## Broadband one-dimensional photonic crystal wave plate containing single-negative materials |

Optics Express, Vol. 18, Issue 19, pp. 19920-19929 (2010)

http://dx.doi.org/10.1364/OE.18.019920

Acrobat PDF (1840 KB)

### Abstract

The properties of the phase shift of wave reflected from one-dimensional photonic crystals consisting of periodic layers of single-negative (permittivity- or permeability-negative) materials are demonstrated. As the incident angle increases, the reflection phase shift of TE wave decreases, while that of TM wave increases. The phase shifts of both polarized waves vary smoothly as the frequency changes across the photonic crystal stop band. Consequently, the difference between the phase shift of TE and that of TM wave could remain constant in a rather wide frequency range inside the stop band. These properties are useful to design wave plate or retarder which can be used in wide spectral band. In addition, a broadband photonic crystal quarter-wave plate is proposed.

© 2010 OSA

## 1. Introduction

*ε*) and permeability (

*μ*) is negative, has been realized [15

15. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. **76**(25), 4773–4776 (1996). [CrossRef] [PubMed]

16. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. **47**(11), 2075–2084 (1999). [CrossRef]

*ε*but positive

*μ*and the mu-negative (MNG) media with negative

*μ*but positive

*ε*. It was shown that stacking alternating layers of ENG and MNG media leads to a type of PBG corresponding to zero effective phase (denoted as zero-

*φ*

_{eff}gap) [17

17. L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B **70**(24), 245102 (2004). [CrossRef]

*φ*

_{eff}gap [18

18. Y. H. Chen, “Defect modes merging in one-dimensional photonic crystals with multiple single-negative material defects,” Appl. Phys. Lett. **92**(1), 011925 (2008). [CrossRef]

19. Y. H. Chen, “Omnidirectional and independently tunable defect modes in fractal photonic crystals containing single-negative materials,” Appl. Phys. B **95**(4), 757–761 (2009). [CrossRef]

*φ*

_{eff}gap and the tunneling modes may be useful for designing omnidirectional filters. However, the properties of the phase shifts of the incident waves in the zero-

*φ*

_{eff}gap have not been reported yet.

*φ*

_{eff}gap. Based on these properties, we design a broadband quarter-wave plate.

## 2. The model and numerical methods

*r*) of the monochromatic plane wave can be obtained as [20

20. W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(1 Pt 2), 016601 (2004). [CrossRef] [PubMed]

*x*(

_{nm}*n*,

*m*= 1,2) are the matrix elements of

*Χ*(

_{s}*ω*). The complex reflection coefficient can be denoted as

*Ф*is the phase shift of TE or TM wave reflected from the PC. The reflectance

*R*of the PC can then be calculated from the reflection coefficient.

21. D. W. Yeh and C. J. Wu, “Analysis of photonic band structure in a one-dimensional photonic crystal containing single-negative materials,” Opt. Express **17**(19), 16666–16680 (2009). [CrossRef] [PubMed]

*β*is the

_{z}*z*component of Bloch wave vector. The passband can be found when the solution for

*β*is real, whereas the forbidden band will be presented if

_{z}*β*is found to be complex valued.

_{z}## 3. Numerical results and discussion

### 3.1 Reflection phase properties of zero-φ_{eff} gap with Drude model dispersion

15. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. **76**(25), 4773–4776 (1996). [CrossRef] [PubMed]

16. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. **47**(11), 2075–2084 (1999). [CrossRef]

22. A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. **51**(10), 2558–2571 (2003). [CrossRef]

25. A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. **92**(10), 5930–5935 (2002). [CrossRef]

22. A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. **51**(10), 2558–2571 (2003). [CrossRef]

23. T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. **46**(5), 476–481 (2005). [CrossRef]

25. A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. **92**(10), 5930–5935 (2002). [CrossRef]

17. L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B **70**(24), 245102 (2004). [CrossRef]

21. D. W. Yeh and C. J. Wu, “Analysis of photonic band structure in a one-dimensional photonic crystal containing single-negative materials,” Opt. Express **17**(19), 16666–16680 (2009). [CrossRef] [PubMed]

*ω*and

_{ep}*ω*are the electronic plasma frequency and the magnetic plasma frequency, respectively.

_{mp}*γ*and

_{e}*γ*denote the respective electric and magnetic damping factors that contribute to the absorption and losses. The angular frequency

_{m}*ω*is in units of gigahertz. In our calculation, the material parameters are selected as

*ε*=

_{a}*μ*= 1,

_{b}*μ*=

_{a}*ε*= 3,

_{b}*ω*=

_{ep}*ω*= 10 GHz, and

_{mp}*γ*=

_{e}*γ*= 1 × 10

_{m}^{6}Hz.

*AB*)

*with*

^{s}*d*= 16 mm,

_{A}*d*= 8 mm. In Fig. 2 , we plot the band structure for the SNG PC. A zero-

_{B}*φ*

_{eff}gap [17

17. L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B **70**(24), 245102 (2004). [CrossRef]

*φ*

_{eff}gap are insensitive to the incident angle and the light polarizations.

*R*and the reflection phase shift

*Ф*are calculated and shown in Fig. 3 . The frequency range of the zero-

*φ*

_{eff}gap in Fig. 3(a) is in accordance with the result in Fig. 2. From Fig. 3(b), we see that the phase shift upon reflection as a function of frequency changes smoothly inside the PBG, while that changes sharply outside it. The dependence of the reflection phase shift

*Ф*on the incident angle is calculated, as shown in Fig. 3(c) – 3(e). It can be seen that, as the incident angle increases, the reflection phase shift of TE wave (

*Ф*

_{TE}) decreases, while that of TM wave (

*Ф*

_{TM}) increases. Moreover, the curves, which represent the dependence of the reflection phase shift on frequency, remain fairly smooth inside the PBG at oblique incidence. We also calculate the difference between the phase shift of TE and that of TM reflected wave, as shown in Fig. 3(c) – 3(e). It is seen that Δ

*Ф*( =

*Ф*

_{TM}

*- Ф*

_{TE}) remains almost constant in a rather wide frequency range inside the zero-

*φ*

_{eff}gap when the incident angle

*θ*is fixed. On the other hand, as the incident angle increases, Δ

*Ф*increases gradually. Such variation of Δ

*Ф*in Fig. 3 is quite different from the case for Δ

*Ф*inside a Bragg gap. In general, Δ

*Ф*of the reflected wave inside the Bragg gap of a conventional 1D PC is sensitive to the frequency.

*ε*

_{eff}and the effective permeability

*μ*

_{eff}of the periodic ENG-MNG layered structures can be written as [26]

*ε*

_{eff}and

*μ*

_{eff}depend on the incident angle

*θ*. The frequency dependence of the values of

*ε*

_{eff}and

*μ*

_{eff}of the considered ENG-MNG structure are plotted in Fig. 4 for both TE and TM waves at incident angle

*θ*= 60°. It is clear shown from Fig. 4 (a)-(c) that the zero-φ

_{eff}gap for TE and TM waves exist in the frequencies where

*ε*

_{eff}of the PC structure is negative and

*μ*

_{eff}is positive.

*x*depend on the effective refractive index (

_{nm}*Ф*

_{eff}has little change in frequencies around 5.0 GHz. Such theoretical result agrees with the numerical simulation in Fig. 3(e). For a given incident angle, the reflection coefficient and the reflection phase of the effective medium depend on the values of

*ε*

_{eff}and

*μ*

_{eff}, which deduced from the parameters in Eqs. (4) and (5). So the phenomena that the reflection phase difference stays constant originate from the frequency dispersion of the permittivity and the permeability of the SNG materials. To further confirm our theoretical results, Fig. 5 shows the angle dependence of the reflection phase corresponding to the central frequency (ω = 5.00 GHz) of the zero-

*φ*

_{eff}gap calculated from numerical simulation and effective medium theoretical calculation, respectively. Clearly, the effective medium theory agrees well with the numerical simulation.

*Ф*

_{TE},

*Ф*

_{TM}, and Δ

*Ф*as functions of frequency at incident angle

*θ*= 60° in PC structure (

*AB*)

^{8}with

*d*= 16 mm and different

_{A}*d*. In our calculation, we found that the bigger the difference between

_{B}*d*and

_{A}*d*is, the wider the zero-

_{B}*φ*

_{eff}gap will be. Such property of the forbidden gap is in accordance with the variation of the reflection phase shift in Fig. 6. It is seen from Fig. 3 that Δ

*Ф*remains invariant in a broader frequency range when the stop band is wider. Moreover, it is found that the changes of the bandwidth of the zero-

*φ*

_{eff}gap would almost not influence the value of Δ

*Ф*at frequencies in the middle of the forbidden gap. For example, Δ

*Ф*remains 0.43

*π*in the middle of the stop band (around 5.00 GHz) with the changing of the bandwidth of the forbidden gap, as shown in Fig. 6.

*π*/2, meaning that the 1D PC can serve as a quarter-wave plate. More importantly, the reflection phase difference can remain constant in a wide frequency range due to the smooth changes of reflection phase shift within the forbidden gap.

*d*= 16 mm,

_{A}*d*= 4 mm and

_{B}*θ*= 65°. The corresponding reflectance as a function of frequency is shown in Fig. 7(a) . It can be seen that the reflectance of TE and TM waves is greater than 0.99 in common reflection band from 3.05 to 6.99 GHz. In Fig. 4(b), the reflection phase shifts

*Ф*

_{TE}(dot line),

*Ф*

_{TM}(dash line), and Δ

*Ф*=

*Ф*

_{TM}

*- Ф*

_{TE}(dash-dot line) are shown, respectively. According to the accuracy of the usual quarter-wave plate, such as 0.005

*π*for the phase precision, Δ

*Ф*is

*π*/2 in the frequency range 4.58–6.03 GHz, as shown in Fig. 4(b), the relative spectral bandwidth Δ

*ω*/

*ω*is over 27%. In principle, we can achieve other phase difference between TE and TM waves in common reflection band by changing the parameters of the PC.

*Ф*for TE and TM waves are different. However, the phase difference Δ

*Ф*between TE and TM waves varies obviously as the frequency of the incident wave changes. So the wave plates based on the metal slabs cannot work efficiently in a broad frequency range. On the other hand, the wave plates based on two-dimensional (2D) metallic photonic crystals, which operate in microwave region [10

10. D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. **82**(7), 1036–1038 (2003). [CrossRef]

11. F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. **82**(16), 2568–2570 (2003). [CrossRef]

### 3.2 Reflection phase properties of zero-φ_{eff} gap with Lorentz model dispersion

16. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. **47**(11), 2075–2084 (1999). [CrossRef]

27. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science **292**(5514), 77–79 (2001). [CrossRef] [PubMed]

30. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. **88**(4), 041109 (2006). [CrossRef]

**47**(11), 2075–2084 (1999). [CrossRef]

27. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science **292**(5514), 77–79 (2001). [CrossRef] [PubMed]

30. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. **88**(4), 041109 (2006). [CrossRef]

*ω*and

_{er}*ω*are respectively the electronic resonant frequency and the magnetic resonant frequency, and

_{mr}*F*

_{1}and

*F*

_{2}are the structural factors. In the following calculation, we take

*F*

_{1}= 0.7,

*F*

_{2}= 0.56,

*ω*=

_{er}*ω*= 4 GHz, and

_{mr}*γ*=

_{e}*γ*= 1 × 10

_{m}^{6}Hz. Figure 8 displays the associated photonic bands of structure (

*AB*)

*with*

^{s}*d*= 4 mm and

_{A}*d*= 20 mm in the frequency range where the corresponding zero-

_{B}*φ*

_{eff}gap is located. As shown in Fig. 8, the zero-

*φ*

_{eff}gap is still insensitive to the incident angle and polarizations although the gap for TM wave is a bit wider at larger incident angle.

*Ф*,

_{TE}*Ф*, and Δ

_{TM}*Ф*on the incident angle in structure (

*AB*)

^{12}are calculated, as shown in Fig. 9 . We can see that

*Ф*and

_{TE}*Ф*change smoothly as the frequency varies across the zero-

_{TM}*φ*

_{eff}gap, and Δ

*Ф*remains almost invariant in the central region of the gap. The value of Δ

*Ф*can be adjusted by varying the incident angle. We also proposed a broad spectral bandwidth quarter-wave plate based on 1D PC containing SNG materials with parameters given by Eqs. (8) and (9), as shown in Fig. 10 . It can be seen from Fig. 10 that Δ

*Ф*is −0.5

*π*± 0.005

*π*and the reflectance of both TE and TM waves is greater than 0.99 in the frequency range 4.83–5.15 GHz.

22. A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. **51**(10), 2558–2571 (2003). [CrossRef]

24. L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **74**(5 Pt 2), 056615 (2006). [CrossRef]

*ε*or/and negative permeability

*μ*have been realized in Terahertz frequency range from split-ring resonators [31

31. J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. **96**(2), 021111 (2010). [CrossRef]

32. O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express **16**(9), 6736–6744 (2008). [CrossRef] [PubMed]

33. J. F. Dong, J. F. Zhou, T. Koschny, and C. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express **17**(16), 14172–14179 (2009). [CrossRef] [PubMed]

*ε*and

*μ*agrees well with the Drude model or Lorentz model. Furthermore, it was demonstrated that nanoscale circuit elements can be obtained using plasmonic and nonplasmonic nanoparticles [34

34. N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. **95**(9), 095504 (2005). [CrossRef] [PubMed]

36. A. Alù and N. Engheta, “All optical metamaterial circuit board at the nanoscale,” Phys. Rev. Lett. **103**(14), 143902 (2009). [CrossRef] [PubMed]

23. T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. **46**(5), 476–481 (2005). [CrossRef]

24. L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **74**(5 Pt 2), 056615 (2006). [CrossRef]

## 4. Conclusion

*φ*

_{eff}gap of the 1D PCs stacking with ENG and MNG materials. The phase difference between TE and TM reflected wave remains invariant in a wide frequency region. According to such property, broadband 1D PC wave plate and retarder can be conveniently designed.

## Acknowledgements

## References and links

1. | E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. |

2. | S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. |

3. | J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science |

4. | K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. |

5. | A. Z. Genack and N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. |

6. | S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. |

7. | S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature |

8. | D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science |

9. | S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. |

10. | D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. |

11. | F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. |

12. | E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. |

13. | Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. |

14. | W. F. Zhang, J. H. Liu, W. P. Huang, and W. Zhao, “Self-collimating photonic-crystal wave plates,” Opt. Lett. |

15. | J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. |

16. | J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. |

17. | L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B |

18. | Y. H. Chen, “Defect modes merging in one-dimensional photonic crystals with multiple single-negative material defects,” Appl. Phys. Lett. |

19. | Y. H. Chen, “Omnidirectional and independently tunable defect modes in fractal photonic crystals containing single-negative materials,” Appl. Phys. B |

20. | W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

21. | D. W. Yeh and C. J. Wu, “Analysis of photonic band structure in a one-dimensional photonic crystal containing single-negative materials,” Opt. Express |

22. | A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. |

23. | T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. |

24. | L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

25. | A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. |

26. | A. Lakhtakia and C. M. Krowne, “Restricted equivalence of paired epsilon-negative and mu-negative layers to a negative phase-velocity material (alias left-handed material),” Optik (Stuttg.) |

27. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science |

28. | T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

29. | R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

30. | D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. |

31. | J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. |

32. | O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express |

33. | J. F. Dong, J. F. Zhou, T. Koschny, and C. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express |

34. | N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. |

35. | N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science |

36. | A. Alù and N. Engheta, “All optical metamaterial circuit board at the nanoscale,” Phys. Rev. Lett. |

**OCIS Codes**

(260.2110) Physical optics : Electromagnetic optics

(160.3918) Materials : Metamaterials

(050.5298) Diffraction and gratings : Photonic crystals

**ToC Category:**

Metamaterials

**History**

Original Manuscript: June 18, 2010

Revised Manuscript: August 16, 2010

Manuscript Accepted: August 23, 2010

Published: September 3, 2010

**Citation**

Yihang Chen, "Broadband one-dimensional photonic crystal wave plate containing single-negative materials," Opt. Express **18**, 19920-19929 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19920

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### References

- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]
- S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]
- J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science 282(5393), 1476–1478 (1998). [CrossRef] [PubMed]
- K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990). [CrossRef] [PubMed]
- A. Z. Genack and N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66(16), 2064–2067 (1991). [CrossRef] [PubMed]
- S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997). [CrossRef]
- S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000). [CrossRef] [PubMed]
- D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003). [CrossRef] [PubMed]
- S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003). [CrossRef]
- D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003). [CrossRef]
- F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. 82(16), 2568–2570 (2003). [CrossRef]
- E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005). [CrossRef]
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