Polarization-Controlled Cavity Input-Output Relations

Cavity input-output relations (CIORs) describe a universal formalism relating each of the far-field amplitudes outside the cavity to the internal cavity fields. Conventionally, they are derived based on a weak-scattering approximation. In this context, the amplitude of the off-resonant field remains nearly unaffected by the cavity, with the high coupling efficiency into cavity modes being attributed to destructive interference between the transmitted (or reflected) field and the output field from the cavity. In this Letter, we show that, in a whispering gallery resonator-waveguide coupled system, in the strong-scattering regime, the off-resonant field approaches to zero, but more than 90% coupling efficiency can still be achieved due to the Purcell-enhanced channeling. As a result, the CIORs turn out to be essentially different than in the weak-scattering regime. With this fact, we propose that the CIOR can be tailored by controlling the scattering strength. This is experimentally demonstrated by the transmission spectra exhibiting either bandstop or bandpass-type behavior according to the polarization of the input light field.

Figure 1

Schematic diagram of a single-mode fiber coupled to a whispering gallery resonator. HWP: half wave plate.

Figure 2

Study of the fiber-microsphere resonator system. The microsphere diameter is $130\mu \mathrm{m}$. The fiber diameters are (a) $d=0.9\mu \mathrm{m}$ and (b) $d=0.4\mu \mathrm{m}$. The laser wavelength in this work is around 980 nm. Right-hand side: measured transmission of the fiber-microsphere resonator system before (solid) and after coating UV adhesive (dashed) on the microsphere. The solid red and green lines correspond to an input field with horizontal ($\mathbf{H}$) and vertical ($\mathbf{V}$) polarization, respectively.

Figure 3

Study of the fiber-microbubble resonator system. (a) A silica microbubble resonator with UV adhesive on one side. (b) Scanning electron microscope (SEM) image of the cross section of the microbubble. (c) Finite element method (FEM) calculation of the fiber transmission with $\mathbf{H}$ and $\mathbf{V}$ polarizations through the coupling region (the blue dashed box in Fig. 1). We used a microbubble diameter of $120\mu \mathrm{m}$ and a wall thickness of $w=0.9\mu \mathrm{m}$. (d) Measured transmission through a tapered fiber of different diameters coupled to a microbubble with UV adhesive present. The small fluctuations could be caused by a change to the coupling position when translating the tapered fiber. (e) Same as (c) except for different wall thicknesses and a fiber diameter of $d=0.5\mu \mathrm{m}$. (f) Measured transmission of two fiber-microbubble (coated with UV adhesive) coupling systems (samples $A$ and $B$) for different input polarizations. The HWP angle 0° (45°) corresponds to $\mathbf{H}$ ($\mathbf{V}$). Here, the fiber diameter $d=0.5\mu \mathrm{m}$ and $w=0.9\pm 0.05\mu \mathrm{m}$ for sample $A$ (blue), $w=1.3\pm 0.05\mu \mathrm{m}$ for sample $B$ (red).

Figure 4

Experimental demonstration of polarization-controlled CIOR with two microbubble resonators, samples $A$ (blue) and $B$ (red), corresponding to Fig. 3. The transmittance is normalized to the transmission of the bare fiber. From top to bottom the input polarization changes from $\mathbf{H}$ to $\mathbf{V}$.