physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, a pulse is a generic term describing a single disturbance that moves through a

transmission medium A transmission medium is a system or substance that can mediate the propagation of signals for the purposes of telecommunication. Signals are typically imposed on a wave of some kind suitable for the chosen medium. For example, data can modulate ...

. This medium may be

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...

(in the case of

electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...

) or

matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...

, and may be indefinitely large or finite.

Pulse reflection

Consider a pulse moving through a medium - perhaps through a rope or a

slinky The Slinky is a helical spring toy invented by Richard James in the early 1940s. It can perform a number of tricks, including travelling down a flight of steps end-over-end as it stretches and re-forms itself with the aid of gravity and its ow ...

. When the pulse reaches the end of that medium, what happens to it depends on whether the medium is fixed in space or free to move at its end. For example, if the pulse is moving through a rope and the end of the rope is held firmly by a person, then it is said that the pulse is approaching a fixed end. On the other hand, if the end of the rope is fixed to a stick such that it is free to move up or down along the stick when the pulse reaches its end, then it is said that the pulse is approaching a free end.

Free end

A pulse will reflect off a free end and return with the same direction of displacement that it had before reflection. That is, a pulse with an upward displacement will reflect off the end and return with an upward displacement. This is illustrated by figures 1 and 2 that were obtained by the numerical integration of the

wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and s ...

Fixed end

A pulse will reflect off a fixed end and return with the opposite direction of displacement. In this case, the pulse is said to have inverted. That is, a pulse with an upward displacement will reflect off the end and return with a downward displacement. This is illustrated by figures 3 and 4 that were obtained by the numerical integration of the

. In addition it is illustrated in the animation of figure 5.

Crossing media

When there exists a pulse in a medium that is connected to another less heavy or less dense medium, the pulse will reflect as if it were approaching a free end (no inversion). Contrarily, when a pulse is traveling through a medium connected to a heavier or denser medium, the pulse will reflect as if it were approaching a fixed end (inversion).

Optical pulse

Dark pulse

Dark pulses are characterized by being formed from a localized reduction of intensity compared to a more intense continuous wave background. Scalar dark

soliton In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium ...

s (linearly polarized dark solitons) can be formed in all normal dispersion fiber lasers mode-locked by the nonlinear polarization rotation method and can be rather stable. Vector dark solitons are much less stable due to the cross-interaction between the two polarization components. Therefore, it is interesting to investigate how the polarization state of these two polarization components evolves. In 2008, the first dark pulse laser was reported in a quantum dot diode laser with a saturable absorber. In 2009, the dark pulse fiber laser was successfully achieved in an all-normal dispersion erbium-doped fiber laser with a polarizer in cavity. Experimentation has revealed that apart from the bright pulse emission, under appropriate conditions the fiber laser could also emit single or multiple dark pulses. Based on numerical simulations, the dark pulse formation in the laser is a result of dark soliton shaping. In 2022, the first free space dark pulse laser using a nonlinear crystal inside of a solid state laser demonstrated.

References

{{reflist Radiation Physical phenomena