The evanescent coupling of a 1.5 µm radius silicon microdisk with one or two Silicon-On-Insulator waveguides is studied. Thanks to the high refractive index contrast between Silica and Silicon materials, this very-small-diameter microdisk exhibits the highest quality factor measured in wavelength range from 1500 nm to 1600 nm. Coupled to a single monomode waveguide, the optical resonator behaves as a stop-band filter. Even if the microdisk is a largely multimode resonator, only its fundamental modes are efficiently excited. The filter’s transmission is measured for different gap between the waveguide and the resonator. The critical coupling is clearly observed and gives access to 1.63 nm linewidth. A 20 dB decrease of the transmission signal is also observed. Coupled to two waveguides, the resonator becomes a compact symmetric wavelength-demultiplexer. In this case, the optimal response comes from a compromise between the gap and the desired linewidth dropped in the second waveguide. Finally, our measurements are also compared to analytic models showing a good agreement especially for the critical gap prediction.
©2006 Optical Society of America
The increase density of metallic-interconnects becomes a real barrier for future generation of Very-Large-Scale-Integrated circuits. Optical interconnects using Silicon-On-Insulator (SOI) technology decrease the propagation delays and give access to higher bandwidth [1, 2]. In order to perform the on-chip information routing, wavelength resonator filter based on cylindrical geometries are investigated for add and drop [3, 4] or stop band filter  applications. Thanks to high refractive-index contrast between silica and silicon materials, ultra-compact structures can be made without using peculiar mirrors. Recently, high-resonant microring cavities  have been achieved with diameters close to 20 µm. The quality factor obtained gives access to several applications on SOI substrate such as high-speed modulator  or compact Raman sources . Compared to other ultra-resonant cavities as microtorus  or microsphere , microring has the great advantage to be integrated on a substrate and to be easily associated to waveguide couplers. Nevertheless, the resonator size can be reduced using microdisk instead of microring . Indeed, the deep etch for designing the inner radius induces a displacement of the field to the external radius. By consequence, the field is less confined in the resonator. It is also more sensible to the roughness on each boundaries of the bend waveguide reducing the quality factor. In this paper, two basic optical-interconnects functions using microdisks are reported. The former is a stop-band filter obtained from a microdisk coupled to a single waveguide. The amplitude transmission of the waveguide is then described by the following relation 
where γ and γc are respectively due to the intrinsic losses of the resonator and the coupling with the waveguide; and ω0 is the resonance frequency of a Whispering-Gallery-Mode (WGM) of the resonator. The gap between the microdisk and the waveguide influences the transmission T, the total quality-factor of the resonator. Indeed, as the gap increases, the coupling losses coefficient γc decreases. On the other hand, the quality-factor increases until the asymptotic quality-factor of the uncoupled microdisk is reached. The condition γ=γc corresponds to the critical coupling of the resonator and it matches a peculiar value of the gap. In this case, a zero transmission is obtained and the structure behaves as a stop-band filter. A second function is obtained when two parallel waveguides are coupled with the microdisk. When the same gap is used for both waveguides as shown in Fig. 1(a), the amplitude transmission T (output 2) and the amplitude transmission R (output 1) are respectively
where γc≫γ for simplicity. In this case, as the gap decreases, the transmission T and the coupling linewidth coefficient γc increase whereas the quality-factor decreases. No critical point is reached with or without the previous approximation , so a compromise between the dropped-frequency band and the transmission T must be chosen. This structure is still a stop-band filter for the first waveguide but also a pass-band filter for the second waveguide. In the following section, the fabrication process and the set-up measurements are described. In section 3 and 4, the results for stop-band and add-and-drop filters are respectively presented. The gap influence is underlined and compared with results given by an analytical method.
2. Realization process and set up characterisation
A 193 nm deep UV lithography is used to reach small propagation losses and a gap close to one hundred nanometers. All the waveguiding structures are realized on a SiO2 layer of 1 µm thickness and are overlayed by a silica box of 1 µm thickness as shown in Fig. 1(a). The thickness of the Silicon structures is set to 300 nm. To obtain monomode waveguides along the wavelength range from 1.5 µm to 1.6 µm, a width of 300 nm was defined on the mask. The measurements are performed only for the transverse magnetic field. As a consequence, a polarization-maintaining fiber is used to inject the TM polarized light from a polarized laser source. To couple the light in and out of these small waveguides, horizontal tapers are put at the input and output of the waveguide. They enlarge the width of the waveguide from 0.3 µm to 2 µm. A SEM picture of the add-and-drop filter is shown in Fig. 1(b). Several small microdisks with diameter of 3 µm have been thus made. In order to characterize the different structures, two three-dimensional (3-D) translation positioners are used to set a polarization-maintaining tapered fiber and a standard tapered fiber at the input and output of the waveguides respectively. A tunable laser source is used to scan the wavelength range from 1.48 µm to 1.62 µm. The output fiber is connected to a photo-detector. The wavelength scan and the power acquisition are controlled by a soft process.
3. Stop band filter
The characterization of the stop-band filter is presented in this part. Examples of power transmission |T|2 are shown in the Fig. 2. To understand those spectra, we shall point out the fact that the microdisk is a multimode structure . A WGM is defined by an azimuthal order m (number of period of the field along the periphery of the microdisk) and a radial order l (number of period in the radial direction in the microdisk). In the transmission response, only two resonance peaks are observed in the chosen wavelength range. These two WGMs have the same radial order l=0 and two different azimuthal orders respectively m and m+1 and a free spectral range of 67.4 nm is measured. Although there is other resonant modes, only the most resonant modes (l=0) are excited  that can be correlated by smallest efficiency of their coupling linewidth. Higher radial-order modes are not efficiently excited since their overlap with the waveguide mode seems to be very poor. In the pass-band wavelength range, the level of the transmission is not constant. With a higher wavelength resolution (Δλ=1 pm), an oscillation is clearly observed. This oscillation comes from the Fabry-Perot resonance induced by Fresnel reflexions at the input and output interfaces of the waveguide.
To study the influence of the gap, the mask included gaps going from 150 nm to 310 nm for the same disk diameter. To obtain the value of the resonant wavelength, the quality-factor and the extinction ratio of the transmission, each amplitude transmission responses is fitted by a Lorentzian lineshape. The results are depicted in Fig. 3(a), Fig. 3(b), and Fig. 3(c).
It is observed in Fig. 3(a) that the resonant wavelength decreases with an increasing gap. The resonant wavelength seems to be directly linked to the confinement of the light in the microdisk. Indeed the waveguide influence changes the field’s map in the resonant structure inducing a resonant wavelength evolution. Theoretical study shows a similar evolution for also a microdisk coupled to a dielectric waveguide . The next evolutions are in good agreement with the description predicted in section 1. It is thus shown in Fig. 3(b) that the quality-factor increases with an increasing gap. In the Fig. 3(c), a maximum of the extinction ratio is observed which allow us to set the critical gap around 230 nm. The quality factor Qc at this critical point gives access to the quality-factor Q0 of the uncoupled microdisk thanks to the following relation Qc=Q0/2 . In order to precisely analyze the spectral distribution of the observed WGM, an analytic calculation method was developed to compute the modes for a given microdisk. Since the Maxwell equations can not be solved exactly for a structure like the microdisk, the problem is splitted in two parts, using the effective index approximation. First, for a given wavelength range, the effective indices neff(λ) of a slab waveguide with the disk thickness and refractive index is computed. Then, the Maxwell equations are solved in an infinite cylinder of the disk diameter replacing the refractive index by the effective one neff(λ). The field’s solutions are Bessel’s functions inside the disk and Hankel’s functions of the second kind outside. The system of two equations coming from the boundary conditions has non zero solutions if the determinant of this system is zero. It occurs for the resonant wavelength λres(neff) of each WGM. Taking into account these two evolutions (neff(λ) and λres(neff)), the resonant wavelength of the 3-D structure can be obtained λres . Applying the coupled-mode-theory with a first-order approximation, the effect of the waveguide on the quality-factor of the structure can be computed. The critical gap can then be reached . The results obtained are sum up in the next table.
Calculated and measured resonant wavelengths are very close. Note that the stronger mismatch for the quality-factor can be explained by the small number of gaps used in the measurements and the rapid variation of the quality-factor around the critical point. A weak roughness of the microdisk sidewalls explains the good quality-factors measured with this small cavity.
4. Symmetric wavelength demultiplexer
In this paragraph, the characterization of the symmetric add-and-drop is finally presented. For a gap equal to 230 nm, two resonance peaks are obtained in our wavelength range shown in Fig. 4(a). On the T (transmission) response only two peaks are also observed which confirm the efficient coupling of only two resonances even if the microdisk is a largely multimode resonator. Similarly to section 1, the resonant peaks are fitted by a Lorentzian lineshape to reach the different optical parameters as shown in the Fig. 4(b). The obtained resonant wavelength and the quality-factor are depicted in Fig. 5(a) and Fig. 5(b) showing similar behaviour to the stop-band filter of section 3.
As expected, no critical point is reached. The maximum value is obtained for a small gap but in this case the quality-factor is very low and induces a large pass bandwith as shown in Fig. 5(b). If a quality factor of 1000 is necessary, the extinction ratio will be slightly 8 dB for a gap around 270 nm. In comparison with the stop band filter results, one may see that the second waveguide decreases the quality-factor for small gaps. Indeed the second coupling waveguide increases the optical light extracted from the microdisk. To obtain a better extinction ratio the gaps of the two waveguides must be different. In this case, due to the intrinsic losses of the single microdisk, the efficiency of the structure is optimized only in one way (demultiplexer or multiplexer functions) . We also measured other add-and-drop with a larger diameter. And for a 3.2 µm diameter instead of 3 µm, extinction ratio of 22 dB with a quality factor of 918 has been measured for a gap of 220 nm. A weak increase of the diameter allows us to reach higher quality factor with the same efficiency for the minimum of transmission in the input waveguide .
In this paper, ultra-compact resonant SOI structures based on 3 µm diameter microdisk coupled to one or two waveguides have been presented. The gap between the microdisk of the waveguides has been especially studied. For the stop-band filter, the critical point has been demonstrated and an extinction ratio of 20 dB is obtained with a quality factor around 1000. The comparison with an analytical method based on the effective index method and the coupled-mode-theory shows a remarkable fit. For the symmetric add-and-drop structure, the exctinction ratio is around 8 dB if the quality factor is at the same order as previously. Finally, it is clearly confirmed that even if the microdisk is a multimode structure only the desired mode are only excited thanks to the poor overlap with the higher radial-order modes.
This work was partially supported by the ACI Program from the French ministry of research and education.
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