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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 12 — Jun. 9, 2008
  • pp: 8623–8628
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Birefringence and optical power confinement in horizontal multi-slot waveguides made of Si and SiO2

Han G. Yoo, Yijing Fu, Daniel Riley, Jung H. Shin, and Philippe M. Fauchet  »View Author Affiliations


Optics Express, Vol. 16, Issue 12, pp. 8623-8628 (2008)
http://dx.doi.org/10.1364/OE.16.008623


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Abstract

Through simulations and measurements, we show that in multi-slot thin film waveguides, the TM polarized modes can be confined mostly in the low refractive index layers of the waveguide. The structure consisted of alternating layers of a-Si and SiO2, in the thickness range between 3 and 40 nm, for which the slots were the SiO2 layers. Simulations were performed using the transfer matrix method and experiments using the m-line technique at 1.55 µm. The dependence of the birefringence and of the power confinement in the slots was studied as a function of the waveguide thickness, the Si and SiO2 layer thicknesses, and the SiO2/Si layer thickness ratio. We find a large birefringence—a refractive index difference between TE and TM modes—as large as 0.8. For TM polarized modes, up to ~85% of the total power in the fundamental mode can be confined in the slots.

© 2008 Optical Society of America

1. Introduction

The goal of achieving optical gain at the telecommunication wavelengths using a silicon platform is driving research on erbium incorporation in CMOS-compatible host materials and structures. Erbium luminescence at 1.55 µm is especially strong if the Er ions reside in a silicon oxide host and are excited by energy transfer from silicon nanocrystals (nc-Si) placed in close proximity [1–6

1. P. G. Kik, M. L. Brongersma, and A. Polman, “Strong exciton-erbium coupling in Si nanocrystal-doped SiO2,” Appl. Phys. Lett. 76, 2325–2327 (2000). [CrossRef]

]. An attractive structure is a stratified multilayer film of alternating thin layers of nc-Si and Er-doped SiO2 [3

3. V. Y. Timoshenko, M. G. Lisachenko, B. V. Kamenev, O. A. Shalygina, P. K. Kashkarov, J. Heitmann, M. Schmidt, and M. Zacharias, “Highly efficient sensitizing of erbium ion luminescence in size-controlled nanocrystalline Si/SiO2 superlattice structures,” Appl. Phys. Lett. 84, 2512–2514 (2004). [CrossRef]

, 4

4. J. H. Shin, W.-H. Lee, and H.-S. Han, “1.54 µm Er3+ photoluminescent properties of erbium-doped Si/SiO2 superlattices,” Appl. Phys. Lett. 74, 1573–1575 (1999). [CrossRef]

]. One of the major hindrances to achieving lasing using Er is the confined (or free) carrier absorption by nc-Si and thus there has been a marked interest in minimizing this type of loss [7

7. D. Navarro-Urrios, M. Melchiorri, N. Daldosso, L. Pavesi, C. Garcia, P. Pellegrino, B. Garrido, G. Pucker, F. Gourbilleau, and R. Rizk, “Optical losses and gain in silicon-rich silica waveguides containing Er ions,” J. Appl. Phys. 91, 534–536 (2002).

, 8

8. P. G. Kik and A. Polman, “Gain limiting processes in Er-doped Si nanocrystal waveguides in SiO2,” J. Lumin. 121, 249–255 (2006). [CrossRef]

].

In this letter, we present simulations and experiments on horizontal multilayer films consisting of alternating nanometer-thin amorphous Si (a-Si) and SiO2 layers. Since the material index of nc-Si is similar to that of a-Si overall [16

16. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

], our results are also applicable to multilayer films of alternating polycrystalline Si and SiO2 layers, which can be formed by post-deposition thermal annealing [17

17. L. Tsybeskov, K. D. Hirschman, S. P. Duttagupta, M. Zacharias, P. M. Fauchet, J. P. McCaffrey, and D. J. Lockwood, “Nanocrystalline-silicon superlattice produced by controlled recrystallization,” Appl. Phys. Lett. 72, 43–45 (1998). [CrossRef]

,18

18. G. F. Grom, D. J. Lockwood, J. P. McCaffrey, H. J. Labbe, P. M. Fauchet, B. White, Jr, J. Diener, D. Kovalev, F. Koch, and L. Tsybeskov, “Ordering and self-organization in nanocrystalline silicon,” Nature (London) 407, 358–361 (2000). [CrossRef] [PubMed]

]. Simulations show that a birefringence of up to 0.8 and a power confinement of up to ~85% can be achieved. It ought to be noted that these effects should also be observable in any multilayer film made of alternating ultra-thin layers with a large material index contrast.

2. Sample

Fig. 1. (a) SEM of a structure made of alternating a-Si and SiO2 layers. (b) Schematic of sample structure with P periods of LSi thick a-Si and LSiO 2 thick SiO2 layers on a 5-µm thick thermal oxide layer. (c) Sample structure as viewed by the prism coupler for m-line measurement. The multilayer film is replaced by a single film with an effective material index of nFilm and thickness LFilm=P(LSi+L SiO2).

Films containing layers of a-Si and SiO2 were deposited by computer-controlled reactive ion RF magnetron sputtering at room temperature on Si substrates covered by a 5-µm thick thermal oxide layer (Fig. 1). The layer thicknesses LSi and L SiO2 of the two materials varied from ~3 to ~40 nm and the number of periods P ranged from 13 to 160, to keep the total film thickness LFilm close to 1 µm, ensuring the presence of multiple guiding modes. Two sets of five films were fabricated: in one set the thickness ratio L SiO2/LSi was kept close to 1, whereas the ratio in the other set ranged between 0.7 and 11.5.

3. Simulations & experimental methods

Simulations were carried out using the transfer matrix method [19

19. J. Chilwell and I. Hodgkinson, “Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1, 742–753 (1984). [CrossRef]

]—equivalently, the Abeles matrix method [20

20. K. Ohta and H. Ishida, “Matrix formalism for calculation of electric field intensity of light in stratified multilayered films,” Appl. Opt. 29, 1952–1959 (1990). [CrossRef] [PubMed]

]—for stratified multilayer films. For the refractive index of the deposited and thermal oxide layers and that of a-Si, we used the values of 1.44 and 3.44 obtained from ellipsometric measurements at 1.55 µm.

Fig. 2. (a) Schematic of m-line measurement. (b) Graph of reflected light intensity as a function of the modal index for a multilayer film of 34 periods of 15.2-nm a-Si and 19.7-nm SiO2. The arrows show the modal indices greater than 1.44 at which a bound mode is established (2.43, 2.16 and 1.75 for TE; and 1.74 and 1.55 for TM). Modal indices between 1.8 and 1.9 were not measurable because of the two prisms used.

4. Modal index & birefringence

Fig. 3. (a) First and second order modal indices versus SiO2/a-Si layer thickness ratio for both polarizations. The curves represent the calculation for 1.00-µm thick film and the dots represent the measured values for film thicknesses ranging from 0.93 to 1.19 µm. (b) Measured (dots) and calculated (curves) modal index difference between the fundamental TE and TM modes as a function of layer thickness ratio for total film thicknesses between 0.4 and 0.9 µm. The maximum difference of ~0.8 is obtained if the thickness ratio is around 0.5 and 0.6.

5. Power profile

Fig. 4. The power profile of the first order TE and TM modes in a 0.60-µm thick film consisting of 10 periods of alternating 30-nm thick a-Si and SiO2 layers. The SiO2 substrate layer is positioned below the 0.0-µm mark and the air above the 0.6-µm mark. The shaded areas represent the SiO2 layers. For TM polarization, the transverse E-field component in the low-index nL region is greater by a factor of nH 2/nL 2 than that in the high-index nH region immediately across the interface.

6. Confinement factor & optimum layer thickness ratio

In Fig. 5(a), the power confinement factor in the SiO2 layers for the fundamental TM mode is plotted as a function of layer thickness ratio for various total film thicknesses. At any given layer thickness ratio, the confinement factor in the SiO2 layers rises as the total film thickness increases, approaching the absolute maximum of ~85%(nH2nL21+nH2nL2) , which can be reached for 0.90-µm or thicker films provided that the thickness ratio is greater than 1.72.

Furthermore, the figure shows that for each film thickness there is an optimum layer thickness ratio at which the confinement in the SiO2 layers is maximum. The confinement factors for thicker films reach their maxima at higher thickness ratios than for thinner films. The optimum layer thickness ratio for a given film thickness follows an empirical linear relationship (Fig. 5(b)). For example, if the film thickness is 0.50 µm, then the optimum ratio is ~0.83. The shaded region in Fig. 5(b) denotes the layer thickness ratio and total film thickness where only one TM mode exists. If a film is to be a single-mode waveguide for TM polarization and to provide the highest SiO2 confinement, then its thickness should be set to 0.80-µm. This thickness is larger than the one producing the largest birefringence (Fig. 3(b)).

Fig. 5. (a) The power confinement factor in the SiO2 layers for first order TM mode as a function of layer thickness ratio at various total film thicknesses. (b) The linear relationship between the total film thickness and its optimum layer thickness ratio. The shaded area represents the region where only one TM mode exists.

Finally, we note that for large SiO2/Si thickness ratios, the confinement factor decreases. This decrease is the result of the increasingly large evanescent tails in the air and the SiO2 substrate, which are produced by the decreasing effective refractive index of the multilayer.

7. Conclusions

Acknowledgments

This study was supported by the US Air Force Office of Scientific Research’s MURI Program (FA9550-06-1-0470) and the Semiconductor Research Corporation through the Center for Advanced Interconnect Science and Technology (2005-KC1292). The authors thank the Optical Manufacturing and Optical & Imaging Sciences groups at the University of Rochester’s Laboratory for Laser Energetics for use of their ellipsometer and prism coupler. Y.F. acknowledges the assistance of Dr. Wenhui Wang with the simulations and the receipt of an Advanced Materials Graduate Fellowship. J.S. acknowledges support in part by grant No. (R11-2003-022) through Optics and Photonics Elite Research Academy (OPERA) and by grant No. (R01-2007-000-21036-0) of the Korea Science and Engineering Foundation (KOSEF).

References and links

1.

P. G. Kik, M. L. Brongersma, and A. Polman, “Strong exciton-erbium coupling in Si nanocrystal-doped SiO2,” Appl. Phys. Lett. 76, 2325–2327 (2000). [CrossRef]

2.

X. W. Zhao, S. Komuro, H. Isshiki, Y. Aoyagi, and T. Sugano, “Fabrication and stimulated emission of Er-doped nanocrystalline Si waveguides formed on Si substrates by laser ablation,” Appl. Phys. Lett. 74, 120–122 (1999). [CrossRef]

3.

V. Y. Timoshenko, M. G. Lisachenko, B. V. Kamenev, O. A. Shalygina, P. K. Kashkarov, J. Heitmann, M. Schmidt, and M. Zacharias, “Highly efficient sensitizing of erbium ion luminescence in size-controlled nanocrystalline Si/SiO2 superlattice structures,” Appl. Phys. Lett. 84, 2512–2514 (2004). [CrossRef]

4.

J. H. Shin, W.-H. Lee, and H.-S. Han, “1.54 µm Er3+ photoluminescent properties of erbium-doped Si/SiO2 superlattices,” Appl. Phys. Lett. 74, 1573–1575 (1999). [CrossRef]

5.

J. Lee, J. H. Shin, and N. Park, “Optical gain at 1.5 µm in nanocrystal Si-sensitized Er-doped silica waveguide using top-pumping 470 nm LEDs,” J. Lightwave Technol. 23, 19–25 (2005). [CrossRef]

6.

L. Dal Negro, J. H. Yi, J. Michel, L. C. Kimerling, S. Hamel, A. Williamson, and G. Galli, “Light-emitting silicon nanocrystals and photonic structures in silicon nitride,” IEEE J. Quantum Electron. 12, 1628–1635 (2006). [CrossRef]

7.

D. Navarro-Urrios, M. Melchiorri, N. Daldosso, L. Pavesi, C. Garcia, P. Pellegrino, B. Garrido, G. Pucker, F. Gourbilleau, and R. Rizk, “Optical losses and gain in silicon-rich silica waveguides containing Er ions,” J. Appl. Phys. 91, 534–536 (2002).

8.

P. G. Kik and A. Polman, “Gain limiting processes in Er-doped Si nanocrystal waveguides in SiO2,” J. Lumin. 121, 249–255 (2006). [CrossRef]

9.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phasematching using an isotropic nonlinear optical-material,” Nature (London) 391, 463–466 (1998). [CrossRef]

10.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004). [CrossRef] [PubMed]

11.

P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9201 (2006). [CrossRef] [PubMed]

12.

N. Feng, J. Michel, and L. C. Kimerling, “Optical field concentration in low-index waveguides,” IEEE J. Quantum Electron. 42, 885–890 (2006). [CrossRef]

13.

R. Sun, P. Dong, N. Feng, C. Hong, J. Michel, M. Lipson, and L. Kimerling, “Horizontal single and multiple slot waveguides: optical transmission at λ=1550 nm,” Opt. Express 15, 17967–17972 (2007). [CrossRef] [PubMed]

14.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-oninsulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006). [CrossRef]

15.

Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29, 1626–1628 (2004). [CrossRef] [PubMed]

16.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

17.

L. Tsybeskov, K. D. Hirschman, S. P. Duttagupta, M. Zacharias, P. M. Fauchet, J. P. McCaffrey, and D. J. Lockwood, “Nanocrystalline-silicon superlattice produced by controlled recrystallization,” Appl. Phys. Lett. 72, 43–45 (1998). [CrossRef]

18.

G. F. Grom, D. J. Lockwood, J. P. McCaffrey, H. J. Labbe, P. M. Fauchet, B. White, Jr, J. Diener, D. Kovalev, F. Koch, and L. Tsybeskov, “Ordering and self-organization in nanocrystalline silicon,” Nature (London) 407, 358–361 (2000). [CrossRef] [PubMed]

19.

J. Chilwell and I. Hodgkinson, “Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1, 742–753 (1984). [CrossRef]

20.

K. Ohta and H. Ishida, “Matrix formalism for calculation of electric field intensity of light in stratified multilayered films,” Appl. Opt. 29, 1952–1959 (1990). [CrossRef] [PubMed]

21.

R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973). [CrossRef] [PubMed]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(230.7390) Optical devices : Waveguides, planar
(230.7400) Optical devices : Waveguides, slab

ToC Category:
Integrated Optics

History
Original Manuscript: March 19, 2008
Revised Manuscript: May 19, 2008
Manuscript Accepted: May 20, 2008
Published: May 28, 2008

Citation
Han G. Yoo, Yijing Fu, Daniel Riley, Jung H. Shin, and Philippe M. Fauchet, "Birefringence and optical power confinement in horizontal multi-slot waveguides made of Si and SiO2," Opt. Express 16, 8623-8628 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8623


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References

  1. P. G. Kik, M. L. Brongersma, and A. Polman, "Strong exciton-erbium coupling in Si nanocrystal-doped SiO2," Appl. Phys. Lett. 76, 2325-2327 (2000). [CrossRef]
  2. X. W. Zhao, S. Komuro, H. Isshiki, Y. Aoyagi, and T. Sugano, "Fabrication and stimulated emission of Er-doped nanocrystalline Si waveguides formed on Si substrates by laser ablation," Appl. Phys. Lett. 74, 120-122 (1999). [CrossRef]
  3. V. Y. Timoshenko, M. G. Lisachenko, B. V. Kamenev, O. A. Shalygina, P. K. Kashkarov, J. Heitmann, M. Schmidt, and M. Zacharias, "Highly efficient sensitizing of erbium ion luminescence in size-controlled nanocrystalline Si/SiO2 superlattice structures," Appl. Phys. Lett. 84, 2512-2514 (2004). [CrossRef]
  4. J. H. Shin, W.-H. Lee, and H.-S. Han, "1.54 ??m Er3+ photoluminescent properties of erbium-doped Si/SiO2 superlattices," Appl. Phys. Lett. 74, 1573-1575 (1999). [CrossRef]
  5. J. Lee, J. H. Shin, and N. Park, "Optical gain at 1.5 ??m in nanocrystal Si-sensitized Er-doped silica waveguide using top-pumping 470 nm LEDs," J. Lightwave Technol. 23, 19-25 (2005). [CrossRef]
  6. L. Dal Negro, J. H. Yi, J. Michel, L. C. Kimerling, S. Hamel, A. Williamson, and G. Galli, "Light-emitting silicon nanocrystals and photonic structures in silicon nitride," IEEE J. Quantum Electron. 12, 1628-1635 (2006). [CrossRef]
  7. D. Navarro-Urrios, M. Melchiorri, N. Daldosso, L. Pavesi, C. Garcia, P. Pellegrino, B. Garrido, G. Pucker, F. Gourbilleau, and R. Rizk, "Optical losses and gain in silicon-rich silica waveguides containing Er ions," J. Appl. Phys. 91, 534-536 (2002).
  8. P. G. Kik and A. Polman, "Gain limiting processes in Er-doped Si nanocrystal waveguides in SiO2," J. Lumin. 121, 249-255 (2006). [CrossRef]
  9. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, "Phasematching using an isotropic nonlinear opticalmaterial," Nature (London) 391, 463-466 (1998). [CrossRef]
  10. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and confining light in void nanostructure," Opt. Lett. 29, 1209-1211 (2004). [CrossRef] [PubMed]
  11. P. A. Anderson, B. S. Schmidt, and M. Lipson, "High confinement in silicon slot waveguides with sharp bends," Opt. Express 14, 9197-9201 (2006). [CrossRef] [PubMed]
  12. N. Feng, J. Michel, and L. C. Kimerling, "Optical field concentration in low-index waveguides," IEEE J. Quantum Electron. 42, 885-890 (2006). [CrossRef]
  13. R. Sun, P. Dong, N. Feng, C. Hong, J. Michel, M. Lipson, and L. Kimerling, "Horizontal single and multiple slot waveguides: optical transmission at ?? = 1550 nm," Opt. Express 15, 17967-17972 (2007). [CrossRef] [PubMed]
  14. M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savio, A. Irrera, and F. Priolo, "Direct evidence of light confinement and emission enhancement in active silicon-oninsulator slot waveguides," Appl. Phys. Lett. 89, 241114 (2006). [CrossRef]
  15. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, "Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material," Opt. Lett. 29, 1626-1628 (2004). [CrossRef] [PubMed]
  16. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  17. L. Tsybeskov, K. D. Hirschman, S. P. Duttagupta, M. Zacharias, P. M. Fauchet, J. P. McCaffrey, and D. J. Lockwood, "Nanocrystalline-silicon superlattice produced by controlled recrystallization," Appl. Phys. Lett. 72, 43-45 (1998). [CrossRef]
  18. G. F. Grom, D. J. Lockwood, J. P. McCaffrey, H. J. Labbe, P. M. Fauchet, B. White, Jr, J. Diener, D. Kovalev, F. Koch, and L. Tsybeskov, "Ordering and self-organization in nanocrystalline silicon," Nature (London) 407, 358-361 (2000). [CrossRef] [PubMed]
  19. J. Chilwell and I. Hodgkinson, "Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides," J. Opt. Soc. Am. A 1, 742-753 (1984). [CrossRef]
  20. K. Ohta and H. Ishida, "Matrix formalism for calculation of electric field intensity of light in stratified multilayered films," Appl. Opt. 29, 1952-1959 (1990). [CrossRef] [PubMed]
  21. R. Ulrich and R. Torge, "Measurement of thin film parameters with a prism coupler," Appl. Opt. 12, 2901-2908 (1973). [CrossRef] [PubMed]

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