Abstract

We report numerical and experimental investigations of asymmetric light propagation in a newly designed photonic structure that is formed by creating a chirped photonic crystal (PC) waveguide. The use of a non-symmetric distribution of unit cells of PC ensures the obtaining of asymmetric light propagation. Properly designing the spatial modulation of a PC waveguide inherently modifies the band structure. That in turn induces asymmetry for the light’s followed path. The investigation of the transmission characteristics of this structure reveals optical diode like transmission behavior. The amount of power collected at the output of the waveguide centerline is different for the forward and backward propagation directions in the designed configuration. The advantageous properties of the proposed approach are the linear optic concept, compact configuration and compatibility with the integrated photonics. These features are expected to hold great potential for implementing practical optical rectifier-type devices.

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  1. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys.76(4), 2023–2026 (1994).
    [CrossRef]
  2. M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
    [CrossRef]
  3. F. Biancalana, “All-optical diode action with quasiperiodic photonic crystals,” J. Appl. Phys.104(9), 093113 (2008).
    [CrossRef]
  4. A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80, 155117 (2009).
    [CrossRef]
  5. A. O. Cakmak, E. Colak, A. E. Serebryannikov, and E. Ozbay, “Unidirectional transmission in photonic-crystal gratings at beam-type illumination,” Opt. Express18(21), 22283–22298 (2010).
    [CrossRef] [PubMed]
  6. M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(5), 056611 (2006).
    [CrossRef] [PubMed]
  7. W.-M. Ye, X.-D. Yuan, C.-C. Guo, and C. Zen, “Unidirectional transmission in non-symmetric gratings made of isotropic material,” Opt. Express18(8), 7590–7595 (2010).
    [CrossRef] [PubMed]
  8. Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
    [CrossRef] [PubMed]
  9. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
    [CrossRef] [PubMed]
  10. H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A78(2), 023804 (2008).
    [CrossRef]
  11. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
    [CrossRef]
  12. X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
    [CrossRef] [PubMed]
  13. Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
    [CrossRef]
  14. C. Wang, C.-Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19(27), 26948–26955 (2011).
    [CrossRef] [PubMed]
  15. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8(3), 173–190 (2001).
    [CrossRef] [PubMed]
  16. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
    [CrossRef]

2011 (3)

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

C. Wang, C.-Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19(27), 26948–26955 (2011).
[CrossRef] [PubMed]

2010 (3)

2009 (3)

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80, 155117 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

2008 (3)

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A78(2), 023804 (2008).
[CrossRef]

F. Biancalana, “All-optical diode action with quasiperiodic photonic crystals,” J. Appl. Phys.104(9), 093113 (2008).
[CrossRef]

2006 (1)

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(5), 056611 (2006).
[CrossRef] [PubMed]

2001 (1)

1995 (1)

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
[CrossRef]

1994 (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys.76(4), 2023–2026 (1994).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Biancalana, F.

F. Biancalana, “All-optical diode action with quasiperiodic photonic crystals,” J. Appl. Phys.104(9), 093113 (2008).
[CrossRef]

Bloemer, M. J.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys.76(4), 2023–2026 (1994).
[CrossRef]

Bowden, C. M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys.76(4), 2023–2026 (1994).
[CrossRef]

Cakmak, A. O.

Chen, Y.-F.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Colak, E.

Dai, Z.

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

Dowling, J. P.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys.76(4), 2023–2026 (1994).
[CrossRef]

Fan, S.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

Feng, L.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Guo, C.-C.

He, C.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

He, Z.

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(5), 056611 (2006).
[CrossRef] [PubMed]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

John, S.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A78(2), 023804 (2008).
[CrossRef]

Johnson, S.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Ke, M.

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

Li, X.-F.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Li, Z. Y.

C. Wang, C.-Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19(27), 26948–26955 (2011).
[CrossRef] [PubMed]

Liu, Z.

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(5), 056611 (2006).
[CrossRef] [PubMed]

Lu, M.-H.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Ni, X.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Ozbay, E.

Peng, S.

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

Qiu, C.

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(5), 056611 (2006).
[CrossRef] [PubMed]

Scalora, M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys.76(4), 2023–2026 (1994).
[CrossRef]

Serebryannikov, A. E.

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Takeda, H.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A78(2), 023804 (2008).
[CrossRef]

Tocci, M. D.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
[CrossRef]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

Wang, C.

C. Wang, C.-Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19(27), 26948–26955 (2011).
[CrossRef] [PubMed]

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

White, K. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(5), 056611 (2006).
[CrossRef] [PubMed]

Ye, W.-M.

Ye, Y.

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

Yu, Z.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

Yuan, X.-D.

Zen, C.

Zhou, C.-Z.

C. Wang, C.-Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19(27), 26948–26955 (2011).
[CrossRef] [PubMed]

Opt. Express (1)

C. Wang, C.-Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19(27), 26948–26955 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

Z. He, S. Peng, Y. Ye, Z. Dai, C. Qiu, M. Ke, and Z. Liu, “Asymmetric acoustic gratings,” Appl. Phys. Lett.98(8), 083505 (2011).
[CrossRef]

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin film nonlinear optical diode,” Appl. Phys. Lett.66(18), 2324–2326 (1995).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

J. Appl. Phys. (2)

F. Biancalana, “All-optical diode action with quasiperiodic photonic crystals,” J. Appl. Phys.104(9), 093113 (2008).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys.76(4), 2023–2026 (1994).
[CrossRef]

Nat. Photonics (1)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Nature (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Rev. A (1)

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A78(2), 023804 (2008).
[CrossRef]

Phys. Rev. B (1)

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80, 155117 (2009).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(5), 056611 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Schematic presentation of asymmetric light propagation mechanism occurring in chirped photonic crystal waveguide.

Fig. 2
Fig. 2

(a) Schematic of a regular photonic crystal waveguide. (b) The dispersion diagram of regular photonic crystal waveguide. (c) Incident light propagation from left-to-right in the waveguide structure.

Fig. 3
Fig. 3

(a) A photonic crystal waveguide that has linearly increased the distance separation between each neighboring column of rods. (b) The spectral content of the contrast ratio. The blue rectangle designates the selected frequency value. (c) Time-domain snapshot of propagation of light from left to right. (d) The transverse field profile across the end face of the structure. (e) The transverse field profile across the front side of the structure. (f) Time-domain snapshot of light propagation from right to left.

Fig. 4
Fig. 4

(a) Another chirped photonic crystal waveguide is shown. The distance between each neighboring column of rods increased in a parabolic pattern. (b) The spectral content of the contrast ratio. The blue rectangle designates the selected frequency value. (c) Time-domain snapshot of propagation of light from left to right. (d) The transverse field profile across the end face of the structure. (e) The transverse field profile across the front side of the structure. (f) Time-domain snapshot of propagation of light from right to left.

Fig. 5
Fig. 5

Schematic representation of a chirped photonic crystal waveguide that enables light’s asymmetric propagation is provided. (a) and (b) correspond to left-to-right and right-to-left propagation, respectively. Yellow boxes in (a) show unit cell variations along the propagation direction.

Fig. 6
Fig. 6

The detailed presentations of the intensity distributions in linearly chirped waveguide configuration for the forward and backward light propagations are shown in (a) and (b), respectively.

Fig. 7
Fig. 7

The simulated intensity distributions are provided at the outside of the structure for microwave region. (a) The transverse field profile across the end face of the linearly chirped waveguide. (b) The transverse field profile across the front face of the same structure. (c) The transverse field profile across the end face of the parabolically chirped waveguide. (d) The transverse field profile across the front face of the same structure.

Fig. 8
Fig. 8

The measured intensity distributions are provided at the outside of the structure. (a) The transverse field profile across the end face of the linearly chirped waveguide. (b) The transverse field profile across the front face of the same structure. (c) The transverse field profile across the end face of the parabolically chirped waveguide. (d) The transverse field profile across the front face of the same structure.

Fig. 9
Fig. 9

Non-normalized transmission spectra for (a) linearly chirped photonic crystals and (b) quadratically chirped photonic crystals are shown for a refractive index of 3.46.

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