Transverse Electromagnetic Modes:

For every axial mode, there is a sequence of electromagnetic configurations
known as "transverse electromagnatic (TEM*mnq*) modes".
The letter *m* gives the number of nodal lines that lie along the
x axis. The letter *n* gives the number of nodal lines that lie along
the y axis. Finally, *q* - 1 indicates the number of nodal lines that
are along the z axis which is usually the axis of the laser cavity.

The linearly polarized electric field distribution for various modes in the xy plane are shown below. The field directions are denoted by arrows. The lines show where the electric field is zero.

^{4
}Figure 3

These field configurations are most commonly referred to as the transverse or spacial mode distributions.

These spacial mode distributions are approximately described by the following equation:

^{5}

where H_{m} and H_{n} are Hermite
polynomials of order m and n respectively. Some of the Hermite polynomials
are shown below:

H_{0} (x) = 1

H_{1} (x) = 2x

H_{2} (x) = 4x^{2}
- 2

H_{3} (x) = 8x^{3}
- 12x abcdef6

These equations can be used to render theoretical representations of the spacial mode distributions shown above in figure 3.

The eigenfrequencies of the modes can be calculated using the equation:

^{7}

where R1 and R2 are the radii of curvature for the two mirrors, L is the laser caavity length, and p, l, and m are numbers descibing the nodal lines of the mode. If squre mirrors are being used insted of circular mirrors, the letters p, l and m can be replaced by the letters m, n and q respectively. These letters indicate the number of nodal lines along each axis for the transverse or spacial mode distributions.