Overview

Recent studies of optical resonators in glass based microspheres, microrings, and microtoroids have highlighted the applications afforded by the extremely long photon lifetime of whispering-gallery-modes (WGMs) supported by these structures. Furthermore, recent work by Ilchenko et al. illustrated the advantages of creating WGMs in crystalline materials. Applications for such devices include quantum networking, low threshold non-linear optical sources, and compact micro-optical circuits. The ability to create similar high quality factor (Q) WGM resonators in III-V or silicon (Si) semiconductors has thus far been hampered by the large refractive index of most semiconductors and the resulting sensitivity to surface roughness. Here we describe measurements of micron-sized Si microdisk resonators supporting transverse-magnetic (TM) WGMs with significantly reduced sensitivity to disk-edge roughness. These modes have measured Q values as high as 5.2×10⁵ and effective modal volumes (V_eff) as small as 5.3 cubic wavelengths in the material. The largest Q/V_eff ratio is measured to be 8.8 × 10⁴, greater than the values measured in ultra-small volume photonic crystals and comparable to the values measured in ultra-high-Q microspheres and microtoroids.

Design and Fabrication

The silicon microdisks in this work are fabricated from a silicon-on-insulator (SOI) wafer consisting of a 344 nm thick p-doped Si layer of resistivity 1-3 Ohm-cm atop a two micron SiO₂ layer. Processing of the microdisks begins with the deposition of a 20 nm SiO₂ protective cap layer using plasma-enhanced chemical vapor-deposition. Electron beam lithography is used to create a polymer resist etch mask, and a lowbias voltage inductively-coupled-plasma reactive-ion-etch with SF₆:C₄F₈ gas chemistry then transfers the circular microdisk pattern into the top Si layer. After dryetching, the sample is immersed in buffered hydrofluoric acid to undercut the bottom SiO₂ cladding, as shown in Figure 1. The thin 20 nm SiO₂ top cap layer is also removed in this process, providing a clean, smooth top Si surface. A final rinse in deionized water is performed, followed by a high-purity nitrogen spray drying step.

Figure 1: SEM micrographs of a R = 2.5 µm Si microdisk: (a) side-view illustrating SiO2 undercut and remaining pedestal, (b) high contrast top-view of disk, and (c) zoomed-in view of top edge showing disk-edge roughness and extracted contour (solid white line). (d) Plot of extracted contour versus arclength. (e) Autocorrelation function of the microdisk contour and its Gaussian fit.

Results

In order to characterize the microdisk resonators, an evanescent fiber taper coupling technique is employed. In this process, an optical fiber is adiabatically drawn to a 1-2 µm diameter so that its evanescent field is made accessible to the environment. In this work, the fiber taper is positioned to the side of the microdisks, with a center height equal to that of the middle of the microdisk. Measurements of the taper transmission as a function of the lateral taper-microdisk gap (g) are then performed using a swept wavelength tunable laser source
(1509-1625 nm) with fine frequency resolution of 10 MHz. A set of paddle wheels are used to adjust the polarization state of the fiber taper mode in the microdisk coupling region, providing selective coupling to the TE-like (TM-like) WGMs with dominant electric field parallel (normal) to the plane of the microdisk. For the 344
nm Si layer thickness of the microdisks studied here, only the fundamental vertical slab mode for TE and TM polarization are strongly guided. As such, we only consider the fundamental vertical modes of the microdisks in what follows, labeling them simply by p_m,n, where p is either TE or TM, and m and n are the characteristic radial and azimuthal number, respectively. Microdisks of two different sizes, radius R = 2.5 and 4.5 µm, are fabricated and tested. A broad wavelength scan covering the 1509-1625 nm wavelength range is initially employed to map out the different microdisk modes. The adjustable polarization state in the taper along with the WGMs’ strength of coupling and linewidth is used to determine sets of modes with a common free spectral range. These measurements provided a reliable determination of radial mode number. An effective index two-dimensional model is then used to estimate the azimuthal number. Using this mode identification technique we found that the highest Q modes in both sizes of microdisks are consistently of TM polarization, and corresponded to the lowest radial number, n ~ 1.

Figure 2 : Fiber taper measurements of a TM44,1 WGM of a microdisk with R = 4.5 µm. (a) Lorentzian full-width halfmaximum (FWHM) linewidth versus taper-microdisk gap. (inset) Taper transmission showing high-Q doublet. (b) Resonant transmission depth versus taper-microdisk gap. (inset) loading versus taper-microdisk gap.

The inset of Fig. 2(a) shows the evanescent coupling to a TM_44,1 WGM of a R = 4.5 µm microdisk, with tapered fiber positioned 1.1 µm laterally from the disk edge. The observed double resonance dip (doublet) is a result of Rayleigh scattering from disk surface roughness as discussed below, which lifts the degeneracy of clockwise (cw) and counter-clockwise (ccw) propagating WGMs in the microdisk. Fitting the shorter wavelength mode of the doublet to a Lorentzian yields a loaded linewidth of 3.9 pm with a 5% coupling depth. These measurements are repeated for varying taper-microdisk gaps and are recorded in Figure 2(a,b). For g > 0.63 µm, the data follows a two-port coupled mode theory with simple exponential loading dependence on taper-microdisk gap. Fits based upon this model are shown as a solid line in each of the plots of Fig. 2. The fiber loading of the microdisk is characterized here by a dimensionless effective quality factor, Qfiber (inset to Fig. 2(b)). The asymptotic unloaded linewidth is found to be 3.0 pm for this WGM, corresponding to a bare-cavity Q of 5.2 × 10⁵. Similar measurements are performed for all n ~ 1 modes (of both polarizations) in each of the two different microdisk sizes, and a summary of the measured barecavity Q and doublet mode-splitting values are given in Table I.

Table I: Summary of theoretical and measured mode parameters for R = 2.5 and 4.5 µm Si microdisks. Theoretical
values are shown in parentheses.

[1] Borselli M, Srinivasan K, Barclay PE, and Painter O, "Rayleigh scattering, mode coupling, and optical loss in silicon microdisks," submitted June 2004, (http://arxiv.org/abs/physics/0406101) (pdf).

Questions?

Please contact Oskar Painter if there are any questions.