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Electromagnetic compatibility

Electromagnetic compatibility (EMC) is the ability of electrical equipment and systems to function acceptably in their electromagnetic environment, by limiting the unintentional generation, propagation and reception of electromagnetic energy which may cause unwanted effects such as electromagnetic interference (EMI) or even physical damage to operational equipment. The goal of EMC is the correct operation of different equipment in a common electromagnetic environment. It is also the name given to the associated branch of electrical engineering.

EMC pursues three main classes of issue. Emission is the generation of electromagnetic energy, whether deliberate or accidental, by some source and its release into the environment. EMC studies the unwanted emissions and the countermeasures which may be taken in order to reduce unwanted emissions. The second class, susceptibility, is the tendency of electrical equipment, referred to as the victim, to malfunction or break down in the presence of unwanted emissions, which are known as Radio frequency interference (RFI). Immunity is the opposite of susceptibility, being the ability of equipment to function correctly in the presence of RFI, with the discipline of "hardening" equipment being known equally as susceptibility or immunity. A third class studied is coupling, which is the mechanism by which emitted interference reaches the victim.

Interference mitigation and hence electromagnetic compatibility may be achieved by addressing any or all of these issues, i.e., quieting the sources of interference, inhibiting coupling paths and/or hardening the potential victims. In practice, many of the engineering techniques used, such as grounding and shielding, apply to all three issues.

Origins
The earliest EMC issue was lightning strike (lightning electromagnetic pulse, or LEMP) on ships and buildings. Lightning rods or lightning conductors began to appear in the mid-18th century. With the advent of widespread electricity generation and power supply lines from the late 19th century on, problems also arose with equipment short-circuit failure affecting the power supply, and with local fire and shock hazard when the power line was struck by lightning. Power stations were provided with output circuit breakers. Buildings and appliances would soon be provided with input fuses, and later in the 20th century miniature circuit breakers (MCB) would come into use.

Early twentieth century
It may be said that radio interference and its correction arose with the first spark-gap experiment of Marconi in the late 1800s. As radio communications developed in the first half of the 20th century, interference between broadcast radio signals began to occur and an international regulatory framework was set up to ensure interference-free communications.

Switching devices became commonplace through the middle of the 20th century, typically in petrol powered cars and motorcycles but also in domestic appliances such as thermostats and refrigerators. This caused transient interference with domestic radio and (after World War II) TV reception, and in due course laws were passed requiring the suppression of such interference sources.

ESD problems first arose with accidental electric spark discharges in hazardous environments such as coal mines and when refuelling aircraft or motor cars. Safe working practices had to be developed.

Postwar period
After World War II the military became increasingly concerned with the effects of nuclear electromagnetic pulse (NEMP), lightning strike, and even high-powered radar beams, on vehicle and mobile equipment of all kinds, and especially aircraft electrical systems.

When high RF emission levels from other sources became a potential problem (such as with the advent of microwave ovens), certain frequency bands were designated for Industrial, Scientific and Medical (ISM) use, allowing emission levels limited only by thermal safety standards. Later, the International Telecommunication Union adopted a Recommendation providing limits of radiation from ISM devices in order to protect radiocommunications. A variety of issues such as sideband and harmonic emissions, broadband sources, and the ever-increasing popularity of electrical switching devices and their victims, resulted in a steady development of standards and laws.

From the late 1970s, the popularity of modern digital circuitry rapidly grew. As the technology developed, with ever-faster switching speeds (increasing emissions) and lower circuit voltages (increasing susceptibility), EMC increasingly became a source of concern. Many more nations became aware of EMC as a growing problem and issued directives to the manufacturers of digital electronic equipment, which set out the essential manufacturer requirements before their equipment could be marketed or sold. Organizations in individual nations, across Europe and worldwide, were set up to maintain these directives and associated standards. In 1979, the American FCC published a regulation that required the electromagnetic emissions of all "digital devices" to be below certain limits. This regulatory environment led to a sharp growth in the EMC industry supplying specialist devices and equipment, analysis and design software, and testing and certification services. Low-voltage digital circuits, especially CMOS transistors, became more susceptible to ESD damage as they were miniaturised and, despite the development of on-chip hardening techniques, a new ESD regulatory regime had to be developed.

Modern era
From the 1980s on the explosive growth in mobile communications and broadcast media channels put huge pressure on the available airspace. Regulatory authorities began squeezing band allocations closer and closer together, relying on increasingly sophisticated EMC control methods, especially in the digital communications domain, to keep cross-channel interference to acceptable levels. Digital systems are inherently less susceptible than analogue systems, and also offer far easier ways (such as software) to implement highly sophisticated protection and error-correction measures.

In 1985, the USA released the ISM bands for low-power mobile digital communications, leading to the development of Wi-Fi and remotely-operated car door keys. This approach relies on the intermittent nature of ISM interference and use of sophisticated error-correction methods to ensure lossless reception during the quiet gaps between any bursts of interference.

Concepts
"Electromagnetic interference" (EMI) is defined as the "degradation in the performance of equipment or transmission channel or a system caused by an electromagnetic disturbance" (IEV 161-01-06) while "electromagnetic disturbance"  is defined as "an electromagnetic phenomenon that can degrade the performance of a device, equipment or system, or adversely affect living or inert matter (IEV 161-01-05).  The terms "electromagnetic disturbance" and "electromagnetic interference" designate respectively the cause and the effect,

Electromagnetic compatibility (EMC) is an equipment characteristic or property and is defined as " the ability of equipment or a system to function satisfactorily in its electromagnetic environment without introducing intolerable electromagnetic disturbances to anything in that environment " (IEV 161-01-07).

EMC ensures the correct operation, in the same electromagnetic environment, of different equipment items which use or respond to electromagnetic phenomena, and the avoidance of any interference. Another way of saying this is that EMC is the control of EMI so that unwanted effects are prevented.

Besides understanding the phenomena in themselves, EMC also addresses the countermeasures, such as control regimes, design and measurement, which should be taken in order to prevent emissions from causing any adverse effect.

Types of interference
EMC is often understood as the control of electromagnetic interference (EMI). Electromagnetic interference divides into several categories according to the source and signal characteristics.

The origin of interference, often called "noise" in this context, can be man-made (artificial) or natural.

Continuous, or continuous wave (CW), interference comprises a given range of frequencies. This type is naturally divided into sub-categories according to frequency range, and as a whole is sometimes referred to as "DC to daylight". One common classification is into narrowband and broadband, according to the spread of the frequency range.

An electromagnetic pulse (EMP), sometimes called a transient disturbance, is a short-duration pulse of energy. This energy is usually broadband by nature, although it often excites a relatively narrow-band damped sine wave response in the victim. Pulse signals divide broadly into isolated and repetitive events.

Coupling mechanisms

When a source emits interference, it follows a route to the victim known as the coupling path. There are four basic coupling mechanisms: conductive, capacitive, magnetic or inductive, and radiative. Any coupling path can be broken down into one or more of these coupling mechanisms working together.

Conductive coupling occurs when the coupling path between the source and victim is formed by direct electrical contact with a conducting body.

Capacitive coupling occurs when a varying electrical field exists between two adjacent conductors, inducing a change in voltage on the receiving conductor.

Inductive coupling or magnetic coupling occurs when a varying magnetic field exists between two parallel conductors, inducing a change in voltage along the receiving conductor.

Radiative coupling or electromagnetic coupling occurs when source and victim are separated by a large distance. Source and victim act as radio antennas: the source emits or radiates an electromagnetic wave which propagates across the space in between and is picked up or received by the victim.

Control
The damaging effects of electromagnetic interference pose unacceptable risks in many areas of technology, and it is necessary to control such interference and reduce the risks to acceptable levels.

The control of electromagnetic interference (EMI) and assurance of EMC comprises a series of related disciplines:
 * Characterising the threat.
 * Setting standards for emission and susceptibility levels.
 * Design for standards compliance.
 * Testing for standards compliance.

The risk posed by the threat is usually statistical in nature, so much of the work in threat characterisation and standards setting is based on reducing the probability of disruptive EMI to an acceptable level, rather than its assured elimination.

For a complex or novel piece of equipment, this may require the production of a dedicated EMC control plan summarizing the application of the above and specifying additional documents required.

Characterisation of the problem requires understanding of:

 * The interference source and signal.
 * The coupling path to the victim.
 * The nature of the victim both electrically and in terms of the significance of malfunction.

Design

Breaking a coupling path is equally effective at either the start or the end of the path, therefore many aspects of good EMC design practice apply equally to potential sources and to potential victims. A design which easily couples energy to the outside world will equally easily couple energy in and will be susceptible. A single improvement will often reduce both emissions and susceptibility. Grounding and shielding aim to reduce emissions or divert EMI away from the victim by providing an alternative, low-impedance path. Techniques include:

 * Grounding or earthing schemes such as star earthing for audio equipment or ground planes for RF. The scheme must also satisfy safety regulations.
 * Shielded cables, where the signal wires are surrounded by an outer conductive layer that is grounded at one or both ends.
 * Shielded housings. A conductive metal housing will act as an interference shield. In order to access the interior, such a housing is typically made in sections (such as a box and lid); an RF gasket may be used at the joints to reduce the amount of interference that leaks through. RF gaskets come in various types. A plain metal gasket may be either braided wire or a flat strip slotted to create many springy "fingers". Where a waterproof seal is required, a flexible elastomeric base may be impregnated with chopped metal fibers dispersed into the interior or long metal fibers covering the surface or both.

Other general measures include:

 * Decoupling or filtering at critical points such as cable entries and high-speed switches, using RF chokes and/or RC elements. A line filter implements these measures between a device and a line.
 * Transmission line techniques for cables and wiring, such as balanced differential signal and return paths, and impedance matching.
 * Avoidance of antenna structures such as loops of circulating current, resonant mechanical structures, unbalanced cable impedances or poorly grounded shielding.
 * Eliminating spurious rectifying junctions that can form between metal structures around and near transmitter installations. Such junctions in combination with unintentional antenna structures can radiate harmonics of the transmitter frequency.

Additional measures to reduce emissions include:

 * Avoid unnecessary switching operations. Necessary switching should be done as slowly as is technically possible.
 * Noisy circuits (e. g. with a lot of switching activity) should be physically separated from the rest of the design.
 * High peaks at single frequencies can be avoided by using the spread spectrum method, in which different parts of the circuit emit at different frequencies.
 * Harmonic wave filters.
 * Design for operation at lower signal levels, reducing the energy available for emission.

Additional measures to reduce susceptibility include:

 * Fuses, trip switches and circuit breakers.
 * Transient absorbers.
 * Design for operation at higher signal levels, reducing the relative noise level in comparison.
 * Error-correction techniques in digital circuitry. These may be implemented in hardware, software or a combination of both.
 * Differential signaling or other common-mode noise techniques for signal routing

Testing
Testing is required to confirm that a particular device meets the required standards. It divides broadly into emissions testing and susceptibility testing. Open-area test sites, or OATS, are the reference sites in most standards. They are especially useful for emissions testing of large equipment systems. However RF testing of a physical prototype is most often carried out indoors, in a specialised EMC test chamber. Types of chamber include anechoic, reverberation and the gigahertz transverse electromagnetic cell (GTEM cell). Sometimes computational electromagnetics simulations are used to test virtual models. Like all compliance testing, it is important that the test equipment, including the test chamber or site and any software used, be properly calibrated and maintained. Typically, a given run of tests for a particular piece of equipment will require an EMC test plan and follow-up test report. The full test program may require the production of several such documents.

Emissions are typically measured for radiated field strength and where appropriate for conducted emissions along cables and wiring. Inductive (magnetic) and capacitive (electric) field strengths are near-field effects, and are only important if the device under test (DUT) is designed for location close to other electrical equipment. For conducted emissions, typical transducers include the LISN (line impedance stabilisation network) or AMN (artificial mains network) and the RF current clamp. For radiated emission measurement, antennas are used as transducers. Typical antennas specified include dipole, biconical, log-periodic, double ridged guide and conical log-spiral designs. Radiated emissions must be measured in all directions around the DUT. Specialized EMI test receivers or EMI analysers are used for EMC compliance testing. These incorporate bandwidths and detectors as specified by international EMC standards. An EMI receiver may be based on a spectrum analyser to measure the emission levels of the DUT across a wide band of frequencies (frequency domain), or on a tunable narrower-band device which is swept through the desired frequency range. EMI receivers along with specified transducers can often be used for both conducted and radiated emissions. Pre-selector filters may also be used to reduce the effect of strong out-of-band signals on the front-end of the receiver. Some pulse emissions are more usefully characterized using an oscilloscope to capture the pulse waveform in the time domain.

Radiated field susceptibility testing typically involves a high-powered source of RF or EM energy and a radiating antenna to direct the energy at the potential victim or device under test (DUT). Conducted voltage and current susceptibility testing typically involves a high-powered signal generator, and a current clamp or other type of transformer to inject the test signal. Transient or EMP signals are used to test the immunity of the DUT against powerline disturbances including surges, lightning strikes and switching noise. In motor vehicles, similar tests are performed on battery and signal lines. The transient pulse may be generated digitally and passed through a broadband pulse amplifier, or applied directly to the transducer from a specialised pulse generator. Electrostatic discharge testing is typically performed with a piezo spark generator called an "ESD pistol". Higher energy pulses, such as lightning or nuclear EMP simulations, can require a large current clamp or a large antenna which completely surrounds the DUT. Some antennas are so large that they are located outdoors, and care must be taken not to cause an EMP hazard to the surrounding environment.

Legislation
Several organizations, both national and international, work to promote international co-operation on standardization (harmonization), including publishing various EMC standards. Where possible, a standard developed by one organization may be adopted with little or no change by others. This helps for example to harmonize national standards across Europe.

International standards organizations include:

 * International Electrotechnical Commission (IEC), which has several committees working full-time on EMC issues. These are:
 * Technical Committee 77 (TC77), working on electromagnetic compatibility between equipment including networks.
 * Comité International Spécial des Perturbations Radioélectriques (CISPR), or International Special Committee on Radio Interference.
 * The Advisory Committee on Electromagnetic Compatibility (ACEC) co-ordinates the IEC's work on EMC between these committees.
 * International Organization for Standardization (ISO), which publishes standards for the automotive industry.

Among the main national organizations are:

 * Europe:
 * Comité Européen de Normalisation (CEN) or European Committee for Standardization).
 * Comité Européen de Normalisation Electrotechniques (CENELEC) or European Committee for Electrotechnical Standardisation.
 * European Telecommunications Standards Institute (ETSI).
 * United States:
 * The Federal Communications Commission (FCC).
 * The Society of Automotive Engineers (SAE).
 * The Radio Technical Commission for Aeronautics (RTCA); see DO-160
 * Britain: The British Standards Institution (BSI).
 * Germany: The Verband der Elektrotechnik, Elektronik und Informationstechnik (VDE) or Association for Electrical, Electronic and Information Technologies.

Compliance with national or international standards is usually laid down by laws passed by individual nations. Different nations can require compliance with different standards.

In European law, EU directive 2014/30/EU (previously 2004/108/EC) on EMC defines the rules for the placing on the market/putting into service of electric/electronic equipment within the European Union. The Directive applies to a vast range of equipment including electrical and electronic appliances, systems and installations. Manufacturers of electric and electronic devices are advised to run EMC tests in order to comply with compulsory CE-labeling. More are given in the list of EMC directives. Compliance with the applicable harmonised standards whose reference is listed in the OJEU under the EMC Directive gives presumption of conformity with the corresponding essential requirements of the EMC Directive.

In 2019, the USA adopted a program for the protection of critical infrastructure against an electromagnetic pulse, whether caused by a geomagnetic storm or a high-altitude nuclear weapon.

title: Electromagnetic compatibility


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Electromagnetic environment

In telecommunication, the term electromagnetic environment (EME) has the following meanings:

 * 1) For a telecommunications system, the spatial distribution of electromagnetic fields surrounding a given site. The electromagnetic environment may be expressed in terms of the spatial and temporal distribution of electric field strength (volts per metre), irradiance (watts per square metre), or energy density (joules per cubic metre).
 * 2) The resulting product of the power and time distribution, in various frequency ranges, of the radiated or conducted electromagnetic emission levels that may be encountered by a military force, system, or platform when performing its assigned mission in its intended operational environment. It is the sum of electromagnetic interference; electromagnetic pulse; hazards of electromagnetic radiation to personnel, ordnance, and volatile materials; and natural phenomena effects of lightning and p-static.
 * 3) All electromagnetic phenomena observable in a given location.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Electromagnetic environment


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Electromagnetic interference control

In Electrical systems, such as telecommunication, power electronics, industrial electronics, power engineering; electromagnetic interference (EMI) control is the control of radiated and conducted energy such that emissions that are unnecessary for system, subsystem, or equipment operation are reduced, minimized, or eliminated.

Note: Electromagnetic radiated and conducted emissions are controlled regardless of their origin within the system, subsystem, or equipment. Successful EMI control with effective susceptibility control leads to electromagnetic compatibility.

title: Electromagnetic interference control


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Nuclear electromagnetic pulse

A nuclear electromagnetic pulse (nuclear EMP or NEMP) is a burst of electromagnetic radiation created by a nuclear explosion. The resulting rapidly varying electric and magnetic fields may couple with electrical and electronic systems to produce damaging current and voltage surges. The specific characteristics of a particular nuclear EMP event vary according to a number of factors, the most important of which is the altitude of the detonation.

The term "electromagnetic pulse" generally excludes optical (infrared, visible, ultraviolet) and ionizing (such as X-ray and gamma radiation) ranges. In military terminology, a nuclear warhead detonated tens to hundreds of miles above the Earth's surface is known as a high-altitude electromagnetic pulse (HEMP) device. Effects of a HEMP device depend on factors including the altitude of the detonation, energy yield, gamma ray output, interactions with the Earth's magnetic field and electromagnetic shielding of targets.

History
The fact that an electromagnetic pulse is produced by a nuclear explosion was known in the earliest days of nuclear weapons testing. The magnitude of the EMP and the significance of its effects were not immediately realized.

During the first United States nuclear test on 16 July 1945, electronic equipment was shielded because Enrico Fermi expected the electromagnetic pulse. The official technical history for that first nuclear test states, "All signal lines were completely shielded, in many cases doubly shielded. In spite of this many records were lost because of spurious pickup at the time of the explosion that paralyzed the recording equipment." During British nuclear testing in 1952–53, instrumentation failures were attributed to "radioflash", which was their term for EMP.

The first openly reported observation of the unique aspects of high-altitude nuclear EMP occurred during the helium balloon-lofted Yucca nuclear test of the Hardtack I series on 28 April 1958. In that test, the electric field measurements from the 1.7 kiloton weapon exceeded the range to which the test instruments were adjusted and was estimated to be about five times the limits to which the oscilloscopes were set. The Yucca EMP was initially positive-going, whereas low-altitude bursts were negative-going pulses. Also, the polarization of the Yucca EMP signal was horizontal, whereas low-altitude nuclear EMP was vertically polarized. In spite of these many differences, the unique EMP results were dismissed as a possible wave propagation anomaly.

The high-altitude nuclear tests of 1962, as discussed below, confirmed the unique results of the Yucca high-altitude test and increased the awareness of high-altitude nuclear EMP beyond the original group of defense scientists. The larger scientific community became aware of the significance of the EMP problem after a three-article series on nuclear EMP was published in 1981 by William J. Broad in Science.

Starfish Prime
In July 1962, the US carried out the Starfish Prime test, exploding a 1.44 MtonTNT bomb 400 km above the mid-Pacific Ocean. This demonstrated that the effects of a high-altitude nuclear explosion were much larger than had been previously calculated. Starfish Prime made those effects known to the public by causing electrical damage in Hawaii, about 1445 km away from the detonation point, disabling approximately 300 streetlights, triggering numerous burglar alarms and damaging a microwave link.

Starfish Prime was the first success in the series of United States high-altitude nuclear tests in 1962 known as Operation Fishbowl. Subsequent tests gathered more data on the high-altitude EMP phenomenon.

The Bluegill Triple Prime and Kingfish high-altitude nuclear tests of October and November 1962 in Operation Fishbowl provided data that was clear enough to enable physicists to accurately identify the physical mechanisms behind the electromagnetic pulses.

The EMP damage of the Starfish Prime test was quickly repaired due, in part, to the fact that the EMP over Hawaii was relatively weak compared to what could be produced with a more intense pulse, and in part due to the relative ruggedness (compared to today) of Hawaii's electrical and electronic infrastructure in 1962.

The relatively small magnitude of the Starfish Prime EMP in Hawaii (about 5.6 kilovolts/metre) and the relatively small amount of damage (for example, only 1% to 3% of streetlights extinguished) led some scientists to believe, in the early days of EMP research, that the problem might not be significant. Later calculations showed that if the Starfish Prime warhead had been detonated over the northern continental United States, the magnitude of the EMP would have been much larger (22 to 30 kV/m) because of the greater strength of the Earth's magnetic field over the United States, as well as its different orientation at high latitudes. These calculations, combined with the accelerating reliance on EMP-sensitive microelectronics, heightened awareness that EMP could be a significant problem.

Soviet Test 184
In 1962, the Soviet Union performed three EMP-producing nuclear tests in space over Kazakhstan, the last in the "Soviet Project K nuclear tests". Although these weapons were much smaller (300 kiloton) than the Starfish Prime test, they were over a populated, large landmass and at a location where the Earth's magnetic field was greater. The damage caused by the resulting EMP was reportedly much greater than in Starfish Prime. The geomagnetic storm–like E3 pulse from Test 184 induced a current surge in a long underground power line that caused a fire in the power plant in the city of Karaganda.

After the dissolution of the Soviet Union, the level of this damage was communicated informally to US scientists. For a few years US and Russian scientists collaborated on the HEMP phenomenon. Funding was secured to enable Russian scientists to report on some of the Soviet EMP results in international scientific journals. As a result, formal documentation of some of the EMP damage in Kazakhstan exists, although it is still sparse in the open-scientific literature.

For one of the K Project tests, Soviet scientists instrumented a 570 km section of telephone line in the area that they expected to be affected by the pulse. The monitored telephone line was divided into sub-lines of 40 to 80 km in length, separated by repeaters. Each sub-line was protected by fuses and by gas-filled overvoltage protectors. The EMP from the 22 October (K-3) nuclear test (also known as Test 184) blew all of the fuses and destroyed all of the overvoltage protectors in all of the sub-lines. Published reports, including a 1998 IEEE article, have stated that there were significant problems with ceramic insulators on overhead electrical power lines during the tests. A 2010 technical report written for Oak Ridge National Laboratory stated that "Power line insulators were damaged, resulting in a short circuit on the line and some lines detaching from the poles and falling to the ground".

Characteristics
Nuclear EMP is a complex multi-pulse, usually described in terms of three components, as defined by the International Electrotechnical Commission (IEC).

The three components of nuclear EMP, as defined by the IEC, are called "E1", "E2", and "E3".

The three categories of high-altitude EMP are divided according to the time duration and occurrence of each pulse. E1 is the fastest or "early time" high-altitude EMP. Traditionally, the term "EMP" often refers specifically to this E1 component of high-altitude electromagnetic pulse.

The E2 and E3 pulses are often further subdivided into additional divisions according to causation. E2 is a much lower intensity "intermediate time" EMP, which is further divided into E2A (scattered gamma EMP) and E2B (neutron gamma EMP).

E3 is a very long-duration "late time" pulse, which is extremely slow in rise and fall times compared to the other components of EMP. E3 is further divided into E3A (blast wave) and E3B (heave). E3 is also called magnetohydrodynamic EMP.

E1
The E1 pulse is a very fast component of nuclear EMP. E1 is a brief but intense electromagnetic field that induces high voltages in electrical conductors. E1 causes most of its damage by causing electrical breakdown voltages to be exceeded. E1 can destroy computers and communications equipment and it changes too quickly (nanoseconds) for ordinary surge protectors to provide effective protection from it. Fast-acting surge protectors (such as those using TVS diodes) will block the E1 pulse.

E1 is produced when gamma radiation from the nuclear detonation ionizes (strips electrons from) atoms in the upper atmosphere. This is known as the Compton effect and the resulting current is called the "Compton current". The electrons travel in a generally downward direction at relativistic speeds (more than 90 per cent of the speed of light). In the absence of a magnetic field, this would produce a large, radial pulse of electric current propagating outward from the burst location confined to the source region (the region over which the gamma photons are attenuated). The Earth's magnetic field exerts a force on the electron flow at a right angle to both the field and the particles' original vector, which deflects the electrons and leads to synchrotron radiation. Because the outward traveling gamma pulse is propagating at the speed of light, the synchrotron radiation of the Compton electrons adds coherently, leading to a radiated electromagnetic signal. This interaction produces a large, brief, pulse.

Several physicists worked on the problem of identifying the mechanism of the HEMP E1 pulse. The mechanism was finally identified by Conrad Longmire of Los Alamos National Laboratory in 1963.

Longmire gives numerical values for a typical case of E1 pulse produced by a second-generation nuclear weapon such as those of Operation Fishbowl. The typical gamma rays given off by the weapon have an energy of about 2MeV (mega electron-volts). The gamma rays transfer about half of their energy to the ejected free electrons, giving an energy of about 1MeV.

In a vacuum and absent a magnetic field, the electrons would travel with a current density of tens of amperes per square metre. Because of the downward tilt of the Earth's magnetic field at high latitudes, the area of peak field strength is a U-shaped region to the equatorial side of the detonation. As shown in the diagram, for nuclear detonations in the Northern Hemisphere, this U-shaped region is south of the detonation point. Near the equator, where the Earth's magnetic field is more nearly horizontal, the E1 field strength is more nearly symmetrical around the burst location.

At geomagnetic field strengths typical of the mid-latitudes, these initial electrons spiral around the magnetic field lines with a typical radius of about 85 m. These initial electrons are stopped by collisions with air molecules at an average distance of about 170 m. This means that most of the electrons are stopped by collisions with air molecules before completing a full spiral around the field lines.

This interaction of the negatively charged electrons with the magnetic field radiates a pulse of electromagnetic energy. The pulse typically rises to its peak value in some five nanoseconds. Its magnitude typically decays by half within 200 nanoseconds. (By the IEC definition, this E1 pulse ends 1000 nanoseconds after it begins.) This process occurs simultaneously on about 1025 electrons. The simultaneous action of the electrons causes the resulting pulse from each electron to radiate coherently, adding to produce a single large-amplitude, short-duration, radiated pulse.

Secondary collisions cause subsequent electrons to lose energy before they reach ground level. The electrons generated by these subsequent collisions have so little energy that they do not contribute significantly to the E1 pulse.

These 2 MeV gamma rays typically produce an E1 pulse near ground level at moderately high latitudes that peaks at about 50,000 volts per metre. The ionization process in the mid-stratosphere causes this region to become an electrical conductor, a process that blocks the production of further electromagnetic signals and causes the field strength to saturate at about 50,000 volts per metre. The strength of the E1 pulse depends upon the number and intensity of the gamma rays and upon the rapidity of the gamma-ray burst. Strength is also somewhat dependent upon altitude.

There are reports of "super-EMP" nuclear weapons that are able to exceed the 50,000 volts per metre limit by unspecified mechanisms. The reality and possible construction details of these weapons are classified and are, therefore, unconfirmed in the open scientific literature

E2
The E2 component is generated by scattered gamma rays and inelastic gammas produced by neutrons. This E2 component is an "intermediate time" pulse that, by IEC definition, lasts from about one microsecond to one second after the explosion. E2 has many similarities to lightning, although lightning-induced E2 may be considerably larger than a nuclear E2. Because of the similarities and the widespread use of lightning protection technology, E2 is generally considered to be the easiest to protect against.

According to the United States EMP Commission, the main problem with E2 is that it immediately follows E1, which may have damaged the devices that would normally protect against E2.

The EMP Commission Executive Report of 2004 states, "In general, it would not be an issue for critical infrastructure systems since they have existing protective measures for defense against occasional lightning strikes. The most significant risk is synergistic because the E2 component follows a small fraction of a second after the first component's insult, which has the ability to impair or destroy many protective and control features. The energy associated with the second component thus may be allowed to pass into and damage systems."

E3
The E3 component is different from E1 and E2. E3 is a much slower pulse, lasting tens to hundreds of seconds. It is caused by the nuclear detonation's temporary distortion of the Earth's magnetic field. The E3 component has similarities to a geomagnetic storm. Like a geomagnetic storm, E3 can produce geomagnetically induced currents in long electrical conductors, damaging components such as power line transformers.

Because of the similarity between solar-induced geomagnetic storms and nuclear E3, it has become common to refer to solar-induced geomagnetic storms as "Solar EMP". "Solar EMP" does not include E1 or E2 components.

Generation
Factors that control weapon effectiveness include altitude, yield, construction details, target distance, intervening geographical features, and local strength of the Earth's magnetic field.

Weapon altitude

According to an internet primer published by the Federation of American Scientists:

 * A high-altitude nuclear detonation produces an immediate flux of gamma rays from the nuclear reactions within the device. These photons in turn produce high energy free electrons by Compton scattering at altitudes between (roughly) 20 and 40 km. These electrons are then trapped in the Earth's magnetic field, giving rise to an oscillating electric current. This current is asymmetric in general and gives rise to a rapidly rising radiated electromagnetic field called an electromagnetic pulse (EMP). Because the electrons are trapped essentially simultaneously, a very large electromagnetic source radiates coherently.

 * The pulse can easily span continent-sized areas, and this radiation can affect systems on land, sea, and air. ... A large device detonated at 400–500 km (250 to 312 miles) over Kansas would affect all of the continental U.S. The signal from such an event extends to the visual horizon as seen from the burst point.

Thus, for equipment to be affected, the weapon needs to be above the visual horizon.

The altitude indicated above is greater than that of the International Space Station and many low Earth orbit satellites. Large weapons could have a dramatic impact on satellite operations and communications such as occurred during Operation Fishbowl. The damaging effects on orbiting satellites are usually due to factors other than EMP. In the Starfish Prime nuclear test, most damage was to the satellites' solar panels while passing through radiation belts created by the explosion.

For detonations within the atmosphere, the situation is more complex. Within the range of gamma ray deposition, simple laws no longer hold as the air is ionised and there are other EMP effects, such as a radial electric field due to the separation of Compton electrons from air molecules, together with other complex phenomena. For a surface burst, absorption of gamma rays by air would limit the range of gamma-ray deposition to approximately 10 mi, while for a burst in the lower-density air at high altitudes, the range of deposition would be far greater.

Weapon yield
Typical nuclear weapon yields used during Cold War planning for EMP attacks were in the range of 1 to 10 MtonTNT. This is roughly 50 to 500 times the size of the Hiroshima and Nagasaki bombs. Physicists have testified at United States Congressional hearings that weapons with yields of 10 ktonTNT or less can produce a large EMP.

The EMP at a fixed distance from an explosion increases at most as the square root of the yield (see the illustration to the right). This means that although a 10 ktonTNT weapon has only 0.7% of the energy release of the 1.44 MtonTNT Starfish Prime test, the EMP will be at least 8% as powerful. Since the E1 component of nuclear EMP depends on the prompt gamma-ray output, which was only 0.1% of yield in Starfish Prime but can be 0.5% of yield in low-yield pure nuclear fission weapons, a 10 ktonTNT bomb can easily be $5 * 8%=40%$ as powerful as the 1.44 MtonTNT Starfish Prime at producing EMP.

The total prompt gamma-ray energy in a fission explosion is 3.5% of the yield, but in a 10 ktonTNT detonation the triggering explosive around the bomb core absorbs about 85.0% of the prompt gamma rays, so the output is only about 0.5% of the yield. In the thermonuclear Starfish Prime the fission yield was less than 100% and the thicker outer casing absorbed about 95% of the prompt gamma rays from the pusher around the fusion stage. Thermonuclear weapons are also less efficient at producing EMP because the first stage can pre-ionize the air which becomes conductive and hence rapidly shorts out the Compton currents generated by the fusion stage. Hence, small pure fission weapons with thin cases are far more efficient at causing EMP than most megaton bombs.

This analysis, however, only applies to the fast E1 and E2 components of nuclear EMP. The geomagnetic storm-like E3 component of nuclear EMP is more closely proportional to the total energy yield of the weapon.

Target distance
In nuclear EMP all of the components of the electromagnetic pulse are generated outside of the weapon.

For high-altitude nuclear explosions, much of the EMP is generated far from the detonation (where the gamma radiation from the explosion hits the upper atmosphere). This electric field from the EMP is remarkably uniform over the large area affected.

According to the standard reference text on nuclear weapons effects published by the U.S. Department of Defense, "The peak electric field (and its amplitude) at the Earth's surface from a high-altitude burst will depend upon the explosion yield, the height of the burst, the location of the observer, and the orientation with respect to the geomagnetic field. As a general rule, however, the field strength may be expected to be tens of kilovolts per metre over most of the area receiving the EMP radiation."

The text also states that, "...over most of the area affected by the EMP the electric field strength on the ground would exceed 0.5Emax. For yields of less than a few hundred kilotons, this would not necessarily be true because the field strength at the Earth's tangent could be substantially less than 0.5Emax."

(Emax refers to the maximum electric field strength in the affected area.)

In other words, the electric field strength in the entire area that is affected by the EMP will be fairly uniform for weapons with a large gamma-ray output. For smaller weapons, the electric field may fall at a faster rate as distance increases.

Super-EMP
Also known as an "Enhanced-EMP", a super-electromagnetic pulse is a relatively new type of warfare in which a nuclear weapon is designed to create a far greater electromagnetic pulse in comparison to standard nuclear weapons of mass destruction. These weapons capitalize on the E1 pulse component of a detonation involving gamma rays, creating an EMP yield of potentially up to 200,000 volts per meter. For decades, numerous countries have experimented with the creation of such weapons, most notably China and Russia.

China
According to a statement made in writing by the Chinese military, the country has super-EMPs and has discussed their use in attacking Taiwan. Such an attack would debilitate information systems in the nation, allowing China to move in and attack it directly using soldiers. The Taiwanese military has subsequently confirmed Chinese possession of super-EMPs and their possible destruction to power grids.

In addition to Taiwan, the possible implications of attacking the United States with these weapons was examined by China. While the United States also possesses nuclear weapons, the country has not experimented with super-EMPs and is hypothetically highly vulnerable to any future attacks by nations. This is due to the country's reliance on computers to control much of the government and economy. Abroad, U.S. aircraft carriers stationed within a reasonable range of an exploding bomb could potentially be subject to complete destruction of missiles on board, as well as telecommunication systems that would allow them to communicate with nearby vessels and controllers on land.

Russia
Since the Cold War, Russia has experimented with the design and effects of EMP bombs.

The Soviet Union designed a system to deliver nuclear weapons from above the Earth's atmosphere. and proposals have been made by Russia to develop satellites supplied with EMP capabilities. This would call for detonations up to 100 km above the Earth's surface, with the potential to disrupt the electronic systems of U.S. satellites suspended in orbit around the planet, many of which are vital for deterrence and alerting the country of possible incoming missiles.

Effects
An energetic EMP can temporarily upset or permanently damage electronic equipment by generating high voltage and high current surges; semiconductor components are particularly at risk. The effects of damage can range from imperceptible to the eye, to devices blowing apart. Cables, even if short, can act as antennas to transmit pulse energy to the equipment.

Vacuum tube vs. solid-state electronics
Older, vacuum tube (valve)-based equipment is generally much less vulnerable to nuclear EMP than solid-state equipment, which is much more susceptible to damage by large, brief voltage and current surges. Soviet Cold War-era military aircraft often had avionics based on vacuum tubes because solid-state capabilities were limited and vacuum-tube gear was believed to be more likely to survive.

Other components in vacuum tube circuitry can be damaged by EMP. Vacuum tube equipment was damaged in the 1962 testing. The solid-state PRC-77 VHF manpackable two-way radio survived extensive EMP testing. The earlier PRC-25, nearly identical except for a vacuum tube final amplification stage, was tested in EMP simulators, but was not certified to remain fully functional.

Electronics in operation vs. inactive
Equipment that is running at the time of an EMP is more vulnerable. Even a low-energy pulse has access to the power source, and all parts of the system are illuminated by the pulse. For example, a high-current arcing path may be created across the power supply, burning out some device along that path. Such effects are hard to predict and require testing to assess potential vulnerabilities.

On aircraft
Many nuclear detonations have taken place using aerial bombs. The B-29 aircraft that delivered the nuclear weapons at Hiroshima and Nagasaki did not lose power from electrical damage, because electrons (ejected from the air by gamma rays) are stopped quickly in normal air for bursts below roughly 10 km, so they are not significantly deflected by the Earth's magnetic field.

If the aircraft carrying the Hiroshima and Nagasaki bombs had been within the intense nuclear radiation zone when the bombs exploded over those cities, then they would have suffered effects from the charge separation (radial) EMP. But this only occurs within the severe blast radius for detonations below about 10 km altitude.

During Operation Fishbowl, EMP disruptions were suffered aboard a KC-135 photographic aircraft flying 300 km from the 410 ktonTNT detonations at 48 and 95 km burst altitudes. The vital electronics were less sophisticated than today's and the aircraft was able to land safely.

Modern aircraft are heavily reliant on solid-state electronics which are very susceptible to EMP blasts. Therefore, airline authorities are creating high intensity radiated fields (HIRF) requirements for new air planes to help prevent the chance of crashes caused by EMPs or electromagnetic interference (EMI). To do this all parts of the airplane must be conductive. This is the main shield from EMP blasts as long as there are no holes for the waves to penetrate into the interior of the airplane. Also, insulating some of the main computers inside the plane adds an extra layer of protection from EMP blasts.

On cars
An EMP would probably not affect most cars, despite modern cars' heavy use of electronics, because cars' electronic circuits and cabling are likely too short to be affected. In addition, cars' metallic frames provide some protection. However, even a small percentage of cars breaking down due to an electronic malfunction would cause traffic jams.

On small electronics
An EMP has a smaller effect on shorter lengths of an electrical conductor. Other factors affect the vulnerability of electronics as well, so no hard cutoff length determines whether some piece of equipment will survive. However, small electronic devices, such as wristwatches and cell phones, would most likely withstand an EMP.

On humans and animals
Though electric potential difference can accumulate in electrical conductors after an EMP, it will generally not flow out into human or animal bodies, and thus contact is safe.

EMPs of sufficient magnitude and length have the potential to affect the human body. Possible side effects include cellular mutations, nervous system damages, internal burns, brain damage, and temporary problems with thinking and memory. However, this would be in extreme cases like being near the center of the blast and being exposed to a large amount of radiation and EMP waves.

A study found that exposure to 200–400 pulses of EMP caused the leaking of vessels in the brain, leakage that has been linked to small problems with thinking and memory recollection. These effects could last up to 12 hours after the exposure. Due to the long exposure time needed to see any of these effects it is unlikely that anyone would see these effects even if exposed for a small period of time. Also, the human body will see little effect as signals are passed chemically and not electrically making it hard to be affected by EMP waves.

Post–Cold War attack scenarios
The United States EMP Commission was created by the United States Congress in 2001. The commission is formally known as the commission to Assess the Threat to the United States from Electromagnetic Pulse (EMP) Attack.

The Commission brought together notable scientists and technologists to compile several reports. In 2008, the Commission released the "Critical National Infrastructures Report". This report describes the likely consequences of a nuclear EMP on civilian infrastructure. Although this report covered the United States, most of the information is applicable to other industrialized countries. The 2008 report was a follow-up to a more generalized report issued by the commission in 2004.

In written testimony delivered to the United States Senate in 2005, an EMP Commission staff member reported:

The United States EMP Commission determined that long-known protections are almost completely absent in the civilian infrastructure of the United States and that large parts of US military services were less-protected against EMP than during the Cold War. In public statements, the Commission recommended making electronic equipment and electrical components resistant to EMP – and maintaining spare parts inventories that would enable prompt repairs. The United States EMP Commission did not look at other nations.

In 2011, the Defense Science Board published a report about the ongoing efforts to defend critical military and civilian systems against EMP and other nuclear weapons effects.

The United States military services developed, and in some cases published, hypothetical EMP attack scenarios.

In 2016, the Los Alamos Laboratory started phase 0 of a multi-year study (through to phase 3) to investigate EMPs which prepared the strategy to be followed for the rest of the study.

In 2017, the US Department of Energy published the "DOE Electromagnetic Pulse Resilience Action Plan", Edwin Boston published a dissertation on the topic and the EMP Commission published "Assessing the threat from electromagnetic pulse (EMP)". The EMP commission was closed in summer 2017. They found that earlier reports had underestimated the effects of an EMP attack on the national infrastructure, highlighted issues with communications from the DoD due to the classified nature of the material, and recommended that the DHS instead of going to the DOE for guidance and direction should directly cooperate with the more knowledgeable parts of the DOE. Several reports are in process of being released to the general public.

Protecting infrastructure
The problem of protecting civilian infrastructure from electromagnetic pulse has been intensively studied throughout the European Union, and in particular by the United Kingdom.

As of 2017, several power utility companies in the United States had been involved in a three-year research program on the impact of HEMP to the United States power grid led by an industry non-profit organization, Electric Power Research Institute (EPRI).

In 2018, the US Department of Homeland Security released the Strategy for Protecting and Preparing the Homeland against Threats from Electromagnetic Pulse (EMP) and Geomagnetic Disturbance (GMD), which was the department's first articulation of a holistic, long-term, partnership-based approach to protecting critical infrastructure and preparing to respond and recover from potentially catastrophic electromagnetic incidents. Progress on that front is described in the EMP Program Status Report.

NuScale, the small modular nuclear reactor company from Oregon, US, has made their reactor resistant to EMP.

In fiction and popular culture
By 1981, a number of articles on nuclear electromagnetic pulse in the popular press spread knowledge of the nuclear EMP phenomenon into the popular culture. EMP has been subsequently used in a wide variety of fiction and other aspects of popular culture.

The popular media often depict EMP effects incorrectly, causing misunderstandings among the public and even professionals, and official efforts have been made in the United States to set the record straight. The United States Space Command commissioned science educator Bill Nye to narrate and produce a video called "Hollywood vs. EMP", so that inaccurate Hollywood fiction would not confuse those who must deal with real EMP events. The video is not available to the general public.

title: Nuclear electromagnetic pulse


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Electromagnetic radiation and health

Electromagnetic radiation can be classified into two types: ionizing radiation and non-ionizing radiation, based on the capability of a single photon with more than 10 eV energy to ionize atoms or break chemical bonds. Extreme ultraviolet and higher frequencies, such as X-rays or gamma rays are ionizing, and these pose their own special hazards: see radiation poisoning. The field strength of electromagnetic radiation is measured in volts per meter (V/m).

The most common health hazard of radiation is sunburn, which causes between approximately 100,000 and 1 million new skin cancers annually in the United States.

In 2011, the World Health Organization (WHO) and the International Agency for Research on Cancer (IARC) have classified radiofrequency electromagnetic fields as possibly carcinogenic to humans (Group 2B).

Hazards
Dielectric heating from electromagnetic radiation can create a biological hazard. For example, touching or standing around an antenna while a high-power transmitter is in operation can cause burns. The mechanism is the same as that used in a microwave oven.

The heating effect varies with the power and the frequency of the electromagnetic energy, as well as the inverse square of distance to the source. The eyes and testes are particularly susceptible to radio frequency heating due to the paucity of blood flow in these areas that could otherwise dissipate the heat buildup.

Workplace exposure
Radio frequency (RF) energy at power density levels of 1–10 mW/cm2 or higher can cause measurable heating of tissues. Typical RF energy levels encountered by the general public are well below the level needed to cause significant heating, but certain workplace environments near high power RF sources may exceed safe exposure limits. A measure of the heating effect is the specific absorption rate or SAR, which has units of watts per kilogram (W/kg). The IEEE and many national governments have established safety limits for exposure to various frequencies of electromagnetic energy based on SAR, mainly based on ICNIRP Guidelines, which guard against thermal damage.

Industrial installations for induction hardening and melting or on welding equipment may produce considerably higher field strengths and require further examination. If the exposure cannot be determined upon manufacturers' information, comparisons with similar systems or analytical calculations, measurements have to be accomplished. The results of the evaluation help to assess possible hazards to the safety and health of workers and to define protective measures. Since electromagnetic fields may influence passive or active implants of workers, it is essential to consider the exposure at their workplaces separately in the risk assessment.

Low-level exposure
The World Health Organization (WHO) began a research effort in 1996 to study the health effects from the ever-increasing exposure of people to a diverse range of EMR sources. In 2011, the WHO/International Agency for Research on Cancer (IARC) has classified radiofrequency electromagnetic fields as possibly carcinogenic to humans (Group 2B), based on an increased risk for glioma, a malignant type of brain cancer, associated with wireless phone use.

Epidemiological studies look for statistical correlations between EM exposure in the field and specific health effects. As of 2019, much of the current work is focused on the study of EM fields in relation to cancer. There are publications which support the existence of complex biological and neurological effects of weaker non-thermal electromagnetic fields (see Bioelectromagnetics), including weak ELF electromagnetic fields and modulated RF and microwave fields.

Effects by frequency

While the most acute exposures to harmful levels of electromagnetic radiation are immediately realized as burns, the health effects due to chronic or occupational exposure may not manifest effects for months or years.

Extremely low frequency
Extremely low frequency EM waves can span from 0 Hz to 3 kHz, though definitions vary across disciplines. The maximum recommended exposure for the general public is 5 kV/m.

ELF waves around 50 Hz to 60 Hz are emitted by power generators, transmission lines and distribution lines, power cables, and electric appliances. Typical household exposure to ELF waves ranges in intensity from 5 V/m for a light bulb to 180 V/m for a stereo, measured at 30 cm and using 240V power. (120V power systems would be unable to reach this intensity unless an appliance has an internal voltage transformer.)

Overhead power lines range from 1kV for local distribution to 1,150 kV for ultra high voltage lines. These can produce electric fields up to 10kV/m on the ground directly underneath, but 50 m to 100 m away these levels return to approximately ambient. Metal equipment must be maintained at a safe distance from energized high-voltage lines.

Exposure to ELF waves can induce an electric current. Because the human body is conductive, electric currents and resulting voltages differences typically accumulate on the skin but do not reach interior tissues. People can start to perceive high-voltage charges as tingling when hair or clothing in contact with the skin stands up or vibrates. In scientific tests, only about 10% of people could detect a field intensity in the range of 2-5 kV/m. Such voltage differences can also create electric sparks, similar to a discharge of static electricity when nearly touching a grounded object. When receiving such a shock at 5 kV/m, it was reported as painful by only 7% of test participants and by 50% of participants at 10 kV/m.

Associations between exposure to extremely low frequency magnetic fields (ELF MF) and various health outcomes have been investigated through a variety of epidemiological studies. A pooled analysis found consistent evidence of an effect of ELF-MF on childhood leukaemia. An assessment of the burden of disease potentially resulting from ELF MF exposure in Europe found that 1.5–2% of childhood leukaemia cases might be attributable to ELF MF, but uncertainties around causal mechanisms and models of dose-response were found to be considerable.

The International Agency for Research on Cancer (IARC) finds "inadequate evidence" for human carcinogenicity.

Shortwave
Shortwave (1.6 to 30 MHz) diathermy (where EM waves are used to produce heat) can be used as a therapeutic technique for its analgesic effect and deep muscle relaxation, but has largely been replaced by ultrasound. Temperatures in muscles can increase by 4–6 °C, and subcutaneous fat by 15 °C. The FCC has restricted the frequencies allowed for medical treatment, and most machines in the US use 27.12 MHz. Shortwave diathermy can be applied in either continuous or pulsed mode. The latter came to prominence because the continuous mode produced too much heating too rapidly, making patients uncomfortable. The technique only heats tissues that are good electrical conductors, such as blood vessels and muscle. Adipose tissue (fat) receives little heating by induction fields because an electrical current is not actually going through the tissues.

Studies have been performed on the use of shortwave radiation for cancer therapy and promoting wound healing, with some success. However, at a sufficiently high energy level, shortwave energy can be harmful to human health, potentially causing damage to biological tissues, for example by overheating or inducing electrical currents. The FCC limits for maximum permissible workplace exposure to shortwave radio frequency energy in the range of 3–30 MHz has a plane-wave equivalent power density of (900/f2) mW/cm2 where f is the frequency in MHz, and 100 mW/cm2 from 0.3 to 3.0 MHz. For uncontrolled exposure to the general public, the limit is 180/f2 between 1.34 and 30 MHz.

Radio and microwave frequencies
The designation of mobile phone signals as "possibly carcinogenic to humans" by the World Health Organization (WHO): "A positive association has been observed between exposure to the agent and cancer for which a causal interpretation is considered by the Working Group to be credible, but chance, bias or confounding could not be ruled out with reasonable confidence." This classification has been interpreted to mean that there is very little scientific evidence as to phone signal carcinogenesis.

In 2011, International Agency for Research on Cancer (IARC) classified mobile phone radiation as Group 2B "possibly carcinogenic" (rather than Group 2A "probably carcinogenic" nor the "is carcinogenic" Group 1). That means that there "could be some risk" of carcinogenicity, so additional research into the long-term, heavy use of mobile phones needs to be conducted. The WHO concluded in 2014 that "A large number of studies have been performed over the last two decades to assess whether mobile phones pose a potential health risk. To date, no adverse health effects have been established as being caused by mobile phone use."

Since 1962, the microwave auditory effect or tinnitus has been shown from radio frequency exposure at levels below significant heating. Studies during the 1960s in Europe and Russia claimed to show effects on humans, especially the nervous system, from low energy RF radiation; the studies were disputed at the time.

In 2019, reporters from the Chicago Tribune tested the level of radiation from smartphones and found that certain models emitted more than reported by the manufacturers and in some cases more than the U.S. Federal Communications Commission exposure limit. It is unclear if this resulted in any harm to consumers. Some problems apparently involved the phone's ability to detect proximity to a human body and lower the radio power. In response, the FCC began testing some phones itself rather than relying solely on manufacturer certifications.

Microwave and other radio frequencies cause heating, and this can cause burns or eye damage if delivered in high intensity, or hyperthermia as with any powerful heat source. Microwave ovens use this form of radiation, and have shielding to prevent it from leaking out and unintentionally heating nearby objects or people.

Millimeter waves
In 2009, the US TSA introduced full-body scanners as a primary screening modality in airport security, first as backscatter X-ray scanners, which use ionizing radiation and which the European Union banned in 2011 due to health and safety concerns. These were followed by non-ionizing millimeter wave scanners. Likewise WiGig for personal area networks have opened the 60 GHz and above microwave band to SAR exposure regulations. Previously, microwave applications in these bands were for point-to-point satellite communication with minimal human exposure.

Infrared
Infrared wavelengths longer than 750 nm can produce changes in the lens of the eye. Glassblower's cataract is an example of a heat injury that damages the anterior lens capsule among unprotected glass and iron workers. Cataract-like changes can occur in workers who observe glowing masses of glass or iron without protective eyewear for prolonged periods over many years.

Exposing skin to infrared radiation near visible light (IR-A) leads to increased production of free radicals. Short-term exposure can be beneficial (activating protective responses), while prolonged exposure can lead to photoaging.

Another important factor is the distance between the worker and the source of radiation. In the case of arc welding, infrared radiation decreases rapidly as a function of distance, so that farther than three feet away from where welding takes place, it does not pose an ocular hazard anymore but, ultraviolet radiation still does. This is why welders wear tinted glasses and surrounding workers only have to wear clear ones that filter UV.

Visible light
Photic retinopathy is damage to the macular area of the eye's retina that results from prolonged exposure to sunlight, particularly with dilated pupils. This can happen, for example, while observing a solar eclipse without suitable eye protection. The Sun's radiation creates a photochemical reaction that can result in visual dazzling and a scotoma. The initial lesions and edema will disappear after several weeks, but may leave behind a permanent reduction in visual acuity.

Moderate and high-power lasers are potentially hazardous because they can burn the retina of the eye, or even the skin. To control the risk of injury, various specifications – for example ANSI Z136 in the US, EN 60825-1/A2 in Europe, and IEC 60825 internationally – define "classes" of lasers depending on their power and wavelength. Regulations prescribe required safety measures, such as labeling lasers with specific warnings, and wearing laser safety goggles during operation (see laser safety).

As with its infrared and ultraviolet radiation dangers, welding creates an intense brightness in the visible light spectrum, which may cause temporary flash blindness. Some sources state that there is no minimum safe distance for exposure to these radiation emissions without adequate eye protection.

Ultraviolet
Sunlight includes sufficient ultraviolet power to cause sunburn within hours of exposure, and the burn severity increases with the duration of exposure. This effect is a response of the skin called erythema, which is caused by a sufficient strong dose of UV-B. The Sun's UV output is divided into UV-A and UV-B: solar UV-A flux is 100 times that of UV-B, but the erythema response is 1,000 times higher for UV-B. This exposure can increase at higher altitudes and when reflected by snow, ice, or sand. The UV-B flux is 2–4 times greater during the middle 4–6 hours of the day, and is not significantly absorbed by cloud cover or up to a meter of water.

Ultraviolet light, specifically UV-B, has been shown to cause cataracts and there is some evidence that sunglasses worn at an early age can slow its development in later life. Most UV light from the sun is filtered out by the atmosphere and consequently airline pilots often have high rates of cataracts because of the increased levels of UV radiation in the upper atmosphere. It is hypothesized that depletion of the ozone layer and a consequent increase in levels of UV light on the ground may increase future rates of cataracts. Note that the lens filters UV light, so if it is removed via surgery, one may be able to see UV light.

Prolonged exposure to ultraviolet radiation from the sun can lead to melanoma and other skin malignancies. Clear evidence establishes ultraviolet radiation, especially the non-ionizing medium wave UVB, as the cause of most non-melanoma skin cancers, which are the most common forms of cancer in the world. UV rays can also cause wrinkles, liver spots, moles, and freckles. In addition to sunlight, other sources include tanning beds, and bright desk lights. Damage is cumulative over one's lifetime, so that permanent effects may not be evident for some time after exposure.

Ultraviolet radiation of wavelengths shorter than 300 nm (actinic rays) can damage the corneal epithelium. This is most commonly the result of exposure to the sun at high altitude, and in areas where shorter wavelengths are readily reflected from bright surfaces, such as snow, water, and sand. UV generated by a welding arc can similarly cause damage to the cornea, known as "arc eye" or welding flash burn, a form of photokeratitis. Fluorescent light bulbs and tubes internally produce ultraviolet light. Normally this is converted to visible light by the phosphor film inside a protective coating. When the film is cracked by mishandling or faulty manufacturing then UV may escape at levels that could cause sunburn or even skin cancer.

Regulation
In the United States, nonionizing radiation is regulated in the Radiation Control for Health and Safety Act of 1968 and the Occupational Safety and Health Act of 1970.

title: Electromagnetic radiation and health


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Electronic switching system

In telecommunications, an electronic switching system (ESS) is a telephone switch that uses solid-state electronics, such as digital electronics and computer ized common control, to interconnect telephone circuits for the purpose of establishing telephone calls.

The generations of telephone switches before the advent of electronic switching in the 1950s used purely electro-mechanical relay systems and analog voice paths. These early machines typically utilized the step-by-step technique. The first generation of electronic switching systems in the 1960s were not entirely digital in nature, but used reed relay-operated metallic paths or crossbar switches operated by stored program control (SPC) systems.

First announced in 1955, the first customer trial installation of an all-electronic central office commenced in Morris, Illinois in November 1960 by Bell Laboratories. The first large-scale electronic switching system was the Number One Electronic Switching System (1ESS) of the Bell System, cut over in Succasunna, New Jersey, in May 1965.

Just three years later, in September 1968, Britain's Post Office opened the world's first all-digital pulse-code modulation (PCM) exchange named Empress (three decades after British scientist Alec Reeves had invented the PCM encoding system without the digital components to take full advantage). Other nations vying to reach the forefront of technical innovation would adopt metal–oxide–semiconductor (MOS) and PCM technologies to make their own transitions from analog to digital telephony throughout the '70s. Later electronic switching systems implemented the digital representation of the electrical audio signals on subscriber loops by digitizing the analog signals and processing the resulting data for transmission between central offices. Time-division multiplexing (TDM) technology permitted the simultaneous transmission of multiple telephone calls on a single wire connection between central offices or other electronic switches, resulting in dramatic capacity improvements of the telephone network.

With the advances of digital electronics starting in the 1960s telephone switches employed semiconductor device components in increasing measure.

In the late 20th century most telephone exchanges without TDM processing were eliminated and the term electronic switching system became largely a historical distinction for the older SPC systems.

title: Electronic switching system


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Electronic warfare support measures

In military telecommunications, electronic support (ES) or electronic support measures (ESM) gather intelligence through passive "listening" to electromagnetic radiations of military interest. They are an aspect of electronic warfare involving actions taken under direct control of an operational commander to detect, intercept, identify, locate, record, and/or analyze sources of radiated electromagnetic energy for the purposes of immediate threat recognition (such as warning that fire control radar has locked on a combat vehicle, ship, or aircraft) or longer-term operational planning. Thus, electronic support provides a source of information required for decisions involving electronic protection (EP), electronic attack (EA), avoidance, targeting, and other tactical employment of forces. Electronic support data can be used to produce signals intelligence (SIGINT), communications intelligence (COMINT) and electronics intelligence (ELINT).

Electronic support measures can provide (1) initial detection or knowledge of foreign systems, (2) a library of technical and operational data on foreign systems, and (3) tactical combat information utilizing that library. ESM collection platforms can remain electronically silent and detect and analyze RADAR transmissions beyond the RADAR detection range because of the greater power of the transmitted electromagnetic pulse with respect to a reflected echo of that pulse. United States airborne ESM receivers are designated in the AN/ALR series.

Desirable characteristics for electromagnetic surveillance and collection equipment include (1) wide-spectrum or bandwidth capability because foreign frequencies are initially unknown, (2) wide dynamic range because the signal strength is initially unknown, (3) narrow bandpass to discriminate the signal of interest from other electromagnetic radiation on nearby frequencies, and (4) good angle-of arrival measurement for bearings to locate the transmitter. The frequency spectrum of interest ranges from 30 MHz to 50 GHz. Multiple receivers are typically required for surveillance of the entire spectrum, but tactical receivers may be functional within a specific signal strength threshold of a smaller frequency range.

title: Electronic warfare support measures


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Electro–optic effect

An electro–optic effect is a change in the optical properties of a material in response to an electric field that varies slowly compared with the frequency of light. The term encompasses a number of distinct phenomena, which can be subdivided into

 * a) change of the absorption
 * Electroabsorption: general change of the absorption constants
 * Franz–Keldysh effect: change in the absorption shown in some bulk semiconductors
 * Quantum-confined Stark effect: change in the absorption in some semiconductor quantum wells
 * Electrochromic effect: creation of an absorption band at some wavelengths, which gives rise to a change in colour
 * b) change of the refractive index and permittivity
 * Pockels effect (or linear electro-optic effect): change in the refractive index linearly proportional to the electric field. Only certain crystalline solids show the Pockels effect, as it requires lack of inversion symmetry
 * Kerr effect (or quadratic electro-optic effect, QEO effect): change in the refractive index proportional to the square of the electric field. All materials display the Kerr effect, with varying magnitudes, but it is generally much weaker than the Pockels effect
 * electro-gyration: change in the optical activity.
 * Electron-refractive effect or EIPM

In December 2015, two further electro-optic effects of type (b) were theoretically predicted to exist but have not, as yet, been experimentally observed.

Changes in absorption can have a strong effect on refractive index for wavelengths near the absorption edge, due to the Kramers–Kronig relation.

Using a less strict definition of the electro-optic effect allowing also electric fields oscillating at optical frequencies, one could also include nonlinear absorption (absorption depends on the light intensity) to category a) and the optical Kerr effect (refractive index depends on the light intensity) to category b). Combined with the photoeffect and photoconductivity, the electro-optic effect gives rise to the photorefractive effect.

The term "electro-optic" is often erroneously used as a synonym for "optoelectronic".

Electro-optic modulators
Electro-optic modulators are usually built with electro-optic crystals exhibiting the Pockels effect. The transmitted beam is phase modulated with the electric signal applied to the crystal. Amplitude modulators can be built by putting the electro-optic crystal between two linear polarizers or in one path of a Mach–Zehnder interferometer. Additionally, Amplitude modulators can be constructed by deflecting the beam into and out of a small aperture such as a fiber. This design can be low loss (<3 dB) and polarization independent depending on the crystal configuration.

Electro-optic deflectors
Electro-optic deflectors utilize prisms of electro-optic crystals. The index of refraction is changed by the Pockels effect, thus changing the direction of propagation of the beam inside the prism. Electro-optic deflectors have only a small number of resolvable spots, but possess a fast response time. There are few commercial models available at this time. This is because of competing acousto-optic deflectors, the small number of resolvable spots and the relatively high price of electro-optic crystals.

Electro-optic field sensors
The electro-optic Pockels effect in nonlinear crystals (e.g. KDP, BSO, K*DP) can be used for electric field sensing via polarisation state modulation techniques. In this scenario, an unknown electric field results in polarisation rotation of a laser beam propagating through the electro-optic crystal; through inclusion of polarisers to modulate the light intensity incident on a photodiode, a time-resolved electric field measurement can be reconstructed from the obtained voltage trace. As the signals obtained from vgcc the crystalline probes are optical, they are inherently resistant to electrical noise pickup, hence can be used for low-noise field measurement even in areas with high levels of electromagnetic noise in the vicinity of the probe. Furthermore, as the polarisation rotation due to the Pockels effect scales linearly with electric field, absolute field measurements are obtained, with no need for numerical integration to reconstruct electric fields, as is the case with conventional probes sensitive to the time-derivative of the electric field.

Electro-optic measurements of strong electromagnetic pulses from intense laser-matter interactions have been demonstrated in both the nanosecond and picosecond (sub-petawatt) laser pulse driver regimes.

title: Electro–optic effect


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Electro-optic modulator

An electro-optic modulator (EOM) is an optical device in which a signal-controlled element exhibiting an electro-optic effect is used to modulate a beam of light. The modulation may be imposed on the phase, frequency, amplitude, or polarization of the beam. Modulation bandwidths extending into the gigahertz range are possible with the use of laser-controlled modulators.

The electro-optic effect describes two phenomena, the change of absorption and the change in the refractive index of a material, resulting from the application of a DC or an electric field with much lower frequency than the optical carrier. This is caused by forces that distort the position, orientation, or shape of the molecules constituting the material. Generally, a nonlinear optical material, such as ferroelectrics like lithium niobate (LiNbO3) or barium titanate (BaTiO3), polymers, or organic electro-optic materials, with an incident static or low frequency optical field will see a modulation of its refractive index.

The simplest kind of EOM consists of a crystal, such as lithium niobate, whose refractive index is a function of the strength of the local electric field. That means that if lithium niobate is exposed to an electric field, light will travel more slowly through it. But the phase of the light leaving the crystal is directly proportional to the length of time it takes that light to pass through it. Therefore, the phase of the laser light exiting an EOM can be controlled by changing the electric field in the crystal.

Note that the electric field can be created by placing a parallel plate capacitor across the crystal. Since the field inside a parallel plate capacitor depends linearly on the potential, the index of refraction depends linearly on the field (for crystals where Pockels effect dominates), and the phase depends linearly on the index of refraction, the phase modulation must depend linearly on the potential applied to the EOM.

The voltage required for inducing a phase change of $$\pi$$ is called the half-wave voltage ($$V_\pi$$). For a Pockels cell, it is usually hundreds or even thousands of volts, so that a high-voltage amplifier is required. Suitable electronic circuits can switch such large voltages within a few nanoseconds, allowing the use of EOMs as fast optical switches.

Liquid crystal devices are electro-optical phase modulators if no polarizers are used.

Phase modulation
Phase modulation (PM) is a modulation pattern that encodes information as variations in the instantaneous phase of a carrier wave.

The phase of a carrier signal is modulated to follow the changing voltage level (amplitude) of modulation signal. The peak amplitude and frequency of the carrier signal remain constant, but as the amplitude of the information signal changes, the phase of the carrier changes correspondingly. The analysis and the final result (modulated signal) are similar to those of frequency modulation.

A very common application of EOMs is for creating sidebands in a monochromatic laser beam. To see how this works, first imagine that the strength of a laser beam with frequency $$\omega$$ entering the EOM is given by

 * $$Ae^{i\omega t}.$$

Now suppose we apply a sinusoidally varying potential voltage to the EOM with frequency $$\Omega$$ and small amplitude $$\beta$$. This adds a time dependent phase to the above expression,

 * $$Ae^{i\omega t + i\beta\sin(\Omega t)}.$$

Since $$\beta$$ is small, we can use the Taylor expansion for the exponential

 * $$Ae^{i\omega t}\left( 1+i\beta\sin(\Omega t)\right) ,$$

to which we apply a simple identity for sine,

 * $$Ae^{i\omega t}\left( 1 + \frac{\beta}{2}\left(e^{i\Omega t} - e^{-i\Omega t}\right)\right) = A\left( e^{i\omega t}+\frac{\beta}{2}e^{i(\omega+\Omega) t}-\frac{\beta}{2}e^{i(\omega-\Omega) t}\right) .$$

This expression we interpret to mean that we have the original carrier signal plus two small sidebands, one at $$\omega+\Omega$$ and another at $$\omega-\Omega$$. Notice however that we only used the first term in the Taylor expansion – in truth there are an infinite number of sidebands. There is a useful identity involving Bessel functions called the Jacobi–Anger expansion which can be used to derive

 * $$Ae^{i\omega t + i\beta\sin(\Omega t)} = Ae^{i\omega t}\left( J_0(\beta) + \sum_{k=1}^\infty J_k(\beta)e^{ik\Omega t} + \sum_{k=1}^\infty (-1)^k J_k(\beta)e^{-ik\Omega t}\right), $$

which gives the amplitudes of all the sidebands. Notice that if one modulates the amplitude instead of the phase, one gets only the first set of sidebands,

 * $$\left( 1 + \beta\sin(\Omega t)\right) Ae^{i\omega t} = Ae^{i\omega t} + \frac{A\beta}{2i}\left( e^{i(\omega+\Omega) t} - e^{i(\omega-\Omega)t} \right) . $$

Amplitude modulation
A phase modulating EOM can also be used as an amplitude modulator by using a Mach–Zehnder interferometer. This alternative technique is often used in integrated optics where the requirements of phase stability is more easily achieved. The beam splitter divides the laser light into two paths, one of which has a phase modulator as described above. The beams are then recombined. Changing the electric field on the phase modulating path will then determine whether the two beams interfere constructively or destructively at the output, and thereby control the amplitude or intensity of the exiting light. This device is called a Mach–Zehnder modulator (MZM) and it is widely used as intensity modulator (IM) in fiber-optic communications.

Polarization modulation
Depending on the type and orientation of the nonlinear crystal, and on the direction of the applied electric field, the phase delay can depend on the polarization direction. A Pockels cell can thus be seen as a voltage-controlled waveplate, and it can be used for modulating the polarization state. For a linear input polarization (often oriented at 45° to the crystal axis), the output polarization will in general be elliptical, rather than simply a linear polarization state with a rotated direction.

Polarization modulation in electro-optic crystals can also be used as a technique for time-resolved measurement of unknown electric fields. Compared to conventional techniques using conductive field probes and cabling for signal transport to read-out systems, electro-optical measurement is inherently noise resistant as signals are carried by fiber-optics, preventing distortion of the signal by electrical noise sources. The polarization change measured by such techniques is linearly dependent on the electric field applied to the crystal, hence providing absolute measurements of the field, without the need for numerical integration of voltage traces, as is the case for conductive probes sensitive to the time-derivative of the electric field.

EOM technologies
EOMs can be based on many operating principles and platforms. One can divide the EOMs in two categories – phase and amplitude modulation. In the following some prominent approaches in SiPh are presented. Operating principles for phase modulation are the plasma dispersion effect, pockels effect, interband transitions, and carrier accumulation/depletion+Franz-Keldysh effect. For the amplitude modulation some operating principles are the Franz-Keldysh effect, quantum confined Stark effect, and electrical gating.

The plasma dispersion effect can be based on carrier injection, depletion, or accumulation. The most established Pockels type modulators are based on the lithium niobate on silicon platform. In recent years, other platforms were introduced, such as BTO on silicon, silicon polymer hybrid, silicon organic hybrids, plasmonics and thin-film lithium niobate. Interband transition rely on 2D materials and the carrier accumulation/depletion+Franz-Keldysh is based on a III-V platform.

The Franz-Keldysh effect is used in electro-absorption modulators which are semiconductor devices. It describes a change in the absorption spectrum due to a shift in the band gap edge when an electric field is present. They are often built on a silicon-germanium platform. Modulators running on the quantum confined stark effect can rely on a III-V platform or on Ge-Si-Ge quantum wells. Electrical gating is built on a 2D material platform.

title: Electro-optic modulator


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Electro-optics

Electro–optics is a branch of electrical engineering, electronic engineering, materials science, and material physics involving components, electronic devices such as lasers, laser diodes, LEDs, waveguides, etc. which operate by the propagation and interaction of light with various tailored materials. It is closely related to photonics, the branch of optics that involves the application of the generation of photons. It is not only concerned with the "electro–optic effect", since it deals with the interaction between the electromagnetic (optical) and the electrical (electronic) states of materials.

Electro-optical devices
The electro-optic effect is a change in the optical properties of an optically active material in response to changes in an electric field. This interaction usually results in a change in the birefringence, and not simply the refractive index of the medium. In a Kerr cell, the change in birefringence is proportional to the square of the electric field, and the material is usually a liquid. In a Pockels cell, the change in birefringence varies linearly with the electric field, and the material is usually a crystal. Non-crystalline, solid electro-optical materials have generated interest because of their low cost of production. These organic, polymer-based materials are also known as organic EO material, plastic EO material, or polymer EO material. They consist of nonlinear optical chromophores in a polymer lattice. The nonlinear optical chromophores can produce Pockels effect.

title: Electro-optics


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Elliptical polarization

In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality.

Circular polarization and linear polarization can be considered to be special cases of elliptical polarization. This terminology was introduced by Augustin-Jean Fresnel in 1822, before the electromagnetic nature of light waves was known.

Mathematical description
The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is (Gaussian units)

 * $$ \mathbf{E} ( \mathbf{r}, t ) = \left| \mathbf{E} \right| \mathrm{Re} \left \{  |\psi\rangle  \exp \left [ i \left  ( kz-\omega t  \right ) \right ] \right \}  $$

 * $$ \mathbf{B} ( \mathbf{r}, t ) = \hat { \mathbf{z} } \times \mathbf{E} ( \mathbf{r} , t )  $$

for the magnetic field, where k is the wavenumber,

 * $$ \omega = c k$$

is the angular frequency of the wave propagating in the +z direction, and $$ c $$ is the speed of light.

Here $$| \mathbf{E} |$$ is the amplitude of the field and

 * $$  |\psi\rangle  \ \stackrel{\mathrm{def}}{=}\  \begin{pmatrix} \psi_x  \\ \psi_y   \end{pmatrix} =   \begin{pmatrix} \cos\theta \exp \left ( i \alpha_x \right )   \\ \sin\theta \exp \left ( i \alpha_y \right )   \end{pmatrix}   $$

is the normalized Jones vector. This is the most complete representation of polarized electromagnetic radiation and corresponds in general to elliptical polarization.

Polarization ellipse
At a fixed point in space (or for fixed z), the electric vector $$ \mathbf{E} $$ traces out an ellipse in the x-y plane. The semi-major and semi-minor axes of the ellipse have lengths A and B, respectively, that are given by
 * $$ A=|\mathbf{E}|\sqrt{\frac{1+\sqrt{1-\sin^2(2\theta)\sin^2\beta}}{2}}$$

and
 * $$ B=|\mathbf{E}|\sqrt{\frac{1-\sqrt{1-\sin^2(2\theta)\sin^2\beta}}{2}}$$,

where $$\beta =\alpha_y-\alpha_x$$ with the phases $$\alpha_x$$ and $$\alpha_y$$. The orientation of the ellipse is given by the angle $$\phi $$ the semi-major axis makes with the x-axis. This angle can be calculated from
 * $$ \tan2\phi=\tan2\theta\cos\beta$$.

If $$\beta= 0$$, the wave is linearly polarized. The ellipse collapses to a straight line $$(A=|\mathbf{E}|, B=0$$) oriented at an angle $$\phi=\theta$$. This is the case of superposition of two simple harmonic motions (in phase), one in the x direction with an amplitude $$|\mathbf{E}| \cos\theta$$, and the other in the y direction with an amplitude $$|\mathbf{E}| \sin\theta $$. When $$\beta$$ increases from zero, i.e., assumes positive values, the line evolves into an ellipse that is being traced out in the counterclockwise direction (looking in the direction of the propagating wave); this then corresponds to left-handed elliptical polarization; the semi-major axis is now oriented at an angle $$\phi\neq\theta $$. Similarly, if $$\beta$$ becomes negative from zero, the line evolves into an ellipse that is being traced out in the clockwise direction; this corresponds to right-handed elliptical polarization.

If $$\beta=\pm\pi/2$$ and $$\theta=\pi/4$$, $$ A=B=|\mathbf{E}|/\sqrt{2}$$, i.e., the wave is circularly polarized. When $$\beta=\pi/2$$, the wave is left-circularly polarized, and when $$\beta=-\pi/2$$, the wave is right-circularly polarized.

Parameterization
Any fixed polarization can be described in terms of the shape and orientation of the polarization ellipse, which is defined by two parameters: axial ratio AR and tilt angle $$\tau$$. The axial ratio is the ratio of the lengths of the major and minor axes of the ellipse, and is always greater than or equal to one.

Alternatively, polarization can be represented as a point on the surface of the Poincaré sphere, with $$2\times \tau$$ as the longitude and $$2\times \epsilon$$ as the latitude, where $$\epsilon=\arccot(\pm AR)$$. The sign used in the argument of the $$\arccot$$ depends on the handedness of the polarization. Positive indicates left hand polarization, while negative indicates right hand polarization, as defined by IEEE.

For the special case of circular polarization, the axial ratio equals 1 (or 0 dB) and the tilt angle is undefined. For the special case of linear polarization, the axial ratio is infinite.

In nature
The reflected light from some beetles (e.g. Cetonia aurata) is elliptical polarized.

title: Elliptical polarization