## Robust absorption broadband in one-dimensional metallic-dielectric quasi-periodic structure

Optics Express, Vol. 14, Issue 5, pp. 2014-2020 (2006)

http://dx.doi.org/10.1364/OE.14.002014

Acrobat PDF (281 KB)

### Abstract

We demonstrated that a broad and robust absorption band for a wide range of incidence angles and for both polarizations can be realized using a one-dimensional metallic-dielectric quasi-periodic structure, when the thickness of the constituent metal is comparable to its skin depth. The absorptance in such peculiar structure can exceed 99% to meet different applications. Furthermore, employing the effective medium approach, a theoretical expression has been deduced to instruct the working frequency of the absorption band. By tuning the permittivity and thickness of the constituent layers, the robust absorption band can cover the wavelength from the visible to the near-infrared.

© 2006 Optical Society of America

## 1. Introduction

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. **58**, 2059–2062 (1987). [CrossRef] [PubMed]

2. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E **53**, 4107–4121 (1996). [CrossRef]

3. J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “AAll-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature (London) **417**, 52–55 (2002). [CrossRef]

*et.al*. [5

5. S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B **20**, 1538–1541 (2003). [CrossRef]

6. S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ=1.5 μm by a three-dimensional tungsten photonic crystal,” Opt. Lett. **28**, 1683–1685 (2003). [CrossRef] [PubMed]

7. G. Veronis, R. W. Dutton, and S. Fan, “Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range,” J. Appl. Phys. **97**, 093104 (2005). [CrossRef]

8. J. F. Yu, Y. F. Shen, X. H. Liu, R. T. Fu, J. Zi, and Z. Q. Zhu, “Absorption in one-dimensional metallic-dielectric photonic crystals,” J. Phys.: Condens. Matter **16**, L51–L56 (2004). [CrossRef]

## 2. Fibonacci photonic crystal and conditions of high absorption band

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

12. J. W. Dong, P. Han, and H. Z. Wang, “Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals,” Chin. Phys. Lett. **20**, 1963–1965 (2003). [CrossRef]

13. S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express **13**, 4113 (2005). [CrossRef] [PubMed]

*S*

_{j+1}= {

*S*

_{j-1}

*S*

_{j},

*j*≥1, where

*S*

_{j}is the

*j*th order sequence. For example, the unit cells of the first three order sequences are

*S*

_{2}=

*MD*,

*S*

_{3}=

*DMD*,

*S*

_{4}=

*MDDMD*, where

*S*

_{0}=

*M*,

*S*

_{1}=

*D*, and

*M*,

*D*represent the thin metal and dielectric layer, respectively. By employing the transfer matrix method [14], the calculated band structures of the first three order Fibonacci MDQPS are shown in Fig. 1. As a numerical example, the refractive index and thickness of the dielectric layer are 1.38 and 180 nm, while the metal is 10nm-thick tungsten for all the Fibonacci MDQPS. The permittivity of tungsten is taken from Palik [15], Insets in Fig. 1 are the unit cells of the corresponding order Fibonacci MDQPS. It is found that a cutoff frequency exists in all the Fibonacci MDQPS due to the Bragg scattering, which is similar to the rigorously period structure. Second, more PBGs appears in the higher order Fibonacci MDQPS, e.g. the

*S*

_{4}structure, than the lower order ones, e.g. the

*S*

_{3}structure, because the former is more difficult to satisfy the Bloch wave condition [14] as its disorder increases. Third, as expected, the slope of photonic band decreases in the higher order Fibonacci MDQPS than the lower order ones between the cut-off frequency and near 1.8μm

^{-1}.

*S*

_{3}with seven periods. The parameters are the same as before. In Fig. 2(a), it can be seen that an absorption broadband (solid line) in the tungsten MDQPS is achieved from 1.17 to 2.05μm, which is corresponding to the first photonic band shown in Fig. 1(b). Obviously, it is significantly stronger than the 100nm-thick tungsten film (dashed line). Note that the skin depth is about 20~30nm in the studied wavelength. Absorptance decays gradually in the long wavelength limit because no propagating mode is allowed below the cutoff frequency in the MDQPS. Moreover, the reflectance of

*S*

_{3}increases substantially within the PBG range due to Bragg scattering. This causes the dips in the absorption spectrum around 1.02 and 0.5μm. Similar behavior of the silver MDQPS structure is shown in Fig. 2(b). The distinct absorption enhancement occurs both in the visible and the near-infrared regions as compared to the 100nm-thick silver film.

## 3. Simulation results

*S*

_{2},

*S*

_{3},

*S*

_{5}(

*DMDMDDMD*), and

*S*

_{7}(

*DMDMDDMDMDDMDDMDMDDMD*) with 10, 7, 3, and 1 period, respectively. The other parameters are the same as Fig. 1.

*S*

_{5}and

*S*

_{7}is 0.76 ~ 1.65μm and 0.74 ~ 1.71 μm, respectively, which cover the whole near-infrared region. For high order MDQPS, the Bragg scattering becomes weaker because of the increasing disorder and the less periods. The reflectance within the PBG range for finite MDQPS is no longer strong although the PBG exists in the infinite MDQPS. Therefore, a broad and robust absorption band can be achieved. Furthermore, it is expected that both the width of the absorption band and the absorptance of the MDQPS are larger than the rigorously period structure, i.e.

*S*

_{2}. Note that a high efficient absorption band (above 99%) is achieved in the

*S*

_{5}and

*S*

_{7}structures with the spectral bandwidth of 163 nm and 267 nm. By optimizing the practical design, one can obtain the best bandwidth 182 nm and 314 nm in the

*S*

_{5}and

*S*

_{7}structures, when the thickness of the dielectric layer is 220 nm and 230 nm, respectively. A further calculation reveals that, for high order MDQPS with several periods, e.g.

*S*

_{7}with 3 periods, the EM wave decays almost completely in the first period of the structure. In other words, the additional periods of the structure are insignificant on optical absorption enhancement.

*S*

_{3}structure. For this particular case, the structure with the unit cell of

*S*

_{3}can be regarded as an effective medium. Due to the mirror symmetry of the stack, the total transfer matrix of a unit cell can be written in the form of matrix of a single layer:

*δ*

_{eff}is the effective phase thickness, and

*ε*

_{eff}is the effective permittivity, written as:

*δ*

_{d}=(

*ω*/

*c*)

*nd*and

*δ*

_{m}= (

*ω*/

*c*)

*n*

_{i}

*d*

_{m}are the phases of the dielectric and metallic layer, respectively.

*n*and

*d*are the refractive index and thickness of dielectric,

*n*

_{i}and

*d*

_{m}are the extinction coefficient and thickness of metal, and

*c*is the speed of light, respectively. After some algebra calculation, Eq. (2) can be deduced using the effective medium approximation:

*ε*

_{0}=

*n*

^{2}and

*δ*

_{m}~

*ω*

_{p}

*d*

_{m}/

*c*in the long wavelength approximation, where

*ω*

_{p}is the plasma frequency of metal. It can be seen from Eq. (5) that the photonic band, as well as the absorption band, can be tuned to the higher frequency range using metal with higher plasma frequency or thin dielectric with lower refractive index. It should be noted that the thickness of the metal thin film should be comparable to its skin depth for the absorption enhancement. Similar guideline is valid in the higher order Fibonacci MDQPS by numerical simulation. For example, if the thickness of tungsten and dielectric layer of

*S*

_{5}is 10 nm and 120nm, the broad absorption band above 90% is from 0.544 to 1.514μm, which covers the whole region from the visible to the near-infrared. Furthermore, similar robust absorption enhancement can also be achieved in other quasi-periodic structure. Take the fifth order Thue-Morse sequence for example. We indeed find out the absorption band exceeding 97% from 0.92 to 1.26μm when the refractive index of dielectric, the thicknesses of dielectric and tungsten layer are 2.67, 80nm and 20nm, respectively.

## 4. Absorption broadband for oblique incidence

*S*

_{5}for both polarizations as a function of incidence angle. It is noted that the absorptance of both polarizations is above 90% over the wavelength range about 0.8 ~ 1.6μm for 0° ~ 50°. In other words, the band edge is nearly unchanged within a wide range of the incidence angle. For larger incidence angles the lower absorptance is due to the impedance mismatch which is similar to the 2D case [7

7. G. Veronis, R. W. Dutton, and S. Fan, “Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range,” J. Appl. Phys. **97**, 093104 (2005). [CrossRef]

## 5. Summary

*S*

_{7}is over 300nm in the near-infrared region. Moreover, we have found that the robust absorption broadband (above 90%) is almost independent within a wide range of incidence angles for both polarizations. By the optimization of the geometric thickness of the simple 1D multilayer structure, the absorption band can be tuned to cover the wavelength from the visible to the near-infrared. Our structures may have wide applications in thermal emission, incandescent light and martial concealment technology because of its peculiar properties, easy fabrication and small size.

## Acknowledgments

## References and links

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

2. | J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E |

3. | J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “AAll-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature (London) |

4. | C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal radiation from photonic crystals: a direct calculation,” Phys. Rev. Lett. |

5. | S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B |

6. | S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ=1.5 μm by a three-dimensional tungsten photonic crystal,” Opt. Lett. |

7. | G. Veronis, R. W. Dutton, and S. Fan, “Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range,” J. Appl. Phys. |

8. | J. F. Yu, Y. F. Shen, X. H. Liu, R. T. Fu, J. Zi, and Z. Q. Zhu, “Absorption in one-dimensional metallic-dielectric photonic crystals,” J. Phys.: Condens. Matter |

9. | A. Narayanaswamy and G. Chen, “Thermal emission control with one-dimensional metallodielectric photonic crystals,” Phys. Rev. B |

10. | A. Rodríguez and F. Domínguez-Adame, “Optical absorption in Fibonacci lattices at finite temperature,” Phys. Rev. B |

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

12. | J. W. Dong, P. Han, and H. Z. Wang, “Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals,” Chin. Phys. Lett. |

13. | S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express |

14. | P. Yeh, |

15. | E. D. Palik, ed., |

**OCIS Codes**

(230.4170) Optical devices : Multilayers

(300.1030) Spectroscopy : Absorption

(310.6860) Thin films : Thin films, optical properties

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: January 3, 2006

Revised Manuscript: February 17, 2006

Manuscript Accepted: February 18, 2006

Published: March 6, 2006

**Virtual Issues**

Vol. 1, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

J. W. Dong, G. Q. Liang, Y. H. Chen, and H. Z. Wang, "Robust absorption broadband in one-dimensional metallic-dielectric quasi-periodic structure," Opt. Express **14**, 2014-2020 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-5-2014

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### References

- E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
- J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996). [CrossRef]
- J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature 417, 52-55 (2002). [CrossRef]
- C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, "Thermal radiation from photonic crystals: a direct calculation," Phys. Rev. Lett. 93, 213905 (2004). [CrossRef] [PubMed]
- S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, "Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal," J. Opt. Soc. Am. B 20, 1538-1541 (2003). [CrossRef]
- S. Y. Lin, J. G. Fleming, and I. El-Kady, "Highly efficient light emission at λ=1.5 μm by a three-dimensional tungsten photonic crystal," Opt. Lett. 28, 1683-1685 (2003). [CrossRef] [PubMed]
- G. Veronis, R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys. 97, 093104 (2005). [CrossRef]
- J. F. Yu, Y. F. Shen, X. H. Liu, R. T. Fu, J. Zi, and Z. Q. Zhu, "Absorption in one-dimensional metallic-dielectric photonic crystals," J. Phys.: Condens. Matter 16, L51-L56 (2004). [CrossRef]
- A. Narayanaswamy and G. Chen, "Thermal emission control with one-dimensional metallodielectric photonic crystals," Phys. Rev. B 70, 125101 (2004). [CrossRef]
- P. Tran, "Optical switching with a nonlinear photonic crystal: a numerical study," Opt. Lett. 21, 1138-1140 (1996). [CrossRef]
- Q. M. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, "Wave propagation in nonlinear photonic band-gap materials," Phys. Rev. B. 53, 15577-15585 (1996). [CrossRef]
- X. Y. Hu, Y. H. Liu, J. Tian, B. Y. Cheng, and D. Z. Zhang, "Ultrafast all-optical switching in two-dimensional organic photonic crystal," Appl. Phys. Lett. 86, 121102 (2005). [CrossRef]
- G. Q. Liang, P. Han, and H. Z. Wang, "Narrow frequency and sharp angular defect mode in one-dimensional photonic crystals from a photonic heterostructure," Opt. Lett. 29, 192-194 (2004). [CrossRef] [PubMed]
- G. Q. Liang, J. W. Dong, and H. Z. Wang, "Tunable sharp angular defect mode with invariant transmitted frequency range in one-dimensional photonic crystals containing negative index materials," Phys. Rev. E. 71, 066610 (2005).
- J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
- P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
- E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, 1985).

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