ is shown by the black dotted line, while the dashed line indicates the splitting between adjacent modes with $\mathrm{\Delta }q=1$. The azimuthal index $m$ determines the number of wavelengths around the circumference and radial index $q$ determines the number of radial nodes. (b) Representative plots of the real part of the electric field (i) in the WGM plane for $m=20$, $q=1$, and (ii) in cross section for $q=1$, 2. (c) Reflectance spectrum for $v$-polarized input. (d) The dispersion of the FSR ${\lambda }_{\mathrm{FSR}}$ is used to identify the strongest mode family as $q=1$. The splitting between the different modes ${\lambda }_{q,1\leftrightarrow 2}$ is used to identify the second as $q=2$. Solid and dashed lines show the calculated dispersions [24] fitted with small adjustments of the sphere radius.

Figure 3

(a) FMR of YIG sphere measured through microwave reflection coefficient $|S_{11}|$ of the antenna as a function of permanent magnet position. The blue dashed line shows the expected dependence of the uniform Kittel mode from the known dependence of the magnetic field on distance from a cuboid magnet [26] and the gyromagnetic ratio $\gamma =28\mathrm{GHz}{\mathrm{T}}^{-1}$. The magnetic field range is $H_{\mathrm{dc}}\approx 100–320\mathrm{mT}$. The $Q$ factor of the magnetic mode is $Q_{\mathrm{FMR}}\approx 400$ (as this is due to Gilbert damping, the rate ${\kappa }_{\mathrm{FMR}}\approx 10–20\mathrm{MHz}$ depends linearly on FMR frequency [27]). (b) Measured spectra of emitted signal (PD II) for $h$ (upper) an $v$ input polarization for ${\omega }_{\mathrm{FMR}}/2\pi \approx 7\mathrm{GHz}$. Orange and blue arrows label Stokes and anti-Stokes peaks, respectively. We can exclude the suppressed sideband down to the signal-to-noise ratio, maximum $\approx 20$ (slightly different for the two input polarizations due to different experimental conditions). (c),(d) Lower panels: maximum of BLS intensity as a function of input laser wavelength, for $h$ and $v$ input, respectively. Upper panels: Reflected optical intensity (PD I), shown for comparison. The $x$ axis is detuning from the resonant wavelength of the $h$ polarized mode. For $v$ input measurements, this is set by the measured $h\text{−}v$ splitting ${\lambda }_{h\text{−}v}^{\text{eff}}$. For the optical modes $Q_v\approx 2\times 10^5$ and $Q_h\approx 1\times 10^5$ (dissipation rates ${\kappa }_v\approx 1\text{GHz}$, ${\kappa }_h\approx 2\mathrm{GHz}$).

Figure 4

BLS scattering amplitudes for different input linear polarizations ($h$, pink, $v$, green). (a) Reflected intensity (PD I) for comparison. Azimuthal mode indices are labeled for clarity. The two curves are plotted on separate scales. (b) Color-plot of BLS intensity for $h$-input polarization as a function of input laser wavelength and FMR frequency. Each scan for fixed FMR frequency has been normalized to the peak amplitude for that scan. (c) As in (b), but for $v$-input polarization. Dashed lines in (b) and (c) indicate the resonant wavelengths for the two polarizations. The $x$ axis in all panels is in detuning from the resonant wavelength of the $h$ polarized mode. For $v$ input measurements, this is set by the measured $h\text{−}v$ splitting.

Figure 5

Comparison between (a) experiment and (b) theory of BLS intensity as a function of input wavelength detuning and FMR frequency for $h$ input polarization. The black lines are the wavelengths corresponding to ${\omega }_h$ and ${\omega }_v-{\omega }_{\mathrm{FMR}}$. Both the experimental data and model are normalized to the peak value at each FMR frequency to allow better comparison of the mode structure. (c) Peak BLS efficiency as a function of FMR frequency. The red line is the expected trend given by the maximum of Eq. (2) for fixed ${\omega }_{\mathrm{FMR}}$.