複式光柵輪廓來自疊合單式光柵的輪廓，雖然原理簡單且疊合後仍為一維週期結構，但許多光學或能源轉換元件僅可由複式光柵的特殊輻射性質達成，卻無法藉單式光柵達成。所以本文主要是針對微米級複式(complex)及其組成單式(simple)光柵，在波長範圍2.5 μm ‐ 25 μm的中紅外光為主之波段，探討雙方向(bi-direction)與方向半球輻射性質(穿透率與反射率)，並且探討影響性質之物理機制以及研究單/複式光柵之間輻射性質、輪廓疊合的相關連性。研究方法有實驗量測與理論模擬兩種方式，其中實驗部分是以半導體製程技術，透過黃光微影將不同週期與線寬之光柵圖案定義在矽晶圓基板，再經由蒸鍍的方式將鈦(Ti)與金(Au)分別沉積於基板上方，接著除去不需要的光阻後便完成樣本製作，形成一維週期金屬狹縫於矽基板上。在量測方面，是使用商用傅立葉轉換紅外線光譜儀(Fourier Transform Infrared spectrometer, FTIR)及其專屬反射率套件，獲得其垂直(θ = 0°)以及斜向(θ = 30°)入射之紅外光輻射性質。而在理論計算方面，數值方法是利用嚴格耦合波理論(Rigorous-Coupled Wave Analysis, RCWA)來模擬該結構之輻射性質。而後將量測與數值結果對照，並探討其輻射性質與物理機制。

The profile of complex grating is composed of simple gratings. Though the composing principle is uncomplicated and the profile is still one-dimensional (1D) periodic structures after superposition. However, there are many optics or energy conversion devices could be only accomplished by complex gratings due to its unique radiative properties. As a result, this work focuses on the bi-directional and directional-hemispherical infrared radiative properties (transmittance and reflectance) of microscale simple/complex gratings at the wavelength from 2.5 μm to 25 μm. In this study, both experiments and simulations are employed to study radiative properties. For experiments, the photoresist patterns with different geometric parameters were defined on silicon substrate by photolithography. Next, the titanium (Ti) and gold (Au) were deposited above the substrate through evaporation, respectively. Finally, the 1D periodic metallic slits were formed on silicon substrate after removing unwanted photoresist area. For measurements, the commercial Fourier transform infrared (FTIR) spectrometer and its specular reflectance accessory were utilized for obtaining infrared radiative properties at normal (θ = 0°) and oblique (θ = 30°) incidence. For theoretical calculations, the employed numerical algorithm is rigorous coupled-wave analysis (RCWA). After that, the measurement results were compared with calculation results to investigate their physical mechanisms and mid-radiative properties.

參考文獻
1. Sandstrom, R. L., Ershov, A. I., Partlo, W. N., Fomenkov, I. V., Smith, S. T., “High Resolution Etalon-Grating Monochromator,” U. S. Patent 6,480,275 B2, 2002.

2. Kanamori, Y., Shimono, M., and Hane, K., “Fabrication of Transmission Color Filters Using Silicon Subwavelength Gratings on Quartz Substrates,” IEEE Photonic Tech. L., Vol. 18, No. 20, pp. 2126-2128, 2006.

3. Yoon, Y. T., Lee, H. S., Lee, S. S., Kim, S. H., Park, J. D., and Lee, K. D., “Color Filter Incorporating a Subwavelength Patterned Grating in Poly Silicon,” Opt. Express, Vol. 16, No. 4, pp. 2374-2380, 2008.

4. Zhang, Z. M., Nano/Microscale Heat Transfer, McGraw-Hill, New York, 2007.

5. Jang, W. G., Beom, T. W., Cui, H., Park, J. R., Hwang, S. J., Lim, Y. J., and Lee, S. H., “Reduction of Viewing-Angle Dependent Color Shift in a Reflective Type Cholesteric Liquid Crystal Color Filter,” Appl. Phys. Express, Vol. 1, No. 3, pp. 032001-1/3, 2008.

6. Sai, H. and Yugami, H., “Thermophotovoltaic Generation with Selective Radiators Based on Tungsten Surface Gratings,” Appl. Phys. Lett., Vol. 85, No. 16, pp. 3399-3401, 2004.

7. Lee, H. S., Yoon, Y. T., Lee, S. S., Kim, S. H., and Lee, K. D., “Color Filter Based on a Subwavelength Patterned Metal Grating,” Opt. Express, Vol. 15, No. 13, pp. 15457-15463, 2007.

8. Tan, W. C., Sambles, J. R, and Preist, T. W., “Double-Period Zero-Order Metal Gratings as Effective Selective Absorbers,” Phys. Rev. B, Vol. 61, No. 19, pp. 177182, 2000.

9. Wang, Y., Chen, Y., Zhang, Y., and Liu, S., “Influence of Grooves in the Electromagnetic Transmission of a Periodic Metallic Grating Filter,” Opt. Commun., Vol. 271, pp. 132-136, 2007.

10. Zayats, A. V., Smolyaninov, I. I., and Maradudin, A. A., “Nano-optics of surface Plasmon polaritons,” Phys. Rep., Vol. 408, pp.131-314, 2005.

11. Hibbins, A. P., Sambles, J. R., and Lawrence, C. R., “Excitation of Remarkably Nondispersive Surface Plasmons on a Nondiffracting, Dual-Pitch Metal Grating,” Appl. Phys. Lett., Vol. 80, No. 13, pp. 2410-2412, 2002.

12. Lockyear, M. J., Hibbins, A. P., Sambles, J. R., and Lawrence, C. R., “Low Angular-Dispersion Microwave Absorption of a Dual-Pitch Nondiffracting Metal Bigrating,” Appl. Phys. Lett., Vol. 83, No. 4, pp. 806-808, 2003.

13. Lockyear, M. J., Hibbins, A. P., Sambles, J. R., and Lawrence, C. R., “Low Angular-Dispersion Microwave Absorption of a Metal Dual-Period Nondiffracting Hexagonal Grating,” Appl. Phys. Lett., Vol. 86, pp. 184103-1/3, 2005.

14. Hibbins, A. P., Hooper, I. R., Lockyear, M. J., and Sambles, J. R., “Microwave Transmission of a Compound Metal Grating,” Phys. Rev. Lett., Vol. 96, No. 25, pp. 257402-1/4, 2006.

15. Fantino, A. N., Grosz, S. I., and Skigin, D. C., “Resonant Effects in Periodic Gratings Comprising a Finite Number of Grooves in Each Period,” Phys. Rev. E, Vol. 64, pp. 016605-1/8, 2001.

16. Grosz, S. I., Skigin, D. C., and Fantino, A. N., “Resonant Effects in Compound Diffraction Gratings: Influence of the Geometrical Parameters of the Surface,” Phys. Rev. E, Vol. 65, pp. 056619-1/6, 2002.

17. Skigin, D. C., Fantino, A. N., and Grosz, S. I., “Phase Resonances in Compound Metallic Gratings,” J. Opt. A: Pure Appl. Opt., Vol. 5, No. 5, pp. s129-s135, 2003.

18. Skigin, D. C. and Depine, R. A., “Transmission Resonances of Metallic Compound Gratings with Subwavelength Slits,” Phys. Rev. Lett., Vol. 95, No. 21, pp. 217402-1/4, 2005.

19. Skigin, D. C. and Depine, R. A., ”Resonances on Metallic Compound Transmission Gratings with Subwavelength Wires and Slits,” Opt. Commun., Vol. 262, No. 2, pp. 270-275, 2006.

20. Skigin, D. C., Loui, H., Popovic, Z., and Kuester, E. F., “Bandwidth Control of Forbidden Transmission Gaps in Compound Structures with Subwavelength Slits,” Phys. Rev. E, Vol. 76, No. 1, pp. 016604-1/6, 2007.

21. Depine, R. A., Fantino, A. N., Grosz, S. I., and Skigin, D. C., “Phase Resonances in Obliquely Illuminated Compound Gratings,” Optik, Vol. 118, No. 1, pp. 42-52, 2007.

22. Navarro-Cia, M., Skigin, D. C., Beruete, M., and Sorolla, M., “Experimental Demonstration of Phase Resonances in Metallic Compound Gratings with Subwavelength Slits in the Millimeter Wave Regime,” Appl. Phys. Lett., Vol. 94, No. 9, pp. 091107-1/3, 2009.

23. Chen, Y. B. and Zhang, Z. M., “Design of Tungsten Complex Gratings for Thermophotovoltaic Radiators,” Opt. Commun., Vol. 269, No. 2, pp. 411-417, 2007.

24. Coutts, T. J., “A Review of Progress in Thermophotovoltaic Generation of Electricity,” Renew. Sust. Energ. Rev. Vol. 3, pp. 77-184, 1999.

25. Lin, S. Y., Moreno, J., and Fleming, J. G., “Three-Dimensional Photonic-Crystal Emitter for Thermal Photovoltaic Power Generation,” Appl. Phys. Lett., Vol. 83, No. 2, pp. 380-382, 2003.

26. Chen, Y. B. and Zhang, Z. M., “Heavily Doped Silicon Complex Gratings as Wavelength-Selective Absorbing Surfaces,” J. Phys. D: Appl. Phys., Vol. 41, No. 9, pp. 095406-1/8, 2008.

27. Madou, M. J., Fundamentals of Microfabrication, CRC Press, 2002.

28. Chen, Y. B., Lee, B. J., and Zhang, Z. M., “Infrared Radiative Properties of Submicron Metallic Slit Arrays,” J. Heat Trans.-T. ASME, Vol. 130, No. 8, pp. 082404-1/8, 2008.

29. Griffiths, P. R. and de Haseth, J. A., Fourier Transform Infrared Spectrometry, John Wiley & Sons, New Jersey, 2007.

30. Neviere, M. and Popov, E., Light Propagation in Periodic Media, Marcel Dekker, United State, 2003.

31. Moharam, M. G., Grann, E. B., and Pommet, D. A., “Formulation for Stable and Efficient Implementation of the Rigorous Coupled-Wave Analysis of Binary Gratings,” J. Opt. Soc. Am. A, Vol. 12, No. 5, pp. 1068-1076, 1995.

32. Choy, T. C., Effective Medium Theory, Oxford University Press, New York, 1999.

33. Born, M. and Wolf, E., Principles of Optics, Cambridge University Press, New York, 1999.

34. Chan, G., Nanoscale Energy Transport and Conversion, Oxford University Press, New York, 2005.

35. Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, United Stated, 2005.

36. Lee, B. J., Khuu, V. P., and Zhang, Z. M., “Partially Coherent Spectral Transmittance of Dielectric Thin Films with Rough Surfaces,” J. Thermophys. Heat Tr., Vol. 19, No. 3, pp. 360-366, 2005.

37. Sai, H., “Numerical Study on Spectral Properties of Tungsten One-Dimensional Surface-Relief Gratings for Spectrally Selective Device,” J. Opt. Soc. Am. A, Vol. 22, No. 9, pp. 1805-1813, 2005.

38. Garnett, J. C. M., “Colours in Metal Glasses and in Metal Film,” Phil. Trans. Royal Soc. London A, Vol. 203, pp. 385-420, 1904.

39. Bruggeman, D. A. G., “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen—Teil I,” Ann. der Physik, Vol. 24, pp. 636-679, 1935.

40. Lee, B. J., Chen, Y. B., and Zhang, Z. M., “Transmission Enhancement through Nanoscale Metallic Slit Arrays from the Visible to Mid-Infrared,” J. Comput. Theor. Nanosci. Vol. 5, No. 2, pp. 201-213, 2008.

41. Siegel, R. and Howell, J. R., Thermal Radiation Heat Transfer, McGraw-Hill, United States, 1972.

42. Ryoo, K., Kim, H. R., Koh, J. S., Seo, G., and Lee, J. H., “Fine Structure of Oxygen Absorption Bands in Si at Low Temperature,” J. Appl. Phys., Vol. 72, No. 11, pp. 5393-5396, 1992.

43. Palik, E. D., Handbook of Optical Constants of Solids, Academic Press, United States, 1985.

44. Hessel, A. and Oliner, A. A., “A New Theory of Wood’s Anomalies on Optical Gratings,” Appl. Opitcs, Vol. 4, No. 10, pp. 1275-1297, 1965.

45. Lee, B. J., Chen, Y. B. and Zhang, Z. M., “Confinement of Infrared Radiation to Nanometer Scales through Metallic Slit Arrays,” J. Quant. Spectrosc. Ra., Vol. 109, pp. 608-619, 2008.

46. Jin, E. X. and Xu, X., “Plasmonic Effects in Near-Field Optical Transmission Enhancement through a Single Bowtie-Shaped Aperture,” Appl. Phys. B, Vol. 84, pp. 3-9, 2006.

47. Sharma, K. K., Optics, Academic Press, United Stated, 2006.

48. Palmer, H. C., “Comment on The Article by Yakovlev and Gerasimov on The Intensity Distribution in The Spectrum of Diffraction Gratings,” J. Opt. Soc. Am., Vol. 51, pp. 1438-1439, 1961.