In this paper, we researched the optical properties of asymmetric transmission devices for onedimensional functions photonic crystals. The refractive indices of media A and B are not constant, it is the functions of space coordinate. By calculated the transmissivity and electric field distribution of asymmetric transmission devices, we found that when the forward incident light can transmit the function photonic crystals, but the backward incident light did not transmit through it, the function photonic crystals can be made into asymmetric transmission devices. Such as optical diodes or optical triode, etc.

The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have given the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems. On this basis, we have given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, we have given the generalized Hamiltonian function for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics.

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In the paper, we have given the quantum transmissivity, probability density and probability current density of photon in one-dimensional photonic crystals (AB) N with the quantum theory approach. We find the quantum transmissivity is identical to the classical transmissivity. When the incident angle θ and periodic number N change the probability density and probability current density are approximate periodic change, and their amplitude are increased with the incident angles θ and periodic number N increasing. Otherwise, we find when the frequency of incident photon is corresponding to transmissivity T = 1, the amplitude of the probability density is the largest. When the frequency of incident photon is corresponding to transmissivity T = 0, the amplitude of the probability density attenuate rapidly to zero, it indicates that there is the quantum tunnel effect of photon in photonic crystals.

The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have generalized the Hamilton principle to the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems, and given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, with the generalized Hamilton principle, we have given the generalized Hamiltonian for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics. PACS: 03.65.-w, 05.70.Ce, 05.30.Rt