Wireless power transfer

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https://en.wikipedia.org/wiki/Wireless_power_transfer 

 

Inductive charging pad for a smartphone as an example of near-field wireless transfer. When the phone is set on the pad, a coil in the pad creates a magnetic field which induces a current in another coil, in the phone, charging its battery.

Wireless power transfer (WPT), wireless power transmission, wireless energy transmission (WET), or electromagnetic power transfer is the transmission of electrical energy without wires as a physical link. In a wireless power transmission system, a transmitter device, driven by electric power from a power source, generates a time-varying electromagnetic field, which transmits power across space to a receiver device, which extracts power from the field and supplies it to an electrical load. The technology of wireless power transmission can eliminate the use of the wires and batteries, thus increasing the mobility, convenience, and safety of an electronic device for all users. Wireless power transfer is useful to power electrical devices where interconnecting wires are inconvenient, hazardous, or are not possible.

Wireless power techniques mainly fall into two categories, near field and far-field. In near field or non-radiative techniques, power is transferred over short distances by magnetic fields using inductive coupling between coils of wire, or by electric fields using capacitive coupling between metal electrodes. Inductive coupling is the most widely used wireless technology; its applications include charging handheld devices like phones and electric toothbrushes, RFID tags, induction cooking, and wirelessly charging or continuous wireless power transfer in implantable medical devices like artificial cardiac pacemakers, or electric vehicles.

In far-field or radiative techniques, also called power beaming, power is transferred by beams of electromagnetic radiation, like microwaves or laser beams. These techniques can transport energy longer distances but must be aimed at the receiver. Proposed applications for this type include solar power satellites and wireless powered drone aircraft.

An important issue associated with all wireless power systems is limiting the exposure of people and other living beings to potentially injurious electromagnetic fields.

Overview

Further information: Coupling (electronics)

 

Generic block diagram of a wireless power system

Wireless power transfer is a generic term for a number of different technologies for transmitting energy by means of electromagnetic fields. The technologies, listed in the table below, differ in the distance over which they can transfer power efficiently, whether the transmitter must be aimed (directed) at the receiver, and in the type of electromagnetic energy they use: time varying electric fields, magnetic fields, radio waves, microwaves, infrared or visible light waves.

In general a wireless power system consists of a "transmitter" device connected to a source of power such as a mains power line, which converts the power to a time-varying electromagnetic field, and one or more "receiver" devices which receive the power and convert it back to DC or AC electric current which is used by an electrical load. At the transmitter the input power is converted to an oscillating electromagnetic field by some type of "antenna" device. The word "antenna" is used loosely here; it may be a coil of wire which generates a magnetic field, a metal plate which generates an electric field, an antenna which radiates radio waves, or a laser which generates light. A similar antenna or coupling device at the receiver converts the oscillating fields to an electric current. An important parameter that determines the type of waves is the frequency, which determines the wavelength.

Wireless power uses the same fields and waves as wireless communication devices like radio, another familiar technology that involves electrical energy transmitted without wires by electromagnetic fields, used in cellphones, radio and television broadcasting, and WiFi. In radio communication the goal is the transmission of information, so the amount of power reaching the receiver is not so important, as long as it is sufficient that the information can be received intelligibly. In wireless communication technologies only tiny amounts of power reach the receiver. In contrast, with wireless power transfer the amount of energy received is the important thing, so the efficiency (fraction of transmitted energy that is received) is the more significant parameter. For this reason, wireless power technologies are likely to be more limited by distance than wireless communication technologies.

Wireless power transfer may be used to power up wireless information transmitters or receivers. This type of communication is known as wireless powered communication (WPC). When the harvested power is used to supply the power of wireless information transmitters, the network is known as Simultaneous Wireless Information and Power Transfer (SWIPT); whereas when it is used to supply the power of wireless information receivers, it is known as a Wireless Powered Communication Network (WPCN).

These are the different wireless power technologies:

Technology	Range	Directivity	Frequency	Antenna devices	Current and/or possible future applications
Inductive coupling	Short	Low	Hz – MHz	Wire coils	Electric tooth brush and razor battery charging, induction stovetops and industrial heaters.
Resonant inductive coupling	Mid-	Low	kHz – GHz	Tuned wire coils, lumped element resonators	Charging portable devices (Qi), biomedical implants, electric vehicles, powering buses, trains, MAGLEV, RFID, smartcards.
Capacitive coupling	Short	Low	kHz – MHz	Metal plate electrodes	Charging portable devices, power routing in large-scale integrated circuits, Smartcards, biomedical implants.
Magnetodynamic coupling	Short	N.A.	Hz	Rotating magnets	Charging electric vehicles, biomedical implants.
Microwaves	Long	High	GHz	Parabolic dishes, phased arrays, rectennas	Solar power satellite, powering drone aircraft, charging wireless devices
Light waves	Long	High	≥THz	Lasers, photocells, lenses	Charging portable devices, powering drone aircraft, powering space elevator climbers.

Field regions

Electric and magnetic fields are created by charged particles in matter such as electrons. A stationary charge creates an electrostatic field in the space around it. A steady current of charges (direct current, DC) creates a static magnetic field around it. The above fields contain energy, but cannot carry power because they are static. However time-varying fields can carry power. Accelerating electric charges, such as are found in an alternating current (AC) of electrons in a wire, create time-varying electric and magnetic fields in the space around them. These fields can exert oscillating forces on the electrons in a receiving "antenna", causing them to move back and forth. These represent alternating current which can be used to power a load.

The oscillating electric and magnetic fields surrounding moving electric charges in an antenna device can be divided into two regions, depending on distance D_range from the antenna. The boundary between the regions is somewhat vaguely defined. The fields have different characteristics in these regions, and different technologies are used for transferring power:

• Near-field or nonradiative region – This means the area within about 1 wavelength (λ) of the antenna. In this region the oscillating electric and magnetic fields are separate and power can be transferred via electric fields by capacitive coupling (electrostatic induction) between metal electrodes, or via magnetic fields by inductive coupling (electromagnetic induction) between coils of wire. These fields are not radiative, meaning the energy stays within a short distance of the transmitter. If there is no receiving device or absorbing material within their limited range to "couple" to, no power leaves the transmitter. The range of these fields is short, and depends on the size and shape of the "antenna" devices, which are usually coils of wire. The fields, and thus the power transmitted, decrease exponentially with distance, so if the distance between the two "antennas" D_range is much larger than the diameter of the "antennas" D_ant very little power will be received. Therefore, these techniques cannot be used for long range power transmission.

Resonance, such as resonant inductive coupling, can increase the coupling between the antennas greatly, allowing efficient transmission at somewhat greater distances,although the fields still decrease exponentially. Therefore the range of near-field devices is conventionally divided into two categories:

• Short range – up to about one antenna diameter: D_range ≤ D_ant. This is the range over which ordinary nonresonant capacitive or inductive coupling can transfer practical amounts of power.
• Mid-range – up to 10 times the antenna diameter: D_range ≤ 10 D_ant. This is the range over which resonant capacitive or inductive coupling can transfer practical amounts of power.

• Far-field or radiative region – Beyond about 1 wavelength (λ) of the antenna, the electric and magnetic fields are perpendicular to each other and propagate as an electromagnetic wave; examples are radio waves, microwaves, or light waves. This part of the energy is radiative, meaning it leaves the antenna whether or not there is a receiver to absorb it. The portion of energy which does not strike the receiving antenna is dissipated and lost to the system. The amount of power emitted as electromagnetic waves by an antenna depends on the ratio of the antenna's size D_ant to the wavelength of the waves λ, which is determined by the frequency: λ = c/f. At low frequencies f where the antenna is much smaller than the size of the waves, D_ant << λ, very little power is radiated. Therefore the near-field devices above, which use lower frequencies, radiate almost none of their energy as electromagnetic radiation. Antennas about the same size as the wavelength D_ant ≈ λ such as monopole or dipole antennas, radiate power efficiently, but the electromagnetic waves are radiated in all directions (omnidirectionally), so if the receiving antenna is far away, only a small amount of the radiation will hit it. Therefore, these can be used for short range, inefficient power transmission but not for long range transmission.

However, unlike fields, electromagnetic radiation can be focused by reflection or refraction into beams. By using a high-gain antenna or optical system which concentrates the radiation into a narrow beam aimed at the receiver, it can be used for long range power transmission. From the Rayleigh criterion, to produce the narrow beams necessary to focus a significant amount of the energy on a distant receiver, an antenna must be much larger than the wavelength of the waves used: D_ant >> λ = c/f. Practical beam power devices require wavelengths in the centimeter region or below, corresponding to frequencies above 1 GHz, in the microwave range or above.

Near-field (nonradiative) techniques

At large relative distance, the near-field components of electric and magnetic fields are approximately quasi-static oscillating dipole fields. These fields decrease with the cube of distance: (D_range/D_ant)⁻³ Since power is proportional to the square of the field strength, the power transferred decreases as (D_range/D_ant)⁻⁶, or 60 dB per decade. In other words, if far apart, doubling the distance between the two antennas causes the power received to decrease by a factor of 2⁶ = 64. As a result, inductive and capacitive coupling can only be used for short-range power transfer, within a few times the diameter of the antenna device D_ant. Unlike in a radiative system where the maximum radiation occurs when the dipole antennas are oriented transverse to the direction of propagation, with dipole fields the maximum coupling occurs when the dipoles are oriented longitudinally.

Inductive coupling

Main article: Inductive charging

 

Generic block diagram of an inductive wireless power system

 

(top) Modern inductive power transfer, an electric toothbrush charger. A coil in the stand produces a magnetic field, inducing an alternating current in a coil in the toothbrush, which is rectified to charge the batteries. (bottom) A light bulb powered wirelessly by induction, in 1910.

In inductive coupling (electromagnetic induction or inductive power transfer, IPT), power is transferred between coils of wire by a magnetic field. The transmitter and receiver coils together form a transformer (see diagram). An alternating current (AC) through the transmitter coil (L1) creates an oscillating magnetic field (B) by Ampere's law. The magnetic field passes through the receiving coil (L2), where it induces an alternating EMF (voltage) by Faraday's law of induction, which creates an alternating current in the receiver. The induced alternating current may either drive the load directly, or be rectified to direct current (DC) by a rectifier in the receiver, which drives the load. A few systems, such as electric toothbrush charging stands, work at 50/60 Hz so AC mains current is applied directly to the transmitter coil, but in most systems an electronic oscillator generates a higher frequency AC current which drives the coil, because transmission efficiency improves with frequency.

Inductive coupling is the oldest and most widely used wireless power technology, and virtually the only one so far which is used in commercial products. It is used in inductive charging stands for cordless appliances used in wet environments such as electric toothbrushes and shavers, to reduce the risk of electric shock. Another application area is "transcutaneous" recharging of biomedical prosthetic devices implanted in the human body, such as cardiac pacemakers and insulin pumps, to avoid having wires passing through the skin. It is also used to charge electric vehicles such as cars and to either charge or power transit vehicles like buses and trains.

However the fastest growing use is wireless charging pads to recharge mobile and handheld wireless devices such as laptop and tablet computers, computer mouse, cellphones, digital media players, and video game controllers. In the United States, the Federal Communications Commission (FCC) provided its first certification for a wireless transmission charging system in December 2017.

The power transferred increases with frequency and the mutual inductance ${\displaystyle M}$ between the coils, which depends on their geometry and the distance ${\displaystyle D_{\text{range}}}$ between them. A widely used figure of merit is the coupling coefficient ${\displaystyle k\;=\;M/{\sqrt {L_{1}L_{2}}}}$. This dimensionless parameter is equal to the fraction of magnetic flux through the transmitter coil ${\displaystyle L1}$ that passes through the receiver coil ${\displaystyle L2}$ when L2 is open circuited. If the two coils are on the same axis and close together so all the magnetic flux from ${\displaystyle L1}$ passes through ${\displaystyle L2}$, ${\displaystyle k=1}$ and the link efficiency approaches 100%. The greater the separation between the coils, the more of the magnetic field from the first coil misses the second, and the lower ${\displaystyle k}$ and the link efficiency are, approaching zero at large separations. The link efficiency and power transferred is roughly proportional to ${\displaystyle k^{2}}$. In order to achieve high efficiency, the coils must be very close together, a fraction of the coil diameter ${\displaystyle D_{\text{ant}}}$, usually within centimeters, with the coils' axes aligned. Wide, flat coil shapes are usually used, to increase coupling. Ferrite "flux confinement" cores can confine the magnetic fields, improving coupling and reducing interference to nearby electronics, but they are heavy and bulky so small wireless devices often use air-core coils.

Ordinary inductive coupling can only achieve high efficiency when the coils are very close together, usually adjacent. In most modern inductive systems resonant inductive coupling (described below) is used, in which the efficiency is increased by using resonant circuits. This can achieve high efficiencies at greater distances than nonresonant inductive coupling.

Prototype inductive electric car charging system at 2011 Tokyo Auto Show

 

Powermat inductive charging spots in a coffee shop. Customers can set their phones and computers on them to recharge.

 

Wireless powered access card.

 

GM EV1 and Toyota RAV4 EV inductively charging at a now-obsolete Magne Charge station

Resonant inductive coupling

Main article: Resonant inductive coupling

Further information: Tesla coil § Resonant transformer

Resonant inductive coupling (electrodynamic coupling, strongly coupled magnetic resonance) is a form of inductive coupling in which power is transferred by magnetic fields (B, green) between two resonant circuits (tuned circuits), one in the transmitter and one in the receiver (see diagram, right). Each resonant circuit consists of a coil of wire connected to a capacitor, or a self-resonant coil or other resonator with internal capacitance. The two are tuned to resonate at the same resonant frequency. The resonance between the coils can greatly increase coupling and power transfer, analogously to the way a vibrating tuning fork can induce sympathetic vibration in a distant fork tuned to the same pitch.

Nikola Tesla first discovered resonant coupling during his pioneering experiments in wireless power transfer around the turn of the 20th century, but the possibilities of using resonant coupling to increase transmission range has only recently been explored. In 2007 a team led by Marin Soljačić at MIT used two coupled tuned circuits each made of a 25 cm self-resonant coil of wire at 10 MHz to achieve the transmission of 60 W of power over a distance of 2 meters (6.6 ft) (8 times the coil diameter) at around 40% efficiency.

The concept behind resonant inductive coupling systems is that high Q factor resonators exchange energy at a much higher rate than they lose energy due to internal damping. Therefore, by using resonance, the same amount of power can be transferred at greater distances, using the much weaker magnetic fields out in the peripheral regions ("tails") of the near fields. Resonant inductive coupling can achieve high efficiency at ranges of 4 to 10 times the coil diameter (D_ant). This is called "mid-range" transfer, in contrast to the "short range" of nonresonant inductive transfer, which can achieve similar efficiencies only when the coils are adjacent. Another advantage is that resonant circuits interact with each other so much more strongly than they do with nonresonant objects that power losses due to absorption in stray nearby objects are negligible.

A drawback of resonant coupling theory is that at close ranges when the two resonant circuits are tightly coupled, the resonant frequency of the system is no longer constant but "splits" into two resonant peaks, so the maximum power transfer no longer occurs at the original resonant frequency and the oscillator frequency must be tuned to the new resonance peak.

Resonant technology is currently being widely incorporated in modern inductive wireless power systems. One of the possibilities envisioned for this technology is area wireless power coverage. A coil in the wall or ceiling of a room might be able to wirelessly power lights and mobile devices anywhere in the room, with reasonable efficiency. An environmental and economic benefit of wirelessly powering small devices such as clocks, radios, music players and remote controls is that it could drastically reduce the 6 billion batteries disposed of each year, a large source of toxic waste and groundwater contamination.

Capacitive coupling

Main article: Capacitive coupling

Capacitive coupling also referred to as electric coupling, makes use of electric fields for the transmission of power between two electrodes (an anode and cathode) forming a capacitance for the transfer of power. In capacitive coupling (electrostatic induction), the conjugate of inductive coupling, energy is transmitted by electric fields between electrodes such as metal plates. The transmitter and receiver electrodes form a capacitor, with the intervening space as the dielectric. An alternating voltage generated by the transmitter is applied to the transmitting plate, and the oscillating electric field induces an alternating potential on the receiver plate by electrostatic induction, which causes an alternating current to flow in the load circuit. The amount of power transferred increases with the frequency the square of the voltage, and the capacitance between the plates, which is proportional to the area of the smaller plate and (for short distances) inversely proportional to the separation.

Capacitive wireless power systems 

Bipolar coupling

 

Monopolar coupling

Capacitive coupling has only been used practically in a few low power applications, because the very high voltages on the electrodes required to transmit significant power can be hazardous, and can cause unpleasant side effects such as noxious ozone production. In addition, in contrast to magnetic fields, electric fields interact strongly with most materials, including the human body, due to dielectric polarization. Intervening materials between or near the electrodes can absorb the energy, in the case of humans possibly causing excessive electromagnetic field exposure. However capacitive coupling has a few advantages over inductive coupling. The field is largely confined between the capacitor plates, reducing interference, which in inductive coupling requires heavy ferrite "flux confinement" cores. Also, alignment requirements between the transmitter and receiver are less critical. Capacitive coupling has recently been applied to charging battery powered portable devices as well as charging or continuous wireless power transfer in biomedical implants, and is being considered as a means of transferring power between substrate layers in integrated circuits.

Two types of circuit have been used:

• Transverse (bipolar) design: In this type of circuit, there are two transmitter plates and two receiver plates. Each transmitter plate is coupled to a receiver plate. The transmitter oscillator drives the transmitter plates in opposite phase (180° phase difference) by a high alternating voltage, and the load is connected between the two receiver plates. The alternating electric fields induce opposite phase alternating potentials in the receiver plates, and this "push-pull" action causes current to flow back and forth between the plates through the load. A disadvantage of this configuration for wireless charging is that the two plates in the receiving device must be aligned face to face with the charger plates for the device to work.
• Longitudinal (unipolar) design: In this type of circuit, the transmitter and receiver have only one active electrode, and either the ground or a large passive electrode serves as the return path for the current. The transmitter oscillator is connected between an active and a passive electrode. The load is also connected between an active and a passive electrode. The electric field produced by the transmitter induces alternating charge displacement in the load dipole through electrostatic induction.

Resonant capacitive coupling

Resonance can also be used with capacitive coupling to extend the range. At the turn of the 20th century, Nikola Tesla did the first experiments with both resonant inductive and capacitive coupling.

Electrodynamic Wireless Power Transfer

An electrodynamic wireless power transfer (EWPT) system utilizes a receiver with a mechanically resonating or rotating permanent magnet. When subjected to a time-varying magnetic field, the mechanical motion of the resonating magnet is converted into electricity by one or more electromechanical transduction schemes (e.g. electromagnetic/induction, piezoelectric, or capacitive). Compared to other WPT schemes, EWPT leverages low-frequency magnetic fields (<1 kHz), which safely pass through conductive media and have higher human field exposure limits (~2 mTrms at 1 kHz), showing promise for potential use in wirelessly recharging biomedical implants. For EWPT devices having identical resonant frequencies, the magnitude of power transfer is entirely dependent on critical coupling coefficient, denoted by ${\displaystyle k}$, between the transmitter and receiver devices. For coupled resonators with same resonant frequencies, wireless power transfer between the transmitter and the receiver is spread over three regimes- under-coupled, critically coupled and over-coupled regimes. As the critical coupling coefficient increases from an under-coupled regime (${\displaystyle k<k_{crit}}$) to the critical coupled regime, the optimum voltage gain curve grows in magnitude (measured at the receiver) and peaks when ${\displaystyle k=k_{crit}}$ and then enters into the over-coupled regime where ${\displaystyle k>k_{crit}}$ and the peak splits into two. This critical coupling coefficient is demonstrated to be a function of distance between the source and the receiver devices.

Magnetodynamic coupling

In this method, power is transmitted between two rotating armatures, one in the transmitter and one in the receiver, which rotate synchronously, coupled together by a magnetic field generated by permanent magnets on the armatures. The transmitter armature is turned either by or as the rotor of an electric motor, and its magnetic field exerts torque on the receiver armature, turning it. The magnetic field acts like a mechanical coupling between the armatures. The receiver armature produces power to drive the load, either by turning a separate electric generator or by using the receiver armature itself as the rotor in a generator.

This device has been proposed as an alternative to inductive power transfer for noncontact charging of electric vehicles. A rotating armature embedded in a garage floor or curb would turn a receiver armature in the underside of the vehicle to charge its batteries. It is claimed that this technique can transfer power over distances of 10 to 15 cm (4 to 6 inches) with high efficiency, over 90%. Also, the low frequency stray magnetic fields produced by the rotating magnets produce less electromagnetic interference to nearby electronic devices than the high frequency magnetic fields produced by inductive coupling systems. A prototype system charging electric vehicles has been in operation at University of British Columbia since 2012. Other researchers, however, claim that the two energy conversions (electrical to mechanical to electrical again) make the system less efficient than electrical systems like inductive coupling.

Zenneck Wave Transmission

A new kind of system using the Zenneck type waves was shown by Oruganti et al., where they demonstrated that it was possible to excite Zenneck wave type waves on flat metal-air interfaces and transmit power across metal obstacles. Here the idea is to excite a localized charge oscillation at the metal-air interface, the resulting modes propagate along the metal-air interface.

Far-field (radiative) techniques

Far field methods achieve longer ranges, often multiple kilometer ranges, where the distance is much greater than the diameter of the device(s). High-directivity antennas or well-collimated laser light produce a beam of energy that can be made to match the shape of the receiving area. The maximum directivity for antennas is physically limited by diffraction.

In general, visible light (from lasers) and microwaves (from purpose-designed antennas) are the forms of electromagnetic radiation best suited to energy transfer.

The dimensions of the components may be dictated by the distance from transmitter to receiver, the wavelength and the Rayleigh criterion or diffraction limit, used in standard radio frequency antenna design, which also applies to lasers. Airy's diffraction limit is also frequently used to determine an approximate spot size at an arbitrary distance from the aperture. Electromagnetic radiation experiences less diffraction at shorter wavelengths (higher frequencies); so, for example, a blue laser is diffracted less than a red one.

The Rayleigh limit (also known as the Abbe diffraction limit), although originally applied to image resolution, can be viewed in reverse, and dictates that the irradiance (or intensity) of any electromagnetic wave (such as a microwave or laser beam) will be reduced as the beam diverges over distance at a minimum rate inversely proportional to the aperture size. The larger the ratio of a transmitting antenna's aperture or laser's exit aperture to the wavelength of radiation, the more can the radiation be concentrated in a compact beam

Microwave power beaming can be more efficient than lasers, and is less prone to atmospheric attenuation caused by dust or aerosols such as fog.

Here, the power levels are calculated by combining the above parameters together, and adding in the gains and losses due to the antenna characteristics and the transparency and dispersion of the medium through which the radiation passes. That process is known as calculating a link budget.

Microwaves

An artist's depiction of a solar satellite that could send energy by microwaves to a space vessel or planetary surface.

Power transmission via radio waves can be made more directional, allowing longer-distance power beaming, with shorter wavelengths of electromagnetic radiation, typically in the microwave range. A rectenna may be used to convert the microwave energy back into electricity. Rectenna conversion efficiencies exceeding 95% have been realized. Power beaming using microwaves has been proposed for the transmission of energy from orbiting solar power satellites to Earth and the beaming of power to spacecraft leaving orbit has been considered.

Power beaming by microwaves has the difficulty that, for most space applications, the required aperture sizes are very large due to diffraction limiting antenna directionality. For example, the 1978 NASA study of solar power satellites required a 1-kilometre-diameter (0.62 mi) transmitting antenna and a 10-kilometre-diameter (6.2 mi) receiving rectenna for a microwave beam at 2.45 GHz. These sizes can be somewhat decreased by using shorter wavelengths, although short wavelengths may have difficulties with atmospheric absorption and beam blockage by rain or water droplets. Because of the "thinned-array curse", it is not possible to make a narrower beam by combining the beams of several smaller satellites.

For earthbound applications, a large-area 10 km diameter receiving array allows large total power levels to be used while operating at the low power density suggested for human electromagnetic exposure safety. A human safe power density of 1 mW/cm² distributed across a 10 km diameter area corresponds to 750 megawatts total power level. This is the power level found in many modern electric power plants. For comparison, a solar PV farm of similar size might easily exceed 10,000 megawatts (rounded) at best conditions during daytime.

Following World War II, which saw the development of high-power microwave emitters known as cavity magnetrons, the idea of using microwaves to transfer power was researched. By 1964, a miniature helicopter propelled by microwave power had been demonstrated.

Japanese researcher Hidetsugu Yagi also investigated wireless energy transmission using a directional array antenna that he designed. In February 1926, Yagi and his colleague Shintaro Uda published their first paper on the tuned high-gain directional array now known as the Yagi antenna. While it did not prove to be particularly useful for power transmission, this beam antenna has been widely adopted throughout the broadcasting and wireless telecommunications industries due to its excellent performance characteristics.

Wireless high power transmission using microwaves is well proven. Experiments in the tens of kilowatts have been performed at the Goldstone Deep Space Communications Complex in California in 1975 and more recently (1997) at Grand Bassin on Reunion Island. These methods achieve distances on the order of a kilometer.

Under experimental conditions, microwave conversion efficiency was measured to be around 54% across one meter.

A change to 24 GHz has been suggested as microwave emitters similar to LEDs have been made with very high quantum efficiencies using negative resistance, i.e., Gunn or IMPATT diodes, and this would be viable for short range links.

In 2013, inventor Hatem Zeine demonstrated how wireless power transmission using phased array antennas can deliver electrical power up to 30 feet. It uses the same radio frequencies as WiFi.

In 2015, researchers at the University of Washington introduced power over Wi-Fi, which trickle-charges batteries and powered battery-free cameras and temperature sensors using transmissions from Wi-Fi routers. Wi-Fi signals were shown to power battery-free temperature and camera sensors at ranges of up to 20 feet. It was also shown that Wi-Fi can be used to wirelessly trickle-charge nickel–metal hydride and lithium-ion coin-cell batteries at distances of up to 28 feet.

In 2017, the Federal Communication Commission (FCC) certified the first mid-field radio frequency (RF) transmitter of wireless power. In 2021 the FCC granted a license to a over-the-air (OTA) wireless charging system that combines near-field and far-field methods by using a frequency of about 900 MHz. Due to the radiated power of about 1 W this system is intended for small IoT devices as various sensors, trackers, detectors and monitors.

Lasers

A laser beam centered on a panel of photovoltaic cells provides enough power to a lightweight model airplane for it to fly.

In the case of electromagnetic radiation closer to the visible region of the spectrum (.2 to 2 micrometers), power can be transmitted by converting electricity into a laser beam that is received and concentrated onto photovoltaic cells (solar cells). This mechanism is generally known as 'power beaming' because the power is beamed at a receiver that can convert it to electrical energy. At the receiver, special photovoltaic laser power converters which are optimized for monochromatic light conversion are applied.

Advantages compared to other wireless methods are:

• Collimated monochromatic wavefront propagation allows narrow beam cross-section area for transmission over large distances. As a result, there is little or no reduction in power when increasing the distance from the transmitter to the receiver.
• Compact size: solid state lasers fit into small products.
• No radio-frequency interference to existing radio communication such as Wi-Fi and cell phones.
• Access control: only receivers hit by the laser receive power.

Drawbacks include:

• Laser radiation is hazardous. Without a proper safety mechanism, low power levels can blind humans and other animals. High power levels can kill through localized spot heating.
• Conversion between electricity and light is limited. Photovoltaic cells achieve a maximum of 40%–50% efficiency.
• Atmospheric absorption, and absorption and scattering by clouds, fog, rain, etc., causes up to 100% losses.
• Requires a direct line of sight with the target. (Instead of being beamed directly onto the receiver, the laser light can also be guided by an optical fiber. Then one speaks of power-over-fiber technology.)

Laser 'powerbeaming' technology was explored in military weapons and aerospace applications. Also, it is applied for the powering of various kinds of sensors in industrial environments. Lately, it is developed for powering commercial and consumer electronics. Wireless energy transfer systems using lasers for consumer space have to satisfy laser safety requirements standardized under IEC 60825.

The first wireless power system using lasers for consumer applications was demonstrated in 2018, capable of delivering power to stationary and moving devices across a room. This wireless power system complies with safety regulations according to IEC 60825 standard. It is also approved by the US Food and Drugs Administration (FDA).

Other details include propagation, and the coherence and the range limitation problem.

Geoffrey Landis is one of the pioneers of solar power satellites and laser-based transfer of energy, especially for space and lunar missions. The demand for safe and frequent space missions has resulted in proposals for a laser-powered space elevator.

NASA's Dryden Flight Research Center has demonstrated a lightweight unmanned model plane powered by a laser beam. This proof-of-concept demonstrates the feasibility of periodic recharging using a laser beam system.

Scientists from the Chinese Academy of Sciences have developed a proof-of-concept of utilizing a dual-wavelength laser to wirelessly charge portable devices or UAVs.

Atmospheric plasma channel coupling

See also: Electrolaser

In atmospheric plasma channel coupling, energy is transferred between two electrodes by electrical conduction through ionized air. When an electric field gradient exists between the two electrodes, exceeding 34 kilovolts per centimeter at sea level atmospheric pressure, an electric arc occurs. This atmospheric dielectric breakdown results in the flow of electric current along a random trajectory through an ionized plasma channel between the two electrodes. An example of this is natural lightning, where one electrode is a virtual point in a cloud and the other is a point on Earth. Laser Induced Plasma Channel (LIPC) research is presently underway using ultrafast lasers to artificially promote development of the plasma channel through the air, directing the electric arc, and guiding the current across a specific path in a controllable manner. The laser energy reduces the atmospheric dielectric breakdown voltage and the air is made less insulating by superheating, which lowers the density (${\displaystyle p}$) of the filament of air.

This new process is being explored for use as a laser lightning rod and as a means to trigger lightning bolts from clouds for natural lightning channel studies, for artificial atmospheric propagation studies, as a substitute for conventional radio antennas, for applications associated with electric welding and machining, for diverting power from high-voltage capacitor discharges, for directed-energy weapon applications employing electrical conduction through a ground return path, and electronic jamming.

Energy harvesting

Main article: Energy harvesting

In the context of wireless power, energy harvesting, also called power harvesting or energy scavenging, is the conversion of ambient energy from the environment to electric power, mainly to power small autonomous wireless electronic devices. The ambient energy may come from stray electric or magnetic fields or radio waves from nearby electrical equipment, light, thermal energy (heat), or kinetic energy such as vibration or motion of the device. Although the efficiency of conversion is usually low and the power gathered often minuscule (milliwatts or microwatts), it can be adequate to run or recharge small micropower wireless devices such as remote sensors, which are proliferating in many fields. This new technology is being developed to eliminate the need for battery replacement or charging of such wireless devices, allowing them to operate completely autonomously.

History

19th century developments and dead ends

The 19th century saw many developments of theories, and counter-theories on how electrical energy might be transmitted. In 1826, André-Marie Ampère discovered a connection between current and magnets. Michael Faraday described in 1831 with his law of induction the electromotive force driving a current in a conductor loop by a time-varying magnetic flux. Transmission of electrical energy without wires was observed by many inventors and experimenters, but lack of a coherent theory attributed these phenomena vaguely to electromagnetic induction. A concise explanation of these phenomena would come from the 1860s Maxwell's equations by James Clerk Maxwell, establishing a theory that unified electricity and magnetism to electromagnetism, predicting the existence of electromagnetic waves as the "wireless" carrier of electromagnetic energy. Around 1884 John Henry Poynting defined the Poynting vector and gave Poynting's theorem, which describe the flow of power across an area within electromagnetic radiation and allow for a correct analysis of wireless power transfer systems. This was followed on by Heinrich Rudolf Hertz' 1888 validation of the theory, which included the evidence for radio waves.

During the same period two schemes of wireless signaling were put forward by William Henry Ward (1871) and Mahlon Loomis (1872) that were based on the erroneous belief that there was an electrified atmospheric stratum accessible at low altitude. Both inventors' patents noted this layer connected with a return path using "Earth currents"' would allow for wireless telegraphy as well as supply power for the telegraph, doing away with artificial batteries, and could also be used for lighting, heat, and motive power. A more practical demonstration of wireless transmission via conduction came in Amos Dolbear's 1879 magneto electric telephone that used ground conduction to transmit over a distance of a quarter of a mile.

Tesla

Tesla demonstrating wireless transmission by "electrostatic induction" during an 1891 lecture at Columbia College.  The two metal sheets are connected to a Tesla coil oscillator, which applies high-voltage radio frequency alternating current.  An oscillating electric field between the sheets ionizes the low-pressure gas in the two long Geissler tubes in his hands, causing them to glow in a manner similar to neon tubes.

After 1890, inventor Nikola Tesla experimented with transmitting power by inductive and capacitive coupling using spark-excited radio frequency resonant transformers, now called Tesla coils, which generated high AC voltages. Early on he attempted to develop a wireless lighting system based on near-field inductive and capacitive coupling and conducted a series of public demonstrations where he lit Geissler tubes and even incandescent light bulbs from across a stage. He found he could increase the distance at which he could light a lamp by using a receiving LC circuit tuned to resonance with the transmitter's LC circuit. using resonant inductive coupling. Tesla failed to make a commercial product out of his findings but his resonant inductive coupling method is now widely used in electronics and is currently being applied to short-range wireless power systems.

(left) Experiment in resonant inductive transfer by Tesla at Colorado Springs 1899. The coil is in resonance with Tesla's magnifying transmitter nearby, powering the light bulb at bottom.

Tesla went on to develop a wireless power distribution system that he hoped would be capable of transmitting power long distance directly into homes and factories. Early on he seemed to borrow from the ideas of Mahlon Loomis, proposing a system composed of balloons to suspend transmitting and receiving electrodes in the air above 30,000 feet (9,100 m) in altitude, where he thought the pressure would allow him to send high voltages (millions of volts) long distances. To further study the conductive nature of low pressure air he set up a test facility at high altitude in Colorado Springs during 1899. Experiments he conducted there with a large coil operating in the megavolts range, as well as observations he made of the electronic noise of lightning strikes, led him to conclude incorrectly that he could use the entire globe of the Earth to conduct electrical energy. The theory included driving alternating current pulses into the Earth at its resonant frequency from a grounded Tesla coil working against an elevated capacitance to make the potential of the Earth oscillate. Tesla thought this would allow alternating current to be received with a similar capacitive antenna tuned to resonance with it at any point on Earth with very little power loss. His observations also led him to believe a high voltage used in a coil at an elevation of a few hundred feet would "break the air stratum down", eliminating the need for miles of cable hanging on balloons to create his atmospheric return circuit. Tesla would go on the next year to propose a "World Wireless System" that was to broadcast both information and power worldwide. In 1901, at Shoreham, New York he attempted to construct a large high-voltage wireless power station, now called Wardenclyffe Tower, but by 1904 investment dried up and the facility was never completed.

Near-field and non-radiative technologies

Inductive power transfer between nearby wire coils was the earliest wireless power technology to be developed, existing since the transformer was developed in the 1800s. Induction heating has been used since the early 1900s and is used for induction cooking.

With the advent of cordless devices, induction charging stands have been developed for appliances used in wet environments, like electric toothbrushes and electric razors, to eliminate the hazard of electric shock. One of the earliest proposed applications of inductive transfer was to power electric locomotives. In 1892 Maurice Hutin and Maurice Leblanc patented a wireless method of powering railroad trains using resonant coils inductively coupled to a track wire at 3 kHz.

In the early 1960s resonant inductive wireless energy transfer was used successfully in implantable medical devices including such devices as pacemakers and artificial hearts. While the early systems used a resonant receiver coil, later systems implemented resonant transmitter coils as well. These medical devices are designed for high efficiency using low power electronics while efficiently accommodating some misalignment and dynamic twisting of the coils. The separation between the coils in implantable applications is commonly less than 20 cm. Today resonant inductive energy transfer is regularly used for providing electric power in many commercially available medical implantable devices.

The first passive RFID (Radio Frequency Identification) technologies were invented by Mario Cardullo (1973) and Koelle et al. (1975) and by the 1990s were being used in proximity cards and contactless smartcards.

The proliferation of portable wireless communication devices such as mobile phones, tablet, and laptop computers in recent decades is currently driving the development of mid-range wireless powering and charging technology to eliminate the need for these devices to be tethered to wall plugs during charging. The Wireless Power Consortium was established in 2008 to develop interoperable standards across manufacturers. Its Qi inductive power standard published in August 2009 enables high efficiency charging and powering of portable devices of up to 5 watts over distances of 4 cm (1.6 inches). The wireless device is placed on a flat charger plate (which can be embedded in table tops at cafes, for example) and power is transferred from a flat coil in the charger to a similar one in the device. In 2007, a team led by Marin Soljačić at MIT used a dual resonance transmitter with a 25 cm diameter secondary tuned to 10 MHz to transfer 60 W of power to a similar dual resonance receiver over a distance of 2 meters (6.6 ft) (eight times the transmitter coil diameter) at around 40% efficiency.

In 2008 the team of Greg Leyh and Mike Kennan of Nevada Lightning Lab used a grounded dual resonance transmitter with a 57 cm diameter secondary tuned to 60 kHz and a similar grounded dual resonance receiver to transfer power through coupled electric fields with an earth current return circuit over a distance of 12 meters (39 ft). In 2011, Dr. Christopher A. Tucker and Professor Kevin Warwick of the University of Reading, recreated Tesla's 1900 patent 0,645,576 in miniature and demonstrated power transmission over 4 meters (13 ft) with a coil diameter of 10 centimetres (3.9 in) at a resonant frequency of 27.50 MHz, with an effective efficiency of 60%.

Microwaves and lasers

Before World War II, little progress was made in wireless power transmission. Radio was developed for communication uses, but could not be used for power transmission since the relatively low-frequency radio waves spread out in all directions and little energy reached the receiver. In radio communication, at the receiver, an amplifier intensifies a weak signal using energy from another source. For power transmission, efficient transmission required transmitters that could generate higher-frequency microwaves, which can be focused in narrow beams towards a receiver.

The development of microwave technology during World War II, such as the klystron and magnetron tubes and parabolic antennas, made radiative (far-field) methods practical for the first time, and the first long-distance wireless power transmission was achieved in the 1960s by William C. Brown. In 1964, Brown invented the rectenna which could efficiently convert microwaves to DC power, and in 1964 demonstrated it with the first wireless-powered aircraft, a model helicopter powered by microwaves beamed from the ground. A major motivation for microwave research in the 1970s and 1980s was to develop a solar power satellite. Conceived in 1968 by Peter Glaser, this would harvest energy from sunlight using solar cells and beam it down to Earth as microwaves to huge rectennas, which would convert it to electrical energy on the electric power grid. In landmark 1975 experiments as technical director of a JPL/Raytheon program, Brown demonstrated long-range transmission by beaming 475 W of microwave power to a rectenna a mile away, with a microwave to DC conversion efficiency of 54%. At NASA's Jet Propulsion Laboratory, he and Robert Dickinson transmitted 30 kW DC output power across 1.5 km with 2.38 GHz microwaves from a 26 m dish to a 7.3 x 3.5 m rectenna array. The incident-RF to DC conversion efficiency of the rectenna was 80%. In 1983 Japan launched Microwave Ionosphere Nonlinear Interaction Experiment (MINIX), a rocket experiment to test transmission of high power microwaves through the ionosphere.

In recent years a focus of research has been the development of wireless-powered drone aircraft, which began in 1959 with the Dept. of Defense's RAMP (Raytheon Airborne Microwave Platform) project which sponsored Brown's research. In 1987 Canada's Communications Research Center developed a small prototype airplane called Stationary High Altitude Relay Platform (SHARP) to relay telecommunication data between points on earth similar to a communications satellite. Powered by a rectenna, it could fly at 13 miles (21 km) altitude and stay aloft for months. In 1992 a team at Kyoto University built a more advanced craft called MILAX (MIcrowave Lifted Airplane eXperiment).

In 2003 NASA flew the first laser powered aircraft. The small model plane's motor was powered by electricity generated by photocells from a beam of infrared light from a ground-based laser, while a control system kept the laser pointed at the plane.

Weak gravitational lensing

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Weak_gravitational_lensing

While the presence of any mass bends the path of light passing near it, this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. Most lines of sight in the universe are thoroughly in the weak lensing regime, in which the deflection is impossible to detect in a single background source. However, even in these cases, the presence of the foreground mass can be detected, by way of a systematic alignment of background sources around the lensing mass. Weak gravitational lensing is thus an intrinsically statistical measurement, but it provides a way to measure the masses of astronomical objects without requiring assumptions about their composition or dynamical state.

Methodology

Distortions of the type produced by lensing, acting on circles and a distribution of ellipses similar to that of real galaxies. The distortion shown here is greatly exaggerated relative to real astronomical systems.

Gravitational lensing acts as a coordinate transformation that distorts the images of background objects (usually galaxies) near a foreground mass. The transformation can be split into two terms, the convergence and shear. The convergence term magnifies the background objects by increasing their size, and the shear term stretches them tangentially around the foreground mass.

To measure this tangential alignment, it is necessary to measure the ellipticities of the background galaxies and construct a statistical estimate of their systematic alignment. The fundamental problem is that galaxies are not intrinsically circular, so their measured ellipticity is a combination of their intrinsic ellipticity and the gravitational lensing shear. Typically, the intrinsic ellipticity is much greater than the shear (by a factor of 3-300, depending on the foreground mass). The measurements of many background galaxies must be combined to average down this "shape noise". The orientation of intrinsic ellipticities of galaxies should be almost entirely random, so any systematic alignment between multiple galaxies can generally be assumed to be caused by lensing.

Another major challenge for weak lensing is correction for the point spread function (PSF) due to instrumental and atmospheric effects, which causes the observed images to be smeared relative to the "true sky". This smearing tends to make small objects more round, destroying some of the information about their true ellipticity. As a further complication, the PSF typically adds a small level of ellipticity to objects in the image, which is not at all random, and can in fact mimic a true lensing signal. Even for the most modern telescopes, this effect is usually at least the same order of magnitude as the gravitational lensing shear, and is often much larger. Correcting for the PSF requires building for the telescope a model for how it varies across the field. Stars in our own galaxy provide a direct measurement of the PSF, and these can be used to construct such a model, usually by interpolating between the points where stars appear on the image. This model can then be used to reconstruct the "true" ellipticities from the smeared ones. Ground-based and space-based data typically undergo distinct reduction procedures due to the differences in instruments and observing conditions.

Angular diameter distances to the lenses and background sources are important for converting the lensing observables to physically meaningful quantities. These distances are often estimated using photometric redshifts when spectroscopic redshifts are unavailable. Redshift information is also important in separating the background source population from other galaxies in the foreground, or those associated with the mass responsible for the lensing. With no redshift information, the foreground and background populations can be split by an apparent magnitude or a color cut, but this is much less accurate.

Weak lensing by clusters of galaxies

The effects of foreground galaxy cluster mass on background galaxy shapes. The upper left panel shows (projected onto the plane of the sky) the shapes of cluster members (in yellow) and background galaxies (in white), ignoring the effects of weak lensing. The lower right panel shows this same scenario, but includes the effects of lensing. The middle panel shows a 3-d representation of the positions of cluster and source galaxies, relative to the observer. Note that the background galaxies appear stretched tangentially around the cluster.

Galaxy clusters are the largest gravitationally bound structures in the Universe with approximately 80% of cluster content in the form of dark matter. The gravitational fields of these clusters deflect light-rays traveling near them. As seen from Earth, this effect can cause dramatic distortions of a background source object detectable by eye such as multiple images, arcs, and rings (cluster strong lensing). More generally, the effect causes small, but statistically coherent, distortions of background sources on the order of 10% (cluster weak lensing). Abell 1689, CL0024+17, and the Bullet Cluster are among the most prominent examples of lensing clusters.

History

The effects of cluster strong lensing were first detected by Roger Lynds of the National Optical Astronomy Observatories and Vahe Petrosian of Stanford University who discovered giant luminous arcs in a survey of galaxy clusters in the late 1970s. Lynds and Petrosian published their findings in 1986 without knowing the origin of the arcs. In 1987, Genevieve Soucail of the Toulouse Observatory and her collaborators presented data of a blue ring-like structure in Abell 370 and proposed a gravitational lensing interpretation. The first cluster weak lensing analysis was conducted in 1990 by J. Anthony Tyson of Bell Laboratories and collaborators. Tyson et al. detected a coherent alignment of the ellipticities of the faint blue galaxies behind both Abell 1689 and CL 1409+524. Lensing has been used as a tool to investigate a tiny fraction of the thousands of known galaxy clusters.

Historically, lensing analyses were conducted on galaxy clusters detected via their baryon content (e.g. from optical or X-ray surveys). The sample of galaxy clusters studied with lensing was thus subject to various selection effects; for example, only the most luminous clusters were investigated. In 2006, David Wittman of the University of California at Davis and collaborators published the first sample of galaxy clusters detected via their lensing signals, completely independent of their baryon content. Clusters discovered through lensing are subject to mass selection effects because the more massive clusters produce lensing signals with higher signal-to-noise.

Observational products

The projected mass density can be recovered from the measurement of the ellipticities of the lensed background galaxies through techniques that can be classified into two types: direct reconstruction and inversion. However, a mass distribution reconstructed without knowledge of the magnification suffers from a limitation known as the mass sheet degeneracy, where the cluster surface mass density κ can be determined only up to a transformation ${\displaystyle \kappa \rightarrow \kappa ^{\prime }=\lambda \kappa +(1-\lambda )}$ where λ is an arbitrary constant. This degeneracy can be broken if an independent measurement of the magnification is available because the magnification is not invariant under the aforementioned degeneracy transformation.

Given a centroid for the cluster, which can be determined by using a reconstructed mass distribution or optical or X-ray data, a model can be fit to the shear profile as a function of clustrocentric radius. For example, the singular isothermal sphere (SIS) profile and the Navarro-Frenk-White (NFW) profile are two commonly used parametric models. Knowledge of the lensing cluster redshift and the redshift distribution of the background galaxies is also necessary for estimation of the mass and size from a model fit; these redshifts can be measured precisely using spectroscopy or estimated using photometry. Individual mass estimates from weak lensing can only be derived for the most massive clusters, and the accuracy of these mass estimates are limited by projections along the line of sight.

Scientific implications

Image of the Bullet Cluster from the Hubble Space Telescope with total mass contours (dominated by dark matter) from a lensing analysis overlaid.

Cluster mass estimates determined by lensing are valuable because the method requires no assumption about the dynamical state or star formation history of the cluster in question. Lensing mass maps can also potentially reveal "dark clusters," clusters containing overdense concentrations of dark matter but relatively insignificant amounts of baryonic matter. Comparison of the dark matter distribution mapped using lensing with the distribution of the baryons using optical and X-ray data reveals the interplay of the dark matter with the stellar and gas components. A notable example of such a joint analysis is the so-called Bullet Cluster. The Bullet Cluster data provide constraints on models relating light, gas, and dark matter distributions such as Modified Newtonian dynamics (MOND) and Λ-Cold Dark Matter (Λ-CDM).

In principle, since the number density of clusters as a function of mass and redshift is sensitive to the underlying cosmology, cluster counts derived from large weak lensing surveys should be able to constrain cosmological parameters. In practice, however, projections along the line of sight cause many false positives. Weak lensing can also be used to calibrate the mass-observable relation via a stacked weak lensing signal around an ensemble of clusters, although this relation is expected to have an intrinsic scatter. In order for lensing clusters to be a precision probe of cosmology in the future, the projection effects and the scatter in the lensing mass-observable relation need to be thoroughly characterized and modeled.

Galaxy-galaxy lensing

Galaxy-galaxy lensing is a specific type of weak (and occasionally strong) gravitational lensing, in which the foreground object responsible for distorting the shapes of background galaxies is itself an individual field galaxy (as opposed to a galaxy cluster or the large-scale structure of the cosmos). Of the three typical mass regimes in weak lensing, galaxy-galaxy lensing produces a "mid-range" signal (shear correlations of ~1%) that is weaker than the signal due to cluster lensing, but stronger than the signal due to cosmic shear.

History

J.A. Tyson and collaborators first postulated the concept of galaxy-galaxy lensing in 1984, though the observational results of their study were inconclusive. It was not until 1996 that evidence of such distortion was tentatively discovered, with the first statistically significant results not published until the year 2000. Since those initial discoveries, the construction of larger, high resolution telescopes and the advent of dedicated wide field galaxy surveys have greatly increased the observed number density of both background source and foreground lens galaxies, allowing for a much more robust statistical sample of galaxies, making the lensing signal much easier to detect. Today, measuring the shear signal due to galaxy-galaxy lensing is a widely used technique in observational astronomy and cosmology, often used in parallel with other measurements in determining physical characteristics of foreground galaxies.

Stacking

Much like in cluster-scale weak lensing, detection of a galaxy-galaxy shear signal requires one to measure the shapes of background source galaxies, and then look for statistical shape correlations (specifically, source galaxy shapes should be aligned tangentially, relative to the lens center.) In principle, this signal could be measured around any individual foreground lens. In practice, however, due to the relatively low mass of field lenses and the inherent randomness in intrinsic shape of background sources (the "shape noise"), the signal is impossible to measure on a galaxy by galaxy basis. However, by combining the signals of many individual lens measurements together (a technique known as "stacking"), the signal-to-noise ratio will improve, allowing one to determine a statistically significant signal, averaged over the entire lens set.

Scientific applications

Galaxy-galaxy lensing (like all other types of gravitational lensing) is used to measure several quantities pertaining to mass:

Mass density profiles

Using techniques similar to those in cluster-scale lensing, galaxy-galaxy lensing can provide information about the shape of mass density profiles, though these profiles correspond to galaxy-sized objects instead of larger clusters or groups. Given a high enough number density of background sources, a typical galaxy-galaxy mass density profile can cover a wide range of distances (from ~1 to ~100 effective radii). Since the effects of lensing are insensitive to the matter type, a galaxy-galaxy mass density profile can be used to probe a wide range of matter environments: from the central cores of galaxies where baryons dominate the total mass fraction, to the outer halos where dark matter is more prevalent.

Mass-to-light ratios

Comparing the measured mass to the luminosity (averaged over the entire galaxy stack) in a specific filter, galaxy-galaxy lensing can also provide insight into the mass to light ratios of field galaxies. Specifically, the quantity measured through lensing is the total (or virial) mass to light ratio – again due to the insensitivity of lensing to matter type. Assuming that luminous matter can trace dark matter, this quantity is of particular importance, since measuring the ratio of luminous (baryonic) matter to total matter can provide information regarding the overall ratio of baryonic to dark matter in the universe.

Galaxy mass evolution

Since the speed of light is finite, an observer on the Earth will see distant galaxies not as they look today, but rather as they appeared at some earlier time. By restricting the lens sample of a galaxy-galaxy lensing study to lie at only one particular redshift, it is possible to understand the mass properties of the field galaxies that existed during this earlier time. Comparing the results of several such redshift-restricted lensing studies (with each study encompassing a different redshift), one can begin to observe changes in the mass features of galaxies over a period of several epochs, leading towards a better understanding of the evolution of mass on the smallest cosmological scales.

Other mass trends

Lens redshift is not the only quantity of interest that can be varied when studying mass differences between galaxy populations, and often there are several parameters used when segregating objects into galaxy-galaxy lens stacks. Two widely used criteria are galaxy color and morphology, which act as tracers of (among other things) stellar population, galaxy age, and local mass environment. By separating lens galaxies based on these properties, and then further segregating samples based on redshift, it is possible to use galaxy-galaxy lensing to see how several different types of galaxies evolve through time.

Cosmic shear

The gravitational lensing by large-scale structure also produces an observable pattern of alignments in background galaxies, but this distortion is only ~0.1%-1% - much more subtle than cluster or galaxy-galaxy lensing. The thin lens approximation usually used in cluster and galaxy lensing does not always work in this regime, because structures can be elongated along the line of sight. Instead, the distortion can be derived by assuming that the deflection angle is always small (see Gravitational Lensing Formalism). As in the thin lens case, the effect can be written as a mapping from the unlensed angular position ${\displaystyle {\vec {\beta }}}$ to the lensed position ${\displaystyle {\vec {\theta }}}$. The Jacobian of the transform can be written as an integral over the gravitational potential ${\displaystyle \Phi }$ along the line of sight

${\displaystyle {\frac {\partial \beta _{i}}{\partial \theta _{j}}}=\delta _{ij}+\int _{0}^{r_{\infty }}drg(r){\frac {\partial ^{2}\Phi ({\vec {x}}(r))}{\partial x^{i}\partial x^{j}}}}$

where ${\displaystyle r}$ is the comoving distance, ${\displaystyle x^{i}}$ are the transverse distances, and

${\displaystyle g(r)=2r\int _{r}^{r_{\infty }}\left(1-{\frac {r^{\prime }}{r}}\right)W(r^{\prime })}$

is the lensing kernel, which defines the efficiency of lensing for a distribution of sources ${\displaystyle W(r)}$.

As in the thin-lens approximation, the Jacobian can be decomposed into shear and convergence terms.

Shear correlation functions

Because large-scale cosmological structures do not have a well-defined location, detecting cosmological gravitational lensing typically involves the computation of shear correlation functions, which measure the mean product of the shear at two points as a function of the distance between those points. Because there are two components of shear, three different correlation functions can be defined:

${\displaystyle \xi _{++}(\Delta \theta )=\langle \gamma _{+}({\vec {\theta }})\gamma _{+}({\vec {\theta }}+{\vec {\Delta \theta }})\rangle }$

${\displaystyle \xi _{\times \times }(\Delta \theta )=\langle \gamma _{\times }({\vec {\theta }})\gamma _{\times }({\vec {\theta }}+{\vec {\Delta \theta }})\rangle }$

${\displaystyle \xi _{\times +}(\Delta \theta )=\xi _{+\times }(\Delta \theta )=\langle \gamma _{+}({\vec {\theta }})\gamma _{\times }({\vec {\theta }}+{\vec {\Delta \theta }})\rangle }$

where ${\displaystyle \gamma _{+~}}$ is the component along or perpendicular to ${\displaystyle {\vec {\Delta \theta }}}$, and ${\displaystyle \gamma _{\times }}$ is the component at 45°. These correlation functions are typically computed by averaging over many pairs of galaxies. The last correlation function, ${\displaystyle \xi _{\times +}}$, is not affected at all by lensing, so measuring a value for this function that is inconsistent with zero is often interpreted as a sign of systematic error.

The functions ${\displaystyle \xi _{++~}}$ and ${\displaystyle \xi _{\times \times }}$ can be related to projections (integrals with certain weight functions) of the dark matter density correlation function, which can be predicted from theory for a cosmological model through its Fourier transform, the matter power spectrum.

Because they both depend on a single scalar density field, ${\displaystyle \xi _{++~}}$ and ${\displaystyle \xi _{\times \times }}$ are not independent, and they can be decomposed further into E-mode and B-mode correlation functions. In analogy with electric and magnetic fields, the E-mode field is curl-free and the B-mode field is divergence-free. Because gravitational lensing can only produce an E-mode field, the B-mode provides yet another test for systematic errors.

The E-mode correlation function is also known as the aperture mass variance

${\displaystyle \langle M_{ap}^{2}\rangle (\theta )=\int _{0}^{2\theta }{\frac {\phi d\phi }{\theta ^{2}}}\left[\xi _{++}(\phi )+\xi _{\times \times }(\phi )\right]T_{+}\left({\frac {\phi }{\theta }}\right)=\int _{0}^{2\theta }{\frac {\phi d\phi }{\theta ^{2}}}\left[\xi _{++}(\phi )-\xi _{\times \times }(\phi )\right]T_{-}\left({\frac {\phi }{\theta }}\right)}$

${\displaystyle T_{+}(x)=576\int _{0}^{\infty }{\frac {dt}{t^{3}}}J_{0}(xt)[J_{4}(t)]^{2}}$

${\displaystyle T_{-}(x)=576\int _{0}^{\infty }{\frac {dt}{t^{3}}}J_{4}(xt)[J_{4}(t)]^{2}}$

where ${\displaystyle J_{0}~}$ and ${\displaystyle J_{4}~}$ are Bessel Functions.

An exact decomposition thus requires knowledge of the shear correlation functions at zero separation, but an approximate decomposition is fairly insensitive to these values because the filters ${\displaystyle T_{+}~}$ and ${\displaystyle T_{-}~}$ are small near ${\displaystyle \theta =0~}$.

Weak lensing and cosmology

The ability of weak lensing to constrain the matter power spectrum makes it a potentially powerful probe of cosmological parameters, especially when combined with other observations such as the cosmic microwave background, supernovae, and galaxy surveys. Detecting the extremely faint cosmic shear signal requires averaging over many background galaxies, so surveys must be both deep and wide, and because these background galaxies are small, the image quality must be very good. Measuring the shear correlations at small scales also requires a high density of background objects (again requiring deep, high quality data), while measurements at large scales push for wider surveys.

While weak lensing of large-scale structure was discussed as early as 1967, due to the challenges mentioned above, it was not detected until more than 30 years later when large CCD cameras enabled surveys of the necessary size and quality. In 2000, four independent groups published the first detections of cosmic shear, and subsequent observations have started to put constraints on cosmological parameters (particularly the dark matter density ${\displaystyle \Omega _{m}~}$ and power spectrum amplitude ${\displaystyle \sigma _{8}~}$) that are competitive with other cosmological probes.

For current and future surveys, one goal is to use the redshifts of the background galaxies (often approximated using photometric redshifts) to divide the survey into multiple redshift bins. The low-redshift bins will only be lensed by structures very near to us, while the high-redshift bins will be lensed by structures over a wide range of redshift. This technique, dubbed "cosmic tomography", makes it possible to map out the 3D distribution of mass. Because the third dimension involves not only distance but cosmic time, tomographic weak lensing is sensitive not only to the matter power spectrum today, but also to its evolution over the history of the universe, and the expansion history of the universe during that time. This is a much more valuable cosmological probe, and many proposed experiments to measure the properties of dark energy and dark matter have focused on weak lensing, such as the Dark Energy Survey, Pan-STARRS, and Large Synoptic Survey Telescope.

Weak lensing also has an important effect on the Cosmic Microwave Background and diffuse 21cm line radiation. Even though there are no distinct resolved sources, perturbations on the origining surface are sheared in a similar way to galaxy weak lensing, resulting in changes to the power spectrum and statistics of the observed signal. Since the source plane for the CMB and high-redshift diffuse 21 cm are at higher redshift than resolved galaxies, the lensing effect probes cosmology at higher redshifts than galaxy lensing.

Negative weak lensing

Minimal coupling of general relativity with scalar fields allows solutions like traversable wormholes stabilized by exotic matter of negative energy density. Moreover, Modified Newtonian Dynamics as well as some bimetric theories of gravity consider invisible negative mass in cosmology as an alternative interpretation to dark matter, which classically has a positive mass.

As the presence of exotic matter would bend spacetime and light differently than positive mass, a Japanese team at the Hirosaki University proposed to use "negative" weak gravitational lensing related to such negative mass.

Instead of running statistical analysis on the distortion of galaxies based on the assumption of a positive weak lensing that usually reveals locations of positive mass "dark clusters", these researchers propose to locate "negative mass clumps" using negative weak lensing, i.e. where the deformation of galaxies is interpreted as being due to a diverging lensing effect producing radial distortions (similar to a concave lens instead of the classical azimuthal distortions of convex lenses similar to the image produced by a fisheye). Such negative mass clumps would be located elsewhere than assumed dark clusters, as they would reside at the center of observed cosmic voids located between galaxy filaments within the lacunar, web-like large-scale structure of the universe. Such test based on negative weak lensing could help to falsify cosmological models proposing exotic matter of negative mass as an alternative interpretation to dark matter.