本論文旨在利用數值模擬方法，研究半導體介電質超表面中利用簡併臨界耦合來增強其紅外（IR）光的吸收。首先，我們研究在太赫茲 (THz）頻率範圍下，利用矽（Si）介電質超表面來實現簡併臨界耦合的條件。我們的結果顯示，當亞波長矽圓柱方形陣列中的電偶極（ED）和磁偶極（MD）兩個共振模態達成簡併時，矽介電質超表面在頻率ν = 1 THz可以達到高吸收率（~ 90%）。我們利用耦合模理論來擬合超表面的吸收光譜，得到上述兩個共振模態的輻射率（γ）和耗散率 (δ），並從而驗證了當兩個共振模態達成簡併臨界耦合時，兩個模態各別的輻射率和耗損率必須滿足 γ = δ的條件。其次，我們設計了一基於砷化鎵 (GaAs) 圓柱的介電質超表面，來增強短波紅外光波段的吸收。首先，當砷化鎵未摻雜時，通過系統性地改變砷化鎵圓柱的直徑（d）和高度（h），我們成功地在波長λ~ 3.8 μm處使超表面的電偶極和磁偶極兩個共振模態達成簡併。在此特定頻率下，砷化鎵圓柱陣列可將入射光完全反射（即反射率R = 1和透射率T = 0）。 我們進而藉由摻雜在砷化鎵中引入自由載子吸收，來臨界耦合超表面中互為簡併的電偶極和磁偶極兩個共振模態。在此條件下，砷化鎵超表面的吸收率在波長λ= 3.8 μm處可達到90 %。我們在以上兩種情況下，成功證明了半導體介電質超表面的紅外光吸收確實能在遠低於半導體能隙的頻率下增強。我們預期，此利用簡併臨界耦合，達成介電質超表面在低於半導體能隙的頻率下光吸收增強的現象，將可以應用於發展包括雷射和光偵測器的新型紅外光電元件上。

關鍵字: 介電質超表面、簡併臨界耦合、紅外光

This thesis is focused on numerical study of degenerate critical coupling in semiconductor dielectric metasurfaces for enhanced infrared (IR) absorption. First, we examine the condition for achieving degenerate critical coupling in a silicon (Si) dielectric metasurface in terahertz (THz) spectral region. We show that high absorption (~ 90 %) can be achieved at ν = 1 THz by spectrally overlapping the electrical dipole (ED) and magnetic dipole (MD) resonance modes supported in a square array of subwavelength Si cylinders. By fitting the absorption spectrum using coupled mode theory, the leakage and dissipation rates, γ and δ, of both resonance modes can be obtained, which in turn verifies the requirement of γ = δ for both modes to be critically coupled. Second, we design a GaAs-cylinder based dielectric metasurface for enhanced absorption in short-wave infrared region. When GaAs is undoped, by systematically varying the diameter (d) and height (h) of GaAs cylinders, we successfully overlap the ED and MD resonance modes at λ ~ 3.8 μm, at which incident light is completely reflected by the GaAs cylinder array (that is, reflectance R = 1 and transmittance T = 0, respectively). Upon introducing free-carrier absorption in GaAs by doping, we show that the absorptance of the GaAs metasurface reaches 90 % at λ= 3.8 μm by critically coupling its degenerate ED and MD resonance modes. In both cases, we demonstrate that enhanced infrared absorption of semiconductor dielectric metasurfaces can indeed occur at an energy far below the semiconductor bandgap. The demonstrated below-bandgap absorption enhancement in dielectric metasurfaces using degenerate critical coupling could potentially be employed for novel infrared optoelectronics including lasers and photodetectors.

Keyword: dielectric metasurface, degenerate critical coupling, infrared

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