Types of modes, Laser modes

http://en.wikipedia.org/wiki/Transverse_mode

Transverse modes are classified into different types:

• TE modes (Transverse Electric) no electric field in the direction of propagation.
• TM modes (Transverse Magnetic) no magnetic field in the direction of propagation.
• TEM modes (Transverse ElectroMagnetic) no electric nor magnetic field in the direction of propagation.
• Hybrid modes nonzero electric and magnetic fields in the direction of propagation.

Modes of hollow metallic waveguides filled with a homogeneous, isotropic material fall into the first two categories. Otherwise, except in cases of special symmetry, modes are generally of hybrid type. For example, light travelling in an optical fiber or other dielectric waveguide forms hybrid-type modes. The fiber modes are usually referred to as LP (linear polarization) modes, which refers to a scalar approximation for the field solution, treating it as if it contains only one transverse field component (this is accurate because of the low refractive index contrast in typical fibers). The transverse electromagnetic (TEM) type. A planar Fabry-Perot resonator or etalon can also exhibit linearly polarized TEM modes. A resonator employing curved mirrors cannot support a TEM mode. Such modes are almost always hybrid except for the special cases of the electric field polarized either radially or azimuthally. The former case corresponds to a TM mode, the latter to a TE mode. Equivalently, linear polarization and TEM modes are mutually exclusive for a Gaussian beam or any other beam with curved wavefronts.

The TEM₀₀ mode corresponds to exactly the same fundamental mode as in the cylindrical geometry. Modes with increasing m and n show lobes appearing in the horizontal and vertical directions, with in general (m+1)(n+1) lobes present in the pattern. As before, higher-order modes have a larger spatial extent than the 00 mode.

The phase of each lobe of a TEM_mn is offset by π radians with respect to its horizontal or vertical neighbours. This is equivalent to the polarization of each lobe being flipped in direction.

The overall intensity profile of a laser's output may be made up from the superposition of any of the allowed transverse modes of the laser's cavity, though often it is desirable to operate only on the fundamental mode.