Brillouin Light Scattering by Magnetic Quasivortices in Cavity Optomagnonics

A ferromagnetic sphere can support optical vortices in the form of whispering gallery modes and magnetic quasivortices in the form of magnetostatic modes with nontrivial spin textures. These vortices can be characterized by their orbital angular momenta. We experimentally investigate Brillouin scattering of photons in the whispering gallery modes by magnons in the magnetostatic modes, zeroing in on the exchange of the orbital angular momenta between the optical vortices and magnetic quasivortices. We find that the conservation of the orbital angular momentum results in different nonreciprocal behavior in the Brillouin light scattering. New avenues for chiral optics and optospintronics can be opened up by taking the orbital angular momenta as a new degree of freedom for cavity optomagnonics.

Figure 1

(a) Transverse magnetization distributions of (1,1,0), $(3,\overline{1},1)$, (3,1,1), and (4,0,1) Walker modes in the equatorial plane. (b) Schematic representations of the heads of the electric fields of TE and TM WGMs on the equatorial plane. These illustrate the difference of OAM for the TE WGM, the inner component of TM WGM, and the outer component of the TM WGM for the case of $m=10$. The hollow circles locate points where the field vectors direct upward for the ease of counting the numbers of the phase rotations in Cartesian coordinates.

Figure 2

Experimental setup for observing the Brillouin scattering. External-cavity diode laser (ECDL) supplies the laser light of 1550-nm wavelength. Its polarization is defined by a PBS and a HWP to be coupled to a particular family of the YIG sphere WGM by the intercession of the silicon prism. Microwaves from a network analyzer excite magnons via a loop coil. Scattered and unscattered light interfere through a HWP and a PBS, and the beat signal is detected by a high-speed PD and analyzed by the network analyzer.

Figure 3

(a) Normalized microwave (MW) reflection spectrum with the mode indices assigned to the Walker modes of our interest. Along the horizontal axis, the relative frequency to the Kittel mode frequency ${\omega }_{\text{Kittel}}/2\pi$ is used. Note that the spectra below (green, left axis) and above (black, right axis) 100 MHz are separately scaled. (b) The signals of the Brillouin scattering of the CCW (red) and the CW (blue) WGMs by (i) (1,1,0), (ii) $(3,\overline{1},1)$, (iii) (3,1,1), and (iv) (4,0,1) Walker modes. Solid lines are Lorentzian fittings to the data as a guide to the eye.

Figure 4

(a)–(c) Densities of states of the relevant WGMs (highlighted, otherwise dotted) for the magnon-induced Brillouin light scattering. Here we assume that the input mode is TM with an azimuthal index of $m_{\mathrm{TM}}$ at a frequency of ${\omega }_{\mathrm{TM}}/2\pi$. The TM modes are split into inner (pink) and outer (purple) components, with the OAM of $m_{\mathrm{TM}}-1$ and $m_{\mathrm{TM}}+1$, respectively. Because of the GB, in our experiment, the TE modes (green) are shifted by $\sim -32\mathrm{GHz}$ in comparison to the TM modes. Two adjacent modes of the same polarization are separated by the $\mathrm{FSR}\sim 40\mathrm{GHz}$. (a)–(c) Situations for the considered Walker mode OAM of ${\mathcal{L}}_z^{(1)}=0$, ${\mathcal{L}}_z^{(0)}=1$, and ${\mathcal{L}}_z^{(-1)}=2$, respectively. The scattered photons are depicted by blue and red arrows, representing, respectively, clockwise and counterclockwise input orbits. (d)–(f) Theoretically predicted nonreciprocal or reciprocal behavior of the Brillouin light scattering (BLS) for the CCW (red) and the CW orbit (blue) inputs, respectively, for cases (a)–(c). The symbol ${\omega }_m^{(i)}$ represents the Walker mode frequency where $i$ designates the OAM.