微共振腔結構中自發放射速率及耦合係數之理論與計算

Abstract

本論文為計算在波導中電偶極(dipole)的自發放射 (spontaneous emission)速率及微小共振腔中之耦合係數。微共振腔包括面射型雷射( surfase emitting lasers)，微碟雷射(micro-disk)及微環雷射(micro- ring )雷射。我們得到自發放射速率與電偶極在結構中之方向有極大的關 係 。如平面波導(slab-waveguide)，當厚度小至波長之0.1倍時，垂直向 的電偶極明顯地對自發放射沒有貢獻，而水平向之電偶極則耦合至最低之 TE模。柱狀波導 (cylindrical waveguide) 中 ，當直徑於0.15-0.25倍 波長時，僅HE11模與徑向電偶極 (radial dipole) 有交互作用。自發放 射速率乃是波導模 (waveguide mode) 及放射模 (radiation mode)的總 和 。由於該自發放射僅有一部份比例能夠耦合至雷射模(lasing mode)。 因此定義參數β為全部自發放射中耦合至雷射模的比例 。該值亦與結構 有關。我們計算得出該係數在micro-ring雷射中可達0.925，在面射型雷 射中為1.85E-3。至於micro-disk雷射，在半徑1-5μm間，β為0.1 ∼0.25 。 In this thesis, we study spontaneous emission in slab and cylindrical dielectric waveguides and the coupling factor in micro-cavity, including surface emitting lasers, micro -disk and micro-ring lasers, by numerical simulations. Strong dependence of spontaneous emission rate on the dipole orientation was found. In planar waveguides, the emission for vertical dipoles was essentially inhibited, while the emission for horizontal dipoles falls into the lowest TE mode when thickness of the waveguide is a fraction of optical wavelength. Total spontaneous emission rates are obtained by adding the contribution from waveguide modes and radiation modes. Spontaneous emission factor β, defined as the fraction of total spontaneous emission into the waveguide or laser mode, was also found to depend strongly on the dimension of the structures. For proton-implanted GaAs surface emitting lasers incorporating AlGaAs/AlAs distributed Bragg reflectors, β is 1.85E-3. For micro-ring,β is as large as 0.925. As for micro- disk lasers,the disk diameter is 1 ∼5μm,when β is 0.1∼0.25 .