Optomechanical properties of a particle-waveguide system

The balances of the electromagnetic powers and momentum flows for the system of a dielectric particle and a dielectric slab waveguide are studied. The emphasis is made on the regime when whispering gallery resonances in the particle are excited. The excitation is achieved by a guided mode that has either transverse electric or magnetic polarization. The scattering problem is solved by using an analytical representation of the solution with subsequent numerical approach to find the scattered fields with high accuracy. It accounts rigorously for the interaction between the particle and the waveguide. It is found that the propelling force on the particle can be comparable to or even exceed the value of the momentum flow of the incident mode. This is related to a highly anisotropic angular distribution of the bulk radiation that can carry some noticeable momentum in the longitudinal direction. The bulk radiation carries also nonvanishing momentum in the transverse direction giving rise to a difference in the transverse forces experienced by the particle and by the waveguide. The strong coupling between the particle and the waveguide operating in the single-mode regime is shown to upshift slightly the resonant frequencies with decreasing gap between the particle and the waveguide.

Figure 1

Geometry of the problem: a particle scatters an incident guided mode supported by the slab.

Figure 2

(a) Scattering ${\sigma }_{\mathrm{sc}}/D$ and (b) radiation pressure ${\sigma }_{\mathrm{rp}}/D$ cross sections as functions of $kR$ for a plane wave with TE or TM polarizations incident on a scattering particle with $\sqrt{{\varepsilon }_s}=1.4$ in free space $\sqrt{{\varepsilon }_b}=1$.

Figure 3

Same as Fig. 2 but for larger $kR$.

Figure 4

(a) Phase index for WGMs with azimuthal numbers $15\le n\le 55$ for a particle with $\sqrt{{\varepsilon }_s}=1.4$. The dots show the calculated values for each mode and the line is a guide to the eyes. The larger dots show the modes with indices which are multiples of five. (b) $Q$ factors for the WGMs. The dots show the calculated values and the straight lines are linear fits that extrapolate $Q$ factors to the values of $kR$ outside of the fitted range.

Figure 5

Dispersion for a slab waveguide with $\sqrt{{\varepsilon }_g}=1.4$. The modes are labeled according to their polarization (TE, TM) and symmetry of the transverse component of the field (s: symmetric; a: antisymmetric). The black dots show the operating points used for Figs. 6 and 8.

Figure 6

(a) Transmitted and (b) reflected powers of the guided mode and scattered bulk radiation in (c) upper and (d) lower half-spaces as functions of $kR$ for $kd=1.5$ and $kL=3$.

Figure 7

Angular distribution of power in the far-field region for (a),(c) $kR=24.597$ and (b),(d) $kR=25.019$. The other parameters are the same as for Fig. 6.

Figure 8

(a) Transmitted power, (b) longitudinal, and (c) transverse forces for the same parameters as Fig. 6. The transmission spectrum is replotted from Fig. 6 for convenience.

Figure 9

Same as Fig. 8 but for $kL=2$.

Figure 10

Momentum flow along the $x$ direction of the scattered bulk radiation for the same parameters as Fig. 9.

Figure 11

Momentum flow of the scattered bulk radiation along the $y$ direction for the same parameters as Fig. 9. Frames (a) and (b) show the flows in the upper and lower half-space for each type of polarization. Frame (c) shows the total momentum flow.

Figure 12

(a) Transmitted power, (b) longitudinal force, and (c) transverse force as functions of wavelength at several values of gap $d$ (in $\mu \mathrm{m}$, labeled for each curve) for $R=5\mu \mathrm{m},L=0.6\mu \mathrm{m}$, and TE polarization.

Figure 13

Same as Fig. 12 but for TM polarization.