## Multiple responses of TPP-assisted near-perfect absorption in metal/Fibonacci quasiperiodic photonic crystal |

Optics Express, Vol. 19, Issue 10, pp. 9759-9769 (2011)

http://dx.doi.org/10.1364/OE.19.009759

Acrobat PDF (1118 KB)

### Abstract

Absorption properties in one-dimensional quasiperiodic photonic crystal composed of a thin metallic layer and dielectric Fibonacci multilayers are investigated. It is found that a large number of photonic stopbands can occur at the dielectric Fibonacci multilayers. Tamm plasmon polaritons (TPPs) with the frequencies locating at each photonic stopband are excited at the interface between the metallic layer and the dielectric layer, leading to almost perfect absorption for the energy of incident wave. By adjusting the length of dielectric layer with higher refractive-index or the Fibonacci order, the number of absorption peaks can be tuned effectively and enlarged significantly.

© 2011 OSA

## 1. Introduction

1. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. **101**(9), 093105 (2007). [CrossRef]

2. A. D. Parsons and D. J. Pedder, “Thin-□lm infrared absorber structures for advanced thermal detectors,” J. Vac. Sci. Technol. A **6**(3), 1686–1689 (1988). [CrossRef]

3. S. Longhi, “Pi-symmetric laser absorber,” Phys. Rev. A **82**(3), 031801 (2010). [CrossRef]

*et al.*[4

4. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. **100**(20), 207402 (2008). [CrossRef] [PubMed]

5. C. G. Hu, X. Li, Q. Feng, X. N. Chen, and X. G. Luo, “Investigation on the role of the dielectric loss in metamaterial absorber,” Opt. Express **18**(7), 6598–6603 (2010). [CrossRef] [PubMed]

6. J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. **96**(25), 251104 (2010). [CrossRef]

7. J. R. Tischler, M. S. Bradley, and V. Bulović, “Critically coupled resonators in vertical geometry using a planar mirror and a 5 nm thick absorbing film,” Opt. Lett. **31**(13), 2045–2047 (2006). [CrossRef] [PubMed]

8. C. G. Hu, Z. Y. Zhao, X. N. Chen, and X. G. Luo, “Realizing near-perfect absorption at visible frequencies,” Opt. Express **17**(13), 11039–11044 (2009). [CrossRef] [PubMed]

10. F. Yu, H. Wang, and S. L. Zou, “Effcient and tunable light trapping thin films,” J. Phys. Chem. C **114**(5), 2066–2069 (2010). [CrossRef]

11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. **10**(7), 2342–2348 (2010). [CrossRef] [PubMed]

12. X. L. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. **104**(20), 207403 (2010). [CrossRef] [PubMed]

*et al.*obtained dual absorption bands at 1.6 THz and 2.8 THz by separating the split ring resonator (SRR) layer from the metal plate layer with a polyimide layer [13

13. H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy, K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, “Highly flexible wide angle of incidence terahertz metamaterial absorber: design, fabricated and characterization,” Phys. Rev. B **78**(24), 241103 (2008). [CrossRef]

14. Q. Y. Wen, H. W. Zhang, Y. S. Xie, Q. H. Yang, and Y. L. Liu, “Dual band terahertz metamaterial absorber: Design, fabrication, and characterization,” Appl. Phys. Lett. **95**(24), 241111 (2009). [CrossRef]

*et al.*in a metal/dielectric Bragg mirror structure both theoretically and experimentally [15

15. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B **76**(16), 165415 (2007). [CrossRef]

16. M. E. Sasin, R. P. Seisyan, M. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasilev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Appl. Phys. Lett. **92**(25), 251112 (2008). [CrossRef]

17. X. Kang, W. Tan, Z. Wang, and H. Chen, “Optic Tamm states: the Bloch-wave-expansion method,” Phys. Rev. A **79**(4), 043832 (2009). [CrossRef]

19. M. Kaliteevski, S. Brand, R. A. Abram, I. Iorsh, A. V. Kavokin, and I. A. Shelykh, “Hybrid states of Tamm plasmons and exciton polaritons,” Appl. Phys. Lett. **95**(25), 251108 (2009). [CrossRef]

*et al.*recently studied the effects of quasibound photonic state within a substrate/metal film/Bragg reflector/air structure [20

20. S. Brand, R. A. Abram, and M. A. Kaliteevski, “Bragg re〉ector enhanced attenuated total re〉ectance,” J. Appl. Phys. **106**(11), 113109 (2009). [CrossRef]

*et al.*experimentally realized optical absorber in heterostructures composed of thick metallic films and truncated all-dielectric photonic crystals [21

21. G. Q. Du, H. T. Jiang, Z. S. Wang, Y. P. Yang, Z. L. Wang, H. Q. Lin, and H. Chen, “Heterostructure-based optical absorbers,” J. Opt. Soc. Am. B **27**(9), 1757–1762 (2010). [CrossRef]

*FT*) of the structure index profile. Finally, conclusions are made in the last section.

## 2. Analysis method and optical propagation properties

*M*on the left, and two semi-infinite dielectric layers

*A*and

*B*on the right arranged with a Fibonacci-sequence. The Fibonacci-sequence was first introduced in optical system by Kohmoto

*et al.*[22

22. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. **58**(23), 2436–2438 (1987). [CrossRef] [PubMed]

*et al.*[23

23. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. **72**(5), 633–636 (1994). [CrossRef] [PubMed]

24. D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. **198**(4-6), 273–279 (2001). [CrossRef]

26. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. **80**(17), 3063–3065 (2002). [CrossRef]

27. Y. K. Gong, X. M. Liu, and L. R. Wang, “High-channel-count plasmonic filter with the metal-insulator-metal Fibonacci-sequence gratings,” Opt. Lett. **35**(3), 285–287 (2010). [CrossRef] [PubMed]

28. R. Riklund and M. Severin, “Optical properties of perfect and non perfect quasiperiodic multilayers a comparison with periodic and disordered multilayers,” J. Phys. C Solid State Phys. **21**(17), 3217–3228 (1988). [CrossRef]

*at al.*experimentally realized a new kind of mirrors with multiple reflection spectral windows based on the one-dimensional Fibonacci chains [29

29. D. T. Nguyen, R. A. Norwood, and N. Peyghambarian, “Multiple spectral window mirrors based on Fibonacci chains of dielectric layers,” Opt. Commun. **283**(21), 4199–4202 (2010). [CrossRef]

*A*and

*B*can be depicted by the following recursive formula:where

*n*and

*j*are positive integers known as the Fibonacci order and Fibonacci generation number, respectively. In our design,

*j*is set as 3, thus the proposed metal/Fibonacci quasiperiodic photonic crystal is

*MF*

_{3}(

*n*)

*= M*(

*B*

^{n}^{−1}

*A*)

*as schematically shown in Fig. 1 .*

^{n}B*F*

_{3}(

*n*)

*=*(

*B*

^{n}^{−1}

*A*)

*. According to the Maxwell boundary condition that the tangential components of electric and magnetic fields must be continuous at the interface between two dielectrics, when optical wave propagates to the structure of*

^{n}B*F*

_{3}(

*n*), the characteristic matrix for dielectric layers

*A*and

*B*can be obtained as [30]:where

*θ*is the incident angle,

*n*, and

_{a,b}*L*are refractive index and length for dielectric layers

_{a,b}*A*and

*B*, respectively.

*β*= 2π

_{a,b}*n*cos(

_{a,b}L_{a,b}*θ*)/λ,

*q*=

_{a,b}*n*cos(

_{a,b}*θ*) is for the

*s*-polarized wave while

*q*= cos(

_{a,b}*θ*)/

*n*is for the

_{a,b}*p*-polarized wave. The operation direction of the transfer matrix is from right to left, and the total characteristic matrix for the structure of of

*F*

_{3}(

*n*) isand the reflection coefficient iswhere

*q*

_{1,2}=

*n*

_{1,2}cos(

*θ*) is for the

*s*-polarized wave, while

*q*

_{1,2}= cos(

*θ*)/

*n*

_{1,2}is for the

*p*-polarized wave. Here,

*n*

_{1}and

*n*

_{2}are the refractive index of the left and the right ambient mediums, respectively. In this paper, we assume

*n*

_{1}and

*n*

_{2}to be 1.

*F*

_{3}(

*n*), TPPs can only be excited when the phase matching condition is satisfied [16

16. M. E. Sasin, R. P. Seisyan, M. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasilev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Appl. Phys. Lett. **92**(25), 251112 (2008). [CrossRef]

*r*is reflection coefficient of the structure of

_{F}*F*

_{3}(

*n*),

*r*

_{m}is reflection coefficient for the wave incident on the metallic layer

*M*and is determined by the Fresnel formula

*r*

_{m}= (

*n*

_{b}-

*n*

_{m})/(

*n*

_{b}+

*n*

_{m}).

*n*

_{m}is refractive index of the metal assuming to be gold in our design. The gold permittivity can be described by the Drude model of

*ε*= 1-

_{m}*w*

_{p}

^{2}/(

*w*

^{2}+ i

*w*γ), where

*w*is the incident optical frequency,

*w*

_{p}= 2.17 × 10

^{15}Hz is plasma frequency, and

*γ =*1.95 × 10

^{13}Hz is the damping constant [11

11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. **10**(7), 2342–2348 (2010). [CrossRef] [PubMed]

*w*

_{p}

^{2}/(

*w*

^{2}+ i

*w*γ) is far larger than 1 and

*w*is far larger than γ, the refractive index of gold

*n*

_{m}can be approximated to

*iw*

_{p}/

*w*. Therefore, the reflection coefficient for the electromagnetic wave incident on the metallic layer

*M*can be expressed as:

*A*and

*B*are selected to be

*Si*(

*n*= 1.23) and

_{a}*TiO*

_{2}(

*n*= 2.13), respectively. The lengths for the gold layer

_{b}*M*, the dielectric

*A*, and the dielectric

*B*are

*L*= 25 nm,

_{m}*L*

_{a}=

*λ*

_{c}/4/

*n*= 120 nm and

_{a}*L*=

_{b}*λ*/4/

_{c}*n*= 70 nm, respectively, where

_{b}*λ*

_{c}is the central wavelength with value of 600 nm. With above parameters, reflection coefficient

*r*for the structure of

_{F}*F*

_{3}(

*n*) are plotted in Table 1 . It shows that when the Fibonacci order

*n*equals to four there is only single photonic stopband, which is similar to the results designed in Ref [15

15. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B **76**(16), 165415 (2007). [CrossRef]

*n*is enlarged, the number of the photonic stopbands will be increased correspondingly. As depicted in Table 1 and Fig. 2 , when

*n*is enlarged to 14, the structure of

*F*

_{3}(

*n*) will possess five photonic stopbands with central wavelengths of 416 nm, 462 nm, 520 nm, 598 nm, and 700nm, respectively. Therefore, the structure of

*F*

_{3}(

*n*) can generate multiple photonic stopbands, with each photonic stopband locating at

*r*−1 and having central frequency of

_{F}=*w*. Since TPPs is generated in the photonic stopbands, we only need to consider the frequencies in each photonic stopband. When an optical wave with frequency

_{i}*w*sufficiently close to the

*w*, the refection coefficient

_{i}*r*in the frequency range near the

_{F}*i-*th photonic stopband can be expressed as [15

15. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B **76**(16), 165415 (2007). [CrossRef]

31. A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Appl. Phys. Lett. **87**(26), 261105 (2005). [CrossRef]

*i*is integer,

*η*is a factor determining the bandwidth of

_{i}*i-*th photonic stopband, and

*w*is the central frequency of the

_{i}*i-*th photonic stopband.

*M*(

*B*

^{n}^{−1}

*A*)

*can be derived asFrom above equation, we can obtain that since there are*

^{n}B*N*photonic stopbands (

*i*= 1, 2,…,

*N*), TPPs with

*N*eigenfrequencies will be excited simultaneously. Meanwhile, because 2

*n*

_{b}/(

*η*) is positive and far smaller than 1, each eigenfrequency will locate in the

_{i}w_{p}*i-*th photonic stopband and is a little smaller than the central frequency of

*w*.

_{i}## 3. Absorption properties and discussions

*M*(

*B*

^{n}^{−1}

*A*)

*. As a design example, the Fabonacci order*

^{n}B*n*is set as 9, so the studied structure becomes

*M*(

*B*)

^{8}A*. With the parameters of*

^{9}B*n*

_{a}= 1.23,

*n*= 2.13,

_{b}*L*= 25 nm,

_{m}*L*= 120 nm, and

_{a}*L*= 70 nm, the spectral properties under normal incidence are calculated by the TMM and demonstrated in Fig. 3 , where transmission (T), reflection (R), and absorption (A) are all plotted. It can be obtained that the transmission is small in the whole range and reaches zero at wavelengths locating at the photonic stopbands of the Fibonacci structure (

_{b}*B*

^{8}

*A*)

^{9}

*B*. There are thee dips in the reflection spectra of Fig. 3(a), which thereby leads to three high absorption peaks in Fig. 3(b) because of A = 1-R-T. The three absorption peaks at the wavelengths of 447.6, 543.8, and 689.3 nm possess value as high as 0.81, 0.97, and 0.96, respectively. Meanwhile, the FWHM of the three stopbands are as narrow as 0.5, 0.9, and 2.2 nm, respectively. The three peaks are in the photonic stopbands while are a little larger than the central wavelength of the photonic stopbands (i.e., 447 nm, 537 nm, and 671 nm, as illustrated in Table 1). The phenomenon is in consistent with the Eq. (8). The absorption spectra for

*s*- and

*p*-polarization at incident angle of 0°, 20°, and 40° are plotted in Figs. 4(a) and 4(b), respectively. When the angle of the incident wave is increased, all the absorption peaks demonstrate a blueshift. It arises from that the photonic stopbands will shift to the shorter wavelength when increasing the incident angle [32

32. X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total-re〉ection frequency range in one dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. **80**(23), 4291–4293 (2002). [CrossRef]

*p*-polarization as shown in Fig. 4, TPPs are able to work with both the

*s*- and the

*p*-polarization. Without loss of generality, we only consider the absorption properties of

*s*-polarization under normal incidence in the following paper.

*E*| simulated by the FDTD method for the structure of

*M*(

*B*

^{8}

*A*)

^{9}

*B*. The FDTD computational domain is schematically shown in Fig. 5(a). The mediums on both sides of the structure are air. The source locates at the left sides with position of

*x*= −1 μm, and normally travels to the right with

*s*-polarization. Perfect matching layer (PML) and periodic boundary condition (PBC) are set along

*x*and

*y*directions at the edge of the computational domain, respectively. The spatial sizes are Δ

*x*= Δ

*y*= 5 nm, and the temporal cell size is Δ

*t*= Δ

*x*/(2

*c*), where

*c*is the velocity of light in vacuum. Figures 5(b) and (c) show the intensity distributions |

*E*| in the structure of

*M*(

*B*

^{8}

*A*)

^{9}

*B*at eigenfrequency of 689.3 nm and off-eigenfrequency of 520 nm, respectively. At the eigenfrequency, the electromagnetic field is trapped at the Au/

*TiO*interface and decrease exponentially inside

_{2}*TiO*

_{2}/

*Si*Fibonacci photonic crystal. Electromagnetic field is barely reflected or transmitted, and almost all the incident energy is absorbed. However, at the off-eigenfrequency of 520 nm

_{,}the electromagnetic field is strongly reflected by the entrance face and no absorption occurs.

## 4. Dependence of the absorption on the structure geometric parameters

*n*on the absorption by varying

_{b}*n*from 2.03 to 2.23 with a step of 0.1. When

_{b}*n*is 2.03, the three absorption peaks are at λ

_{b}_{1}= 427.9 nm, λ

_{2}= 518 nm, λ

_{3}= 657.6 nm, respectively. While it is increased to 2.13 and 2.23, the peaks shift to λ

_{1}= 447.6 nm, λ

_{2}= 542.8 nm, λ

_{3}= 689.3 nm, and λ

_{1}= 467.5 nm, λ

_{2}= 567.5 nm, λ

_{3}= 721.3 nm, respectively. Increasing

*n*with the same step of 0.1 as indicated in Fig. 6(b), each absorption peak will exhibit a redshift, which is similar to the behavior of increasing

_{a}*n*. Note that the redshifts induced by increasing

_{b}*n*is significantly smaller than that by increasing

_{a}*n*. To explain this phenomenon, Fourier transform (FT) of the structure refractive index can be utilized [33]. The refractive index profile for the structure (

_{b}*B*

^{8}

*A*)

^{9}

*B*is

*i*= 1, 2,…,

*n*, and

*z*is the coordinate along the structure (

*B*)

^{8}A*.*

^{9}B*FT*of refractive index profile is expressed aswhere

*L*is the length of the structure (

*B*)

^{8}A*, and*

^{9}B*β*is wave number in the medium. Inserting Eq. (9) to Eq. (10) we can obtain that

*FT*result gives characteristics of photonic stopband in the structure (

*B*)

^{8}A*, and each peak at a given*

^{9}B*β*domain corresponds to a photonic stopband. The

*FT*spectra of the structure

*F*

_{3}(9) under different values of

*n*are calculated by Eq. (11) and plotted in Fig. 7 . It shows that the

_{b}*FT*results agree well with the results calculated by the TMM in Fig. 6(a). In Eq. (11) which contains three polynomials, the coefficient for

*n*in the first and third polynomial is far larger than the coefficient for

_{b}*n*in the second polynomial. Therefore, although with the same changes of 0.1,

_{a}*n*have a larger influence on absorption than

_{b}*n*does as observed in Fig. 6.

_{a}*L*and

_{a}*on the absorption spectra are depicted in Fig. 8 . Seen from Eq. (11), dependence of*

_{.}L_{b}*FT*on

*L*is determined by the term of exp(

_{b}*jβ*(

*i*-1)(

*n*-1)

*L*). Since

_{b}*n*-1 is a large value and any change in

*L*multiplies it, the peak density will be increased dramatically even with a small change of

_{b}*L*in the

_{b}*FT*spectrum at a given range. As shown in Fig. 8(b), when

*L*varies from 25 nm to 50 nm, 70 nm, 95 nm, and 120 nm, the number of absorption peaks in visual frequency is tuned from 1 to 2, 3, 4, and 5, respectively. The dependence of

_{b}*FT*on

*L*is determined by the term of exp(

_{a}*jβ*(

*i*-1)

*L*) which do not involve the large

_{a}*n-*1. As a result, increasing

*L*as illustrated in Fig. 8(a) will not introduce obvious influence on the number of absorption peaks as that by increasing

_{a}*L*, and can only redshift the absorption peaks as increasing

_{b}*n*and

_{a}*n*does as shown in Fig. 5. We can also obtain from Eq. (11) that increasing

_{b}*n*will also increase the number of absorption peaks as the behavior of increasing

*L*, which can well explain the phenomena in Table 1. When

_{b}*n*= 9,

*n*

_{a}= 1.23,

*n*= 2.13,

_{b}*L*= 25 nm,

_{m}*L*= 120 nm, and

_{a}*L*= 280 nm, PA with twelve channels and 1-nm FWHM for each channel are designed as shown in Fig. 9 . This ultranarrow FWHM is significantly narrower than that of the PAs proposed in [11

_{b}11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. **10**(7), 2342–2348 (2010). [CrossRef] [PubMed]

12. X. L. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. **104**(20), 207403 (2010). [CrossRef] [PubMed]

*n*or

*L*.

_{b}## 5. Conclusions

*F*

_{3}(

*n*) at

*r*= −1. TPPs with the frequencies locating at each photonic stopband will be excited at the interface between the metallic layer and the dielectric layer, leading to multiple peaks in the absorption spectra. The dependence of the absorption spectra on the structure geometric parameters of

_{F}*n*,

*n*,

_{a}*n*,

_{b}*L*, and

_{a}*L*are studied in detail. It is found that

_{b}*n*and

*L*play the dominate roles in the multiple absorption responses. To explain above phenomena, a

_{b}*FT*technique is utilized. As a design example, finally, a PA with channel number as high as twelve and bandwidth as narrow as 1 nm is achieved, which is very attractive in sensor/detector technology and highly integrated dense wavelength division multiplexing networks. Although the PAs in this paper are designed to work in the visual frequency, it can be further applied to other frequency ranges by scaling the structure geometric.

## Acknowledgments

## References and links

1. | S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. |

2. | A. D. Parsons and D. J. Pedder, “Thin-□lm infrared absorber structures for advanced thermal detectors,” J. Vac. Sci. Technol. A |

3. | S. Longhi, “Pi-symmetric laser absorber,” Phys. Rev. A |

4. | N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. |

5. | C. G. Hu, X. Li, Q. Feng, X. N. Chen, and X. G. Luo, “Investigation on the role of the dielectric loss in metamaterial absorber,” Opt. Express |

6. | J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. |

7. | J. R. Tischler, M. S. Bradley, and V. Bulović, “Critically coupled resonators in vertical geometry using a planar mirror and a 5 nm thick absorbing film,” Opt. Lett. |

8. | C. G. Hu, Z. Y. Zhao, X. N. Chen, and X. G. Luo, “Realizing near-perfect absorption at visible frequencies,” Opt. Express |

9. | T. V. Teperik, F. J. Garcia, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nature |

10. | F. Yu, H. Wang, and S. L. Zou, “Effcient and tunable light trapping thin films,” J. Phys. Chem. C |

11. | N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. |

12. | X. L. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. |

13. | H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy, K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, “Highly flexible wide angle of incidence terahertz metamaterial absorber: design, fabricated and characterization,” Phys. Rev. B |

14. | Q. Y. Wen, H. W. Zhang, Y. S. Xie, Q. H. Yang, and Y. L. Liu, “Dual band terahertz metamaterial absorber: Design, fabrication, and characterization,” Appl. Phys. Lett. |

15. | M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B |

16. | M. E. Sasin, R. P. Seisyan, M. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasilev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Appl. Phys. Lett. |

17. | X. Kang, W. Tan, Z. Wang, and H. Chen, “Optic Tamm states: the Bloch-wave-expansion method,” Phys. Rev. A |

18. | S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B |

19. | M. Kaliteevski, S. Brand, R. A. Abram, I. Iorsh, A. V. Kavokin, and I. A. Shelykh, “Hybrid states of Tamm plasmons and exciton polaritons,” Appl. Phys. Lett. |

20. | S. Brand, R. A. Abram, and M. A. Kaliteevski, “Bragg re〉ector enhanced attenuated total re〉ectance,” J. Appl. Phys. |

21. | G. Q. Du, H. T. Jiang, Z. S. Wang, Y. P. Yang, Z. L. Wang, H. Q. Lin, and H. Chen, “Heterostructure-based optical absorbers,” J. Opt. Soc. Am. B |

22. | M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. |

23. | W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. |

24. | D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. |

25. | X. Q. Huang, S. S. Jiang, R. W. Peng, and A. Hu, “Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

26. | R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. |

27. | Y. K. Gong, X. M. Liu, and L. R. Wang, “High-channel-count plasmonic filter with the metal-insulator-metal Fibonacci-sequence gratings,” Opt. Lett. |

28. | R. Riklund and M. Severin, “Optical properties of perfect and non perfect quasiperiodic multilayers a comparison with periodic and disordered multilayers,” J. Phys. C Solid State Phys. |

29. | D. T. Nguyen, R. A. Norwood, and N. Peyghambarian, “Multiple spectral window mirrors based on Fibonacci chains of dielectric layers,” Opt. Commun. |

30. | M. Born, and E. Wolf, Principles of Optics, fourth ed., Pergamon, Oxford, 1970, 58–68. |

31. | A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Appl. Phys. Lett. |

32. | X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total-re〉ection frequency range in one dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. |

33. | J. Nakayama, ““Periodic Fourier transform and its application to wave scattering from a finite periodic surface: Two-dimensional case,” IEICE Trans. Electron,” E |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(240.0240) Optics at surfaces : Optics at surfaces

(050.5298) Diffraction and gratings : Photonic crystals

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: March 25, 2011

Revised Manuscript: April 30, 2011

Manuscript Accepted: May 2, 2011

Published: May 4, 2011

**Citation**

Yongkang Gong, Xueming Liu, Leiran Wang, Hua Lu, and Guoxi Wang, "Multiple responses of TPP-assisted near-perfect absorption in metal/Fibonacci quasiperiodic photonic crystal," Opt. Express **19**, 9759-9769 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9759

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