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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 20 — Oct. 7, 2002
  • pp: 1139–1144
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Coupling anomalies in SimGen/Si/SiO2 waveguide systems

Amy E. Bieber and T. G. Brown  »View Author Affiliations


Optics Express, Vol. 10, Issue 20, pp. 1139-1144 (2002)
http://dx.doi.org/10.1364/OE.10.001139


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Abstract

Sharp coupling anomalies exist in a SiGe superlattice buried in a silicon-on-insulator waveguide structure. We study these anomalies using a rigorous coupled wave analysis and examine their suitability for silicon-compatible waveguide-mode resonant filters for optical telecommunications. Active functions could include optical detection, switching, and modulation. We predict that a very weak, sub band-edge absorption can improve filter contrast or provide high quantum efficiency detection.

© 2002 Optical Society of America

1. Introduction

Guided-mode resonances have long been of both practical and fundamental interest in optics and optoelectronics. They are most often seen in reflection anomalies in dielectric or metallic gratings and are associated with resonant grating coupling between an external wave and a local wave. A good deal of theoretical and experimental research was carried out in the 1990’s [1–5

1. M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105 (1983). [CrossRef]

]; most of these studies were aimed at the use of buried periodic dielectric structures to achieve narrowband filtering for such applications as wavelength division multiplexing. When optimized, and fabricated with very low loss waveguides, such structures are predicted to exhibit sub-Angstrom linewidths for notch or line filters.

The physical mechanism for a guided-mode resonant filter is based on the principle of diffractive coupling between an incident external wave (e.g. a radiation mode of the cover or substrate) and a guided wave or other locally confined wave (e.g. a surface plasmon). Gaylord and Moharam [1

1. M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105 (1983). [CrossRef]

,2

2. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett. 23, 700 (1998). [CrossRef]

], Morris and coworkers [3

3. S. M. Norton, G. M. Morris, and T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,” J. Opt. Soc. Am A 15, 464 (1998). [CrossRef]

,4

4. S. Peng and G. M. Morris, “Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1087 (1995). [CrossRef]

], and Magnusson and Wang [5

5. S. S. Wang and R. Magnusson, “Theory and Applications of Guided Mode Resonance Filters,” Applied Optics , 32, pp. 2606 (1993). [CrossRef] [PubMed]

] have all made excellent contributions to the theoretical understanding, numerical modeling, and experimental design of these structures.

During the same period, considerable work was carried out on waveguide interactions, including free-space coupling, in semiconductor waveguides fabricated from a silicon-on-insulator platform. Semiconductors offer a variety of active device functions ranging from electronic tunability and/or modulation to all-optical switching. Sankey, Prelewitz and Brown [6

6. N. D. Sankey, D.F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic waveguide structure,” Appl. Phys. Lett. 60, 1427 (1992). [CrossRef]

,7

7. N. D. Sankey, D.F. Prelewitz, and T. G. Brown, “Optical switching dynamics of the nonlinear Bragg reflector: comparison of theory and experiment,” J. Appl. Phys. 73, 7111 (1993). [CrossRef]

], and later Bieber and Brown [8

8. Amy E. Bieber and T. G. Brown, “Integral coupler-resonator for silicon-based switching and modulation,” Appl. Phys. Lett. 71, 861 (1997). [CrossRef]

,9

9. Amy E. Bieber, D. F. Prelewitz, T. G. Brown, and R. Tiberio, “Optical Switching in a Metal-Semiconductor-Metal Waveguide Structure,” Appl. Phys. Lett. 66, 3401 (1995). [CrossRef]

], experimentally investigated optical switching in a silicon-on-insulator platform using grating couplers, Bragg-reflectors, and integrated couplers/Bragg reflectors. The silicon-on-insulator platform combines a natural waveguide structure with an increasingly common platform for high-speed electronics. This structure can be integrated with interdigitated periodic electrodes (optically-resonant periodic electrode structures) to achieve tunable, high-speed grating couplers for switching or modulation. Most structures that include metal electrodes, however, possess a limit on the resonance width due to the damping of the metal. Indeed, most waveguide loss mechanisms will reduce the strength of the resonance and result in broad, shallow resonances rather than the extremely sharp resonances needed for many switching and filter applications.

Structures suitable for active functions such as detection require absorption in the structure. The interplay of absorption and filter contrast is, however, not an obvious one. In this paper, we study a variation on the familiar silicon-on-insulator (SOI) structure that incorporates a small volume of SimGen superlattice material to provide optical functionality in the transparency region of silicon. The structure exhibits sharp waveguide mode resonances in which a small amount of absorption in the SimGen region plays a beneficial role both for passive filters and for active functions such as detection and modulation in dense wavelength-division multiplexed (DWDM) optical systems.

2. Analysis of SiGe/SOI guided wave structures

Figure 1 shows a schematic of the structure, in which a silicon substrate supports a prescribed number of silicon/SiO2 layer pairs; one silicon region contains an active SimGen (device) layer buried at the center. The active layer can either perform a detection function or be otherwise active, e.g. by allowing injected electrons (or optically-produced electron-hole pairs) to modify either the absorption or the refractive index. The optical constants can be varied, in a bulk semiconductor, by free carrier effects, or band edge shifts. Band filling in an indirect quantum well or quantum wire structure can also result in a carrier-induced change in absorption or refractive index. Both these and other means of tuning the refractive index of group IV compounds have been discussed extensively by Soref [10

10. R. A. Soref and B. R. Bennett, “Electro-optical Effects in Silicon,” IEEE J. Quantum Electron. , QE-23, pp. 123 (1987). [CrossRef]

,11

11. R.A. Soref, et.al, “Optical Waveguiding in a Single-Crystal Layer of Germanium-Silicon Grown on Silicon,” Opt. Lett , 15, p. 270 (1990). [CrossRef] [PubMed]

].

This work made use of a rigorous coupled wave (RCW) algorithm, introduced by Peng and Morris [4

4. S. Peng and G. M. Morris, “Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1087 (1995). [CrossRef]

], especially suited to study the characteristics of strong reflection/transmission anomalies in complex, subwavelength buried grating structures. RCW theory is based on the Rayleigh expansion of electric and magnetic fields at a series of lamellar-type layers, employing a truncated Fourier expansion of the dielectric constant in each layer, and casting the boundary conditions between layers into a matrix eigenvalue problem which can either yield the eigenmodes of the entire structure or, in this case, the response of the structure to an external field. All of the structures in this study were examined at wavelengths near 1550 nm (below the band edge for both silicon and SiGe) and assumed to be illuminated by a monochromatic, TE-polarized plane wave at near-normal incidence (for normal incidence, TE polarization assumes the electric field to be parallel to the grating lines). This is an important geometry for free-space interconnects and is amenable to integration with conventional VLSI components.

Fig. 1. Cross sectional schematic of the SiGe/SOI structure. In the example shown, four silicon layers are separated by SiO2 cladding regions. A thin (160 nm) corrugated layer of SimGen is inserted into one c-Si layers and functions as the guiding layer. For the Cartesian axes shown, z denotes the direction of light propagation, y the orientation of the grating lines and the direction of incident polarization, and x is the direction of propagation of light within the guiding layer.

The structure of Fig. 1 has the general characteristics of a high-reflectivity multilayer with a phase shift placed in one high-index layer (for example, a Bragg mirror with a λ/4 phase shift in the middle will exhibit a reflection anomaly at the center of the Bragg resonance). Figure 2 shows a plot of the broad spectral features of a structure with four silicon layers surrounded by SiO2 cladding. The SimGen superlattice layer is inserted into one of the silicon layers. The thicknesses of the Si and SiO2 layers are adjusted as for a thin- film dielectric mirror; the maximum reflectivity of the structure, illuminated from the cover region, is 0.9998. For comparison, two cases are considered in Fig. 2: 1) A buried SimGen grating (50% duty cycle, period 715 nm) of refractive index 3.765; 2) A uniform layer of refractive index 3.615, which is equivalent to the volume-weighted average of the Si and SimGen superlattice in the grating region. It is clear that the reflection anomaly is associated with a waveguide mode resonance of the grating coupler and not simply with a phase shift in the central layer. Adjustment of the grating period can locate the resonance anywhere in the high reflectance band, a useful feature for DWDM telecommunications.

Figure 3 illustrates the intrinsic tunability of these structures with a higher resolution plot of the coupling resonance at two different refractive indices of the SiGe region. Changing the refractive index of the SiGe region by 0.01 (0.13 percent by volume of the central layer) yields a clear shift of the resonance by 0.4 nm (about one channel spacing in a dense wavelength division multiplexed system). Thus, tuning the refractive index of the grating layer (thermally, by carrier injection, or by a suitable electro-optic effect) permits modulation of the reflectance of a fixed wavelength or channel selection of a WDM detector.

Fig. 2. Blue trace: reflectance of a structure with a buried grating (715 nm period) comprised of a SimGen superlattice. The red trace shows the reflectance of a structure in which the grating is replaced with an equivalent uniform layer of refractive index 3.615.
Fig. 3. The narrowband reflectance of a waveguide mode resonance near λ=1550 nm shows tunability with refractive index: (a) nSiGe=3.75; (b) nSiGe=3.76.

As is typical of all resonant filters, the resonance wavelength can also be angle-tuned. However, because it is a waveguide-mode resonance, oblique angles of incidence both forward and backward traveling modes can be excited. Figure 4 illustrates the reflectance spectrum of a structure at normal incidence and detuned by 0.1 degrees. The accompanying movie shows the evolution of the resonance when detuned from normal incidence to 0.15 degrees. Both the appearance of the extra resonance and the rate at which it shifts with angle are characteristic of the dispersion relation of this structure. Since both the overall SOI structure and the individual, central guiding layer support many modes, the dispersion relation in the presence of a corrugation is a complex one. That this is true even for simple SOI structures was noted in an earlier paper by Brown, Weiss and Fabrizzio [12

12. T. G. Brown, R. P. Fabrizzio, and S. M. Weiss, “Semiconductor periodic structures for out-of-plane optical switching and Bragg-soliton excitation,” Opt. Express 3, 433 (1998). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-11-433 [CrossRef] [PubMed]

].

Fig. 4. Waveguide mode resonance (a) for normally incident radiation and (b) detuned by 0.1 degree for cover illumination. Clicking on the figure will play a movie which shows the evolution of the resonance over an angular range from 0 to 0.15 degrees. [Media 1]

3. The role of absorption in SiGe/SOI guided mode resonances

Si1-xGex can, in principle, exist in any stoichiometry. For unstrained alloys, the fraction x of germanium is typically constrained by the lattice mismatch. However, fractions of germanium of 50% or higher can be incorporated into thin SimGen superlattices. The choice of composition will determine both the refractive index and absorption [13

13. T. P. Pearsall, H. Polatoglou, H. Presting, and Erich Kasper“Optical absorption spectroscopy of Si-Ge alloys and superlattices,” Phys. Rev. B 54, 1545 (1996). [CrossRef]

]. A detailed comparison of SiGe superlattices and alloys is out of the scope of this discussion; suffice it to say that the choice of stoichiometry and ordering allows a high degree of flexibility in placement of the absorption edge in the 1100 nm to 1550 nm wavelength range.

Fig. 5. Waveguide mode resonance (a) with absorption in the SiGe layer (k=3×10-4) and (b) without absorption in the SiGe layer.
Fig. 6 (a) Fraction of light absorbed and on/off contrast plotted against extinction k in the SiGe layer. (b) Comparison of contrast against extinction for substrate versus cover illumination.

4. Conclusions

In summary, we have applied rigorous coupled wave theory to the study of SiGe/SOI structures and have identified high-contrast waveguide-mode resonances near 1550 nm, which offer several possible functions for optoelectronic telecommunications. A small amount of residual absorption in the SiGe significantly improves the contrast and can provide total absorption of nearly 80%.

Acknowledgments

This work was supported in part by a grant from the City University of New York PSC-CUNY Research Award Program.

References and Links

1.

M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105 (1983). [CrossRef]

2.

D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett. 23, 700 (1998). [CrossRef]

3.

S. M. Norton, G. M. Morris, and T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,” J. Opt. Soc. Am A 15, 464 (1998). [CrossRef]

4.

S. Peng and G. M. Morris, “Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1087 (1995). [CrossRef]

5.

S. S. Wang and R. Magnusson, “Theory and Applications of Guided Mode Resonance Filters,” Applied Optics , 32, pp. 2606 (1993). [CrossRef] [PubMed]

6.

N. D. Sankey, D.F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic waveguide structure,” Appl. Phys. Lett. 60, 1427 (1992). [CrossRef]

7.

N. D. Sankey, D.F. Prelewitz, and T. G. Brown, “Optical switching dynamics of the nonlinear Bragg reflector: comparison of theory and experiment,” J. Appl. Phys. 73, 7111 (1993). [CrossRef]

8.

Amy E. Bieber and T. G. Brown, “Integral coupler-resonator for silicon-based switching and modulation,” Appl. Phys. Lett. 71, 861 (1997). [CrossRef]

9.

Amy E. Bieber, D. F. Prelewitz, T. G. Brown, and R. Tiberio, “Optical Switching in a Metal-Semiconductor-Metal Waveguide Structure,” Appl. Phys. Lett. 66, 3401 (1995). [CrossRef]

10.

R. A. Soref and B. R. Bennett, “Electro-optical Effects in Silicon,” IEEE J. Quantum Electron. , QE-23, pp. 123 (1987). [CrossRef]

11.

R.A. Soref, et.al, “Optical Waveguiding in a Single-Crystal Layer of Germanium-Silicon Grown on Silicon,” Opt. Lett , 15, p. 270 (1990). [CrossRef] [PubMed]

12.

T. G. Brown, R. P. Fabrizzio, and S. M. Weiss, “Semiconductor periodic structures for out-of-plane optical switching and Bragg-soliton excitation,” Opt. Express 3, 433 (1998). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-11-433 [CrossRef] [PubMed]

13.

T. P. Pearsall, H. Polatoglou, H. Presting, and Erich Kasper“Optical absorption spectroscopy of Si-Ge alloys and superlattices,” Phys. Rev. B 54, 1545 (1996). [CrossRef]

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(250.3140) Optoelectronics : Integrated optoelectronic circuits

ToC Category:
Research Papers

History
Original Manuscript: September 20, 2002
Revised Manuscript: September 27, 2002
Published: October 7, 2002

Citation
Amy Bieber and Thomas Brown, "Coupling anomalies in SimGen/Si/SiO2 waveguide systems," Opt. Express 10, 1139-1144 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-20-1139


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References

  1. M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 73, 1105 (1983). [CrossRef]
  2. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, �??Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,�?? Opt. Lett. 23, 700 (1998). [CrossRef]
  3. S. M. Norton, G. M. Morris, and T. Erdogan, �??Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,�?? J. Opt. Soc. Am A 15, 464 (1998). [CrossRef]
  4. S. Peng and G. M. Morris, �??Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings,�?? J. Opt. Soc. Am. A 12, 1087 (1995). [CrossRef]
  5. S. S. Wang and R. Magnusson, "Theory and Applications of Guided Mode Resonance Filters," Appl. Opt. 32, 2606 (1993). [CrossRef] [PubMed]
  6. N. D. Sankey, D.F. Prelewitz and T. G. Brown, "All-optical switching in a nonlinear periodic waveguide structure," Appl. Phys. Lett. 60, 1427 (1992). [CrossRef]
  7. N. D. Sankey , D.F. Prelewitz and T. G. Brown, "Optical switching dynamics of the nonlinear Bragg reflector: comparison of theory and experiment," J. Appl. Phys. 73, 7111 (1993). [CrossRef]
  8. Amy E. Bieber and T. G. Brown, "Integral coupler-resonator for silicon-based switching and modulation," Appl. Phys. Lett. 71, 861 (1997). [CrossRef]
  9. Amy E. Bieber, D. F. Prelewitz, T. G. Brown, and R. Tiberio, "Optical Switching in a Metal-Semiconductor-Metal Waveguide Structure," Appl. Phys. Lett. 66, 3401 (1995). [CrossRef]
  10. R. A. Soref and B. R. Bennett, "Electro-optical Effects in Silicon," IEEE J. Quantum Electron. QE-23, 123 (1987). [CrossRef]
  11. R.A. Soref, et.al, "Optical Waveguiding in a Single-Crystal Layer of Germanium-Silicon Grown on Silicon," Opt. Lett. 15, 270 (1990). [CrossRef] [PubMed]
  12. T. G. Brown, R. P. Fabrizzio and S. M. Weiss, "Semiconductor periodic structures for out-of-plane optical switching and Bragg-soliton excitation," Opt. Express 3, 433 (1998). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-11-433">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-11-433</a> [CrossRef] [PubMed]
  13. T. P. Pearsall, H. Polatoglou, H. Presting, and Erich Kasper "Optical absorption spectroscopy of Si-Ge alloys and superlattices," Phys. Rev. B 54, 1545 (1996). [CrossRef]

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