| Summary: | 碩士 === 國立成功大學 === 物理學系 === 107 === This work simulates the Hong-Ou-Mandel (HOM) interference phenomenon by using the theoretical framework of the photon wave mechanics (PWM). Here, comparing with the creation operator and annihilation operator formalism of the quantum field theory (QFT), photon wave function (PWF) describes the photon state explicitly in the E+icB form, and the equation of motion obeyed is just the Maxwell’s equations in the classical electromagnetics. Therefore, the finite-difference time domain method is suitable for numerical calculations. The probability of the photon wave function is given in the form of non-local integral. This form requires the introduction of dual modes to form the biorthogonal basis system with the wave-packet mode, thus possessing the Lorentz-invariance. Therefore, their modulus square is interpreted as the local energy density. The two-dimensional beam splitter is designed in the mechanism of evanescent wave coupling. Through the numerical calculation, the medium refractive index of √3 ensures that the splitting effects of different incident modes are the same. After the simulation, the result is different from HOM experiment. But interestingly, its lower envelope matches the shape of the HOM dip. This work shows that the theoretical interest of PWM is not only for the completeness of theories or the demand of simulations, but also helping us to understand more deeply the properties of fundamental particles.
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