Photonic crystal is a new field which combines optics and condensed matter physics. It is also a great important research field of applied physics in recent years.This is an artificial multi-dimension periodic structure in the two background media which possess different dielectric constants. It is so called beca use its structure and characteristics resemble that of solid crystal. Photonicb and gap (PBG) structure is a periodic modulation of dielectric and it can exhibit "forbidden" frequency regions where electromagnetic waves can not propagate along any directions in the crystal. This may bring about some peculiar physical phenomena

as well as wide applications in several scientific and technical areas. Some great a chievements made in this paperare listed as follows. (1) PBG structures with absolute band gaps are designed via the calculation of photonic band structures by plane-wave expansion method. A two-dimensional photonic crystal is periodic along two of its axes and homogeneous along the third. A typical specimen

consisting of a square lattice of dielectric columns is shown in Fig.1. For certain values of the column

spacing this crystal can have a photonic band gap in the x

1

-x

2

plane. The rods forming photonic crystal are characterized by a dielectric constant ε

a

=17

they are embedded in a background medium whose dielectric constant is ε

b

=1.The rods are of circular cross-section with radius

r

and the lattice constant of the square lattice is

a

with

a

>

2

r

. The main idea is to lift the band degeneracy at high symmetry points in the Bril louin zone of crystals by lowering the structure symmetry of crystal. (2) It also gives a complete deduction for the electromagnetic wave theory of photonic crystal of two dimensions and Bloch wave solution in stratified periodic dielectric

offers the academic foundation of the existence of stop band

and for an example of two dimensional photonic crystal of square lattice demonstrates that dielectric rods in air background can generate a common band gap

which is called absolute photonic band gap

for both orthogonal polarization

E

and

H

.As to two dimensional (2D) PBG structures

a novel method is applied to substantially improve absolute band gaps by quasi-independently adjusting the refractive indices for

E

-polarization and

H

-polarization modes. This is acco mplished b y fabricating 2D PBG structures from an isotropic materials and selecting the extraordinaryaxis of uniaxial crystal parallel to the extension direction of cylinders. Such a novel mechanism should open up a new scope to design 2D photonic band gaps.