Polarization-Dependent Forces and Torques at Resonance in a Microfiber-Microcavity System

Spin-orbit interactions in evanescent fields have recently attracted significant interest. In particular, the transfer of the Belinfante spin momentum perpendicular to the propagation direction generates polarization-dependent lateral forces on particles. However, it is still elusive as to how the polarization-dependent resonances of large particles synergize with the incident light’s helicity and resultant lateral forces. Here, we investigate these polarization-dependent phenomena in a microfiber-microcavity system where whispering-gallery-mode resonances exist. This system allows for an intuitive understanding and unification of the polarization-dependent forces. Contrary to previous studies, the induced lateral forces at resonance are not proportional to the helicity of incident light. Instead, polarization-dependent coupling phases and resonance phases generate extra helicity contributions. We propose a generalized law for optical lateral forces and find the existence of optical lateral forces even when the helicity of incident light is zero. Our work provides new insights into these polarization-dependent phenomena and an opportunity to engineer polarization-controlled resonant optomechanical systems.

Figure 1

A generalized law for polarization-dependent optical lateral forces at resonances. (a) Schematic of a microfiber-microcavity system. Two counterpropagating modes with the opposite helicity (forward, $\sigma =+\sin \varphi$; backward, $\sigma =-\sin \varphi$) are input. The radius of the microfiber $r_f$ and the microcavity $r_s$ is 1.33 and $5.32\mathrm{\mu }\mathrm{m}$, respectively. The refractive index of the microfiber $n_{\mathrm{core}}$, the microcavity $n_s$, and the environment (water) $n_{\mathrm{clad}}$ is 1.45, 1.68, and 1.33, respectively. The gap between the fiber and the microcavity is 133 nm. (b) Electric field amplitude spectra inside the microcavity for the ${\mathrm{HE}}_{11}^y$ and ${\mathrm{HE}}_{11}^z$ modes. ${\lambda }_1$ (1048.6 nm) and ${\lambda }_2$ (1057.7 nm) are the resonance wavelength of the ${\mathrm{HE}}_{11}^y$ and ${\mathrm{HE}}_{11}^z$ modes, respectively. (c) Calculated optical lateral force $F_t$, gradient force $F_g$, and scattering force $F_s$ on the microcavity when $\varphi =\pi /2$. (d) Schematic shows two polarization-dependent phase shifts. $\mathrm{\Delta }{\varphi }_c$, the coupling phase shift when light couples from the fiber to the microcavity; $\mathrm{\Delta }{\varphi }_{\mathrm{WGM}}$, the WGM resonance phase shift. For simplicity, light incidents from the right-hand side (the principle keeps the same when light incidents from the left-hand side). (e) Calculated optical lateral force on the microcavity. (f) Calculated optical lateral force for a nanoparticle with $r_s=250\mathrm{nm}$. The black dashed lines in (e) and (f) are the contour lines for $F_t=0$ because the helicity of incident light (f) or the effective helicity after considering the phase shift effect (e) is zero on these lines. (g) Calculated gradient force on the microcavity.

Figure 2

Optical spin torques of the microcavity when varying the helicities of the two counterpropagating modes. (a) Schematic of the microfiber-microcavity system and the microcavity experienced optical spin torques when the two counterpropagating modes have different helicities. (b)–(g) Simulated longitudinal $T_x^S$ (b),(e), transverse $T_y^S$ (c),(f), and vertical $T_z^S$ (d),(g) optical spin torques at the resonance wavelengths of ${\lambda }_1=1048.6\mathrm{nm}$ (b)–(d) and ${\lambda }_2=1057.7\mathrm{nm}$ (e)–(g) when varying ${\varphi }_1$ and ${\varphi }_2$. The black dashed lines forming diamond shapes in (b),(e) and (d),(g) are contour lines for $F_t=0$, which can be predicted by Eqs. (3) and (4), respectively. The unit in (b)–(g) is $\mathrm{pN}\mathrm{\mu }\mathrm{m}/\mathrm{W}$.

Figure 3

Arbitrary control of optical spin torque and orbit torque in the microfiber-microcavity system. (a) Schematic of the microcavity and the longitudinal optical orbit torque and spin torque when the two counterpropagating modes have opposite helicity $\sigma$ and opposite degree of diagonal polarization $\chi$. The optical spin torques $T_y^S$ and $T_z^S$ are canceled out in this case. (b) Calculated optical spin torques $T_{x,y,z}^S$ of the microcavity when $\varphi =\pi /2$. (c),(d) Calculated optical orbit torque $T_x^O$ (c) and optical spin torque $T_x^S$ (d) of the microcavity when varying $\varphi$. (e) Light-induced spinning and orbiting motions of the microcavity for the four selected polarizations and wavelengths (triangle, $\varphi =3\pi /2$ and $\lambda =1058\mathrm{nm}$; diamond, $\varphi =\pi /2$ and $\lambda =1058\mathrm{nm}$; star, $\varphi =\pi /2$ and $\lambda =1069\mathrm{nm}$; circle, $\varphi =3\pi /2$ and $\lambda =1069\mathrm{nm}$).