Desktop version

Home arrow Engineering arrow Cellular Image Classification

Solution to LP2i Mode

From Maxwell equations, we can obtain natural modes, TE and TH modes. However, the TE and TH modes only exist when m = 0; when m is not zero, TE mode and TH mode cannot exist. Only in the form of Ez and Hz coexistence can they exist, and when Ez accounts for a large proportion they are called EH modes, otherwise are named HE modes. Linear polarized mode is constituted by the degeneration of the EH mode and the HE mode, LPmn = EHm+1nHEm-1,n, where EHm+1n and HEm-1,n are two solutions to Maxwell equations under the same boundary conditions [11].

In order to facilitate the discussion of mode polarization, we transform the polar coordinates into Cartesian coordinates via following equations:

We solved for HE31, EH11 mode using:

where 60 can take either 0° or 90°, standing for even or odd mode respectively, indicating that both are mutually orthogonal. In this way, by the expression LP21 = HE31 + EH11, we can derive the formula of LP21 mode as follows:

In Eq. 3.5, it can be obtained that the transverse component along the X-direction is zero, i.e., the light field is only in the Y-direction of polarization, and contains 60 = 0° and 90° two modes. Similarly, LP21 mode can be derived from the expression LP21 = HE31 - EH11:

In this condition, the transverse component in Y direction is zero, that is to say, only in the X direction exists the polarized light field, and comprising of two modes with в0 = 0° and 90°.

< Prev   CONTENTS   Source   Next >

Related topics