January 1, 2000 / Vol. 25, No. 1 / OPTICS LETTERS
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Pedestal antiresonant reflecting waveguides for robust coupling to microsphere resonators and for microphotonic circuits B. E. Little, J.-P. Laine, D. R. Lim, and H. A. Haus Research Laboratory of Electronics, Department of Electrical Engineering and Computer Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
L. C. Kimerling Department of Material Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
S. T. Chu National Institute of Standards and Technology, Gaithersburg, Maryland 20899 Received September 10, 1999 Strip-line pedestal antiresonant ref lecting waveguides are high-conf inement, silica integrated optical waveguides in which the optical modes are completely isolated from the substrate by thin high-index layers. These waveguides are particularly well suited for whispering-gallery mode excitation in high-Q microspheres. They can also be used in microphotonic circuits, such as for microring resonators. The theory and design of these structures are highlighted. Experiments that show high coupling eff iciency to microspheres are also demonstrated. 2000 Optical Society of America OCIS codes: 230.7370, 230.5750, 130.2790.
Silica-based microsphere resonators1 support whispering-gallery modes that exhibit Q values in excess of 1010 . Harnessing these huge Q values may enable microspheres to find potential for unprecedented performance in applications calling for ultranarrow linewidths, long energy decay times, large energy densities, or fine sensing of environmental changes. It is also of practical and commercial significance that these spheres are compact (they have submillimeter diameters), simple to fabricate, and inexpensive. Controlling the excitation and external Q’s of the whispering-gallery modes is vital to device performance. Although bulk1 and discrete2 – 5 optical components have been used to couple energy efficiently into microspheres, more widespread deployment of microspheres in practical devices will call for their integration with robust planar waveguide technology. Doing this represents an interesting challenge for conventional waveguides. That is, high-Q microspheres are composed of high-purity silica, a material whose low refractive-index value is commonly used for the cladding of planar waveguides. As a result, a silica sphere coupled to a conventional surface waveguide will lose most of its energy to substrate and cladding radiation. This loss may spoil the Q and reduce the device efficiency. Q spoiling could be alleviated if the waveguide cladding index were made signif icantly lower than that of silica. Unfortunately, such low-index materials are not readily available. In this Letter we demonstrate numerically and experimentally how simple silica-based strip-line pedestals, antiresonant ref lecting waveguides6, (ARROW’s), or SPARROW’s for short here, can be used as a robust and 0146-9592/00/010073-03$15.00/0
eff icient integrated-optics means to excite microsphere modes. We also show how these waveguides might find applicability in microphotonic circuits. Numerous methods have been developed for the excitation of whispering-gallery modes in microsphere resonators, as depicted in Fig. 1. The devices used include the prism coupler,1 the tapered fiber coupler,2,3 the polished half-block coupler,4 and, more recently, the hybrid fiber–prism coupler.5 The prism coupler is eff icient and tunable, but it uses bulk components and is therefore less desirable for applications that call for robustness. It also lacks guided-wave control. The tapered fiber coupler is eff icient and uses guided modes as the input –output waves, but it requires delicately drawn fibers less than 5 mm in diameter suspended in air. The polished half-block coupler offers a more robust coupling platform but yields low
Fig. 1. Methods for exciting whispering-gallery modes of high-Q microspheres. 2000 Optical Society of America
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OPTICS LETTERS / Vol. 25, No. 1 / January 1, 2000
eff iciencies because, as was mentioned above, energy in the sphere couples to the cladding radiation modes of the half-block. The hybrid fiber–prism makes use of the efficiency of the bulk prism, with the versatility of optical fibers. The SPARROW, depicted in Fig. 2, overcomes the limitations of the foregoing couplers by providing mode isolation from the substrate, guided mode control, and a robust integrated optics platform. A cross-sectional view of the SPARROW is shown schematically in Fig. 2(a). Lateral mode conf inement is achieved by deep etching; vertical confinement is accomplished by means of high ref lection. High ref lection is produced by an alternating series of highand low-index layers. In analogy with quarter-wave stacks, the thicknesses of the layers correspond to a quarter of the vertically directed guide wavelength (explained below). The optimum thickness of the SPARROW cladding layers (dL and dH ) for low-leakage loss can be calculated with good accuracy by a simple effective-index method and can be followed by numerical ref inement, if so desired. It is assumed that the high- and low-index values nL and nH , respectively, are given and that the waveguide core thicknesses W and d are selected to give a certain effective index. Only TE modes will be considered here, because TM ARROW modes are generally much lossier.6 The procedure to calculate dL and dH is as follows: First we compute the TM-polarized effective index of an air-clad slab waveguide of thickness W and core index nL . The effective index value so computed is labeled NL here. Next we choose a thickness d for the waveguide core layer. The optical field of a SPARROW goes to zero at some point in the first thin high-index layer, near the core–high-index layer boundary. The vertical cladding layers of the SPARROW can then be replaced by a mirror plane (in the ideal case). A conventional mode with this property is the second-order mode of a symmetric slab waveguide with thickness 2d. That is, the second-order mode has a null in the center of the waveguide, a distance d from the core –clad interface, similar to our SPARROW. Thus we compute the effective index for the TE-polarized second-order mode of an air –clad slab of thickness 2d and core index NL. This effective index, which we label here Neff , is the approximate real part of the exact SPARROW effective mode index. The optimum thicknesses of the low- and high-index cladding layer(s) are dL 苷
1 l0 , p 4 NL 2 2 Neff 2
dH 苷
index is substituted for Neff in Eqs. (1), and the ref inement process is repeated. For example, consider a SiO2 Si-based SPARROW with the geometry shown in Fig. 2(a) and with the parameters nL 苷 1.45, nH 苷 3.5, d 苷 2.0 mm, l0 苷 1.55 mm, and W 苷 6.0 mm. In the approximate method one obtains NL 苷 1.4446, Neff 苷 1.4026, and thus dL 苷 1.12 mm and dH 苷 120 nm, from Eqs. (1). An exact numerical solution to this structure yields an effective index of 1.4025 (in excellent agreement with the approximate method) and a leakage loss of less than 0.5 dB兾cm. Figure 2(b) shows the field prof ile of the SPARROW mode. Note that the optical field is almost entirely contained within the top core layer and is isolated from the substrate. A SiO2 Si-based SPARROW similar to that depicted in Fig. 2(a) was fabricated in the Microsystems Technology Laboratory at the Massachusetts Institute of Technology. In this device the substrate was silicon, and therefore there was only one high-index and one low-index cladding layer. The ARROW stack was fabricated upon 10.16-Vcm silicon wafers, with the initial step being a thermal oxidation process to grow 1.6-mm-thick silica. This oxidation was followed by the deposition of 120 nm of amorphous silicon by lowpressure chemical-vapor deposition, which was in turn followed by the deposition of 1.7 mm of low-temperature oxide by plasma-enhanced chemical-vapor deposition. The ARROW stack was then patterned, and the lowtemperature oxide was wet etched in a buffered oxide etcher. The remainder of the stack was then etched by reactive ion etching to form the SPARROW waveguides. The waveguide width was designed to be 8 mm, but as a result of the etching process the top core layer eroded to approximately 6 mm. The wafer was diced and the facets of the waveguide samples were polished before they were used to couple light into the microspheres. A silica microsphere 250 mm in diameter was fabricated and coupled to the SPARROW by direct contact. Figure 3 shows the transmission spectrum near a wavelength of 1.55 mm. Resonant dips are observed as the microsphere extracts power from the waveguide. These preliminary results show greater than 85% extraction eff iciency. The transmitted power levels in the absence of the sphere remain within approximately 5% of the peak values observed in Fig. 3. The calculated effective index of the fundamental whispering-gallery mode is approximately 1.43,8 whereas that of the SPARROW is 1.4025. We therefore
1 l0 , p 4 nH 2 2 Neff 2 (1)
respectively, which are a quarter of the vertically directed guide wavelength, and where l0 is the desired operating wavelength. Note that we use nH in the expression for dH , rather than some effective index NH in analogy with NL for dL , because nH and NH turn out to be almost identical. These starting values for dL and dH can be refined by use of a numerical mode solver,7 if so desired. In the refinement process the numerically computed value of the effective mode
Fig. 2. (a) Cross-sectional geometry of a SPARROW. Hatched regions, thin high-index layers. ( b) Numerically simulated fundamental mode field, showing complete isolation from the substrate.
January 1, 2000 / Vol. 25, No. 1 / OPTICS LETTERS
Fig. 3. Waveguide transmission response of a microsphere coupled to a SPARROW. The center wavelength is close to 1.55 mm.
Fig. 4. Calculated net loss (bending plus ARROW leakage) per round trip in a microring resonator SPARROW.
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calculated numerically for the SPARROW of Fig. 2(a) with parameters nL 苷 1.45, nH 苷 3.5, d 苷 2.5 um, l0 苷 1.55 mm, W 苷 3.0 mm, dL 苷 1.37 um, and dH 苷 120 nm. Figure 4 shows the bending-induced loss in decibels per resonator round trip. Note that bending loss exceeds ARROW leakage loss (dashed line) only when the radius becomes smaller than approximately 8 mm. In practice, because of the low leakage loss, SPARROW rings will be limited only by etch-induced surface roughness. In conclusion, strip-line pedestal antiresonant ref lecting waveguides are low-index, high-confinement waveguides that achieve vertical conf inement and substrate isolation by means of a few thin, high-index layers. They are ideally suited as robust couplers for microsphere whispering-gallery mode excitation and can phase match deep radial modes. SiO2 Si-based SPARROW’s were fabricated and showed whisperinggallery mode excitation of approximately 85%. (As this manuscript went to press, we observed Q values of the order of 108 and single-coupler efficiencies of approximately 98%.) High-confinement SPARROW’s can also be bent into microring resonators with negligible loss for radii as small as 10 mm. They might therefore serve in microphotonic circuits. This research was supported in part by a Charles Stark Draper Laboratories research grant. D. R. Lim was supported in part by HIDE U.S. Army Research Off ice grant DAAG55-97-1-0366. B. E. Little’s e-mail address is
[email protected]. References
believe that this SPARROW is exciting higher-order radial (or deeper) whispering-gallery modes. Different device dimensions and (or) different refractive-index values for the low-index core can be used to phase match most microsphere modes, including the fundamental. Because dust and moisture on the surface of the sphere are thought to be responsible for the degradation of the Q values over time, it may be beneficial to excite deeper radial whispering-gallery modes, which interact less with the sphere surface. In addition to serving as robust couplers for microsphere resonators, SPARROW’s might find application as a technology for microphotonic resonator circuits. For instance, because of the air cladding and substrate isolation, these high-confinement waveguides can be bent into low-loss microring resonators. Unlike the conventional high-index waveguides used for microrings,9 these devices make use of low-index silica, which may have better matching properties for optical fibers. Further, compared with compound-glass microrings,10 SPARROW’s use two more widely available materials and do not directly rely on core– substrate index contrast to achieve low bending loss. As an example, net loss as a function of ring radius was
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