## Experimental demonstration of light bending at optical frequencies using a non-homogenizable graded photonic crystal |

Optics Express, Vol. 20, Issue 4, pp. 4776-4783 (2012)

http://dx.doi.org/10.1364/OE.20.004776

Acrobat PDF (2007 KB)

### Abstract

Experimental results on light bending in a non-homogenizable graded photonic crystal operating at optical wavelengths are presented in this paper. A square lattice silicon on insulator photonic crystal made of a two-dimensional chirp of the air-hole filling factor is exploited to produce the bending effect in a near bandgap frequency range. The sensitivity of light paths to wavelength tuning is also exploited to show demultiplexing capability with low insertion loss (<2dB) and low crosstalk (~-20dB). This experimental demonstration opens opportunities for light manipulation using a generalized two-dimensional chirp of photonic crystal lattice parameters. It also constitutes an alternative solution to the use of photonic metamaterials combining dielectric and metallic materials with sub-wavelength unit cells.

© 2012 OSA

## 1. Introduction

1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science **305**(5685), 788–792 (2004). [CrossRef] [PubMed]

5. A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. **33**(1), 43–45 (2008). [CrossRef] [PubMed]

10. W. Ding, D. Tang, Y. Liu, L. Chen, and X. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. **96**(4), 041102 (2010). [CrossRef]

11. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. **8**(7), 568–571 (2009). [CrossRef] [PubMed]

12. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics **3**(8), 461–463 (2009). [CrossRef]

13. P. S. J. Russel, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt. **38**(8), 1599–1619 (1991). [CrossRef]

16. K. Ren and X. Ren, “Controlling light transport by using a graded photonic crystal,” Appl. Opt. **50**(15), 2152–2157 (2011). [CrossRef] [PubMed]

17. E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. **92**(13), 133501 (2008). [CrossRef]

18. E. Cassan, K. V. Do, C. Caer, D. Marris-Morini, and L. Vivien, “Short-wavelength light propagation in graded photonic crystals,” J. Lightwave Technol. **29**(13), 1937–1943 (2011). [CrossRef]

19. areV. K. Do, X. L. Roux, C. Caer, D. Marris-Morini, N. Izard, L. Vivien, and E. Cassan, “Wavelength demultiplexer based on a two-dimensional graded photonic crystal,” IEEE Photon. Technol. Lett. **23**(15), 1094–1096 (2011). [CrossRef]

## 2. Device design and fabrication

*a*= 390nm. The variation of hole radius in x-y coordinate is governed by

*r*/

*a*(

*ρ*) = 0.35.exp(-

*ρ*

^{2}/2

*R*

^{2}), where

*ρ*= √(

*x*

^{2}+

*y*

^{2}) is distance from the bottom left corner of GPhC area, as shown in Fig. 1(a) ), with

*R*= 62µm. To minimize the light incident angle around zero, the PhC lattice was also rotated by 45°.

*R*distance from the (0,0) point.

*a*(2.6µm) served to excite the electric field in transverse electric (TE) polarization at (

*x*= 0,

*y*=

*R*/2) incident point, which was optimized first using Hamiltonian optics light propagation.

*a*/

*λ*around 0.25, i.e. close to the bandgap between band 1 and band 2 but below the light line to minimize out-off plane losses. In reciprocal space, the exploited iso-frequency curves are centered at the M points of the employed square lattice and not at the Γ point [18

18. E. Cassan, K. V. Do, C. Caer, D. Marris-Morini, and L. Vivien, “Short-wavelength light propagation in graded photonic crystals,” J. Lightwave Technol. **29**(13), 1937–1943 (2011). [CrossRef]

*r*= 85nm (

*r*/

*a*= 0.219) to the hole radius value at the current point along the input interface of the GPhC area (varying itself from 136 to 85nm along the (

*x*= 0,

*y*>0) and (

*x*>0,

*y*= 0) interfaces according to the

*r*/

*a*(

*ρ*) = 0.35.exp(-

*ρ*

^{2}/2

*R*

^{2}) law). By itself, the reduction of r is responsible for the decrease of the band-edge frequency of the PhC band 1, leading to strong reflection in the considered normalized frequency range around 0.25. A linear increase of the lattice period was thus simultaneously considered to maintain the normalized frequency

*a*/

*λ*below the band-edge limit. In practice, a linear increase of

*a*from 305nm to 390nm at the input of the GPhC area was considered. As a whole, the designed input and output tapers are thus made of a two-dimensional chirp of the air hole radius and a one-dimensional chirp of the lattice period.

*a*/

*λ*, and the overall power transmission spectra of the two structures with and without the input/output tapers as function of light wavelength, respectively. As it can be seen in Fig. 2(a), there exists a local photonic bandgap of Δ

*ω*≈0.02 between band 1 (

*ω*≈0.26) and band 2 (

_{1}*ω*≈0.28) at the point M (edge corner of the first Brillouin zone). Since light is injected into the studied structure along the Γ-M direction, it is totally reflected for frequencies inside the photonic bandgap. We can see in Fig. 2(a) and 2(b) that a good agreement is obtained between the dispersion diagram and the calculated transmission that drops in the frequency range 0.26<

_{2}*a*/

*λ*<0.28. Considering Fig. 2(c), we see that the wavelength range for which light is bended by 90° is roughly extended from 1510nm to 1690nm (i.e

*ω*≈0.23-0.257 in Fig. 2(b)). Wavelengths shorter than

*λ*= 1490nm (

*ω*>0.26) lie in the local photonic bandgap between the first band and the second band of the photonic crystal, which explains the drop in transmission. Transmission after the 90°-turn also drops for wavelengths above λ = 1700nm because we then enter the ‘long-wavelength’ homogenization (or sub-wavelength) approximation of the periodic medium, and light then propagates across the corrugated graded medium mostly in the straight direction. The maximum of 90°-turn transmission power is about −2.5dB for the GPhC configuration without taper (red curve), while it is around −0.5dB when I/O tapers are introduced (blue curve).

_{6}/O

_{2}anisotropic etching process. Our optimized process carefully took into account the proximity effects in the e-beam lithography step.

18. E. Cassan, K. V. Do, C. Caer, D. Marris-Morini, and L. Vivien, “Short-wavelength light propagation in graded photonic crystals,” J. Lightwave Technol. **29**(13), 1937–1943 (2011). [CrossRef]

*λ*= 1550nm. Such configurations were also considered here. Figure 4 shows a fabricated structure with two output strip waveguides adjusted at proper positions using FDTD simulation to collect transmission power of two expected wavelength channels.

## 3. Characterization

### 3.1. Light bending effect

### 3.2. Two-channel wavelength demultiplexer

19. areV. K. Do, X. L. Roux, C. Caer, D. Marris-Morini, N. Izard, L. Vivien, and E. Cassan, “Wavelength demultiplexer based on a two-dimensional graded photonic crystal,” IEEE Photon. Technol. Lett. **23**(15), 1094–1096 (2011). [CrossRef]

## 4. Conclusion

5. A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. **33**(1), 43–45 (2008). [CrossRef] [PubMed]

8. Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. **105**(10), 104913 (2009). [CrossRef]

25. B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express **18**(19), 20321–20333 (2010). [CrossRef] [PubMed]

## References and links

1. | D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science |

2. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science |

3. | N. Engheta and R. W. Ziolkowski, |

4. | Z. Saïd, A. Sihvola, and A. P. Vinogradov, |

5. | A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. |

6. | M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. |

7. | M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express |

8. | Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. |

9. | N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express |

10. | W. Ding, D. Tang, Y. Liu, L. Chen, and X. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. |

11. | J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. |

12. | L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics |

13. | P. S. J. Russel, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt. |

14. | P. S. J. Russel and T. A. Birks, “Hamiltonian optics of nonuniform photonic crystals,” J. Lightwave Technol. |

15. | E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B |

16. | K. Ren and X. Ren, “Controlling light transport by using a graded photonic crystal,” Appl. Opt. |

17. | E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. |

18. | E. Cassan, K. V. Do, C. Caer, D. Marris-Morini, and L. Vivien, “Short-wavelength light propagation in graded photonic crystals,” J. Lightwave Technol. |

19. | areV. K. Do, X. L. Roux, C. Caer, D. Marris-Morini, N. Izard, L. Vivien, and E. Cassan, “Wavelength demultiplexer based on a two-dimensional graded photonic crystal,” IEEE Photon. Technol. Lett. |

20. | Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

21. | E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. |

22. | F. Grillot, L. Viv, S. Laval, and E. Cassan, “Propagation loss in single-mode ultrasmall square silicon-on-insulator optical waveguides,” J. Lightwave Technol. |

23. | E. Cassan, S. Laval, S. Lardenois, and A. Koster, “On-chip optical interconnects with compact and low-loss light distribution in silicon-on-insulator rib waveguides,” IEEE Sel. Top. Quantum Electron. |

24. | L. Vivien, S. Lardenois, D. Pascal, S. Laval, E. Cassan, J. L. Cercus, A. Koster, J. M. Fédéli, and M. Heitzmann, “Experimental demonstration of a low-loss optical H-tree distribution using silicon-on-insulator microwaveguides,” Appl. Phys. Lett. |

25. | B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(130.5296) Integrated optics : Photonic crystal waveguides

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: November 23, 2011

Revised Manuscript: January 15, 2012

Manuscript Accepted: February 6, 2012

Published: February 10, 2012

**Citation**

Khanh-Van Do, Xavier Le Roux, Delphine Marris-Morini, Laurent Vivien, and Eric Cassan, "Experimental demonstration of light bending at optical frequencies using a non-homogenizable graded photonic crystal," Opt. Express **20**, 4776-4783 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4776

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### References

- D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (John Wiley and Sons, 2006), pp. 211–221.
- Z. Saïd, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modelling, Applications (Springer-Verlag, 2008), pp. 3–10, Chap. 3, p. 106.
- A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett.33(1), 43–45 (2008). [CrossRef] [PubMed]
- M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008). [CrossRef] [PubMed]
- M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express16(15), 11555–11567 (2008). [CrossRef] [PubMed]
- Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys.105(10), 104913 (2009). [CrossRef]
- N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express17(17), 14872–14879 (2009). [CrossRef] [PubMed]
- W. Ding, D. Tang, Y. Liu, L. Chen, and X. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett.96(4), 041102 (2010). [CrossRef]
- J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009). [CrossRef] [PubMed]
- L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009). [CrossRef]
- P. S. J. Russel, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt.38(8), 1599–1619 (1991). [CrossRef]
- P. S. J. Russel and T. A. Birks, “Hamiltonian optics of nonuniform photonic crystals,” J. Lightwave Technol.17(11), 1982–1988 (1999). [CrossRef]
- E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B73(23), 235119 (2006). [CrossRef]
- K. Ren and X. Ren, “Controlling light transport by using a graded photonic crystal,” Appl. Opt.50(15), 2152–2157 (2011). [CrossRef] [PubMed]
- E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett.92(13), 133501 (2008). [CrossRef]
- E. Cassan, K. V. Do, C. Caer, D. Marris-Morini, and L. Vivien, “Short-wavelength light propagation in graded photonic crystals,” J. Lightwave Technol.29(13), 1937–1943 (2011). [CrossRef]
- areV. K. Do, X. L. Roux, C. Caer, D. Marris-Morini, N. Izard, L. Vivien, and E. Cassan, “Wavelength demultiplexer based on a two-dimensional graded photonic crystal,” IEEE Photon. Technol. Lett.23(15), 1094–1096 (2011). [CrossRef]
- Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(3), 036612 (2004). [CrossRef] [PubMed]
- E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett.30(17), 2278–2280 (2005). [CrossRef] [PubMed]
- F. Grillot, L. Viv, S. Laval, and E. Cassan, “Propagation loss in single-mode ultrasmall square silicon-on-insulator optical waveguides,” J. Lightwave Technol.24(2), 891–896 (2006). [CrossRef]
- E. Cassan, S. Laval, S. Lardenois, and A. Koster, “On-chip optical interconnects with compact and low-loss light distribution in silicon-on-insulator rib waveguides,” IEEE Sel. Top. Quantum Electron.9(2), 460–464 (2003).
- L. Vivien, S. Lardenois, D. Pascal, S. Laval, E. Cassan, J. L. Cercus, A. Koster, J. M. Fédéli, and M. Heitzmann, “Experimental demonstration of a low-loss optical H-tree distribution using silicon-on-insulator microwaveguides,” Appl. Phys. Lett.85(5), 701–703 (2004). [CrossRef]
- B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express18(19), 20321–20333 (2010). [CrossRef] [PubMed]

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