球体热辐射的空间相干性
Spatial Coherence of Thermal Emission by a Sphere
摘要：
本文给出了计算任意尺寸和材料的均匀等温球热辐射的能量密度和空间关联函数的解析表达式。在近场和远场制度的碳化硅，硅和钨球的各种尺寸参数范围从X = 0.002到5的光谱分布和幂律的距离依赖的能量密度的影响。研究了球体辐射热场在径向和极向的空间相干性。对于所有尺寸和材料，远场的能量密度都遵循d^-2（d是观测距离）的幂律。近场的幂律与材料、尺寸参数和比值d/a（a是球体半径）密切相关。在近场中，当X<<1且d/a>>1时，能量密度遵循d^-6的幂律（类似于电偶极子）。随着X的增加或d/a的减小，多极子对能量密度的贡献增加，导致d的幂次增加，直到幂律收敛到半无限介质的幂律。径向上的空间相关长度在远场、中间近场和极端近场中分别为$λ$、0.1 $λ$和0.001 $λ$的数量级。在极端近场中的相关角强烈地依赖于球体尺寸参数，使得当X从0.002增加到5时，其减小三个数量级（从0.5 $π$到0.001 $π$）。在中间近场和远场中，对于所有考虑的X，相关角保持相同的数量级（0.15 $π$ - 0.7 $π$）。虽然偶极局域表面声子（LSPh）的激发不影响相关长度和角度，但多极LSPh降低了两个方向上的空间相干性。
英文摘要：
Analytical expressions for calculating the energy density and spatial correlation function of thermal emission by a homogeneous, isothermal sphere of arbitrary size and material are presented. The spectral distribution and the power law governing the distance-dependent energy density are investigated in the near-field and far-field regimes for silicon carbide, silicon and tungsten spheres of various size parameters ranging from X = 0.002 to 5. The spatial coherence of thermal field emitted by spheres is also studied in both radial and polar directions. The energy density follows a power law of d^-2 (d is the observation distance) in the far field for all sizes and materials. The power law in the near field is strongly dependent on the material, size parameter, and the ratio d/a (a is the sphere radius). In the near field, the energy density follows a power law of d^-6 when X<<1 and d/a>>1 (similar to an electric point dipole). With increasing X or decreasing d/a, the contribution of multipoles to the energy density increases resulting in an increase in the power of d until the power law converges to that for a semi-infinite medium. The spatial correlation length in the radial direction is in the orders of $λ$, 0.1$λ$, and 0.001$λ$ in the far field, intermediate near field, and extreme near field, respectively. The correlation angle in the extreme near field is strongly dependent on the sphere size parameter, such that it decreases by three orders of magnitude (from 0.5$π$ to 0.001$π$) when X increases from 0.002 to 5. In the intermediate near field and far field, the correlation angle retains the same order of magnitude (0.15$π$ - 0.7$π$) for all considered Xs. While the excitation of dipolar localized surface phonons (LSPhs) does not affect the correlation length and angle, the multipolar LSPhs reduce the spatial coherence in both directions.
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