## Giant resonance absorption in ultra-thin metamaterial periodic structures |

Optics Express, Vol. 20, Issue 4, pp. 3693-3702 (2012)

http://dx.doi.org/10.1364/OE.20.003693

Acrobat PDF (1517 KB)

### Abstract

We study the interaction of an incident plane wave with a metamaterial periodic structure consisting of alternating layers of positive and negative refractive index with average zero refractive index. We show that the existence of very narrow resonance peaks for which giant absorption - 50% at layer thickness of 1% of the incident wavelength - is exhibited. Maximum absorption is obtained at a specific layer thickness satisfying the critical coupling condition. This phenomenon is explained by the Rayleigh anomaly and by the excitation of Fabry Perot modes in the periodic layer. In addition, we investigate the modes supported by the structures for several limiting cases, and show that zero phase accumulation in the periodic metamaterial is obtained at resonance.

© 2012 OSA

## 1. Introduction

2. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of *ε* and *μ*,” Sov. Phys. Usp. **10**, 509 (1968). [CrossRef]

3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. **85**, 3966 (2000). [CrossRef] [PubMed]

4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**, 4184–4187 (2000). [CrossRef] [PubMed]

5. S. Nefedov and S. A. Tretyakov, “Photonic band gap structure containing metamaterial with negative permittivity and permeability,” Phys. Rev. E **66**, 036611 (2002). [CrossRef]

6. J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. **90**(8), 083901 (2003). [CrossRef] [PubMed]

7. L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B **67**, 235103 (2003). [CrossRef]

8. A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. **51**, 2558–2571 (2003). [CrossRef]

9. D. R. Fredkin and A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett. **81**, 1753–1755 (2002). [CrossRef]

*ɛ*and negative

*μ*materials (ENG and MNG) can behave effectively as structures with alternating DPS and DNG layers. Experimental measurements of the zero refractive index band gap were also reported [10

10. Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, “Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials,” Opt. Express **14**, 2220–2227 (2006). [CrossRef] [PubMed]

11. S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. **102**, 203905 (2009). [CrossRef] [PubMed]

12. Y. Jin, S. Xiao, N. A. Mortensen, and S. He, “Arbitrarily thin metamaterial structure for perfect absorption and giant magnification,” Opt. Express **19**, 11114–11119 (2011). [CrossRef] [PubMed]

7. L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B **67**, 235103 (2003). [CrossRef]

13. L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Opt. Express **11**, 1283–1290 (2003). [CrossRef] [PubMed]

*ω*

_{0}, for alternating DPS-DNG structures the Bragg reflection dominates, resulting in very narrow transmission peaks. Hereby, we use the Rigorous Coupled Wave Analysis (RCWA) method [14

14. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A **12**, 1068–1076 (1995). [CrossRef]

17. T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Derivation of plasmonic resonances in the Fourier modal method with adaptive spatial resolution and matched coordinates,” J. Opt. Soc. Am. A **28**, 238–244 (2011). [CrossRef]

## 2. Modes of a DPS-DNG structure with infinite thickness

*n̄*, i.e. a structure which satisfies

*h*= ∞. Using the TMM, the dispersion relation for TM (

*H*) modes can be written as (with nearly the same notation as used in Ref. [7

_{y}7. L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B **67**, 235103 (2003). [CrossRef]

*n*takes a positive sign for DPS media and a negative sign for DNG media),

_{i}*ɛ*=

*ɛ*

_{2}/

*ɛ*

_{1},

*n*=

*n*

_{2}/

*n*

_{1},

*K*is the Bloch wavevector. As shown in Fig. 1,

_{B}*ɛ*

_{1,2}and

*μ*

_{1,2}are the permittivity and permeability of the DPS and DNG layers, respectively. It has been shown, that for an infinitely thick (

*h*→ ∞) periodic stack of layers with average refractive index of

*n̄*= 0, a band gap is formed resulting in 100% reflection from the stack for plane waves propagating in the x-direction, except for discrete frequencies which satisfy the Fabry Perot condition (

*k*

_{x}_{1}

*L*

_{1}=

*mπ, k*

_{x}_{2}

*L*

_{2}= −

*pπ*where m,p are nonzero integers) for which the periodic stack has full transmission. We consider this structure, but for transverse illumination (light propagating perpendicular to the periodicity of the structure, namely in z direction of Fig. 1) in contrast to the configurations discussed in the various references presented in the introduction. The normally incident plane-wave has a vacuum wavelength

*λ*

_{0}and a transverse magnetic (TM) polarization. The modes of the structure are studied by observing the diffraction of the incident plane wave from the periodic structure which is semi-infinite in the z direction (

*h*= ∞). The incidence medium (labeled as region I in Fig. 1(a)) and the outgoing medium (region III) are assumed to be vacuum, while the grating (region II) is defined by the parameters

*ɛ*

_{1}= 1,

*ɛ*

_{2}= −1,

*μ*

_{1}= 1,

*μ*

_{2}= −1, with

*n̄*= 0 condition. The effect of loss will be included starting from the next paragraph, and dispersion will also be considered towards the last section of this manuscript. The zeroth diffraction order in region II has

*k*

*= 0, and*

_{x}*k*

*= ±*

_{z}*k*

_{0}yielding no power flow (zero Poynting vector

*P*

*) as a result of the anti-parallel and equal amplitude Poynting vectors at the two media i.e.*

_{z}*P*

_{z}_{1}= −

*P*

_{z}_{2}where

*k*

*= ±*

_{x}*mK*, where K is the grating vector given by

*K*= 2

*π*/

*L*. In the specific configuration we study, the periodicity is equal to the vacuum wavelength, i.e.

*K*=

*k*

_{0}, thus all the diffraction orders satisfy the Fabry-Perot condition along the x axis and thus are propagating along the structure interface (x directed surface modes), with either zero

*k*

*for the ±1 diffraction order, or purely imaginary*

_{z}*k*

*for higher diffraction orders). It therefore follows that the grating will not allow any power propagation in the z direction.*

_{z}## 3. Resonant modes of a DPS-DNG slab with finite thickness

*L*=

*λ*

_{0}. As found in the previous section, all eigenmodes are complex valued, resulting in a decay of the electromagnetic field in the positive Z direction. Therefore, for a structure with semi infinite thickness no transmission is expected and the structure performs as a good mirror, reflecting the incident power with some losses. On the other hand, for a structure, thinner than the effective “skin depth” (of the order of the wavelength) of the gratings, one would expect some tunneling from region I to region III such that significant transmission is obtained. However while this prediction is true for most wavelengths, it is not the case for wavelengths in the vicinity of

*λ*

_{0}, denoted as the resonance. The above expectation is supported by Fig. 3 which presents the transmission, reflection, and absorption as a function of the normalized gratings thickness and the normalized wavelength. The obtained results indicate a steep increase in the absorption followed by a steep drop in transmission around resonance. Therefore, the structure may be considered as a “super absorber” for the resonance wavelength.

20. A. Hessel and A. A. Oliner, “A new theory of Wood anomalies on optical gratings,” Appl. Opt. **4**, 1275–1297 (1965). [CrossRef]

23. C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red-shifts and red tails in hole array transmission spectra,” Opt. Commun. **225**, 331–336 (2003). [CrossRef]

*ε*= 1 and

*μ*= 1 in both the incident and outgoing regions, the Rayleigh wavelength is equal to the period, i.e.

*λ*

*=*

_{R}*L*. A guided mode resonance is the consequence of the matching of the diffracted orders to a leaky mode which is propagating along the x axis in region II. To gain further understanding of the physics behind the obtained transmission/absorption/reflection maps we plot (Fig. 4) the field distribution within the metamaterial structure and its vicinity. We consider a thin periodic metamaterial with thickness of h=0.01L. First, it can be seen from Figs. 4(a) and 4(b) that in regions I and III the diffracted wave occupies precisely a single unit cell and therefore can be identified as the Fabry Perot mode, discussed in Section 2, which is consistent with the choice of

*L*≈

*λ*. The resonance in these regions is therefore in agreement with the Rayleigh anomaly. In region II, the excited mode is resonantly guided in the periodic layer as indicated by the fact that the mode periodicity is identical to the gratings period. This is somewhat similar to the very well known case of guided mode resonance [20

20. A. Hessel and A. A. Oliner, “A new theory of Wood anomalies on optical gratings,” Appl. Opt. **4**, 1275–1297 (1965). [CrossRef]

24. A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A **14**, 2985–2993 (1997). [CrossRef]

25. S. M. Norton, T. Erdogan, and G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A **14**, 629–639 (1997). [CrossRef]

*ω*

_{0}× 10

^{−6}for

*h*/

*λ*

_{0}= 0.01) is explained by the sensitivity of the Fabry Perot resonance, where small change in wavelength shifts the domination to the Bragg regime over the Fabry Perot regime, as discussed in Section 2, following references [7

**67**, 235103 (2003). [CrossRef]

13. L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Opt. Express **11**, 1283–1290 (2003). [CrossRef] [PubMed]

26. V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express **17**(24), 21897–21909 (2009). [CrossRef] [PubMed]

*H*

*for a slightly off resonance case (*

_{y}*λ*= 1.001

*L*). From the results (See Fig. 4(c)) it can be seen that the magnetic field no longer builds up coherently in the unit cell.

27. R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter **13**(9), 1811–1818 (2001). [CrossRef]

28. S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. **225**, 233–240 (2003). [CrossRef]

*ε*and

*μ*simultaneously change their sign over a very small region [29

29. N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. **33**, 2350–2352 (2008). [CrossRef] [PubMed]

*n*

*) of light propagation in the z-direction, in the resonant frequencies. The phase index is calculated according to:*

_{ph}*ϕ*is the phase difference between the transmitted and incident waves, and

*ω*= 2

*π*

*c*/

*λ*. In Fig. 5, we have plotted both the absorption and the phase index as function of frequency near resonance for h=0.01L. It can be seen that at the peak of absorption,

*n*

*crosses zero (marked in Fig. 5 by the crossing of the dotted lines), indicating an asymptotically infinite phase velocity at this wavelength. This indicates again that at the absorption peak, the fields are evenly distributed between the DPS and DNG media. Since the phase velocity in both media is opposite, inside the grating there is full cancellation of the phase accumulation in the z direction.*

_{ph}24. A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A **14**, 2985–2993 (1997). [CrossRef]

25. S. M. Norton, T. Erdogan, and G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A **14**, 629–639 (1997). [CrossRef]

31. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. **4**, 321–322 (2000). [CrossRef]

*λ*= (1 + 6 × 10

^{−7})

*L*. It can be seen that for this wavelength, the optimal coupling into the periodic layer is obtained around

*h*/

*L*≈ 0.01. For smaller or larger values of h/L the internal losses in the resonator are detuned from their optimal value due to variations in mode confinement and the absorption in the periodic layers is reduced. Furthermore, it can be seen from Fig. 6(b) that the resonant absorption peak near

*h*/

*L*= 0.01, is a sharp peak in a slowly varying envelope of the absorption. This slowly varying envelope is the consequence of interference of waves inside Region II, similar to interference effects in a conventional lossy homogeneous dielectric slab, and is not the consequence of a transverse resonant mode (e.g. the transverse Fabry – Perot mode discussed above).

33. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A **20**, 569–572 (2003). [CrossRef]

*r*

*and*

_{D}*t*

*are the direct (off resonance) transmission and reflection coefficients respectively,*

_{D}*ω*

_{res}is the resonant frequency,

*τ*is the decay time in the resonator due to coupling and

*γ*is the decay time due to internal losses in the resonator. In Fig. 7, fitting results for h=0.01L are shown, with

*γ*= 1.49 × 10

^{6}

*L*/(2

*π*

*c*) and

*τ*= 1.22 × 10

^{6}

*L*/(2

*π*

*c*). This indeed indicates that the resonator is near critical coupling (

*γ*is of the order of

*τ*) [30,33

33. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A **20**, 569–572 (2003). [CrossRef]

*ε*

_{1}= 1,

*μ*

_{1}= 1,

*γ*

*= 1 × 10*

_{ε}^{−3}

*ω*

*and*

_{p}*γ*

*= 1 × 10*

_{μ}^{−2}

*ω*

*. As can be observed from Fig. 8 the resonance near*

_{p}*λ*

_{0}≈

*L*is very similar to the resonance in the dispersionless case discussed above.

## 4. Conclusions

## Acknowledgments

## References

1. | N. Engheta and R. Ziolkowski, |

2. | V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of |

3. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

4. | D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. |

5. | S. Nefedov and S. A. Tretyakov, “Photonic band gap structure containing metamaterial with negative permittivity and permeability,” Phys. Rev. E |

6. | J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. |

7. | L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B |

8. | A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. |

9. | D. R. Fredkin and A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett. |

10. | Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, “Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials,” Opt. Express |

11. | S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. |

12. | Y. Jin, S. Xiao, N. A. Mortensen, and S. He, “Arbitrarily thin metamaterial structure for perfect absorption and giant magnification,” Opt. Express |

13. | L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Opt. Express |

14. | M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A |

15. | L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A |

16. | P. Lalanne and G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A |

17. | T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Derivation of plasmonic resonances in the Fourier modal method with adaptive spatial resolution and matched coordinates,” J. Opt. Soc. Am. A |

18. | P. Yeh, |

19. | S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B |

20. | A. Hessel and A. A. Oliner, “A new theory of Wood anomalies on optical gratings,” Appl. Opt. |

21. | U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. |

22. | M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B |

23. | C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red-shifts and red tails in hole array transmission spectra,” Opt. Commun. |

24. | A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A |

25. | S. M. Norton, T. Erdogan, and G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A |

26. | V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express |

27. | R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter |

28. | S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. |

29. | N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. |

30. | H. A. Haus, |

31. | A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. |

32. | H. Raether, |

33. | S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A |

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(240.0240) Optics at surfaces : Optics at surfaces

(240.6690) Optics at surfaces : Surface waves

(310.2790) Thin films : Guided waves

**ToC Category:**

Metamaterials

**History**

Original Manuscript: November 21, 2011

Revised Manuscript: January 12, 2012

Manuscript Accepted: January 18, 2012

Published: January 31, 2012

**Citation**

Avner Yanai, Meir Orenstein, and Uriel Levy, "Giant resonance absorption in ultra-thin metamaterial periodic structures," Opt. Express **20**, 3693-3702 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3693

Sort: Year | Journal | Reset

### References

- N. Engheta and R. Ziolkowski, Metamaterials: Physics and Engineering Explorations, (Wiley, 2006).
- V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp.10, 509 (1968). [CrossRef]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966 (2000). [CrossRef] [PubMed]
- D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000). [CrossRef] [PubMed]
- S. Nefedov and S. A. Tretyakov, “Photonic band gap structure containing metamaterial with negative permittivity and permeability,” Phys. Rev. E66, 036611 (2002). [CrossRef]
- J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003). [CrossRef] [PubMed]
- L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B67, 235103 (2003). [CrossRef]
- A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag.51, 2558–2571 (2003). [CrossRef]
- D. R. Fredkin and A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett.81, 1753–1755 (2002). [CrossRef]
- Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, “Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials,” Opt. Express14, 2220–2227 (2006). [CrossRef] [PubMed]
- S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett.102, 203905 (2009). [CrossRef] [PubMed]
- Y. Jin, S. Xiao, N. A. Mortensen, and S. He, “Arbitrarily thin metamaterial structure for perfect absorption and giant magnification,” Opt. Express19, 11114–11119 (2011). [CrossRef] [PubMed]
- L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Opt. Express11, 1283–1290 (2003). [CrossRef] [PubMed]
- M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A12, 1068–1076 (1995). [CrossRef]
- L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A13, 1870–1876 (1996). [CrossRef]
- P. Lalanne and G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A13, 779–784 (1996). [CrossRef]
- T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Derivation of plasmonic resonances in the Fourier modal method with adaptive spatial resolution and matched coordinates,” J. Opt. Soc. Am. A28, 238–244 (2011). [CrossRef]
- P. Yeh, Optical waves in layered media, (John Wiley & Sons, New York, 1988).
- S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B79, 035120 (2009). [CrossRef]
- A. Hessel and A. A. Oliner, “A new theory of Wood anomalies on optical gratings,” Appl. Opt.4, 1275–1297 (1965). [CrossRef]
- U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124, 1866–1878 (1961). [CrossRef]
- M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67, 085415 (2003). [CrossRef]
- C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red-shifts and red tails in hole array transmission spectra,” Opt. Commun.225, 331–336 (2003). [CrossRef]
- A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A14, 2985–2993 (1997). [CrossRef]
- S. M. Norton, T. Erdogan, and G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A14, 629–639 (1997). [CrossRef]
- V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express17(24), 21897–21909 (2009). [CrossRef] [PubMed]
- R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter13(9), 1811–1818 (2001). [CrossRef]
- S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun.225, 233–240 (2003). [CrossRef]
- N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett.33, 2350–2352 (2008). [CrossRef] [PubMed]
- H. A. Haus, Waves and fields in Optoelectronics, (New Jersey, Prentice-Hall Inc., 1984).
- A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.4, 321–322 (2000). [CrossRef]
- H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer-Verlag, New York, 1988).
- S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20, 569–572 (2003). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.