Surely laser cavity is also very important for a laser in many other aspects, for example, its dimension decides the longitudinal laser modes. Then what is a laser mode?

Generally speaking light modes means possible standing EM waves in a system. The number of modes in this meaning is huge. Laser mode means the possible standing waves in laser cavity. We see that stimulated lights are transmitted back and forth between the mirrors and interfere with each other, as a result only light whose round trip distance is integer multiples of the wavelength l can become a standing wave. That is:

m = 2L/(c/f) =2L/l , or f = m c/(2L), D f = c/(2L)

Where L is the length of cavity, c is the light speed in laser cavity, f is the frequency of standing wave, l is the wavelength, m is an integer, D f is the frequency difference between two consecutive modes. The number of longitudinal modes may be very large, it can also be as small as only a few (below 10).

If we intersect the output laser beam and study the transverse beam cross section, we find the light intensity can be of different distributions (patterns). These are called Transverse Electromagnetic Modes (TEM). Three index are used to indicate the TEM modes—TEMplq, p is the number of radial zero fields, l is the number of angular zero fields, q is the number of longitudinal fields. We usually use the first two index to specify a TEM mode, like TEM00, TEM10, etc. Clearly, the higher the order of the modes the more difficult it is poor to focus the beam to a fine spot. That is why some times TEM00 mode or Gaussian beam is preferred. Detailed discussion about laser modes can be found in higher level sections.