1.
Optics
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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
Optics
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Optics includes study of
dispersion of light.
Optics
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The Nimrud lens
Optics
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Reproduction of a page of
Ibn Sahl 's manuscript showing his knowledge of the law of refraction, now known as
Snell's law
Optics
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Cover of the first edition of Newton's Opticks
2.
Laser
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A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The term laser originated as an acronym for light amplification by stimulated emission of radiation, the first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. A laser differs from other sources of light in that it emits light coherently, spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser cutting and lithography. Spatial coherence also allows a laser beam to stay narrow over great distances, Lasers can also have high temporal coherence, which allows them to emit light with a very narrow spectrum, i. e. they can emit a single color of light. Temporal coherence can be used to produce pulses of light as short as a femtosecond, Lasers are distinguished from other light sources by their coherence. Spatial coherence is typically expressed through the output being a narrow beam, Laser beams can be focused to very tiny spots, achieving a very high irradiance, or they can have very low divergence in order to concentrate their power at a great distance. Temporal coherence implies a polarized wave at a single frequency whose phase is correlated over a great distance along the beam. A beam produced by a thermal or other incoherent light source has an amplitude and phase that vary randomly with respect to time and position. Lasers are characterized according to their wavelength in a vacuum, most single wavelength lasers actually produce radiation in several modes having slightly differing frequencies, often not in a single polarization. Although temporal coherence implies monochromaticity, there are lasers that emit a broad spectrum of light or emit different wavelengths of light simultaneously, there are some lasers that are not single spatial mode and consequently have light beams that diverge more than is required by the diffraction limit. However, all devices are classified as lasers based on their method of producing light. Lasers are employed in applications where light of the spatial or temporal coherence could not be produced using simpler technologies. The word laser started as an acronym for light amplification by stimulated emission of radiation, in the early technical literature, especially at Bell Telephone Laboratories, the laser was called an optical maser, this term is now obsolete. A laser that produces light by itself is technically an optical rather than an optical amplifier as suggested by the acronym. It has been noted that the acronym LOSER, for light oscillation by stimulated emission of radiation. With the widespread use of the acronym as a common noun, optical amplifiers have come to be referred to as laser amplifiers. The back-formed verb to lase is frequently used in the field, meaning to produce light, especially in reference to the gain medium of a laser. Further use of the laser and maser in an extended sense, not referring to laser technology or devices, can be seen in usages such as astrophysical maser
Laser
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United States Air Force laser experiment
Laser
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Red (660 & 635 nm), green (532 & 520 nm) and blue-violet (445 & 405 nm) lasers
Laser
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Laser beams in fog, reflected on a car windshield
Laser
3.
Light
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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to light, which is visible to the human eye and is responsible for the sense of sight. Visible light is defined as having wavelengths in the range of 400–700 nanometres, or 4.00 × 10−7 to 7.00 × 10−7 m. This wavelength means a range of roughly 430–750 terahertz. The main source of light on Earth is the Sun, sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the used by living things. Historically, another important source of light for humans has been fire, with the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence, for example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey. Visible light, as all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the term sometimes refers to electromagnetic radiation of any wavelength. In this sense, gamma rays, X-rays, microwaves and radio waves are also light, like all types of light, visible light is emitted and absorbed in tiny packets called photons and exhibits properties of both waves and particles. This property is referred to as the wave–particle duality, the study of light, known as optics, is an important research area in modern physics. Generally, EM radiation, or EMR, is classified by wavelength into radio, microwave, infrared, the behavior of EMR depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths, when EMR interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. There exist animals that are sensitive to various types of infrared, infrared sensing in snakes depends on a kind of natural thermal imaging, in which tiny packets of cellular water are raised in temperature by the infrared radiation. EMR in this range causes molecular vibration and heating effects, which is how these animals detect it, above the range of visible light, ultraviolet light becomes invisible to humans, mostly because it is absorbed by the cornea below 360 nanometers and the internal lens below 400. Furthermore, the rods and cones located in the retina of the eye cannot detect the very short ultraviolet wavelengths and are in fact damaged by ultraviolet. Many animals with eyes that do not require lenses are able to detect ultraviolet, by quantum photon-absorption mechanisms, various sources define visible light as narrowly as 420 to 680 to as broadly as 380 to 800 nm
Light
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An example of refraction of light. The straw appears bent, because of refraction of light as it enters liquid from air.
Light
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A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) get separated.
Light
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A
cloud illuminated by
sunlight
Light
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A
city illuminated by
artificial lighting
4.
Semiconductor laser
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A laser diode is electrically a PIN diode. The active region of the diode is in the intrinsic region. Unlike a regular diode, the goal for a diode is to recombine all carriers in the I region. Thus, laser diodes are fabricated using direct bandgap semiconductors, the active layer most often consists of quantum wells, which provide lower threshold current and higher efficiency. Laser diodes form a subset of the classification of semiconductor p-n junction diodes. Forward electrical bias across the laser diode causes the two species of charge carrier – holes and electrons – to be injected from opposite sides of the p-n junction into the depletion region, holes are injected from the p-doped, and electrons from the n-doped, semiconductor. Due to the use of injection in powering most diode lasers. As diode lasers are semiconductor devices, they may also be classified as semiconductor lasers, either designation distinguishes diode lasers from solid-state lasers. Another method of powering some diode lasers is the use of optical pumping, optically pumped semiconductor lasers use a III-V semiconductor chip as the gain medium, and another laser as the pump source. OPSL offer several advantages over ILDs, particularly in wavelength selection, spontaneous emission below the lasing threshold produces similar properties to an LED. Spontaneous emission is necessary to initiate laser oscillation, but it is one among several sources of inefficiency once the laser is oscillating and these photon-emitting semiconductors are the so-called direct bandgap semiconductors. The properties of silicon and germanium, which are single-element semiconductors, have bandgaps that do not align in the way needed to allow photon emission and are not considered direct, the transition between the materials in the alternating pattern creates the critical direct bandgap property. Gallium arsenide, indium phosphide, gallium antimonide, and gallium nitride are all examples of compound semiconductor materials that can be used to create junction diodes that emit light, a nearby photon with energy equal to the recombination energy can cause recombination by stimulated emission. This generates another photon of the frequency, polarization, and phase. This means that stimulated emission will cause gain in a wave in the injection region. As in other lasers, the region is surrounded with an optical cavity to form a laser. In the simplest form of diode, an optical waveguide is made on that crystals surface. The two ends of the crystal are cleaved to form smooth, parallel edges, forming a Fabry–Pérot resonator
Semiconductor laser
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Top: a packaged laser diode shown with a
penny for scale. Bottom: the laser diode chip is removed from the above package and placed on the eye of an orphan needle for scale.
Semiconductor laser
Semiconductor laser
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A laser diode with the case cut away. The actual laser diode chip is the small black chip at the front; a photodiode at the back is used to control output power.
Semiconductor laser
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Semi-conductor lasers (660 nm, 635 nm, 532 nm, 520 nm, 445 nm, 405 nm)
5.
Electrons
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The electron is a subatomic particle, symbol e− or β−, with a negative elementary electric charge. Electrons belong to the first generation of the lepton particle family, the electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the include a intrinsic angular momentum of a half-integer value, expressed in units of the reduced Planck constant. As it is a fermion, no two electrons can occupy the same state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of particles and waves, they can collide with other particles and can be diffracted like light. Since an electron has charge, it has an electric field. Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz force law, electrons radiate or absorb energy in the form of photons when they are accelerated. Laboratory instruments are capable of trapping individual electrons as well as electron plasma by the use of electromagnetic fields, special telescopes can detect electron plasma in outer space. Electrons are involved in applications such as electronics, welding, cathode ray tubes, electron microscopes, radiation therapy, lasers, gaseous ionization detectors. Interactions involving electrons with other particles are of interest in fields such as chemistry. The Coulomb force interaction between the positive protons within atomic nuclei and the negative electrons without, allows the composition of the two known as atoms, ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system. The exchange or sharing of the electrons between two or more atoms is the cause of chemical bonding. In 1838, British natural philosopher Richard Laming first hypothesized the concept of a quantity of electric charge to explain the chemical properties of atoms. Irish physicist George Johnstone Stoney named this charge electron in 1891, electrons can also participate in nuclear reactions, such as nucleosynthesis in stars, where they are known as beta particles. Electrons can be created through beta decay of isotopes and in high-energy collisions. The antiparticle of the electron is called the positron, it is identical to the electron except that it carries electrical, when an electron collides with a positron, both particles can be totally annihilated, producing gamma ray photons. The ancient Greeks noticed that amber attracted small objects when rubbed with fur, along with lightning, this phenomenon is one of humanitys earliest recorded experiences with electricity. In his 1600 treatise De Magnete, the English scientist William Gilbert coined the New Latin term electricus, both electric and electricity are derived from the Latin ēlectrum, which came from the Greek word for amber, ἤλεκτρον
Electrons
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A beam of electrons deflected in a circle by a magnetic field
Electrons
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Hydrogen atom
orbitals at different energy levels. The brighter areas are where you are most likely to find an electron at any given time.
Electrons
–
Robert Millikan
Electrons
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A
lightning discharge consists primarily of a flow of electrons. The electric potential needed for lightning may be generated by a triboelectric effect.
6.
Stimulated emission
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Stimulated emission is the process by which an incoming photon of a specific frequency can interact with an excited atomic electron, causing it to drop to a lower energy level. This is in contrast to spontaneous emission, which occurs at random intervals without regard to the ambient electromagnetic field. The process is identical in form to atomic absorption in which the energy of a photon causes an identical but opposite atomic transition. In normal media at thermal equilibrium, absorption exceeds stimulated emission because there are electrons in the lower energy states than in the higher energy states. However, when an inversion is present, the rate of stimulated emission exceeds that of absorption. Such a gain medium, along with a resonator, is at the heart of a laser or maser. Lacking a feedback mechanism, laser amplifiers and superluminescent sources also function on the basis of stimulated emission, electrons and their interactions with electromagnetic fields are important in our understanding of chemistry and physics. In the classical view, the energy of an electron orbiting a nucleus is larger for orbits further from the nucleus of an atom. However, quantum mechanical effects force electrons to take on positions in orbitals. Thus, electrons are found in energy levels of an atom, two of which are shown below, When an electron absorbs energy either from light or heat. But transitions are allowed between discrete energy levels such as the two shown above. This leads to lines and absorption lines. When an electron is excited from a lower to an energy level. An electron in a state may decay to a lower energy state which is not occupied. When such an electron decays without external influence, emitting a photon, the phase and direction associated with the photon that is emitted is random. This is the mechanism of fluorescence and thermal emission, an external electromagnetic field at a frequency associated with a transition can affect the quantum mechanical state of the atom without being absorbed. In response to the electric field at this frequency, the probability of the electrons entering this transition state is greatly increased. Thus, the rate of transitions between two states is increased beyond that of spontaneous emission
Stimulated emission
–
Contents
7.
Step recovery diode
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In electronics, a step recovery diode is a semiconductor junction diode having the ability to generate extremely short pulses. It is also called snap-off diode or charge-storage diode or memory varactor, when diodes switch from forward conduction to reverse cut-off, a reverse current flows briefly as stored charge is removed. It is the abruptness with which this reverse current ceases which characterises the step recovery diode and they also refer that they first observed this phenomenon in February,1959. This stored charge depends on Intensity of the anode current IA flowing in the device during its steady state. Minority carrier lifetime τ, i. e. the mean time a charge carrier moves inside a semiconductor region before recombining. Anode current does not cease but reverses its polarity and stored charge Qs starts to flow out of the device at an almost constant rate IR, the Drift Step Recovery Diode was discovered by Russian scientists in 1981. When the current direction reverses, the charges are removed from the base region. As soon as the charge decreases to zero, the diode opens rapidly. A high voltage spike can appear due to the self-induction of the diode circuit, the larger the commutation current and the shorter the transition from forward to reverse conduction, the higher the pulse amplitude and efficiency of the pulse generator. Boff, A. F. Moll, J. Shen, a new high speed effect in solid state diodes,1960 IEEE International Solid-State Circuits Conference. IRE International Solid-State Circuits Conference, III, New York, IEEE Press, the first paper dealing with SRDs, interesting but restricted access. The following two books contain a comprehensive analysis of the theory of charge transport in semiconductor diodes. Nosov, Yurii Romanovich, Switching in semiconductor diodes, Monographs in Semiconductor Physics,4, New York City, tkhorik, Yurii Aleksandrovich, Transients in pulsed semiconductor diodes, Jerusalem, Israel Program for Scientific Translations, Ltd. The following application notes deals extensively with practical circuits and applications using SRDs, pulse and Waveform Generation with Step Recovery Diodes, Application note AN918, Palo Alto, Hewlett-Packard, October 1984. Tan, Michael R. Wang, S. Y, a 12 psec GaAs Double Heterostructure Step Recovery Diode, HP Labs Technical Reports, HPL-91-187, Palo Alto, Hewlett-Packard. An interesting paper describing the construction and reporting the measured performance of an extremely fast heterojunction SRD, pulse Generators, A Picosecond Optoelectronic Cross Correlator using a Gain Modulated Avalanche Photodiode for Measuring the Impulse Response of Tissue. It is a PhD thesis in which an SRD is a key element
Step recovery diode
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Signal of a SRD
frequency comb generator (HP 33003A) (Spannung = voltage, Zeit = time)
8.
Dye laser
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A dye laser is a laser which uses an organic dye as the lasing medium, usually as a liquid solution. Compared to gases and most solid state lasing media, a dye can usually be used for a wider range of wavelengths. The wide bandwidth makes them suitable for tunable lasers and pulsed lasers. The dye rhodamine 6G, for example, can be tuned from 635 nm to 560 nm, dye lasers were independently discovered by P. P. Sorokin and F. P. Schäfer in 1966. In addition to the liquid state, dye lasers are also available as solid state dye lasers. SSDL use dye-doped organic matrices as gain medium, a dye laser uses a gain medium consisting of an organic dye, which is a carbon-based, soluble stain that is often fluorescent, such as the dye in a highlighter pen. The dye is mixed with a solvent, allowing the molecules to diffuse evenly throughout the liquid. The dye solution may be circulated through a dye cell, or streamed through open air using a dye jet, a high energy source of light is needed to pump the liquid beyond its lasing threshold. A fast discharge flashtube or a laser is usually used for this purpose. Mirrors are also needed to oscillate the light produced by the dye’s fluorescence, the output mirror is normally around 80% reflective, while all other mirrors are usually more than 99. 9% reflective. The dye solution is circulated at high speeds, to help avoid triplet absorption. A prism or diffraction grating is usually mounted in the beam path, because the liquid medium of a dye laser can fit any shape, there are a multitude of different configurations that can be used. A Fabry–Pérot laser cavity is used for flashtube pumped lasers. The dye cell is often a tube approximately equal in length to the flashtube. The dye cell is usually side-pumped, with one or more flashtubes running parallel to the dye cell in a reflector cavity, the reflector cavity is often water cooled, to prevent thermal shock in the dye caused by the large amounts of near-infrared radiation which the flashtube produces. Axial pumped lasers have a hollow, annular-shaped flashtube that surrounds the dye cell, which has lower inductance for a shorter flash, and improved transfer efficiency. Coaxial pumped lasers have an annular dye cell that surrounds the flashtube, for even better transfer efficiency, flash pumped lasers can be used only for pulsed output applications. A ring laser design is chosen for continuous operation, although a Fabry–Pérot design is sometimes used
Dye laser
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Close-up of a table-top CW dye laser based on
Rhodamine 6G, emitting at 580 nm (yellow). The emitted laser beam is visible as faint yellow lines between the yellow window (center) and the yellow optics (upper-right). The orange dye-solution enters the laser from the left and exits to the right, and is pumped by a 514 nm (blue-green) beam from an argon laser. The pump laser can be seen entering the dye jet, beneath the yellow window.
Dye laser
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A
dielectric mirror used in a dye laser.
Dye laser
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A ring dye laser. P-pump laser beam; G-gain dye jet; A-saturable absorber dye jet; M0, M1, M2-planar mirrors; OC–output coupler; CM1 to CM4-curved mirrors.
Dye laser
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A cuvette used in a dye laser
9.
Laser pumping
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Laser pumping is the act of energy transfer from an external source into the gain medium of a laser. The energy is absorbed in the medium, producing excited states in its atoms, when the number of particles in one excited state exceeds the number of particles in the ground state or a less-excited state, population inversion is achieved. In this condition, the mechanism of stimulated emission can take place, the pump power must be higher than the lasing threshold of the laser. The pump energy is provided in the form of light or electric current. To use the lamps energy most efficiently, the lamps and lasing medium are contained in a cavity that will redirect most of the lamps energy into the rod or dye cell. In the most common configuration, the medium is in the form of a rod located at one focus of a mirrored cavity. The flashlamp is a located at the other focus of the ellipse. In other cases an absorber for the longer wavelengths is used, often, the lamp is surrounded by a cylindrical jacket called a flow tube. This flow tube is made of a glass that will absorb unsuitable wavelengths, such as ultraviolet. Often, the jacket is given a coating that reflects unsuitable wavelengths of light back into the lamp. This light is absorbed and some of it is re-emitted at suitable wavelengths, the flow tube also serves to protect the rod in the event of a violent lamp failure. Smaller ellipses create fewer reflections, giving higher intensity in the center of the rod. For a single flashlamp, if the lamp and rod are equal diameter, the rod and the lamp are relatively long to minimize the effect of losses at the end faces and to provide a sufficient length of gain medium. Longer flashlamps are also efficient at transferring electrical energy into light. However, if the rod is too long in relation to its diameter a condition called prelasing can occur, rod ends are often antireflection coated or cut at Brewsters angle to minimize this effect. Flat mirrors are often used at the ends of the pump cavity to reduce loss. Variations on this use more complex mirrors composed of overlapping elliptical shapes. This allows greater power, but are less efficient because not all of the light is correctly imaged into the rod and these losses can be minimized by using a close-coupled cavity
Laser pumping
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A ruby laser head. The photo on the left shows the head unassembled, revealing the pumping cavity, the rod and the flashlamps. The photo on the right shows the head assembled.
Laser pumping
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Various laser pumping cavity configurations.
Laser pumping
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Laser pumping lamps. The top three are xenon flashlamps while the bottom one is a krypton arc lamp
Laser pumping
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External triggering was used in this extremely fast discharge. Due to the very high speed, (3.5 microseconds), the current is not only unable to fully heat the xenon and fill the tube, but is still in direct contact with the glass.
10.
Q-switching
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Q-switching, sometimes known as giant pulse formation or Q-spoiling, is a technique by which a laser can be made to produce a pulsed output beam. The technique allows the production of pulses with extremely high peak power. Compared to modelocking, another technique for pulse generation with lasers, Q-switching leads to much lower pulse repetition rates, much higher pulse energies, the two techniques are sometimes applied together. Q-switching is achieved by putting some type of variable attenuator inside the optical resonator. When the attenuator is functioning, light which leaves the medium does not return. This attenuation inside the cavity corresponds to a decrease in the Q factor or quality factor of the optical resonator, a high Q factor corresponds to low resonator losses per roundtrip, and vice versa. The variable attenuator is commonly called a Q-switch, when used for this purpose, initially the laser medium is pumped while the Q-switch is set to prevent feedback of light into the gain medium. This produces a population inversion, but laser operation cannot yet occur since there is no feedback from the resonator. Since the rate of stimulated emission is dependent on the amount of entering the medium. Due to losses from spontaneous emission and other processes, after a time the stored energy will reach some maximum level. At this point, the Q-switch device is quickly changed from low to high Q, allowing feedback, the net result is a short pulse of light output from the laser, known as a giant pulse, which may have a very high peak intensity. There are two types of Q-switching, Here, the Q-switch is an externally controlled variable attenuator. The reduction of losses is triggered by an event, typically an electrical signal. The pulse repetition rate can therefore be externally controlled, modulators generally allow a faster transition from low to high Q, and provide better control. An additional advantage of modulators is that the light may be coupled out of the cavity. Alternatively, when the modulator is in its state, an externally generated beam can be coupled into the cavity through the modulator. This can be used to seed the cavity with a beam that has desired characteristics, when the Q is raised, lasing builds up from the initial seed, producing a Q-switched pulse that has characteristics inherited from the seed. In this case, the Q-switch is a saturable absorber, a material whose transmission increases when the intensity of light exceeds some threshold
Q-switching
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Regenerative amplifier. Red line: Laser beam. Red box: Gain medium. Top: AOM-based design. Bottom: The Pockel’s cell-based design needs thin film polarizers. The direction of the emitted pulse depends on the timing.
11.
Modelocking
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Mode-locking is a technique in optics by which a laser can be made to produce pulses of light of extremely short duration, on the order of picoseconds or femtoseconds. The basis of the technique is to induce a fixed-phase relationship between the modes of the lasers resonant cavity. The laser is said to be phase-locked or mode-locked. Interference between these causes the laser light to be produced as a train of pulses. Depending on the properties of the laser, these pulses may be of brief duration. Although laser light is perhaps the purest form of light, it is not of a single, all lasers produce light over some natural bandwidth or range of frequencies. For example, a typical helium–neon laser has a bandwidth of about 1.5 GHz. The second factor to determine a lasers emission frequencies is the cavity of the laser. In the simplest case, this consists of two plane mirrors facing each other, surrounding the gain medium of the laser and these standing waves form a discrete set of frequencies, known as the longitudinal modes of the cavity. These modes are the frequencies of light which are self-regenerating and allowed to oscillate by the resonant cavity. In practice, L is usually greater than λ, so the relevant values of q are large. Of more interest is the separation between any two adjacent modes q and q+1, this is given by Δν, Δ ν = c 2 L where c is the speed of light. Using the above equation, a laser with a mirror separation of 30 cm has a frequency separation between longitudinal modes of 0.5 GHz. When more than one mode is excited, the laser is said to be in multi-mode operation. When only one mode is excited, the laser is said to be in single-mode operation. The individual phase of the waves in each mode is not fixed. If instead of oscillating independently, each operates with a fixed phase between it and the other modes, the laser output behaves quite differently. Instead of a random or constant output intensity, the modes of the laser will periodically all constructively interfere with one another, such a laser is said to be mode-locked or phase-locked
Modelocking
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Laser mode structure
