In optics, polarized light can be described using the Jones calculus, invented by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by Jones matrices. When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light. Note that Jones calculus is only applicable to light that is already fully polarized. Light which is randomly polarized, partially polarized, or incoherent must be treated using Mueller calculus.
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.
In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave.
Polarization is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image), for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves in solids.
A waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. Two common types of waveplates are the half-wave plate, which rotates the polarization direction of linearly polarized light, and the quarter-wave plate, which converts between different elliptical polarizations
Birefringence means double refraction. It is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are described as birefringent or birefractive. The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress.
A Lyot filter, named for its inventor and French astronomer Bernard Lyot, is a type of optical filter that uses birefringence to produce a narrow passband of transmitted wavelengths. Lyot filters are used in astronomy, particularly for solar astronomy, lasers, biomedical photonics and Raman chemical imaging.
An optical vortex is a zero of an optical field; a point of zero intensity. The term is also used to describe a beam of light that has such a zero in it. The study of these phenomena is known as singular optics.
A solid-state laser is a laser that uses a gain medium that is a solid, rather than a liquid as in dye lasers or a gas as in gas lasers. Semiconductor-based lasers are also in the solid state, but are generally considered as a separate class from solid-state lasers, called laser diodes.
A fiber laser is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such as erbium, ytterbium, neodymium, dysprosium, praseodymium, thulium and holmium. They are related to doped fiber amplifiers, which provide light amplification without lasing.
A depolarizer or depolariser is an optical device used to scramble the polarization of light. An ideal depolarizer would output randomly polarized light whatever its input, but all practical depolarizers produce pseudo-random output polarization.
In physical optics or wave optics, a vector soliton is a solitary wave with multiple components coupled together that maintains its shape during propagation. Ordinary solitons maintain their shape but have effectively only one (scalar) polarization component, while vector solitons have two distinct polarization components. Among all the types of solitons, optical vector solitons draw the most attention due to their wide range of applications, particularly in generating ultrafast pulses and light control technology. Optical vector solitons can be classified into temporal vector solitons and spatial vector solitons. During the propagation of both temporal solitons and spatial solitons, despite being in a medium with birefringence, the orthogonal polarizations can copropagate as one unit without splitting due to the strong cross-phase modulation and coherent energy exchange between the two polarizations of the vector soliton which may induce intensity differences between these two polarizations. Thus vector solitons are no longer linearly polarized but rather elliptically polarized.
A polarization controller is an optical device which allows one to modify the polarization state of light.
The angular momentum of light is a vector quantity that expresses the amount of dynamical rotation present in the electromagnetic field of the light. While traveling approximately in a straight line, a beam of light can also be rotating around its own axis. This rotation, while not visible to the naked eye, can be revealed by the interaction of the light beam with matter.
The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. OAM can be split into two types. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position and its total linear momentum.
An acousto-optic programmable dispersive filter (AOPDF) is a special type of collinear-beam acousto-optic modulator capable of shaping spectral phase and amplitude of ultrashort laser pulses. AOPDF was invented by Pierre Tournois. Typically, quartz crystals are used for the fabrication of the AOPDFs operating in the UV spectral domain, paratellurite crystals are used in the visible and the NIR and calomel in the MIR (3–20 μm). Recently introduced lithium niobate crystals allow for high-repetition rate operation (> 100 kHz) owing to their high acoustic velocity. The AOPDF is also used for the active control of the carrier-envelope phase of few-cycle optical pulses, as a part of pulse-measurement schemes and multi-dimensional spectroscopy techniques. Although sharing a lot in principle of operation with an acousto-optic tunable filter, the AOPDF should not be confused with it, since in the former the tunable parameter is the transfer function and in the latter it is the impulse response.
Rotating-polarization coherent anti-Stokes Raman spectroscopy, (RP-CARS) is a particular implementation of the coherent anti-Stokes Raman spectroscopy (CARS). RP-CARS takes advantage of polarization-dependent selection rules in order to gain information about molecule orientation anisotropy and direction within the optical point spread function.
A q-plate is an optical device that can form a light beam with orbital angular momentum (OAM) from a beam with well-defined spin angular momentum (SAM). Q-plates are based on the SAM-OAM coupling that may occur in media that are both anisotropic and inhomogeneous, such as an inhomogeneous anisotropic birefringent waveplate. Q-plates are also currently realized using total internal reflection devices, liquid crystals, metasurfaces based on polymers, and sub-wavelength gratings.
Anisotropic terahertz microspectroscopy (ATM) is a spectroscopic technique in which molecular vibrations in an anisotropic material are probed with short pulses of terahertz radiation whose electric field is linearly polarized parallel to the surface of the material. The technique has been demonstrated in studies involving single crystal sucrose, fructose, oxalic acid, and molecular protein crystals in which the spatial orientation of molecular vibrations are of interest.
Sergio Carbajo is a Basque-Spanish-American scientist and educator, musician and composer, and creative writer. He is an assistant professor at the University of California, Los Angeles Samueli School of Engineering and Applied Sciences with appointments in the Electrical & Computer Engineering (ECE) and Physics & Astronomy departments. He is also a scientist at Stanford University’s Photon Science Division at SLAC National Accelerator Laboratory.
