Abstract

We report here a polarization-independent drop filter (PIDF) based on a photonic crystal self-collimation ring resonator (SCRR). Despite of the large birefringence associated with the polarization-dependent dispersion properties, we demonstrate a PIDF based on multiple-beam interference theory and polarization peak matching (PPM) technique. The PIDF performance was also investigated based on finite-difference time-domain (FDTD) technique, with excellent agreement between the theory and the simulation. For the designed drop wavelength of 1550 nm, the polarization-independent free spectral range is about 36.1 nm, which covers the whole optical communication C-band window. The proposed PIDFs are highly desirable for applications in photonic integrated circuits (PICs).

© 2009 OSA

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  1. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
    [CrossRef]
  2. J. Witzens, M. Loncar, and A. Scherer, “Self-Collimation in Planar Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1246–1257 (2002).
    [CrossRef]
  3. L. Wu, M. Mazilu, and T. F. Krauss, “Beam Steering in Planar-Photonic Crystals: From Superprism to Supercollimator,” J. Lightwave Technol. 21(2), 561–566 (2003).
    [CrossRef]
  4. X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
    [CrossRef]
  5. P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
    [CrossRef]
  6. D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
    [CrossRef]
  7. D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D Appl. Phys. 41(11), 15108–15112 (2008).
    [CrossRef]
  8. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
    [CrossRef]
  9. V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdré, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. 32(5), 530–532 (2007).
    [CrossRef] [PubMed]
  10. Y. Zhang, Y. Zhang, and B. Li, “Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals,” Opt. Express 15(15), 9287–9292 (2007).
    [CrossRef] [PubMed]
  11. X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
    [CrossRef]
  12. J. Hou, D. Gao, H. Wua, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
    [CrossRef]
  13. P. Yeh, “Electromagnetic propagation in birefringent layered media,” J. Opt. Soc. Am. 69(5), 742–756 (1979).
    [CrossRef]
  14. B. E. A. Saleh, and M. C. Teich, “Fundamentals of Photonics,” (A Wiley-Interscience publication, New York, 1991).

2009 (1)

J. Hou, D. Gao, H. Wua, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

2008 (2)

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D Appl. Phys. 41(11), 15108–15112 (2008).
[CrossRef]

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

2007 (4)

V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdré, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. 32(5), 530–532 (2007).
[CrossRef] [PubMed]

Y. Zhang, Y. Zhang, and B. Li, “Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals,” Opt. Express 15(15), 9287–9292 (2007).
[CrossRef] [PubMed]

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

2006 (1)

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

2003 (2)

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
[CrossRef]

L. Wu, M. Mazilu, and T. F. Krauss, “Beam Steering in Planar-Photonic Crystals: From Superprism to Supercollimator,” J. Lightwave Technol. 21(2), 561–566 (2003).
[CrossRef]

2002 (1)

J. Witzens, M. Loncar, and A. Scherer, “Self-Collimation in Planar Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1246–1257 (2002).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

1979 (1)

Chen, C.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Chen, X.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Dahlem, M. S.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Dunbar, L. A.

Fan, S.

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
[CrossRef]

Gao, D.

J. Hou, D. Gao, H. Wua, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

Gong, Q.

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D Appl. Phys. 41(11), 15108–15112 (2008).
[CrossRef]

Han, K.

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

Hou, J.

J. Hou, D. Gao, H. Wua, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

Houdré, R.

Ibanescu, M.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Ippen, E. P.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Jiang, X.

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D Appl. Phys. 41(11), 15108–15112 (2008).
[CrossRef]

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Joannopoulos, J. D.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Kolodziejski, L. A.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Kotlyar, M. V.

Krauss, T. F.

Le Thomas, N.

Li, B.

Li, H. P.

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

Loncar, M.

J. Witzens, M. Loncar, and A. Scherer, “Self-Collimation in Planar Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1246–1257 (2002).
[CrossRef]

Martin, R.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Mazilu, M.

Miao, B.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Murakowski, J.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

O’Faolain, L.

Pakich, P. T.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Petrich, G. S.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Prather, D. W.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Scherer, A.

J. Witzens, M. Loncar, and A. Scherer, “Self-Collimation in Planar Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1246–1257 (2002).
[CrossRef]

Schneider, G. J.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Sharkawy, A.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Shen, X. P.

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

Shi, S.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

Soljacic, M.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Tandon, S.

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Wang, Z. Y.

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

Witzens, J.

J. Witzens, M. Loncar, and A. Scherer, “Self-Collimation in Planar Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1246–1257 (2002).
[CrossRef]

Wu, L.

Wua, H.

J. Hou, D. Gao, H. Wua, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

Yao, P.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Yeh, P.

Yu, X.

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
[CrossRef]

Yuan, F.

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

Zabelin, V.

Zhang, J.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Zhang, Y.

Zhao, D.

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D Appl. Phys. 41(11), 15108–15112 (2008).
[CrossRef]

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

Zhong, Q.

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

Zhou, C.

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D Appl. Phys. 41(11), 15108–15112 (2008).
[CrossRef]

Zhou, Z.

J. Hou, D. Gao, H. Wua, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

Appl. Phys. Lett. (3)

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
[CrossRef]

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Chin. Phys. Lett. (1)

X. P. Shen, K. Han, F. Yuan, H. P. Li, Z. Y. Wang, and Q. Zhong, “New configuration of ring resonator in photonic crystal based on self-collimation,” Chin. Phys. Lett. 25(12), 4288–4291 (2008).
[CrossRef]

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

J. Witzens, M. Loncar, and A. Scherer, “Self-Collimation in Planar Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1246–1257 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Phys. D (1)

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40(9), 2635–2651 (2007).
[CrossRef]

J. Phys. D Appl. Phys. (1)

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D Appl. Phys. 41(11), 15108–15112 (2008).
[CrossRef]

Nat. Mater. (1)

P. T. Pakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef]

Opt. Commun. (1)

J. Hou, D. Gao, H. Wua, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

B. E. A. Saleh, and M. C. Teich, “Fundamentals of Photonics,” (A Wiley-Interscience publication, New York, 1991).

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Figures (5)

Fig. 1
Fig. 1

(a) Square lattice air hole photonic crystal structure dispersion curves for two polarizations (TE and TM) along ΓΜ direction; Equal frequency contours (EFCs) of the first band for (b) TE modes and (c) TM modes. The air hole radius r equals 0.33a, where a is the lattice constant. The dielectric constant is assumed to be 12.25. The highlighted regions correspond to the SC frequency window.

Fig. 2
Fig. 2

(a) Schematic of polarization-independent drop filters based on self-collimation ring resonators (SCRRs) consisting of two beam splitters (BS1, BS2) and two mirrors (M1, M2); (b) Zoom-ins of the mirrors and beam splitters with key parameters defined; and (c) simulated reflection and transmission spectra for polarization-dependent mirrors and beam-splitters.

Fig. 3
Fig. 3

Theoretical (dash lines) and FDTD simulated (solid lines) transmission spectra for the drop channel in the proposed SCRR based drop filters, with (a) l=372a , and (b) l=472a .

Fig. 4
Fig. 4

Theoretically calculated peak frequencies shown in blue circles and red dots for (a) TE and (b) TM polarizations, respectively, at each geometrical length (SCRR size) l. The corresponding integer values jTE and jTM are also shown. (c) Polarization peak matching (PPM) map with triangles identifying polarization independent operation conditions where TE (blue circles) and TM (red dots) peaks overlap.

Fig. 5
Fig. 5

(a) FDTD simulated drop channel transmission (solid blue lines) and through channel output (dash red lines) for both TE and TM polarizations at SCRR loop size l1=432a . Notice PPM occurs at f1 = 0.1824 c/a, which agrees very well with the results shown in Fig. 4(c) based on the theoretical calculations. (b, c) FDTD simulated magnetic-field distribution for TE polarization (top) and electric-field distribution for TM polarization (bottom) at (b) matching condition f1 = 0.1824 c/a for drop channel, and (c) f2 = 0.1800 c/a for through channel.

Equations (4)

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

f=(c/2πne)k+f0
IdI0=TS2(1RSRM)211+[4RSRM/(1RSRM)2]sin2(ϕ/2)
ϕ=kle+θ=k(l+lp)+θ
2jTEπ=kTE(l+lp,TE)+θTE,2jTMπ=kTM(l+lp,TM)+θTM

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