Ideality in a Fiber-Taper-Coupled Microresonator System for Application to Cavity Quantum Electrodynamics

The ability to achieve near lossless coupling between a waveguide and a resonator is fundamental to many quantum-optical studies as well as to practical applications of such structures. The nature of loss at the junction is described by a figure of merit called ideality. It is shown here that under appropriate conditions ideality in excess of $99.97\%$ is possible using fiber-taper coupling to high-$Q$ silica microspheres. To verify this level of coupling, a technique is introduced that can both measure ideality over a range of coupling strengths and provide a practical diagnostic of parasitic coupling within the fiber-taper-waveguide junction.

Figure 1

Coupling and loss parameters in a taper-microresonator system. The input field is a fundamental taper mode which couples into the resonator with amplitude ${\kappa }_0$ (transmission amplitude $t_0$). The output field couples into the fundamental taper mode and higher-order taper modes with coupling constants ${\kappa }_0$ and ${\kappa }_i$, respectively [16]. The presence of the waveguide can also result in a radiated field. The higher-order taper modes are radiated or coupled to cladding modes upon transition of the taper back to single-mode fiber. The round-trip resonator intrinsic power loss is given by ${\sigma }_0^2$.

Figure 2

$K$ vs position for various taper diameters for a $67\mathrm{\text{−}}\mu \mathrm{m}$-diameter microsphere. The data represent taper diameters of approximately $1.2\mu \mathrm{m}$ (circles), $1.35\mu \mathrm{m}$ (stars), and $1.65\mu \mathrm{m}$ (triangles). Solid curves are fits using Eq. (6). The ideality at contact in the data (extrapolating fits to zero gap) is $>99.98\%$, $99\%$, and $88\%$, respectively. Data show that for increased taper diameter higher-order-mode coupling causes a deviation from the ideal case (dashed line). The dash-dotted line represents $K_P$, which is related to ideality through Eq. (5). Dotted lines mark the critical coupling point.

Figure 3

Coupling parameter $K$ vs taper-sphere separation for a $65\mathrm{\text{−}}\mu \mathrm{m}$-diameter microsphere. The data show a linear relation between $\ln K$ and $x$, with a least squares fit (solid line). Ideality inferred at contact is greater than $99.99\%$. The dotted line marks the critical coupling point ($K=1$ at $x=0.91\mu \mathrm{m}$). The inset shows transmission vs position data.