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**Laser cavity modes** are particular sets of standing wave patterns in a laser cavity. Standing waves, also known as stationary waves, are created when two waves of the same frequency and amplitude but opposite phases interfere with each other. The output of a laser may consist of one mode or a superposition of several modes. These modes that are sustained depend on the boundary conditions, which are determined by the mirrors in a laser cavity, such as the geometry and alignment, as well as the wavelength of the laser.

A laser cavity is an optical resonator in a laser where the lasing action takes place. The cavity is typically made up of two mirrors at each end of the cavity, one of which is partially reflective and allows some of the light to pass through.

The light that is trapped inside the cavity between the mirrors is amplified as it bounces back and forth. However, the mirrors at each end lead to the development of both longitudinal and transverse modes superimposed on the beam. The longitudinal modes are standing wave patterns along the optical axis of the laser, whereas the transverse modes are perpendicular to the direction of propagation of the laser beam.

The number of modes, Mc(ν), that exist in a closed cavity of volume, Vc, over a frequency interval Δν is given by:

where c is the velocity of light.

These standing waves are created when the electromagnetic radiation is forced to move back and forth inside the cavity. In a standing wave, the point at which the amplitude of the waves is at a minimum is called a **node**, while the point at which the amplitude is at a maximum is called an **anti-node**. The positive integers m, n, and p give the number of nodes that the standing wave has along the y, z, and x axes, respectively. Each set of values of m, n, and p represents a well-defined cavity mode with a well-defined resonant frequency.

**Conditions for creating standing waves are:**

- Two waves of the same frequency and amplitude moving in opposite directions
- The optical path between the mirrors must be the length of the laser cavity.
- The wave must start with the same phase
- The length between the mirrors is constant; L is an integral multiple (p) of half wavelengths since only those frequencies that create nodes at both mirrors are allowed.

The wavelengths which create standing waves can be expressed as:

**Longitudinal modes**

The longitudinal modes are standing wave patterns along the optical axis of the laser. When different modes have the same values for m and n with a unit difference in the p-value, the corresponding difference in frequency of oscillationis:

Thus, these modes differ in their field distribution along the longitudinal axis. This explains why only specific frequencies are possible inside the cavity. Longitudinal modes appear as a single spot in the laser output. These modes are created by the length of the laser cavity and are determined by the distance between the cavity mirrors and the wavelength of the laser.

The number of longitudinal modes can be controlled by controlling the length of the laser cavity, for example, by reducing the cavity length, and adding an extra mirror inside the cavity.

**Transverse modes**

Transverse modes are standing wave patterns that are perpendicular to the direction of propagation of the laser beam. When the modes have the same p-value but differ in m and n values, the resulting field distributions differ in the transverse direction.

where a is the mirror dimension.

The transverse modes give an indication of the distribution of intensity within the beam crcross-sectionThese modes appear as a pattern of spots and are referred to as transverse electromagnetic, or TEM modes. These modes are created by the width of the laser cavity, which develops a few diagonal modes, and are determined by the shape of the laser beam. A little misalignment of the laser mirrors causes different path lengths for different rays inside the cavity.

The most common transverse mode is the Gaussian mode, which has a bell-shaped intensity profile and is designated by TEM_{mn}.

The number of transverse cavity modes can be controlled by choosing a pinhole diameter equal to the diameter of the lower mode.

Laser cavity modes depend on the frequency of the laser light, the direction in which it is emitted, and the intensity of the light. The length, shape, and optical properties of the cavity, such as the refractive index of the material within the cavity, also affect the laser cavity modes.

**Properties of Laser Cavity Modes**

- Spatial dependence
- Frequency dependence
- Mode competition

**Applications**

Laser cavity modes determine the output characteristics of the laser, such as wavelength, polarization, and spatial distribution of the laser light. The selection of a specific mode of operation is important for many applications, including laser spectroscopy, metrology, and material processing.