Yi-Heng Wu

Function photonic crystals

Abstract In this paper, we present a new kind of function photonic crystals (PCs), whose refractive index is a function of space position. Conventional PCs structure grows from two materials, A and B, with different dielectric constants e A and e B . Based on Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we give the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals, and we find the following: (1) For the vertical and non-vertical incidence light of function photonic crystals, there are band gap structures, and for only the vertical incidence light, the conventional PCs have band gap structures. (2) By choosing various refractive index distribution functions n(z), we can obtain more wider or more narrower band gap structure than conventional photonic crystals.

Quantum Wave Equation of Photon

In this paper, we give the quantum wave equations of single photon when it is in the vacuum and medium. With these wave equations, we can study light interference and diffraction with the approach of quantum theory, and also can study the quantum property of photon when it is in a general crystal and photonic crystal. Otherwise, it can be applied in quantum optics and condensed matter feld.

Two-dimensional function photonic crystals

In this paper, we have firstly proposed two-dimensional function photonic crystals, which the dielectric constants of medium columns are the functions of space coordinates

Finite Temperature Schrödinger Equation

\vec{r}

The Quantum Well of One-Dimensional Photonic Crystals

, it is different from the two-dimensional conventional photonic crystals constituting by the medium columns of dielectric constants are constants. We find the band gaps of two-dimensional function photonic crystals are different from the two-dimensional conventional photonic crystals, and when the functions form of dielectric constants are different, the band gaps structure should be changed, which can be designed into the appropriate band gaps structures by the two-dimensional function photonic crystals.

Quantum theory of light diffraction

We know Schrödinger equation describes the dynamics of quantum systems, which don’t include temperature. In this paper, we propose finite temperature Schrödinger equation, which can describe the quantum systems in an arbitrary temperature. When the temperature T=0, it become Shrödinger equation.

Quantum Theory of Atom Laser Cooling

We have studied the transmissivity of one-dimensional photonic crystals quantum well (QW) with quantum theory approach. By calculation, we find that there are photon bound states in the QW structure , and the numbers of the bound states are equal to . We have found that there are some new features in the QW, which can be used to design optic amplifier, attenuator, and optic filter of multiple channel.

Derivation of Nonlinear Schrödinger Equation

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.

A new quantum approach of one-dimensional photonic crystals

In this paper, we study the laser cooling mechanisms with new Schrodinger quantum wave equation, which can describe a particle in conservative and non-conservative force field. We prove the atom in laser field can be cooled with the new theory, and predict that the atom cooling temperature T is directly proportional to the atom vibration frequency ω, which is in accordance with experiment result. PACS: 03.65.-w, 37.10.De, 37.10.Mn

Dirac Equation at Finite Temperature

We propose some nonlinear Schrödinger equations by adding some higher order terms to the Lagrangian density of Schrödinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. In addition, we prove the coefficient of nonlinear term is very small, i.e., the nonlinearity of Schrödinger equation is weak.