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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 10 — Oct. 2, 2009
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T-shaped plasmonic array as a narrow-band thermal emitter or biosensor

Chih-Ming Wang, Yia-Chung Chang, Mohammed Nadhim Abbas, Ming-Hsiung Shih, and Din Ping Tsai  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 13526-13531 (2009)
http://dx.doi.org/10.1364/OE.17.013526


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Abstract

A T-shaped plasmonic array is proposed for application as an effective thermal emitter or biosensor. The reflection and thermal radiation properties of a T-shaped array are investigated theoretically. The angular dependent reflectance spectrum shows a clear resonant dip at 0.36eV for full polar angles. No other significant localized resonant mode is found in the investigated spectral range from 0.12eV to 0.64eV. According to the Kirchhoff’s law, the thermal radiation of the proposed structure can lead to a sharp peak at 3.5µm with low sideband emission. We have also found that the T-shaped structure filled with organic material such as PMMA with different thicknesses (10 nm -50 nm) can lead to significant shift of the resonance wavelength. Thus, the T-shaped structure can also be used as a good sensor for organic materials.

© 2009 Optical Society of America

1. Introduction

According to the well-known Kirchhoff’s law [1

1. R. Siegel and J. Howell, Thermal Radiation Heat Transfer (New York: Hemisphere Publishing Corporation, 1981).

], good light absorbers are good light emitters when they are heated. At structured surfaces, the absorption may strongly depend on the angle of incidence and the polarization of the impinging light. Strong grating anomalies, where the absorption of a metallic surface rises up to nearly 100% of the impinging light flux, are expected to behave like a black body which leads to a perfect emitter [2

2. M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168, 117–122 (1999). [CrossRef]

]. Thermal radiation of structured surfaces, such as laminated structures [3

3. P. Ben-Abdallah and B. Ni, “Single-defect Bragg stacks for high-power narrow-band thermal emission,” J. Appl. Phys. 97, 104910 (2005). [CrossRef]

,4

4. I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72, 075127 (2005). [CrossRef]

], 2D/3D photonic crystals (PhC) [5

5. M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81, 4685–4687 (2002). [CrossRef]

8

8. S. Y. Lin, J. G. Fleming, and I. El-Kady, “Experimental observation of photonic-crystal emission near a photonic band edge,” Appl. Phys. Lett. 83, 593–595 (2003). [CrossRef]

], nanoparticle arrays [9

9. E. V. Shevchenko, D. V. Talapin, N. A. Kotov, S. O’Brien, and C.B. Murray, “Structural diversity in binary nanoparticle superlattices,” Nature 439, 55–59 (2006). [CrossRef] [PubMed]

,10

10. V. Yannopapas “Thermal emission from three-dimensional arrays of gold nanoparticles,” Phys. Rev. B 73, 113108 (2006). [CrossRef]

], and plasmonic crystals [11

11. I. Puscasu, M. Pralle, M. McNeal, J. Daly, A. Greenwald, E. Johnson, R. Biswas, and C. G. Ding, “Extraordinary emission from two-dimensional plasmonic-photonic crystals,” J. Appl. Phys. 98, 013531 (2005). [CrossRef]

13

13. T. H. Chuang, M. W. Tsai, Y. T. Chang, and S. C. Lee, “Remotely coupled surface plasmons in a two-colored plasmonic thermal emitter,” App. Phys. Lett. 89, 173128 (2006). [CrossRef]

], has been widely investigated. In addition, the grating anomaly highly depends on the incident angle of the impinging light so that the enhanced thermal radiation is observed only at a specific observation polar angle, the so-called Wolf effect [14

14. E. Wolf, “Non-cosmological red-shifts of spectral lines,” Nature 326, 363–365 (1987). [CrossRef]

,15

15. E. Wolf and D. F. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996). [CrossRef]

]. Recently, we demonstrated a narrow band thermal radiation of a plasmonic multilayer structure [16

16. C. M. Wang, Y. C. Chang, M. W. Tsai, Y. H. Ye, C. Y. Chen, Y. W. Jiang, S. C. Lee, and D. P. Tsai, “Reflection and emission properties of an infrared emitter,” Opt. Express. 15, 14673–14678 (2007). [CrossRef] [PubMed]

] which can be fabricated more easily than the PhC structure. The thermal radiation peaks coincide with angular-independent localized surface plasmon polariton (LSPP) modes of the structure. Thus, reducing the unwanted LSPP mode becomes an alternative for suppressing the sideband of the thermal radiation.

In this paper, we demonstrate the thermal radiation properties of a T-shaped array. Comparing to our pervious work [16

16. C. M. Wang, Y. C. Chang, M. W. Tsai, Y. H. Ye, C. Y. Chen, Y. W. Jiang, S. C. Lee, and D. P. Tsai, “Reflection and emission properties of an infrared emitter,” Opt. Express. 15, 14673–14678 (2007). [CrossRef] [PubMed]

], the multiple LSPP peaks of the metal/dielectric/metal cavity are suppressed. The reflectance spectrum of the proposed structure shows only one resonance dip, which leads to a sharp thermal radiation peak with a low sideband emission.

2. Thermal radiation and angular-dependent reflectance spectrum

Emission(λ,T)=B(λ,T)([1R(λ,θ,ϕ)]cos(θ)dΩ)
(1)

where R(λ, θ, ϕ) is the reflectance of the proposed structure at an incident angle, (θ,ϕ) confined in the upper hemisphere, and 1-R(λ,θ,ϕ) is the absorption efficiency of the structure, assuming the effect of higher-order reflectivities is negligible. B(λ,T) denotes the thermal radiation spectrum at temperature T without the grating structure. Through Eq. (1) one can quickly obtain an estimate of the thermal radiation spectrum of a structured surface by investigating the reflectance properties.

3. Device descriptions

In this paper, we study the thermal radiation and reflection properties of T-shaped plasmonic structures. Figure 1 shows a schematic picture of the analyzed structures. For reference, a plasmonic multilayer structure, which has been extensively investigated [12

12. M. W. Tsai, T. H. Chuang, C. Y. Meng, Y. T. Chang, and S. C. Lee, “High performance midinfrared narrow-band plasmonic thermal emitter,” App. Phys. Lett. 89, 173116 (2006). [CrossRef]

,13

13. T. H. Chuang, M. W. Tsai, Y. T. Chang, and S. C. Lee, “Remotely coupled surface plasmons in a two-colored plasmonic thermal emitter,” App. Phys. Lett. 89, 173128 (2006). [CrossRef]

,16

16. C. M. Wang, Y. C. Chang, M. W. Tsai, Y. H. Ye, C. Y. Chen, Y. W. Jiang, S. C. Lee, and D. P. Tsai, “Reflection and emission properties of an infrared emitter,” Opt. Express. 15, 14673–14678 (2007). [CrossRef] [PubMed]

], is shown in Fig. 1(a). The proposed T-shaped array on a metallic substrate is depicted in Fig. 1(b). The material of T-shaped array and the substrate is Ag. The periodicity of the T-shaped array is denoted by Λg. The widths at the top and the bottom of the T-shaped metallic line are wAg and wT, respectively. The thickness of the top of the T-shaped metallic line is tAg. To make the structure more robust, the bottom of the T-shaped metallic line are buried in a thin SiO2 layer with a thickness of tw. The substrate thickness is assumed to be infinite. The structure is illuminated with an incident plane wave at an angle θi. The reflectance of the structure is calculated by using the Rigorous Coupled Wave Analysis (RCWA) as described in ref. [17

17. 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); “Stable implementation of the rigorous coupled-wave analysis of surface-relief gratings: enhance transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995). [CrossRef]

]. The input light is TM (or TE) polarized in which the magnetic (electric) field is parallel to the grating grooves (i.e., parallel to the y-axis). The frequency-dependent complex dielectric constants of SiO2 and Ag are taken from ref. [18

18. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Boston, 1985).

]. It is found that around 50 plane waves are needed to obtain convergent results due to the localized nature of the solutions.

Fig. 1. Basic geometry of the investigated structures, (a) plasmonic multilayer structure and (b) T-shaped array.

4. Angle-dependent reflectance spectrum and thermal emission

Figure 2(a) shows the angle-dependent reflectance spectra of the plasmonic multilayer structure with geometric parameters of Λg=3000nm, wAg=1500nm, tAg=100nm and tw=50nm. The red and blue colors respectively represent high and low reflectance. Figure 2(a) displays three resonant dips at 0.21eV, 0.37eV and 0.55eV. Figures 2(b) and 2(c) shows the Hy 2 distribution within one pitch of the periodic structure respectively for 0.37eV (θi=89°) and 0.55eV (θ i=0°). From these nodal structures, we can identify the three resonant dips at 0.21eV, 0.37eV and 0.55eV as the n=1, n=2 and n=3 Fabry-Perot cavity modes, respectively.

With the same geometric parameters, the T-shaped array with wT=800nm displays a very different property. As shown in Fig. 3, the TM mode angle-dependent reflectance spectrum shows only one clear resonant dip at 0.36eV within a wide spectrum range from 0.12eV to 0.64eV for full polar incident angles. The geometric parameters of the T-shaped array are adopted as follows: Λg=3000nm, wAg=1500nm, tAg=100nm, tw=50nm and wT=800nm.

Fig. 2. (a). Simulated angle-dependent reflectance spectra of the plasmonic multilayer structure. Hy 2 distribution within one pitch of the periodic structure (b) at 0.37eV for θi=89° and (c) at 0.55eV for θi=0°. The bar charts on the right side of each panel indicate the relative strength of the reflectance or field intensity.
Fig. 3. (a).TM mode simulated angle-dependent reflectance spectra of the proposed T-shaped array structure. (b) Hy2 distribution within one pitch of the T-shaped array at 0.36eV for θi=0°. (c)TE mode simulated angle-dependent reflectance spectra of the proposed T-shaped array structure. (d) Ey2 distribution within one pitch of the T-shaped array at 0.4eV for θi=0°. The bar charts on the right side of each panel indicate the relative strength of the reflectance or field intensity.

Figure 3(b) shows the Hy 2 distribution within one pitch of the periodic T-shaped array at 0.36eV for θi=0°. The Hy 2 field distribution is symmetric with respect to the center plane (x=0nm) and localized under the cap of the T-shaped line. The Hy 2 field is localized within a one-closed-end cavity under the cap of the T-shaped, with a cavity length of Lc=(wAg-wT)/2. The wave function has a node at the open end and an antinode at the closed end. Ideally, the resonant wavelength satisfies the relation, λ=4neffLc. Here, the effective index of the resonant cavity, neff is a function of resonant wavelength and the dimensions of the cavity, so the relation is not quite linear. The Lc-dependent resonant wavelength will be discussed later. The TE mode reflectance spectra and mode pattern for the resonance dip are shown in Figs. 3(c) and 3(d). For the TE mode, there is no SPP mode since it follows different boundary conditions as the TM mode, and the Ey 2 field distribution at the resonance dip is not localized under the cap of the T-shaped line as illustrated in Fig. 3 (d).

Figure 4(a) shows the absorption spectrum for both TE and TM modes. It is clear in the figure that for TE mode most of the wave is reflected for all wavelengths, while for TM mode, there is strong absorption near the resonance wavelength. The thermal radiation spectra of the above mentioned structures are also calculated according to Eq. (1). The integration was done over 18 polar angles and 18 azimuthal angles (with 5 degree steps between 0 and 90 degrees) and B(λ,T) is taken to be the idea blackbody radiation curve at 500°C and it shows a maximum around 3.75µm. Figure 4(b) shows the simulated thermal radiation spectra of the structures. The solid and the dot-dashed lines represent the thermal radiation of the T-shaped array and plasmonic multilayer structure, respectively. The ideal blackbody radiation at 500°C is shown as dotted line. The plasmonic multilayer structure gives three thermal radiation peaks at 2.2µm, 3.1µm and 6µm, which correspond to the Fabry-Perot resonant dips at 0.55eV, 0.37eV, and 0.21eV shown in Fig. 2(a). The radiation spectrum of T-shaped array shows a single peak around 3.5µm. The other peaks due to the Fabry-Perot resonant dips, at 2.2µm and 6µm, are suppressed. Both the normal-incidence absorption spectrum and the thermal emission spectrum (integrated over all solid angles) display a strong peak near 3.5µm with similar lineshapes. This indicates that the emission pattern is nearly independent of angles, consistent to what’s displayed in Fig. 3(a). There is also a very narrow resonance peak in the normal-incidence absorption spectrum, which is caused by the angle-dependent SPP mode and it merges with the LSPP mode after the average over solid angles.

Fig. 4. (a). Absorption spectra of the proposed T-shaped array structure for TM mode (solid line) and TE mode (dashed line) for θi=0°. (b) Emission spectra of the proposed T-shaped array structure (solid line) and the plasmonic multilayer structure (dashed line).

From the point of view for applications, one can modify the resonant wavelength of the T-shaped array, i.e. engineer the thermal emission peak wavelength, through adjusting the cavity length, Lc. Figure 5(a) shows the resonant wavelength as a function of Lc. wT is fixed at 800nm, while wAg is allowed to vary from 1000nm to 2000nm in steps of 20nm. Two different SiO2 thickness, tw=20nm (black square) and tw=50nm (red circle), were considered. It can be seen that the resonant wavelength red shifts almost linearly with increasing Lc. The slopes for tw=20nm and tw=50nm are 9.21 and 7.35, respectively. For a thinner tw, the effective index of the cavity (defined as the slope divided by 4) is larger. Therefore the slope for tw=20nm is larger than that for tw=50nm. The single-mode behavior remains as the cavity length changes. However, the resonance peak is less sharp as the cavity length reduces. Besides the cavity length, the refractive index inside the cavity also plays a crucial role for tuning the reflection/emission properties. Thus a T-shaped structure without SiO2 could be used as material sensor, since the reflectance spectra would be sensitive to the refractive index of the filling material.

Fig. 5. (a). Resonant wavelength as a function of the cavity length, Lc. Two different SiO2 thickness, tw=20nm (black square) and tw=50nm (red circle), are used in the simulation. The thin straight lines are included for checking the linearity of the behavior. (b). Reflectance versus wavelength for various PMMA thicknesses. The insert shows the shift of resonance wavelength, Δλ versus the thickness, t of PMMA.

6. Sensitivity to organic materials

7. Conclusion

Acknowledgement

The authors acknowledge fruitful discussions with Ming-Wei Tsai, Yi-Han Ye, Chia-Yi Chen, Yu-Wei Jiang, Yi-Tsung Chang and Si-Chen Lee. This work is supported by Academia Sinica.

References and Links

1.

R. Siegel and J. Howell, Thermal Radiation Heat Transfer (New York: Hemisphere Publishing Corporation, 1981).

2.

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168, 117–122 (1999). [CrossRef]

3.

P. Ben-Abdallah and B. Ni, “Single-defect Bragg stacks for high-power narrow-band thermal emission,” J. Appl. Phys. 97, 104910 (2005). [CrossRef]

4.

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72, 075127 (2005). [CrossRef]

5.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81, 4685–4687 (2002). [CrossRef]

6.

I. Puscasu and W. L. Schaich, “Narrow-band, tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92, 233102 (2008). [CrossRef]

7.

S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional Photonic-Crystal Emitter for Thermal Photovoltaic Generation,” Appl. Phys. Lett. 83, 380–382 (2003). [CrossRef]

8.

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Experimental observation of photonic-crystal emission near a photonic band edge,” Appl. Phys. Lett. 83, 593–595 (2003). [CrossRef]

9.

E. V. Shevchenko, D. V. Talapin, N. A. Kotov, S. O’Brien, and C.B. Murray, “Structural diversity in binary nanoparticle superlattices,” Nature 439, 55–59 (2006). [CrossRef] [PubMed]

10.

V. Yannopapas “Thermal emission from three-dimensional arrays of gold nanoparticles,” Phys. Rev. B 73, 113108 (2006). [CrossRef]

11.

I. Puscasu, M. Pralle, M. McNeal, J. Daly, A. Greenwald, E. Johnson, R. Biswas, and C. G. Ding, “Extraordinary emission from two-dimensional plasmonic-photonic crystals,” J. Appl. Phys. 98, 013531 (2005). [CrossRef]

12.

M. W. Tsai, T. H. Chuang, C. Y. Meng, Y. T. Chang, and S. C. Lee, “High performance midinfrared narrow-band plasmonic thermal emitter,” App. Phys. Lett. 89, 173116 (2006). [CrossRef]

13.

T. H. Chuang, M. W. Tsai, Y. T. Chang, and S. C. Lee, “Remotely coupled surface plasmons in a two-colored plasmonic thermal emitter,” App. Phys. Lett. 89, 173128 (2006). [CrossRef]

14.

E. Wolf, “Non-cosmological red-shifts of spectral lines,” Nature 326, 363–365 (1987). [CrossRef]

15.

E. Wolf and D. F. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996). [CrossRef]

16.

C. M. Wang, Y. C. Chang, M. W. Tsai, Y. H. Ye, C. Y. Chen, Y. W. Jiang, S. C. Lee, and D. P. Tsai, “Reflection and emission properties of an infrared emitter,” Opt. Express. 15, 14673–14678 (2007). [CrossRef] [PubMed]

17.

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); “Stable implementation of the rigorous coupled-wave analysis of surface-relief gratings: enhance transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995). [CrossRef]

18.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Boston, 1985).

19.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature , 416, 61–64 (2002) [CrossRef] [PubMed]

20.

B. Lahiri, A. Z. Khokhar, R. M. De La Rue, S. G. McMeekin, and N. P. Johnson, “Asymmetric split ring resonators for optical sensing of organic materials,” Opt. Express. 17,1107–1115 (2009) [CrossRef] [PubMed]

21.

D. H. Williams and I. Fleming, Spectroscopic methods in Organic Chemistry (McGraw Hill Publications, 2nd Edition1973), Chap. 2

OCIS Codes
(260.3060) Physical optics : Infrared
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optoelectronics

History
Original Manuscript: June 2, 2009
Revised Manuscript: July 17, 2009
Manuscript Accepted: July 17, 2009
Published: July 22, 2009

Virtual Issues
Vol. 4, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Yia-Chung Chang, Chih-Ming Wang, Mohammed N. Abbas, Ming-Hsiung Shih, and Din Ping Tsai, "T-shaped plasmonic array as a narrow-band thermal emitter or biosensor," Opt. Express 17, 13526-13531 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-16-13526


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References

  1. R. Siegel and J. Howell, Thermal Radiation Heat Transfer (New York: Hemisphere Publishing Corporation, 1981).
  2. M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, "Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons," Opt. Commun. 168, 117-122 (1999). [CrossRef]
  3. P. Ben-Abdallah and B. Ni, "Single-defect Bragg stacks for high-power narrow-band thermal emission," J. Appl. Phys. 97, 104910 (2005). [CrossRef]
  4. I. Celanovic, D. Perreault, and J. Kassakian, "Resonant-cavity enhanced thermal emission," Phys. Rev. B 72, 075127 (2005). [CrossRef]
  5. M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002). [CrossRef]
  6. I. Puscasu, and W. L. Schaich, "Narrow-band, tunable infrared emission from arrays of microstrip patches," Appl. Phys. Lett. 92, 233102 (2008). [CrossRef]
  7. S. Y. Lin, J. Moreno, and J. G. Fleming, "Three-dimensional Photonic-Crystal Emitter for Thermal Photovoltaic Generation," Appl. Phys. Lett. 83, 380-382 (2003). [CrossRef]
  8. S. Y. Lin, J. G. Fleming, and I. El-Kady, "Experimental observation of photonic-crystal emission near a photonic band edge," Appl. Phys. Lett. 83, 593-595 (2003). [CrossRef]
  9. E. V. Shevchenko, D. V. Talapin, N. A. Kotov, S. O'Brien, and C.B. Murray, "Structural diversity in binary nanoparticle superlattices," Nature 439, 55-59 (2006). [CrossRef] [PubMed]
  10. V. Yannopapas "Thermal emission from three-dimensional arrays of gold nanoparticles," Phys. Rev. B 73, 113108 (2006). [CrossRef]
  11. I. Puscasu, M. Pralle, M. McNeal, J. Daly, A. Greenwald, E. Johnson, R. Biswas, and C. G. Ding, "Extraordinary emission from two-dimensional plasmonic-photonic crystals," J. Appl. Phys. 98, 013531 (2005). [CrossRef]
  12. M. W. Tsai, T. H. Chuang, C. Y. Meng, Y. T. Chang, and S. C. Lee, "High performance midinfrared narrow-band plasmonic thermal emitter," App. Phys. Lett. 89, 173116 (2006). [CrossRef]
  13. T. H. Chuang, M. W. Tsai, Y. T. Chang, and S. C. Lee, "Remotely coupled surface plasmons in a two-colored plasmonic thermal emitter," App. Phys. Lett. 89, 173128 (2006). [CrossRef]
  14. E. Wolf, "Non-cosmological red-shifts of spectral lines," Nature 326, 363-365 (1987). [CrossRef]
  15. E. Wolf and D. F. James, "Correlation-induced spectral changes," Rep. Prog. Phys. 59, 771-818 (1996). [CrossRef]
  16. C. M. Wang, Y. C. Chang, M. W. Tsai, Y. H. Ye, C. Y. Chen, Y. W. Jiang, S. C. Lee, and D. P. Tsai, "Reflection and emission properties of an infrared emitter," Opt. Express. 15, 14673-14678 (2007). [CrossRef] [PubMed]
  17. 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); "Stable implementation of the rigorous coupled-wave analysis of surface-relief gratings: enhance transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995). [CrossRef]
  18. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Boston, 1985).
  19. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy and Y. Chen, "Coherent emission of light by thermal sources," Nature,  416, 61-64 (2002) [CrossRef] [PubMed]
  20. B. Lahiri, A. Z. Khokhar, R. M. De La Rue, S. G. McMeekin, and N. P. Johnson, "Asymmetric split ring resonators for optical sensing of organic materials," Opt. Express. 17,1107-1115 (2009) [CrossRef] [PubMed]
  21. D. H. Williams and I. Fleming, Spectroscopic methods in Organic Chemistry (McGraw Hill Publications, 2nd Edition 1973), Chap. 2

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