Round-trip gain refers to the laser physics

Laser Physics

Laser Physics is an international scientific journal published by Nauka/Interperiodica. It is distributed through the Springer.-Topics covered:The journal specializes in laser physics, but also publishes papers about:...

, and laser cavitys (or laser resonators).
It is gain, integrated along a ray, which makes a round-trip in the cavity.

At the continuous-wave operation, the round-trip gain gain exactly compensate both, the output coupling of the cavity and its background loss.

Round-trip gain in geometric optics

Generally, the Round-trip gain may depend on the frequency, on the position and tilt of the ray, and even on the
polarization of light. Usually, we may assume that at some moment of time, at reasonable frequency of operation, the gain

Gain (lasers)

Gain in laser physics is a process, where the medium transfers part of its energy to the emitted electromagnetic radiation, resulting in an increase in laser power...

is function of the Cartesian coordinates
,
, and
. Then, assuming that the geometrical optics

Geometrical optics

Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as far as they travel in...

 is applyable
the round-trip gain can be expressed as follows:
,
where is path along the ray, parametrized with functions
,
,
; the integration is performed along the whole ray, which is supposed to
form the closed loop.

In simple models, the flat-top distribution of pump and
gain is assumed to be constant. In the case of simlest cavity, the round-trip gain
, where is length of the cavity; the laser light is supposed
to go forward and back, this leads to the coefficient 2 in the estimate.

In the steady-state continuous wave

Continuous wave

A continuous wave or continuous waveform is an electromagnetic wave of constant amplitude and frequency; and in mathematical analysis, of infinite duration. Continuous wave is also the name given to an early method of radio transmission, in which a carrier wave is switched on and off...

 operation of a laser, the round-trip gain is determined by the
reflectivity of the mirrors (in the case of stable cavity) and the magnification coefficient in the
case of unstable resonator (unstable cavity).

Coupling parameter

The coupling parameter of a laser resonator determines, what part of the
energy of the laser field in the cavity goes out at each round-trip. This output can be deermined by the
transmitivity of the output coupler

Output coupler

An output coupler is a partially reflective mirror used in lasers to extract a portion of the laser beam from the optical resonator....

, or the magnification coefficient in the case of unstable cavity
.

Round-trip loss (background loss)

The background loss, of the round-trip loss determines, what part of the energy of the laser field
becomes unusable at each round-trip; it can be absorbed or scattered.

At the self-pulsation

Self-pulsation

Self-pulsation takes place at the beginning of laser action.As the pump is switched on, the gainin the active medium rises and exceeds the steady-state value...

, the gain lates to respond the variation of number of photons in the cavity. Within the simple model,
the round-trip loss and the output coupling determine the damping parameters of the equivalent oscillator Toda

Oscillator Toda

In physics, the Toda oscillator is special kind of nonlinear oscillator; it is vulgarization of the Toda field theory, which is a continuous limit of Toda's chain, of chain of particles, with exponential potential of interaction between neighbors. These concepts are named afterMorikazu Toda...

.

At the steady-state operation, the round-trip gain exactly compensate both,
the output coupling and losses:
.
Assuming, that the gain is small (), this relation can be written as follows:



Such as relation is used in analytic estimates of the performance of lasers
. In particular, the
round-trip loss may be one of important parameters which limit the
output power of a disk laser

Disk laser

A disk laser or active mirror is a type of solid-state laser characterized by a heat sink and laser output that are realized on opposite sides of a thin layer of active gain medium...

; at the power scaling, the gain should be decreased
(in order to avoid the exponential growth

Exponential growth

Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...

 of the amplified spontaneous emission

Amplified spontaneous emission

Amplified spontaneous emission or superluminescence is light, produced by spontaneous emission, that has been optically amplified by the process of stimulated emission in a gain medium. It is inherent in the field of random lasers....

), and the round-trip gain
should remain larger than the background loss ;
this requires to increase of the thickness of the slab of the gain medium; at certain thickness, the
overheating

Overheating

Overheating may refer to:*Hyperthermia, also called sunstroke, an elevated body temperature due to failed thermoregulation*Thermal shock, the overheating of a device leading to reduced efficiency, damage or even destruction...

prevents the efficient operation
.

For the analysis of processes in active medium, the sum can be also called
"loss"
. This notation leads to confusions as soon as one is interested, which part of the
energy is absorbed and scattered, and which part of such a "loss" is actually wanted and useful output of the laser.