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We present polarization-dependent optical transmission properties of a completely symmetric silicon-on-insulator (SOI) microphotonic material system. In contrast to typical SOI based photonic materials, here an insulator-on-silicon-on-insulator (IOSOI) material system has been fabricated. This symmetric structure exhibits average losses between 1510 and 1630 nm of around 0.5 dB/mm for TE and 0.3 dB/mm for TM-polarization. The good transmission for TM-polarization can be explained by the thick insulting cladding layer of 3 μm thickness. Moreover, group index dispersion diagrams are presented and discussed for both polarizations.
©2009 Optical Society of America
1. Introduction
In the last years great efforts lead to a strong miniaturization of optical components analog to the evolution process of microelectronics. One of the greatest steps forward was the realization of integrated optical components within the silicon-on-insulator (SOI) platform which is completely compatible to CMOS technology. Typically, the waveguiding structures are etched into a thin silicon (Si) membrane on top of a silicon oxide cladding layer and a Si substrate. The very high refractive index contrast between the Si core (n=3.5) and the oxide cladding (n=1.45) and air (n=1), respectively, leads to a high confinement of light inside a waveguide.
To meet the demands of next generation networks with bandwidths of more than 100 Gbit/s adequate modulators and modulation techniques have to be realized on a Si platform. The state-of-the-art methods for high-bandwidth modulation require polarization diversity, e.g., the Dual Polarization Quadrature Phase Shift Keying (DP QPSK) technique which uses four step phase shift keying and polarization multiplexing simultaneously. For polarization multiplexing an appropriate material system which provides equably propagation of TE and TM-polarization is essential.
In addition, to realize photonic crystal based polarization sensitive devices a fully symmetrical material system is needed to avoid polarization mixing. In a photonic crystal an asymmetric index profile leads to coupling of the linear polarization states and therefore an independent guiding of TE and TM-polarization is not possible [1].
These two conditions are not fulfilled simultaneously by most of the approaches presented in literature. For most of the (symmetric) SOI-based structures no transmission for TM-polarized light was reported [2,3] or for TM-polarization a large deviation between theory and experiment was observed [4]. In contrast, SOI structures which support a low-loss guided TM mode are typically not symmetric [5].
In this paper, we present the results of our basic investigation of the waveguiding characteristics of an SOI-based material, the insulator-on-silicon-on-insulator (IOSOI) material system. It offers low-loss guiding of TM-polarized light as well as a vertical symmetry for photonic crystal applications at the same time. Ridge waveguides with two different widths were realized and low-loss propagation of light could be demonstrated.
Due to the large index contrast and the resulting small cross-section of the IOSOI waveguides the waveguide dispersion becomes more important than the material dispersion and group indices larger than the phase index of the core material can be reached. Hence, the group index dispersion of the waveguides is investigated and compared with calculations.
2. Material system
The IOSOI material system is a layer system similar to the standard SOI. An additional silica layer is brought on the top of the Si membrane, as it is schematically shown in Fig. 1. The waveguide structures are etched into the material in a completely symmetrical manner: below and above the 200 nm thin Si layer the oxide is equally structured. Thus, the IOSOI material has to be etched up to 500 nm deep into the lower oxide.
The fabrication process of an IOSOI-structure is reported in detail elsewhere [6, 7]. Here, a short summary of the process is given. It starts with a commercial available SOI wafer. It has a device-layer thickness of 1.5 μm and a oxide thickness of 3 μm [Fig. 1(a)]. Then, a multistage oxidation and wet-etching procedure follows and ends up with a 200 nm thin device layer and a 500 nm thin oxide layer on top [Fig. 1(b)]. With respect to the above characteristics of the IOSOI material, a direct etching of a three-layer structure SiO2/Si/SiO2 is not possible using only a usual resist mask. It would be removed too fast during the process, therefore one has to choose a hard etching mask. This is realized by a 150 nm thin chromium (Cr) layer, which is sputtered on top of the wafer [Fig. 1(c)]. Cr fulfills the requirements, because it is hard, strongly adhering to the silica, and resistant to the dry etching process with fluorine-based plasmas (commonly used in Si and silica etching). After applying an e-beam resist [Fig. 1(d)], the patterning via an e-beam lithography step occurs [Fig. 1(e)]. Then, the Cr mask is opened by RIE etching, while the patterned resist works as the etching mask for the Cr [Fig. 1(f)]. Afterwards, the e-beam resist is removed [Fig. 1(g)]. Finally, the pores are etched into the IOSOI material using a combined RIE and ICP etching process [Fig. 1(h)], with the patterned Cr layer as the etching mask, and the residual Cr is removed by wet-etching [Fig. 1(i)]. These single steps, especially the etching processes are explained more detailed elsewhere. The quality of the samples is very good, as shown in Fig. 2. The different layers can be clearly identified, the surface roughness is low and the etched walls are almost vertical. Ridge waveguides with two different widths, 890 nm and 2 μm, respectively, were fabricated. The 890 nm wide ridge waveguide supports the even fundamental and an odd propagating mode for TE-polarization and only the fundamental mode for TM-polarization. The 2 μm wide ridge waveguide is multi-mode for both polarizations.
Fig. 1. Overview of the fabrication process of an IOSOI waveguide structure. Details in the main text.
After the structures are etched, single dices have to be cut out of the whole wafer. This process is very critical for the optical loss measurements since the facets will limit the precision of the measurement. Moreover, simple cleaving is not possible in the multi-layer system. Therefore, a process consisting of a sawing step followed by several polishing steps had been developed. The dicing of the samples is carried out by a diamond wire saw. The sawn edge has a typical roughness of about 40 μm. The following polishing steps are performed with varying grain sizes, going from large to small. The polished coupling facets of the IOSOI ridge waveguides have a final roughness of well below 50 nm.
Fig. 2. SEM micrograph of a ridge waveguide etched into the IOSOI material as described in the main text. One can clearly identify the Si layer surrounded by the silicon oxide claddings. On top of the structure the remaining Cr mask is visible.
3. Optical characterization
Transmission measurements through IOSOI waveguides were performed to determine the losses and the group indices. The characterization setup is schematically shown in Fig. 3. The light emitted from a tunable laser source is guided via optical fibers through an automatic polarization controller (PC) to a lensed fiber (LF). The lensed fiber focuses the light on a spot size of around 2 μm and is used for coupling light into the sample (device under test, DUT). A similar LF is used to collect the light on the output side of the DUT. Finally, the light is guided to a detector (PD) connected with an optical multimeter. By tuning the laser system, a wavelength dependent transmission spectrum can be recorded. The intrinsic optical losses of the setup with fiber-to-fiber coupling, including fiber connectors and PC, is around -12 dB. The output power of the laser system is adjusted to 5 dBm to get a constant output for wavelengths from 1510 till 1630 nm. The optical multi-meter has a lower detection limit of about -70 dBm. Alternatively to the LF a microscope objective and an infrared (IR)-camera can be installed on the output side, which are used to control the coupling of light into the DUT.
Fig. 3. Scheme of the used setup for the transmission measurements. For a detailed description see the text. PC: polarization controller, LF: lensed fiber, XYZ: micropositioners, DUT: device under test, -10dB: -10 dB-coupler, PD: detector, E: electronics
Typical transmission spectra of an 890 nm wide IOSOI ridge waveguide for both, TE and TM-polarization, are depicted in Fig. 4. Here, TE-polarization denotes the state where the electric field vector is parallel to the plane of the sample. Because of the finite reflectivity of the end faces of the waveguides Fabry-Perot oscillations are generated. Due to a higher reflection coefficient the Fabry-Perot oscillations for TE-polarized light are much more intensive than in the TM case.
Fig. 4. Typical transmission spectra of an 890 nm wide IOSOI ridge waveguide. left: TE-polarization; right: TM-polarization.
The propagation of light in an arbitrary lossy waveguide is described by Eq. 1:
whereas 𝓔k,l(x,y) is the electric field distribution of the (k,l)-mode of the waveguide and βk,l its propagation constant. The propagation direction is z, t is the time and ω the (angular) frequency of light. The entire optical losses during the propagation of the waveguide mode are described by the absorption coefficient α.
For the group index ng for the (k,l)-mode of a waveguide holds Eq. 2:
whereas λ is the wavelength of light and nk,l is the phase index of the mode. It can be calculated with (c is the speed of light) Eq. 3:
The signal-to-noise ratio (SNR) is especially for TM-polarization measurements very low (see Fig. 4). Therefore, the determination of the losses is carried out by analyzing the recorded transmission spectra by Fourier analysis [9, 10] since it is more precise than the Fabry-Perot method [8]. The Fourier method can only give reliable results if light propagates within one single mode through the waveguide and no heavy imperfections of the waveguide structure cause a significant distortion of the transmitted signal [11]. For the IOSOI material system, the sufficient uniformity of the ridge waveguides is assured by the fabrication process. The single-mode behavior of the waveguides is checked by Fourier analysis and if it can be confirmed one gets plausible results: In case of the IOSOI ridge waveguides, for the Fabry-Perot method measurement errors are up to three times larger than for the Fourier method.
The Fourier transformation of a typical transmission spectrum of a waveguide shows not only the fundamental contribution of the Fabry-Perot oscillation but also the harmonics of higher orders. An example of a Fourier spectrum is depicted in Fig. 5.
For the calculation of the Fourier transformation 𝓕{IT} the wavelength values λ of the recorded transmission spectrum are changed into wavevectors k by k = 2π/λ. Now the conjugated variable after the Fourier transformation is the optical length d. If the value for d belonging to the fundamental peak of the Fabry-Perot oscillation can be determined in the Fourier spectrum, the group index ng can be determined by division of d and the geometrical length of the waveguide, d geo.
Fig. 5. Fourier transformation of the transmission spectrum in Fig. 4. The two arrows mark the fundamental peak (left) and the first harmonic (right) of the Fabry-Perot oscillation.
The relation of the amplitudes of the Fourier components of a Fabry-Perot oscillation, 𝓕{IT}((i + 1)L) and 𝓕{IT}(iL) located at the optical lengths iL and (i + 1)L(i ∊ ℕ), respectively, gives the product of reflectivity R and the absorption term A = exp(−αd geo) (equation 4) [12].
The absorption coefficient can now be determined by equation 5:
4. Results
The losses of 890 nm wide ridge waveguides were measured with the method described above for both, TE and TM-polarization. In Fig. 6 the measured absorption coefficient α is plotted against the wavelength. Furthermore, the analysis of the Fourier spectra shows that for both polarizations the light propagates mono-mode through the waveguide.
Fig. 6. Absorption coefficient α of an 890 nm wide IOSOI ridge waveguide for TE-polarization (left) and TM-polarization (right) determined via the Fourier method.
The average absorption coefficients are for both polarizations in the same order of magnitude. For TE-polarization it is α 890nm,TE = 0.5 ± 0.3 dB/mm and for TM-polarization it is α 890nm,TM = 0.3 ± 0.2 dB/mm.
The measured losses of 2 μm wide ridge waveguides for both polarizations are depicted in Fig. 7. The analysis of the Fourier spectra shows that even for this structure for both polarizations the light propagates mono-mode through the waveguide.
Fig. 7. Absorption coefficient α of a 2 μm wide IOSOI ridge waveguide for TE-polarization (left) and TM-polarization (right) determined via the Fourier method.
The strong variation of the measured absorption coefficients for TM-polarization is a result of the low SNR. So, the two values with the strongest deviation are not considered for calculating the average absorption coefficient. The average absorption coefficients are for TE-polarization α 2μm,TE = 0.4 + 0.1 dB/mm and for TM-polarization α 2μm,TM = 0.3 ± 0.1 dB/mm.
The group index dispersions were determined from the Fourier transformation of the transmission spectrum as described above (see Section 3). In Fig. 8 the group index is plotted versus the wavelength for an 890 nm and a 2 μm wide waveguide for both polarizations. The experimental data are plotted in black and theoretical curves are plotted in red. The theoretical curves were calculated with a commercial available 2D FEM code (COMSOL, http://www.comsol.com).
5. Discussion
Up to now no data for absorption coefficients and group index dispersion for the completely symmetric IOSOI ridge waveguides have been published. Only data for absorption coefficients of two types of similar structures were published. On the one hand, these are SOI ridge waveguides buried with PECVD oxide [2] or flowable oxide [3]. On the other hand, an absorption coefficient for a 500 nm wide SOI waveguide with a 250 μm thick hydrogen silsesquioxane (HSQ) layer on top was published [13]. In Table 1 the absorption coefficients of the 890 nm and 2 μm wide IOSOI ridge waveguides are compared with these different waveguides and with a state-of-the-art SOI waveguide [5].
First of all, it should be noted that IOSOI ridge waveguides transmit TM-polarized light with slightly lower losses than TE-polarized light. For most of the published SOI waveguides, e.g., references [14–16], and also for the buried structures no transmission for TM-polarized light was reported. This is due to the fact that the buffering oxide is not thick enough to prevent the TM-polarized light from coupling to the Si substrate. This assumption is supported by results reported in [4], where the experimental results for the group index dispersion of an SOI ridge waveguide for TM-polarized light showed a cut-off at smaller wavelengths than theoretically predicted. The authors explained this behavior also with the leakage of light into the substrate. In contrast, the ridge waveguides presented in [5] have also a 3 μm thick buffering oxide and absorption coefficients for both, TE and TM-polarization are presented.
Fig. 8. Group index dispersion ng(λ) of an 890 nm wide (top) and a 2 μm wide (bottom) IOSOI ridge waveguide for TE-polarization (left) and TM-polarization (right). Experimental data are drawn in black and theoretical curves are drawn in red.
To analyze the field dependence in detail, the field distributions were calculated by 2D FEM. Exemplarily, the field distributions for the fundamental guided modes for TE and TM-polarization of an 890 nm wide IOSOI ridge waveguide are depicted in Fig. 9. The boundaries of the different materials are marked with black lines. It becomes apparent that the guided modes are not purely TE or TM-polarized. They have only a quasi-TE and a quasi-TM character. The maxima of the Ey-field and the Ex-field (TE-polarization) have a ratio of 1/5 as well as the maxima of the Hy-field and the Hy-field have a ratio of 1/10. Due to the high birefringence of the waveguide the polarizations cannot couple to each other. For all field distributions, the modes exhibit a perfect vertical and horizontal symmetry, respectively. Accordingly, the barycenter of the field distributions matches perfectly the center of the Si core of the waveguide. Thus, the perfect symmetry of the waveguide structure leads to a perfect symmetry of the guided modes. The constitution of the field distributions differs between TE and TM: In the TE-case the field is more concentrated towards the center of the waveguide core than in the TM-case. In both cases significant parts of the fields leak into the cladding and beyond the side walls. For the conventional SOI ridge waveguide the field distributions have no vertical symmetry due to the non-symmetric index profile [15].
The comparison of the absorption coefficients with the cited references above is shown in Table 1. Considering the measurement errors, for structures with similar cross sections all reported absorption coefficients are of the same magnitude. The SOI waveguide with an HSQ layer on top seems to be clearly better than the rest [13]. With respect to the larger Si thickness and the refractive index of the HSQ layer of approximately n=1.7 as well as the fact that this structure is mono-mode the gap to the IOSOI structures decreases.
Fig. 9. Calculated field distributions of the fundamental guided modes of an 890 nm wide IOSOI waveguide. For TE-polarization, the Ey-field distribution (top left) and the Ex-field distribution (bottom left, multiplied by a factor of 5) are displayed. For TM-polarization, the Hy-field distribution (top right) and the Hx-field distribution (bottom right, multiplied by a factor of 10) are displayed.
In case of the IOSOI structures, the main reason for loss is scattering at the side walls of the waveguides. In Fig. 9 the significant overlap of the fields and the side walls can be clearly seen. Hence, two effects contribute to the measured losses: Due to the scattering light from the guided mode couples to radiating modes and to higher order guided modes. For the 890 nm wide waveguide and TM-polarization the absorption coefficient is smaller than in the TE-case although the overlap with the side walls seems to be larger (see Fig. 9). Here, no further guided mode exists and therefore the second effect cannot contribute to the entire loss. In addition, for the 2 μm wide waveguides the number of guided modes is lower for TM-polarization and therefore the contribution of the second effect to the entire loss is smaller. An improvement of the IOSOI structures would be possible by reducing the sidewall roughness within the fabrication process or by wet chemical postprocessing [16].
The standard SOI structures absorb less light and show absorption coefficients of approximately the half of the ones measured for the IOSOI ridge waveguides. This is due to the highly developed fabrication process used in Ref. [5], which results into a very small roughness of the side walls of the ridge waveguides.
The measured group index dispersion of the IOSOI waveguides are for TE-polarization in very good agreement with the theoretical curves. For TM-polarized light, there exists a very high sensitivity of the group index to the thickness of the waveguide.
For the 890 nm wide ridge waveguide the measured group index dispersion does not fit very well the theoretical curve for wavelengths above 1580 nm. Therefore, the calculations were done with the assumption of a thinner Si membrane. For the 890 nm wide waveguide a thickness of 190 nm fits leads to a curve which fits the measured data very well in the designated spectral region but not for lower wavelengths (see Fig. 8 top right). This inconsistence is the consequence of the very low SNR of the measurements for TM-polarized light.
Table 1. Overview and comparison of absorption coefficients of silicon based ridge waveguides characterized by different groups.
In case of the 2 μm wide IOSOI ridge waveguide the calculated curve for a Si thickness of 170 nm fits the measured group index dispersion very well (see Fig. 8 bottom right). Here, the SNR of the recorded transmission spectrum is much larger and the only reason for the deviation between experiment and theory are fabrication tolerances.
Altogether, the qualitative behavior of the group index dispersions the IOSOI ridge waveguides is very similar to those of SOI waveguides with similar cross sections. Because of the missing upper oxide layer, the absolute values of the group indices for the SOI structures are slightly higher [4].
6. Conclusion
In conclusion, the IOSOI ridge waveguides and the buried SOI ridge waveguides are on a par in terms of propagation losses. Low absorption coefficients for mono-mode propagation of light in an 890 nm wide ridge waveguide and a 2 μm wide waveguide were measured. For the 890 nm wide structure an absorption coefficient of 0,5 ± 0,2 dB/mm for TE-polarization and 0,3 ± 0,2 dB/mm, respectively, were obtained. The 2 μm wide structures absorption coefficients are 0,4±0,1 dB/mm (TE) and 0,3±0,1 dB/mm (TM). Due to the thick cladding oxide, both polarizations are guided with low losses, an important requirement for future microphotonic devices.
The group index dispersions of the IOSOI ridge waveguides show a trend typical for nanophotonic SOI-based ridge waveguides. Due to the upper oxide cladding the absolute values of the group indices are slightly lower than for conventional SOI ridge waveguides. Furthermore, a strong sensitivity of the TM mode to variations of the Si membrane thickness was measured and verified by 2D FEM calculations. This will be an important design rule for future polarization dependent devices.
The large benefit of the IOSOI material system compared to the buried SOI structures is its high refractive contrast in horizontal direction. This unique property is promising in view of etching photonic crystals and other integrated devices in such a material system. In contrast to the situation in SOI photonic crystals, the nearly perfect symmetry of the material with respect to the Si membrane should lead to a decoupling of TE and TM-polarization [1]. Hence, this material system is the most promising candidate for the fabrication of polarization maintaining photonic crystal structures.
Acknowledgments
The authors want to acknowledge the financial support of the BMBF within the project “HiPhoCs” and the Center for Innovation Competence “SiLi-nano” (Grant-No: 03Z2HN12). We gratefully acknowledge fruitful discussions with C. Jamois and great support with the fabrication of IOSOI samples by A.P. Milenin at the Max-Planck Institute of Microstructure Physics, Halle.
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