Abstract

A two-dimensional photonic crystal asymmetric Mach-Zehnder filter (AMZF) based on the self-collimation effect is studied by numerical simulations and experimental measurements in microwave region. A self-collimated beam is effectively controlled by employing line-defect beam splitters and mirrors. The measured transmission spectra at the two output ports of the AMZF sinusoidally oscillate with the phase difference of π in the self-collimation frequency range. Position of the transmission peaks and dips can be controlled by varying the size of the defect rod of perfect mirrors, and therefore this AMZF can be used as a tunable power filter.

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References

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, NJ, 1995).
  2. S. G. Johnson, P. Villeneuve, S. Fan, and J. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
    [CrossRef]
  3. 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]
  4. 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]
  5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
    [CrossRef]
  6. 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]
  7. S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 29(6), 617–619 (2004).
    [CrossRef] [PubMed]
  8. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29(1), 50–52 (2004).
    [CrossRef] [PubMed]
  9. D. M. Pustai, S. Shi, C. Chen, A. Sharkawy, and D. W. Prather, “Analysis of splitters for self-collimated beams in planar photonic crystals,” Opt. Express 12(9), 1823–1831 (2004).
    [CrossRef] [PubMed]
  10. S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
    [CrossRef]
  11. M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
    [CrossRef]
  12. S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
    [CrossRef] [PubMed]
  13. X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251 (2003).
    [CrossRef]
  14. T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
    [CrossRef]
  15. A. W. Snyder and J. D. Love, “Goos-Hänchen shift,” Appl. Opt. 15(1), 236–238 (1976).
    [CrossRef] [PubMed]
  16. A. F. Matthews and Y. S. Kivshar, “Tunable Goos-Hänchen shift for the self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372, 3098–3101 (2008).
  17. A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos-Hänchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93(13), 131901 (2008).
    [CrossRef]
  18. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (2nd Ed. Artech House INC, Norwood, 2000).
  19. D. M. Pozar, Microwave Engineering, (John Wiley & Sons, New York, 1998), Chap. 3.2.

2009 (1)

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
[CrossRef]

2008 (3)

A. F. Matthews and Y. S. Kivshar, “Tunable Goos-Hänchen shift for the self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372, 3098–3101 (2008).

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos-Hänchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93(13), 131901 (2008).
[CrossRef]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
[CrossRef] [PubMed]

2007 (3)

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]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[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]

2005 (1)

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
[CrossRef]

2004 (3)

2003 (1)

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

2000 (1)

S. G. Johnson, P. Villeneuve, S. Fan, and J. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

1976 (1)

Chen, C.

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]

Choi, J.-S.

Fan, S.

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

S. G. Johnson, P. Villeneuve, S. Fan, and J. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

Jiang, 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]

Joannopoulos, J.

S. G. Johnson, P. Villeneuve, S. Fan, and J. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

Johnson, S. G.

S. G. Johnson, P. Villeneuve, S. Fan, and J. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

Kee, C.-S.

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
[CrossRef]

Kim, J.-E.

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
[CrossRef]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
[CrossRef]

Kim, M.-W.

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
[CrossRef]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[CrossRef]

Kim, T.-T.

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
[CrossRef]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[CrossRef]

Kivshar, Y. S.

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos-Hänchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93(13), 131901 (2008).
[CrossRef]

A. F. Matthews and Y. S. Kivshar, “Tunable Goos-Hänchen shift for the self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372, 3098–3101 (2008).

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

Lee, S.-G.

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
[CrossRef]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
[CrossRef]

Li, B.

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]

Love, J. D.

Matthews, A. F.

A. F. Matthews and Y. S. Kivshar, “Tunable Goos-Hänchen shift for the self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372, 3098–3101 (2008).

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos-Hänchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93(13), 131901 (2008).
[CrossRef]

Murakowski, J.

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

Oh, S. S.

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
[CrossRef]

Park, H. Y.

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
[CrossRef]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
[CrossRef] [PubMed]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
[CrossRef]

Prather, D. W.

Pustai, D. M.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[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.

Sharkawy, A.

Shi, S.

Snyder, A. W.

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

Venkataraman, S.

Villeneuve, P.

S. G. Johnson, P. Villeneuve, S. Fan, and J. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[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]

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]

Yu, X.

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

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, 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]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

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

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95(1), 011119 (2009).
[CrossRef]

A. F. Matthews and Y. S. Kivshar, “Experimental studies of the internal Goos-Hänchen shift for self-collimated beams in two-dimensional microwave photonic crystals,” Appl. Phys. Lett. 93(13), 131901 (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]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87(18), 181106 (2005).
[CrossRef]

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 90(11), 113121 (2007).
[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]

Opt. Express (3)

Opt. Lett. (2)

Phys. Lett. A (1)

A. F. Matthews and Y. S. Kivshar, “Tunable Goos-Hänchen shift for the self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372, 3098–3101 (2008).

Phys. Rev. B (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[CrossRef]

S. G. Johnson, P. Villeneuve, S. Fan, and J. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

Other (3)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, NJ, 1995).

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (2nd Ed. Artech House INC, Norwood, 2000).

D. M. Pozar, Microwave Engineering, (John Wiley & Sons, New York, 1998), Chap. 3.2.

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Figures (4)

Fig. 1
Fig. 1

Asymmetric Mach-Zehnder interferometer composed of two 50:50 beam splitters and two mirrors. Arrows indicate the direction of light propagation.

Fig. 2
Fig. 2

(a) Schematic diagram of the experimental apparatus of a PC asymmetric Mach-Zehnder filter (AMZF). Two aluminum plates hold alumina rods vertically. (b) Layout of the square lattice 2D PC-AMZF composed of two 50:50 line-defect beam splitters and two perfect mirrors. The ARS are introduced at the input and two output ports. (c) Simulated spatial distribution of the steady-state electric field at the frequency f = 12.5 GHz in the line-defect beam splitter with the radii rd aligned in the ΓΧ direction. The inset shows the top view of the beam splitter structure. (d) Power spectra for the split beams by a line-defect beam splitter as a function of the radius of defect rods rd .

Fig. 3
Fig. 3

Transmittance of microwaves (a) without any ARS and (b) with the ARS applied to the proposed 2D AMZF. Two solid lines represent the experimentally measured values at the two output ports, port 1 (black line) and port 2 (red line), respectively, while the dashed lines correspond to the simulation results. Simulated spatial distributions of the steady-state electric fields of the self-collimated beams at frequencies (c) f1 = 12.67 GHz and (d) f2 = 12.44 GHz.

Fig. 4
Fig. 4

Transmittance of microwaves (a) without any ARS and (b) with the ARS applied to the proposed 2D AMZF. Two solid lines represent the experimentally measured values at the two output ports, port 1 (black line) and port 2 (red line), respectively, while the dashed lines correspond to the simulation results. Simulated spatial distributions of the steady-state electric fields of the self-collimated beams at frequencies (c) f1 = 12.67 GHz and (d) f2 = 12.44 GHz.

Equations (2)

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I 1 = I 0 sin 2 ( δ 2 )
I 2 = I 0 cos 2 ( δ 2 )

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