Enhancement of microcavity lifetimes using highly dispersive materials

We show analytically and numerically that highly dispersive media can be used to drastically increase lifetimes of high-$Q$ microresonators. In such a resonator, lifetime is limited either by undesired coupling to radiation, or by intrinsic absorption of the constituent materials. The presence of dispersion weakens coupling to the undesired radiation modes and also effectively reduces the material absorption.

Figure 1

(Color) The photonic crystal microcavity system used in all our numerical experiments. The top panel is a sketch of the system (red denotes $n=3.464$, the rest is $n=1$). If we denote the thickness of the monorail with $a$, then the distance between successive holes is also $a$, except for the defect in the periodicity which presents the cavity, where the distance between the holes is increased to $1.4a$. The radius of each hole is $0.35a$. In various numerical simulations in this paper, we change only the properties of the “central,” shaded region of this structure; the thickness of this region is the same as the monorail, while its width is $0.6a$. The central panel shows the magnetic field of the confined mode, which is perpendicular to the plane everywhere, while the electric field lies in the plane. The bottom panel shows results of a transmission “measurement” through the system.

Figure 2

(Color) Transmission curves for all the microcavities (sketched in Fig. 1) that were simulated. Solid blue and red lines denote transmission through cavities made from nondispersive material: blue is for the case with three holes on each side of the cavity, while red is for the case of four holes on each side. Solid green and black curves denote transmission through cavities in which dispersive material was included in the shaded “central” region of Fig. 1; in each case, there were three holes on each side of the cavity. The green curve is for the cavity whose $n\left(\omega \right)$ is shown in Fig. 3; it has $v_G\left({\omega }_{\mathrm{res}}\right)∕c=0.0453$. The black curve is for the cavity that has $v_G\left({\omega }_{\mathrm{res}}\right)∕c=0.0150$. Dashed curves are for the cavities that are exactly the same as their corresponding-color solid curve counterparts, but now also including absorption: $\mathrm{lm}\left\{n\right\}=0.0077$.

Figure 3

Example of an $n\left(\omega \right)$ used in our simulations; both imaginary and real parts are shown. The column on the left shows $n\left(\omega \right)$ over a broad frequency range. The column on the right shows the same $n\left(\omega \right)$, but over the frequency regime relevant for the microcavities studied. In the case shown here, $v_G∕c\approx 0.0453$ in the region of interest.