Round-trip gain refers to the
laser physics
Laser science or laser physics is a branch of optics that describes the theory and practice of lasers.
Laser science is principally concerned with quantum electronics, laser construction, optical cavity design, the physics of producing a popula ...
, and
laser cavities (or
laser resonator An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that forms a cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and provid ...
s). It is gain, integrated along a ray, which makes a round-trip in the cavity.
At the
continuous-wave operation, the round-trip gain exactly compensates 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
Polarization ( also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of t ...
. Usually, we may assume that at some moment of time, at reasonable frequency of operation, the
gain
Gain or GAIN may refer to:
Science and technology
* Gain (electronics), an electronics and signal processing term
* Antenna gain
* Gain (laser), the amplification involved in laser emission
* Gain (projection screens)
* Information gain in de ...
is function of the
Cartesian coordinates ,
, and
. Then, assuming that the
geometrical optics
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of ''rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
is applicable 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 simplest 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
A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particle ...
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
Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in siz ...
in the case of
unstable resonator
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be m ...
(
unstable cavity
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be m ...
).
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 determined by the transmitivity of the
output coupler
An output coupler (OC) is the component of an optical resonator that allows the extraction of a portion of the light from the laser's intracavity beam. An output coupler most often consists of a partially reflective mirror, allowing a certain po ...
, or the
magnification coefficient
Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in siz ...
in the case of
unstable cavity
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be m ...
.
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 is a transient phenomenon in continuous-wave lasers. Self-pulsation takes place at the beginning of laser action. As the pump is switched on, the gain in the active medium rises and exceeds the steady-state value. The number of ...
, the gain is late 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
In physics, the Toda oscillator is a special kind of nonlinear oscillator. It represents a chain of particles with exponential potential interaction between neighbors. These concepts are named after Morikazu Toda. The Toda oscillator is used as ...
.
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
A disk laser or active mirror (Fig.1) is a type of diode pumped 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.
Despite their name, disk lasers do not hav ...
; at the power scaling, the gain
should be decreased (in order to avoid the
exponential growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a q ...
of the
amplified spontaneous emission Amplified spontaneous emission (ASE) 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.
Origins ...
), 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
The active laser medium (also called gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a h ...
; at certain thickness, the
overheating prevents the efficient operation.
{dead link, date=April 2018 , bot=InternetArchiveBot , fix-attempted=yes
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.
References
Laser science