Laser cavity modes are particular sets of standing wave patterns in a laser cavity. Specific resonant modes, often referred to as cavity modes, are supported by the laser cavity and are distinguished by their particular characteristics. These characteristics affect the laser's behaviour and are crucial for understanding and controlling the output of the laser. The properties of laser cavity modes are wavelength of the laser cavity modes, spatial distribution of laser intensity, frequency of  modes, and mode competition inside the laser cavity.

Wavelength: The wavelength is among the most significant characteristics of laser cavity modes. It is determined by the size of the cavity and the type of material used in the cavity. The cavity is designed in such a manner that the length of the cavity is an integer multiple of  half wavelengths, which ensures that the light is confined within the cavity and the intensity can be increased.

Spatial Dependence: The mode shape is influenced by the spatial distribution of a mode's electric and magnetic fields. Different modes have different mode shapes, this affects the output intensity and beam quality of the laser. Even though all operating modes use mostly the same gain medium, they can access different spatial regions within the laser cavity. Each mode in a typical two mirror cavity with its associated mode number (n, l, m) is a distinct standing wave pattern that has an electric field value of zero at the mirrors. 

Each transverse mode must be associated with a specific longitudinal mode number, n, and unique transverse mode numbers l and m. Thus, the distinct standing wave pattern for each mode is a distinct spatial distribution of laser intensity that is slightly different from that of any other mode.

Frequency Dependence: The frequency difference between consecutive modes in the cavity is known as the mode spacing. The geometry of the cavity and the properties of the material influence the mode spacing, which is often quite small. This indicates that there are numerous modes within a constrained frequency range, and that a particular mode can be chosen for laser operation by varying the cavity length or the material's refractive index.

Each mode also has a slightly different frequency. For example, two transverse modes with the same "n" number can have different frequencies due to l and m mode numbers. However, two longitudinal modes typically have a greater frequency difference than transverse modes.

Mode Competition: Mode competition refers to a phenomenon where multiple optical modes compete for the same energy levels in a laser system. Although the laser cavity is capable of supporting several modes, the laser output will only use one mode. This is accomplished using mode selection techniques that identify the mode with the maximum gain, such as loss or feedback. A key component of laser construction and operation is the mode selection mechanism, which influences the laser's output power, wavelength, and stability.

For homogeneous broadening, all the waves associated with different modes are competing for the same upper laser level within the laser cavity and are attempting reach saturation. The mode at the centre of the gain profile will reach saturation first. Since the upper laser level is affected by saturation, the entire gain curve begins to decrease in amplitude. This makes it difficult for more than one mode to lase. The weaker mode depends on the spatial region of gain that is distinct from that of the strong mode. Since the transverse modes have distinct spatial regions, it is common for more than one transverse mode but only a single longitudinal mode to lase.

For inhomogeneous broadening, different longitudinal modes operate independently if their natural bandwidths do not overlap, because they are not competing for the same upper laser level. Even if the distinct longitudinal modes are sufficiently seperated in frequency, transverse modes with the same longitudinal mode number n with similar frequency compete for the same upper laser level. Because of their radically diverse spatial regions, it is common to saturate one longitudinal mode while leaving the transverse modes associated with that mode gaining.

Mode Polarization: The direction of the electric field vector inside the cavity is referred to as the mode polarization. Polarization can be divided into two categories: linear and circular. The laser's output intensity and beam quality are impacted by the polarization type. For instance, while circular polarization creates a beam with a more distinct spiral shape, linear polarization creates a beam that is more homogeneous.

Quality Factor: Quality factor of cavity mode defined as the ratio of the energy stored in the cavity to the energy lost every cycle, is influenced by the losses in the cavity, such as absorption and reflection. It measures confinement and determines energy storage duration for the mode in the cavity. The more energy that can be stored in the cavity, the greater the quality factor, and the more effective the laser will be.

Effect of modes on the gain of laser

Figure: Effect of modes

Laser modes that reach saturation intensity have a significant effect on the gain profile. When a laser beam consisting of n photons bounces back and forth, the population of the upper laser level can be reduced compared to the population before the beam developed. Each stimulated photon results in a decrease in the population at the upper laser level. Thus, the gain can be reduced. The two effects of mode competition that have a significant impact on the gain profile are spectral and spatial hole burning.