Mode volume

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In fiber optics, mode volume is the number of bound modes that an optical fiber is capable of supporting.

A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular to the radiation's propagation direction. Transverse modes occur in radio waves and microwaves confined to a waveguide, and also in light waves in an optical fiber and in a laser's optical resonator.

Optical fiber light-conducting fiber

An optical fiber is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss; in addition, fibers are immune to electromagnetic interference, a problem from which metal wires suffer excessively. Fibers are also used for illumination and imaging, and are often wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also used for a variety of other applications, some of them being fiber optic sensors and fiber lasers.

The mode volume M is approximately given by and , respectively for step-index and power-law index profile fibers, where g is the profile parameter, and V is the normalized frequency, which must be greater than 5 for this approximation to be valid.

For an optical fiber, a step-index profile is a refractive index profile characterized by a uniform refractive index within the core and a sharp decrease in refractive index at the core-cladding interface so that the cladding is of a lower refractive index. The step-index profile corresponds to a power-law index profile with the profile parameter approaching infinity. The step-index profile is used in most single-mode fibers and some multimode fibers.

For optical fibers, a power-law index profile is an index of refraction profile characterized by

In an optical fiber, the normalized frequency, V, is given by

See also

The equilibrium mode [power] distribution of light travelling in an optical waveguide or fiber, is the distribution of light that is no longer changing with fibre length or with input modal excitation. This phenomenon requires both mode filtering and mode mixing to occur in the fibre to produce a state that is independent of the mode power distribution launched by the light source. At propagation distances exceeding the equilibrium length, intramodal pulse distortion increases as the square root of length.

In telecommunications, a mode scramblermode mixer is a device for inducing mode coupling in an optical fiber, or a device that, itself, exhibits a uniform output intensity profile independent of the input mode volume or modal excitation condition. Mode scramblers are used to provide a modal distribution that is independent of the optical source for purposes of laboratory, manufacturing, or field measurements or tests. Mode scramblers are primarily used to improve reproducibility of multimode fiber bandwidth measurements.

In multimode fiber optics, mandrel wrapping is a technique used to preferentially attenuate high-order mode power of a propagating optical signal. Consequently, if the fibre is propagating substantial energy in affected modes, the modal distribution will be changed.

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In fiber optics, a graded index is an optical fiber whose core has a refractive index that decreases with increasing radial distance from the optical axis of the fiber.

Numerical aperture dimensionless number that characterizes the range of angles over which the system can accept or emit light

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

Single-mode optical fiber

In fiber-optic communication, a single-mode optical fiber (SMF) is an optical fiber designed to carry light only directly down the fiber - the transverse mode. Modes are the possible solutions of the Helmholtz equation for waves, which is obtained by combining Maxwell's equations and the boundary conditions. These modes define the way the wave travels through space, i.e. how the wave is distributed in space. Waves can have the same mode but have different frequencies. This is the case in single-mode fibers, where we can have waves with different frequencies, but of the same mode, which means that they are distributed in space in the same way, and that gives us a single ray of light. Although the ray travels parallel to the length of the fiber, it is often called transverse mode since its electromagnetic oscillations occur perpendicular (transverse) to the length of the fiber. The 2009 Nobel Prize in Physics was awarded to Charles K. Kao for his theoretical work on the single-mode optical fiber.

Dispersion (optics) Dependence of phase velocity on frequency

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

The laser diode rate equations model the electrical and optical performance of a laser diode. This system of ordinary differential equations relates the number or density of photons and charge carriers (electrons) in the device to the injection current and to device and material parameters such as carrier lifetime, photon lifetime, and the optical gain.

Laser beam welding

Laser beam welding (LBW) is a welding technique used to join pieces of metal or thermoplastics through the use of a laser. The beam provides a concentrated heat source, allowing for narrow, deep welds and high welding rates. The process is frequently used in high volume applications using automation, such as in the automotive industry. It is based on keyhole or penetration mode welding.

Multi-mode optical fiber

Multi-mode optical fiber is a type of optical fiber mostly used for communication over short distances, such as within a building or on a campus. Typical multi-mode links have data rates of 10 Mbit/s to 10 Gbit/s over link lengths of up to 600 meters. Multi-mode fiber has a fairly large core diameter that enables multiple light modes to be propagated and limits the maximum length of a transmission link because of modal dispersion.

Fiber Bragg grating

A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror. A fiber Bragg grating can therefore be used as an inline optical filter to block certain wavelengths, or as a wavelength-specific reflector.

Double-clad fiber

Double-clad fiber (DCF) is a class of optical fiber with a structure consisting of three layers of optical material instead of the usual two. The inner-most layer is called the core. It is surrounded by the inner cladding, which is surrounded by the outer cladding. The three layers are made of materials with different refractive indices.

In Riemannian geometry, the unit tangent bundle of a Riemannian manifold (M, g), denoted by T1M, UT(M) or simply UTM, is the unit sphere bundle for the tangent bundle T(M). It is a fiber bundle over M whose fiber at each point is the unit sphere in the tangent bundle:

In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can hear the shape of a drum is: given the Dirichlet eigenvalues, what features of the shape of the drum can one deduce. Here a "drum" is thought of as an elastic membrane Ω, which is represented as a planar domain whose boundary is fixed. The Dirichlet eigenvalues are found by solving the following problem for an unknown function u ≠ 0 and eigenvalue λ

Cladding in optical fibers is one or more layers of materials of lower refractive index, in intimate contact with a core material of higher refractive index. The cladding causes light to be confined to the core of the fiber by total internal reflection at the boundary between the two. Light propagation in the cladding is suppressed in typical fiber. Improving transmission through fibers by applying a cladding was discovered in 1953 by Dutch scientist Bram van Heel. Some fibers can support cladding modes in which light propagates in the cladding as well as the core.

Orbital angular momentum multiplexing

Orbital angular momentum (OAM) multiplexing is a physical layer method for multiplexing signals carried on electromagnetic waves using the orbital angular momentum of the electromagnetic waves to distinguish between the different orthogonal signals.

JCMsuite is a finite element analysis software package for the simulation and analysis of electromagnetic waves, elasticity and heat conduction. It also allows a mutual coupling between its optical, heat conduction and continuum mechanics solvers. The software is mainly applied for the analysis and optimization of nanooptical and microoptical systems. Its applications in research and development projects include dimensional metrology systems, photolithographic systems, photonic crystal fibers, VCSELs, Quantum-Dot emitters, light trapping in solar cells, and plasmonic systems. The design tasks can be embedded into the high-level scripting languages MATLAB and Python, enabling a scripting of design setups in order to define parameter dependent problems or to run parameter scans.

References

General Services Administration United States government agency

The General Services Administration (GSA), an independent agency of the United States government, was established in 1949 to help manage and support the basic functioning of federal agencies. GSA supplies products and communications for U.S. government offices, provides transportation and office space to federal employees, and develops government-wide cost-minimizing policies and other management tasks.

MIL-STD-188 series of U.S. military standards relating to telecommunications

MIL-STD-188 is a series of U.S. military standards relating to telecommunications.