Abstract

In this paper, we propose a Silicon-On-Insulator waveguide structure which when excited with TM guided light emits controlled TE polarized radiation from one side of the structure only. The validity of the proposed structure is analyzed using eigenmode expansion and supermode techniques. It is shown that care must be taken to select the gap between the radiating elements such that both the phase and the amplitude of the radiating modes are maintained along the propagation direction to achieve the desired directional control of radiation. Steps toward practical demonstration of the proposed structure are identified.

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  1. M. Lipson, “Silicon photonics: the optical spice rack,” Electron. Lett. 45(12), 576–578 (2009).
    [CrossRef]
  2. B. Jalali, “Can silicon change photonics?” Phys. Stat. Solidi A 2(205), 213–224 (2008).
    [CrossRef]
  3. B. Jalali and S. Fathpour, “Silicon Photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
    [CrossRef]
  4. R. Soref, “Silicon Photonics: A Review of Recent Literature,” Springer 2(1), 1–6 (2010).
  5. D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
    [CrossRef]
  6. M. Webster, R. Pafchek, A. Mitchell, and T. Koch, “Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19(6), 429–431 (2007).
    [CrossRef]
  7. M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005).
    [CrossRef]
  8. R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen, and T. L. Koch, “Low-loss silicon-on-insulator shallow-ridge TE and TM waveguides formed using thermal oxidation,” Appl. Opt. 48(5), 958–963 (2009), http://ao.osa.org/abstract.cfm?URI=ao-48-5-958 .
    [CrossRef] [PubMed]
  9. T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers,” IEEE Photon. Technol. Lett. 21(7), 486–488 (2009).
    [CrossRef]
  10. A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides: Part II—New physical effects,” IEEE Trans. Microw. Theory Tech. 29(9), 855–869 (1981).
    [CrossRef]
  11. T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Lateral leakage of TM-like mode in thin-ridge Silicon-on-Insulator bent waveguides and ring resonators,” Opt. Express 18(7), 7243–7252 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7243 .
    [CrossRef] [PubMed]
  12. D. Lioubtchenko, S. Tretyakov, and S. Dudorov, Millimeter-wave waveguides (Kluwer Academic Publisher, Boston, 2003), Chap. 8.
  13. A. S. Sudbo, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” J. Opt. A, Pure Appl. Opt. 3, 381–388 (1994).
  14. K. Ogusu, “Optical strip waveguide-A detailed analysis including leaky modes,” J. Opt. Soc. Am. 73(3), 353–357 (1983).
    [CrossRef]
  15. W. S. C. Chang, Fundamentals of Guided-Wave Optoelectronic Devices (Cambridge University Press, New York, 2010), Chap. 2.

2010 (3)

R. Soref, “Silicon Photonics: A Review of Recent Literature,” Springer 2(1), 1–6 (2010).

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[CrossRef]

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Lateral leakage of TM-like mode in thin-ridge Silicon-on-Insulator bent waveguides and ring resonators,” Opt. Express 18(7), 7243–7252 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7243 .
[CrossRef] [PubMed]

2009 (3)

M. Lipson, “Silicon photonics: the optical spice rack,” Electron. Lett. 45(12), 576–578 (2009).
[CrossRef]

R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen, and T. L. Koch, “Low-loss silicon-on-insulator shallow-ridge TE and TM waveguides formed using thermal oxidation,” Appl. Opt. 48(5), 958–963 (2009), http://ao.osa.org/abstract.cfm?URI=ao-48-5-958 .
[CrossRef] [PubMed]

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers,” IEEE Photon. Technol. Lett. 21(7), 486–488 (2009).
[CrossRef]

2008 (1)

B. Jalali, “Can silicon change photonics?” Phys. Stat. Solidi A 2(205), 213–224 (2008).
[CrossRef]

2007 (1)

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, “Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19(6), 429–431 (2007).
[CrossRef]

2006 (1)

2005 (1)

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005).
[CrossRef]

1994 (1)

A. S. Sudbo, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” J. Opt. A, Pure Appl. Opt. 3, 381–388 (1994).

1983 (1)

1981 (1)

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides: Part II—New physical effects,” IEEE Trans. Microw. Theory Tech. 29(9), 855–869 (1981).
[CrossRef]

Bowers, J. E.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[CrossRef]

Chen, E.

Fathpour, S.

Hsu, T. I.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides: Part II—New physical effects,” IEEE Trans. Microw. Theory Tech. 29(9), 855–869 (1981).
[CrossRef]

Jalali, B.

B. Jalali, “Can silicon change photonics?” Phys. Stat. Solidi A 2(205), 213–224 (2008).
[CrossRef]

B. Jalali and S. Fathpour, “Silicon Photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
[CrossRef]

Koch, T.

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, “Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19(6), 429–431 (2007).
[CrossRef]

Koch, T. L.

Li, J.

Liang, D.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[CrossRef]

Lipson, M.

M. Lipson, “Silicon photonics: the optical spice rack,” Electron. Lett. 45(12), 576–578 (2009).
[CrossRef]

Mitchell, A.

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Lateral leakage of TM-like mode in thin-ridge Silicon-on-Insulator bent waveguides and ring resonators,” Opt. Express 18(7), 7243–7252 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7243 .
[CrossRef] [PubMed]

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers,” IEEE Photon. Technol. Lett. 21(7), 486–488 (2009).
[CrossRef]

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, “Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19(6), 429–431 (2007).
[CrossRef]

Nguyen, T. G.

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Lateral leakage of TM-like mode in thin-ridge Silicon-on-Insulator bent waveguides and ring resonators,” Opt. Express 18(7), 7243–7252 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7243 .
[CrossRef] [PubMed]

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers,” IEEE Photon. Technol. Lett. 21(7), 486–488 (2009).
[CrossRef]

Ogusu, K.

Oliner, A. A.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides: Part II—New physical effects,” IEEE Trans. Microw. Theory Tech. 29(9), 855–869 (1981).
[CrossRef]

Pafchek, R.

R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen, and T. L. Koch, “Low-loss silicon-on-insulator shallow-ridge TE and TM waveguides formed using thermal oxidation,” Appl. Opt. 48(5), 958–963 (2009), http://ao.osa.org/abstract.cfm?URI=ao-48-5-958 .
[CrossRef] [PubMed]

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, “Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19(6), 429–431 (2007).
[CrossRef]

Pafchek, R. M.

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005).
[CrossRef]

Peng, S. T.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides: Part II—New physical effects,” IEEE Trans. Microw. Theory Tech. 29(9), 855–869 (1981).
[CrossRef]

Sanchez, A.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides: Part II—New physical effects,” IEEE Trans. Microw. Theory Tech. 29(9), 855–869 (1981).
[CrossRef]

Soref, R.

R. Soref, “Silicon Photonics: A Review of Recent Literature,” Springer 2(1), 1–6 (2010).

Sudbo, A. S.

A. S. Sudbo, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” J. Opt. A, Pure Appl. Opt. 3, 381–388 (1994).

Sukumaran, G.

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005).
[CrossRef]

Tummidi, R.

Tummidi, R. S.

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Lateral leakage of TM-like mode in thin-ridge Silicon-on-Insulator bent waveguides and ring resonators,” Opt. Express 18(7), 7243–7252 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7243 .
[CrossRef] [PubMed]

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers,” IEEE Photon. Technol. Lett. 21(7), 486–488 (2009).
[CrossRef]

Webster, M.

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, “Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19(6), 429–431 (2007).
[CrossRef]

Webster, M. A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005).
[CrossRef]

Electron. Lett. (1)

M. Lipson, “Silicon photonics: the optical spice rack,” Electron. Lett. 45(12), 576–578 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, “Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers,” IEEE Photon. Technol. Lett. 21(7), 486–488 (2009).
[CrossRef]

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, “Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 19(6), 429–431 (2007).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides: Part II—New physical effects,” IEEE Trans. Microw. Theory Tech. 29(9), 855–869 (1981).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

A. S. Sudbo, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” J. Opt. A, Pure Appl. Opt. 3, 381–388 (1994).

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[CrossRef]

Opt. Express (1)

Phys. Stat. Solidi A (1)

B. Jalali, “Can silicon change photonics?” Phys. Stat. Solidi A 2(205), 213–224 (2008).
[CrossRef]

Springer (1)

R. Soref, “Silicon Photonics: A Review of Recent Literature,” Springer 2(1), 1–6 (2010).

Other (2)

D. Lioubtchenko, S. Tretyakov, and S. Dudorov, Millimeter-wave waveguides (Kluwer Academic Publisher, Boston, 2003), Chap. 8.

W. S. C. Chang, Fundamentals of Guided-Wave Optoelectronic Devices (Cambridge University Press, New York, 2010), Chap. 2.

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Figures (6)

Fig. 1
Fig. 1

(a) X-Y cross section of a single SOI shallow ridge waveguide and plan view of the structure showing TM to TE mode coupling at the side wall of the ridge, (b) X-Y cross section of two identical and parallel SOI shallow ridge waveguides and plan view of the structure showing the mechanism of the summation of the radiation of the two waveguides in both sides of the structure. Waveguide dimensions are shown.

Fig. 2
Fig. 2

Electric field components of the guided mode of the waveguide of Fig. 1 with width 1µm to maximize TE radiation at λ = 1.55μm. (a) real component; (b) imaginary component.

Fig. 3
Fig. 3

The magnitude of the y-component of the electric fields of the TM-like modes of (a) the original SOI waveguide; (b) the additional identical SOI waveguides with a 4.58µm lateral translation and a π/2 phase shift and (c) the coherent superposition of these two modes; (d) the magnitude (in Log scale) of the super-imposed radiation fields of identical modes at two symmetric fixed points (y1 = + 8µm and y2 = −8µm, x1 = x2 = midpoint of the Si film) on right & left hand sides of both waveguides versus the gap (S) between the waveguides and the magnitude of the summation of the TE radiation waves as obtained from Eq. (1) and (2) which account for the phase difference between the two TE waves.

Fig. 4
Fig. 4

.Real (a) and imaginary (b) parts of the effective refractive indices of the even and odd supermodes of the structure versus the waveguide separation, respectively. The magnitude of the y-component of the electric fields of the TM-like supermodes of the structure with 4.54µm waveguide separation respectively: (c) even mode (d) odd mode.

Fig. 5
Fig. 5

(a) Magnitude of the y-component of the electric field of the superimposed TM-like even and odd supermodes of the structure with a phase difference of π/2 and 4.54µm waveguide separation; (b) magnitude (Log scale) of the radiation field from the superposition of the supermodes for two symmetric fixed points (y1 = + 8µm and y2 = −8µm, x1 = x2 = middle point of the Si film) to the right and left of the structure as a function of waveguide separation.

Fig. 6
Fig. 6

Poynting vector magnitude of Y-Z cross section of the structure for waveguide separations of, (a) 4.36μm, (b) 4.54μm and (c) 4.45μm; Poynting vector magnitude at two symmetric fixed points to the right and left of the structure (y1 = + 8µm and y2 = −8µm, x1 = x2 = midpoint of the Si-film) as a function of propagation distance in the z-direction for (d) 4.36μm, (e) 4.54μm and (f) 4.45μm.

Equations (2)

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Δ φ R = Φ +  k 0 n TE d
Δ φ L = Φ  k 0 n TE d

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