Editing Pockels effect (section)

==Pockels cells==
The key component of a Pockels cell is a non-centrosymmetric single crystal with an optic axis whose refractive index is controlled by an external electric field. In other words, the Pockels effect is the basis of the operation of Pockels cells. By controlling the refractive index, the optical retardance of the crystal is altered so the polarization state of incident light beam is changed. Therefore, Pockels cells are used as voltage-controlled [[wave plate]]s as well as other photonics applications. See [[#Applications|applications]] below for uses. Pockels cells are divided into two configurations depending on the crystals' electro-optic properties: longitudinal and transverse.

Longitudinal Pockels cells operate with electric field applied along the crystal optic axis or along incident beam propagation. Such crystals include KDP, KD*P, and ADP. Electrodes are coated as transparent metal oxide films on crystal faces where the beam is propagating through or metal rings (usually made out of gold) coated around the crystal body. Terminals for voltage application are in contact with the electrodes. The optical retardance ''Δφ'' for longitudinal Pockels cells proportional to the ordinary refractive index ''n''<sub>o</sub>, electro-optic constant ''r''<sub>63</sub> (units of m/V), and applied voltage ''V'' and inversely proportional to the incident beam wavelength ''λ''<sub>0</sub>. For an example, the halfwave voltage is approximately 7.6 kV for a KDP crystal with a ''n''<sub>o</sub> = 1.51, ''r''<sub>63</sub> = {{val|10.6e-12|u=m/V}} at ''λ''<sub>0</sub>, and Δφ = π.<ref>{{cite book |last1=Hecht |first1=Eugene |title=Optics |date=2002 |publisher=Addison Wesley |isbn=0-8053-8566-5 |edition=4th}}</ref> The advantage of using longitudinal Pockels cells is that the voltage requirements for quarter wave or half wave retardance is not dependent on crystal length or diameter.

Transverse Pockels cells operate with electric field being applied perpendicular to beam propagation. Crystals used in transverse Pockels cells include BBO, LiNbO<sub>3</sub>, [[CdTe]], [[ZnSe]], and [[CdSe]].<ref>{{Cite journal |year=1984 |title=Properties of the II-VI Crystals  |url=https://cdn.sanity.io/files/8jt7x1sz/production/c4acc2ba55ea779842622b2c93d88ea305853417.pdf |journal=Information Sheet |publisher=Cleveland Crystals, Inc.}}</ref>
The long sides of the crystal are coated with electrodes. Optical retardance ''Δφ'' for transverse Pockels cells is similar to that of longitudinal Pockels cells but it is dependent on crystal dimensions. The quarter wave or half wave voltage requirements increase with crystal aperture size, but the requirements can be reduced by lengthening the crystal.

Two or more crystal can be incorporated into a transverse Pockels cell. One reason is to reduce the voltage requirement by extending the overall length of the Pockels cell. Another reason is the fact that KDP is biaxial and possesses two electro-optic constants, ''r''<sub>63</sub> for longitudinal configuration and ''r''<sub>41</sub> for transverse configuration. A transverse Pockels cell that uses a KDP (or one of its isomorphs) consists of two crystals in opposite orientation, which together give a zero-order waveplate when the voltage is turned off. This is often not perfect and drifts with temperature. But the mechanical alignment of the crystal axis is not so critical and is often done by hand without screws; while misalignment leads to some energy in the wrong ray (either ''e'' or ''o''{{spaced ndash}} for example, horizontal or vertical), in contrast to the longitudinal case, the loss is not amplified through the length of the crystal.

Alignment of the crystal axis with the ray axis is critical, regardless of configuration. Misalignment leads to [[birefringence]] and to a large phase shift across the long crystal. This leads to [[Polarization (waves)|polarization]] [[optical rotation|rotation]] if the alignment is not exactly parallel or perpendicular to the polarization.

=== Dynamics within the cell ===
Because of the high relative [[dielectric constant]] of ε<sub>r</sub> ≈ 36 inside the crystal, changes in the electric field propagate at a speed of only ''c''/6. Fast non-fiber optic cells are thus embedded into a matched transmission line. Putting it at the end of a transmission line leads to reflections and doubled switching time. The signal from the driver is split into parallel lines that lead to both ends of the crystal. When they meet in the crystal, their voltages add up.
Pockels cells for [[optical fiber|fiber optics]] may employ a traveling wave design to reduce current requirements and increase speed.

Usable crystals also exhibit the [[piezoelectric effect]] to some degree<ref>{{cite journal |first=J. |last=Valasek |title=Properties of Rochelle salt related to the piezo-electric effect |journal=Physical Review |volume=20 |issue=6 |page=639 |date=1922 |doi=10.1103/PhysRev.20.639 |bibcode=1922PhRv...20..639V }}</ref> ([[Rubidium Titanyl Phosphate|RTP]] ({{chem2|RbTiOPO4}}) has the lowest, [[Beta barium borate|BBO]] and [[lithium niobate]] are the highest). After a voltage change, sound waves start propagating from the sides of the crystal to the middle. This is important not for [[pulse picker]]s, but for [[boxcar window]]s. Guard space between the light and the faces of the crystals needs to be larger for longer holding times.
Behind the sound wave the crystal stays deformed in the equilibrium position for the high electric field.
This increases the polarization. Due to the growing of the polarized volume the electric field in the crystal in front of the wave increases
linearly, or the driver has to provide a constant current leakage.

=== The driver electronics ===
A Pockels cell, by design, is a [[capacitor]], and often require high voltages to change the state of the polarization of the laser beam to effectively operate as a switchable waveplate.  The voltage required depends on the type of Pockels cell, the wavelength of the light, and the size of the crystal; but typically, the voltage range is in the order of 1–10 kV. Pockels cell drivers provide this high voltage in the form of very fast pulses, which typically have rise times of less than 10 nanoseconds.

There are basically two types of drivers: a quick or Q drive which has a fast rise time, then slowly decays. A Pockels cell that uses a Q-drive is sometimes referred to as a Q-switch. The other type of driver is referred to as a regenerative or R drive. R drives will have a fast rise time and a fast fall time.  The driver's output pulse width can be from nanoseconds to microseconds long, depending on the application.  The type of drive and its repetition rate will depend on the laser and the intended application.

===Applications===
Pockels cells are used in a variety of scientific and technical applications. A Pockels cell, combined with a polarizer, can be used for switching between initial polarization state and half-wave phase retardance, creating a fast shutter capable of "opening" and "closing" in [[nanosecond]]s. The same technique can be used to impress information on the beam by modulating the rotation between 0° and 90°; the exiting beam's [[Intensity (physics)|intensity]], when viewed through the polarizer, contains an [[amplitude modulation|amplitude-modulated]] signal. This modulated signal can be used for time-resolved electric field measurements when a crystal is exposed to an unknown electric field.<ref>{{cite journal|last1=Consoli|first1=F.|last2=De Angelis|first2=R.|last3=Duvillaret|first3=L.|last4=Andreoli|first4=P. L.|last5=Cipriani|first5=M.|last6=Cristofari|first6=G.|last7=Di Giorgio|first7=G.|last8=Ingenito|first8=F.|last9=Verona|first9=C.|title=Time-resolved absolute measurements by electro-optic effect of giant electromagnetic pulses due to laser-plasma interaction in nanosecond regime|journal=Scientific Reports|date=15 June 2016|volume=6|issue=1|page=27889|doi=10.1038/srep27889|bibcode=2016NatSR...627889C|pmc=4908660|pmid=27301704}}</ref><ref>{{cite journal|last1=Robinson|first1=T. S.|last2=Consoli|first2=F.|last3=Giltrap|first3=S.|last4=Eardley|first4=S. J.|last5=Hicks|first5=G. S.|last6=Ditter|first6=E. J.|last7=Ettlinger|first7=O.|last8=Stuart|first8=N. H.|last9=Notley|first9=M.|last10=De Angelis|first10=R.|last11=Najmudin|first11=Z.|last12=Smith|first12=R. A.|title=Low-noise time-resolved optical sensing of electromagnetic pulses from petawatt laser-matter interactions|journal=Scientific Reports|date=20 April 2017|volume=7|issue=1|page=983|doi=10.1038/s41598-017-01063-1|bibcode=2017NatSR...7..983R|pmc=5430545|pmid=28428549}}</ref>

Pockels cells are used as a [[Q-switching|Q-switch]] to generate short, high-intensity laser pulse. The Pockels cell prevents optical amplification by introducing a polarization dependent loss in the laser cavity. This allows the [[gain medium]] to have a high [[population inversion]]. When the [[Active laser medium|gain medium]] has the desired [[population inversion]], the Pockels cell is switched "open", and a short high energy laser pulse is created. Q-switched lasers are used in a variety of applications, such as medical aesthetics, metrology, manufacturing, and holography.

Pulse picking is another application that uses a Pockels cell. A pulse picker is typically composed of an oscillator, electro-optic modulator, amplifiers, high voltage driver, and a frequency doubling modulator along with a Pockels cell.<ref>{{cite journal |last1=Zhao |first1=Zhi |title=An ultrafast laser pulse picker technique for high-average-current high-brightness photoinjectors |journal=Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment |year=2020 |volume=959 |page=163586 |publisher=Elsevier |doi=10.1016/j.nima.2020.163586 |bibcode=2020NIMPA.95963586Z |s2cid=213227045 |doi-access=free }}</ref> The Pockels cell can pick up a pulse from a laser induced bunch while blocking the rest by synchronized electro-optic switching.

Pockels cells are also used in [[Regenerative amplification|regenerative amplifiers]], [[chirped pulse amplification]], and [[Q-switching#Variants|cavity dumping]] to let optical power in and out of lasers and optical amplifiers.<ref>{{cite journal |last1=Pichon |first1=Pierre |last2=Taleb |first2=Hussein |last3=Druon |first3=Frédéric |last4=Blanchot |first4=Jean-Philippe |last5=Georges |first5=Patrick |last6=Balembois |first6=François |title=Tunable UV source based on an LED-pumped cavity-dumped Cr:LiSAF laser |journal=Optics Express |date=5 August 2019 |volume=27 |issue=16 |pages=23446–23453 |doi=10.1364/OE.27.023446 |pmid=31510620 |bibcode=2019OExpr..2723446P |s2cid=201256144 |issn=1094-4087|doi-access=free }}</ref>

Pockels cells can be used for [[quantum key distribution]] by [[Photon polarization|polarizing]] [[photon]]s.

Pockels cells in conjunction with other EO elements can be combined to form electro-optic probes.

Pockels cells are used in [[two-photon microscopy]] to adjust the transmitted laser intensity at a time scale of microseconds.<ref>{{cite web |title=Conoptics Model 350-80LA Electro-Optic Modulator |url=https://www.conoptics.com/modulation-systems-mpm/ |website=Conoptics Homepage |access-date=30 August 2024}}</ref>

In recent years, Pockels cells are employed at the [[National Ignition Facility]] located at [[Lawrence Livermore National Laboratory]]. Each Pockels cell for one of the 192 lasers acts as an optical trap before exiting through an amplifier. The beams from all of the 192 lasers eventually converge onto a single target of deuterium-tritium fuel in hopes to trigger a fusion reaction.<ref>{{cite web |title=How NIF Works |url=https://lasers.llnl.gov/about/how-nif-works |website=lasers.llnl.gov |access-date=25 April 2023}}</ref>