Abstract

The fundamental quasi-TE and quasi-TM modes of a sub-wavelength strip silicon waveguide are not purely TE or TM as the plane waves in free space. We investigate theoretically and experimentally the far-field polarization compositions of the two waveguide modes after they emanate from the waveguide facet. The measured polarization extinction ratios (PERs) of 31 dB for the quasi-TM mode and 26 dB for quasi-TE mode using free-space polarizers are consistent with our numerical analysis. Moreover, our far-field simulations show that the free-space measurement of PERs is influenced, and in many cases limited, by the sizes of various apertures in the experimental setup. This suggests a potential trade-off between achievable PERs and overall power detection/collection efficiency.

© 2013 Optical Society of America

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Y. Ding, B. Huang, H. Ou, F. Da Ros, and C. Peucheret, Opt. Express 21, 7828 (2013).
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J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

2011 (3)

2010 (3)

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A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
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M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
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2008 (1)

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Almeida, V. R.

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T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
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M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

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[CrossRef]

Bowers, J. E.

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P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y. Chen, in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012), paper Th3B1.

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L. Chen, C. R. Doerr, and Y. Chen, Opt. Lett. 36, 469 (2011).
[CrossRef]

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y. Chen, in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012), paper Th3B1.

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L. Chen, C. R. Doerr, and Y. Chen, Opt. Lett. 36, 469 (2011).
[CrossRef]

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y. Chen, in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012), paper Th3B1.

Da Ros, F.

Dai, D.

Ding, Y.

Doerr, C. R.

Dong, P.

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y. Chen, in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012), paper Th3B1.

Fan, L.

J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

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T. Feuchter and C. Thirstrup, IEEE Photon. Technol. Lett. 6, 1244 (1994).
[CrossRef]

Folkenberg, J.

Fukuda, H.

Haus, H. A.

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

Huang, B.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Ippen, E. I.

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

Ippen, E. P.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Itabashi, S.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Kartner, F. X.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Khan, M. H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

Kikuchi, K.

Kwong, D.

J. Zhang, M. Yu, G. Lo, and D. Kwong, IEEE J. Sel. Top. Quantum Electron. 16, 53 (2010).
[CrossRef]

Leaird, D. E.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

Lipson, M.

Lo, G.

J. Zhang, M. Yu, G. Lo, and D. Kwong, IEEE J. Sel. Top. Quantum Electron. 16, 53 (2010).
[CrossRef]

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Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Ou, H.

Ouyang, J.

J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
[CrossRef]

Panepucci, R. R.

Peucheret, C.

Popovic, M. A.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Qi, M.

J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

Rakich, P. T.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

Shinojima, H.

Smith, H. I.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

Socci, L.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

Thirstrup, C.

T. Feuchter and C. Thirstrup, IEEE Photon. Technol. Lett. 6, 1244 (1994).
[CrossRef]

Tsuchizawa, T.

Varghese, L. T.

J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

Wang, J.

J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

Watanabe, T.

Watts, M. R.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

Weiner, A.

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

Wirth, J. C.

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

Xiao, S.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

Xie, C.

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y. Chen, in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012), paper Th3B1.

Xuan, Y.

J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

Yamada, K.

Yu, M.

J. Zhang, M. Yu, G. Lo, and D. Kwong, IEEE J. Sel. Top. Quantum Electron. 16, 53 (2010).
[CrossRef]

Zhang, J.

J. Zhang, M. Yu, G. Lo, and D. Kwong, IEEE J. Sel. Top. Quantum Electron. 16, 53 (2010).
[CrossRef]

Zhao, L.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

Adv. Opt. Mater. (1)

J. Wang, J. Ouyang, L. T. Varghese, L. Fan, Y. Xuan, and M. Qi, Adv. Opt. Mater. 1, 740 (2013).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Zhang, M. Yu, G. Lo, and D. Kwong, IEEE J. Sel. Top. Quantum Electron. 16, 53 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Feuchter and C. Thirstrup, IEEE Photon. Technol. Lett. 6, 1244 (1994).
[CrossRef]

Nat. Photonics (2)

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, Nat. Photonics 4, 117 (2010).
[CrossRef]

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Other (3)

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. T. Varghese, D. E. Leaird, and A. Weiner, in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper JW4A.83.

M. R. Watts, M. Qi, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, H. I. Smith, and H. A. Haus, in Optical Fiber Communication Conference (Optical Society of America, 2005), paper PDP11.

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y. Chen, in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012), paper Th3B1.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Near-field FDTD simulations of the fundamental TM mode emanating from a silicon waveguide to air. |Ex| and |Ez| are normalized to their respective maxima. (b) The radiation patterns of |E| of the TM and TE waveguide modes are plotted at the yz and xz planes.

Fig. 2.
Fig. 2.

Calculated far-field profiles of the TM and TE modes at a plane 1 mm away from the waveguide exit facet.

Fig. 3.
Fig. 3.

Energy compositions, Uei, for (a) the TM mode and (b) TE mode at the 1 mm plane vary with the aperture diameter d. The insets are the profiles of the electric field energy densities |E|2. (c) The PERs of both TM and TE modes vary with the aperture diameter d.

Fig. 4.
Fig. 4.

(a) Experimental setup. TLD, tunable laser diode; PC, polarization controller; DUT, device under test; OBJ, objective; POLs, polarizers; LIA, locked-in amplifier. (b) Transmission spectra taken with both TE and TM linearly polarized CW inputs.

Tables (1)

Tables Icon

Table 1. Parameters Used in the FP Model

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E(r)=Sds{iω(n×B(r))G+(n×E(r))×G+(n·E(r))G},
T=ηt2e2αL(1re2αL)2+4re2αLsin2(θ/2),
γ=1rTmax/Tmin1Tmax/Tmin+1.

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