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Pockels Cells

Definition: electro-optic devices, used for building modulators

Alternative term: electro-optic modulators

German: Pockelszelle

Category: photonic devices

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URL: https://www.rp-photonics.com/pockels_cells.html

A Pockels cell is a device consisting of an electro-optic crystal (with some electrodes attached to it) through which a light beam can propagate. The phase delay in the crystal (→ Pockels effect) can be modulated by applying a variable electric voltage. The Pockels cell thus acts as a voltage-controlled waveplate. Pockels cells are the basic components of electro-optic modulators and optical switches, used e.g. for Q switching lasers. They can also be used as sensors for electric voltages.

Geometries and Materials

Pockels cells can have two different geometries concerning the direction of the applied electric field:

  • Longitudinal devices have the electric field in the direction of the light beam. The light may e.g. pass through holes in the electrodes, or (less frequently) through transparent electrodes. Large apertures can easily be realized, as the required drive voltage is basically independent of the aperture. The electrodes can be metallic rings (Figure 1, left) or transparent layers on the end faces (right) with metallic contacts.
Pockels cells with longitudinal electric field
Figure 1: Pockels cells with longitudinal electric field. The electrodes are either rings on the end faces (left side) or on the outer face (right side).
  • Transverse devices have the electric field perpendicular to the light beam. The field is applied through electrodes at the sides of the crystal. For small apertures, they can have lower switching voltages.
Pockels cells with transverse electric field
Figure 2: Pockels cells with transverse electric field. On the left is a bulk modulator and on the right a waveguide modulator.

Common nonlinear crystal materials for Pockels cells are potassium di-deuterium phosphate (KD*P = DKDP), potassium titanyl phosphate (KTP), β-barium borate (BBO) (the latter for higher average powers and/or higher switching frequencies), lithium niobate (LiNbO3), lithium tantalate (LiTaO3), and ammonium dihydrogen phosphate (NH4H2PO4, ADP). For applications in the mid-infrared, special materials like cadmium telluride (CdTe) are required.

Half-wave Voltage

Pockels cell
Figure 3: A Pockels cell based on KD*P, which can be used for Q switching of solid-state lasers. The photograph has been kindly provided by EKSMA Optics.

An important property of a Pockels cell is the half-wave voltage Uπ (also called Uλ/2 or Vλ/2). This is the voltage required for inducing a phase change of π, equivalent to a half an optical wavelength. In an amplitude modulator, the applied voltage has to be changed by that value in order to go from the operation point with minimum transmission to that with maximum transmission.

The half-wave voltage of a Pockels cell with transverse electric field depends on the crystal material, the electrode separation, and the length of the region where the electric field is applied. It may be reduced, for example, by using a longer crystal. For larger open apertures, the electrode separation needs to be larger, and hence also the voltages.

For a Pockels cell with longitudinal electric field, the crystal length does not matter, since e.g. a shorter length also increases the electric field strength for a given voltage. Larger apertures are possible without increasing the half-wave voltage.

Typical Pockels cell have half-wave voltages of hundreds or even thousands of volts, so that a high-voltage amplifier is required for large modulation depths. Relatively small half-wave voltages are possible for highly nonlinear crystal materials such as LiNbO3, and for integrated optical modulators with a small electrode separation, but such devices have a limited power handling capability.

Example for Intensity Modulation with a Pockels Cell

As an example, consider a simple intensity modulator based on a Pockels cell, where the input beam has its linear polarization at an angle of 45° against the optical axis of the nonlinear crystal. We assume that the crystal has no birefringence without an applied electric field, and that it has a given half-wave voltage Uπ. Behind the crystal, we have a polarizer which is aligned such that we obtain 100 % transmission (disregarding some parasitic losses) without an applied voltage. In that situation, we can consider the transmitted field to be a superposition of two in-phase field components of equal strength. With an applied electric field, those field components acquire a phase difference of Δφ = πU / Uπ. The total transmitted amplitude is then proportional to 0.5 · (1 + exp iΔφ), and we obtain the following result for the power transmission:

transmission of intensity modulator

If the polarizer is rotated such that we get zero transmission for zero voltage, the formula contains sin instead of cos.

The calculation demonstrates that in order to switch the transmission of an identity modulator between zero and 100%, one needs to modify the applied voltage just by one half-wave voltage. Typically, one would vary the voltage between zero and the half-wave voltage, although in principle one may also vary it between Uπ / 2 and +Uπ / 2.

Electric Current Requirements

In order to maintain a certain voltage level at a Pockels cell, virtually no electric current at all is required, since the crystal material is a dielectric, i.e., an electric insulator. However, a Pockels cell can have a significant electric capacitance, which implies that some electric charge needs to be supplied or removed when changing the applied voltage. For a very fast and large voltage changes, substantial electric currents may be needed.

One may also need to take into account the inductance of the connecting wires, which do not modify the required current, but influence the voltage drop and can lead to resonant phenomena.

Modulation Bandwidth

The possible modulation bandwidth with a Pockels cell can be very high – many megahertz, possibly even multiple gigahertz. It is essentially limited only by the speed with which the electric field strength in the electro-optic crystal can be modified. As such, it is essentially limited by the used Pockels cell driver electronics, and possibly by the cable connection between the driver and the cell. However, Pockels cells with a high electrical capacitance make it more difficult for the driver to achieve a high bandwidth. Therefore, it is beneficial to use crystal materials with a low dielectric susceptibility εr. Besides, the chosen electrode geometry can play a role, and that may also be influenced e.g. by requirements concerning the open aperture.

Plasma Electrodes

For some applications, one requires Pockels cells which can handle optical pulses with extremely high optical energy. For such cases, very large apertures are required, and longitudinal electrode designs with ring electrodes are then not feasible. Conventional transparent electrodes are also problematic because they limit the applicable pulse fluence. Therefore, a concept with transparent electrodes formed by a low-pressure ionized gas has been developed [4]. Here, the ionized gas is generated in a glow discharge, which is obtained with transverse electrodes.

Additional Effect to Consider

In practical applications of Pockels cells, one may need to consider some additional physical effects:

  • Particularly for operation with large beam radius, it can be important to optimize electrode design (possibly with additional auxiliary electrodes [9]) for high uniformity of the generated electric field, as otherwise one may obtain a spatially varying modulation.
  • Even when the end faces of the used crystal contain high-quality anti-reflection coatings, etalon effects can affect the optical performance if the beam direction is exactly perpendicular to those faces [6].
  • There is some temperature dependence of the obtain phase changes. Therefore, a Pockels cell which is adjusted to produce perfect high-contrast amplitude modulation, for example, may require a readjustment of the applied voltages when the temperature changes. There are thermally compensated double crystal designs where that problem can be largely avoided.
  • At high optical power levels, some residual absorption of the crystal material may cause thermal effects. Low-absorption materials our therefore preferable for high power operation.
  • The crystals used in Pockels cells are nonlinear crystal materials, exhibiting substantial optical nonlinearities. For example, one may obtain self-phase modulation and nonlinear self-focusing for light pulses with substantial peak power.
  • Nonlinear crystals often exhibit substantial piezo-electric and elastooptic effects, which can have substantial influences on the performance at high modulation frequencies [1, 12].

Suppliers

The RP Photonics Buyer's Guide contains 36 suppliers for Pockels cells. Among them:

Questions and Comments from Users

2021-07-31

What is the acceptance angle of an electro-optic modulator and its dependence on the crystal length?

Answer from the author:

That very much depends on the type of modulator. It matters not only that a light beam can get through the device without clipping, but also that the modulation works with sufficiently high quality. Tentatively, modulators based on longer crystals may have a smaller acceptance angle, unless the aperture size is also increased.

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Bibliography

[1]R. P. Hilberg and W. R. Hook, “Transient elastooptic effects and Q-switching performance in lithium niobate and KD*P Pockels cells”, Appl. Opt. 9 (8), 1939 (1970), doi:10.1364/AO.9.001939
[2]W. R. Hook and R. P. Hilberg, “Lossless KD*P Pockels cell for high-power Q switching”, Appl. Opt. 10 (5), 1179 (1971), doi:10.1364/AO.10.001179
[3]D. Milam, “Brewster-Angle Pockels cell design”, Appl. Opt. 12 (3), 602 (1973), doi:10.1364/AO.12.000602
[4]J. Goldhar and M. A. Henesian, “Electro-optical switches with plasma electrodes”, Opt. Lett. 9 (3), 73 (1984), doi:10.1364/OL.9.000073
[5]M. A. Rhodes et al., “Performance of large-aperture optical switches for high-energy inertial-confinement fusion lasers”, Appl. Opt. 34 (24), 5312 (1995), doi:10.1364/AO.34.005312
[6]C. Tian, S. Goldstein and E. S. Fry, “On the etalon effect generated by a Pockels cell with high-quality antireflection coatings”, Appl. Opt. 39 (10), 1600 (2000), doi:10.1364/AO.39.001600
[7]M. A. Brubaker and C. Yakymyshyn, “Pockels cell voltage probe for noninvasive electron-beam measurements”, Appl. Opt. 39 (7), 1164 (2000), doi:10.1364/AO.39.001164
[8]Y. Li, C. Li and T. Yoshino, “Optical electric-power-sensing system using Faraday and Pockels cells”, Appl. Opt. 40 (31), 5738 (2001), doi:10.1364/AO.40.005738
[9]H. Chu, Y. Li and S. Zhao, “Improving deuterated potassium dihydrogen phosphate’s electro-optical Q-switched characteristics by adding a pair of auxiliary electrodes”, Appl. Opt. 50 (3), 360 (2011), doi:10.1364/AO.50.000360
[10]A. Starobor and O. Palashov, “Thermal effects in the DKDP Pockels cells in the 215–300 K temperature range”, Appl. Opt. 55 (26), 7365 (2016), doi:10.1364/AO.55.007365
[11]J. Zhang et al., “Aperture scalable, high-average power capable, hybrid-electrode Pockels cell”, Opt. Lett. 42 (9), 1676 (2017), doi:10.1364/OL.42.001676
[12]J. Vengelis et al., “Investigation of piezoelectric ringing effects in Pockels cells based on beta barium borate crystals”, Appl. Opt. 58 (33), 9240 (2019), doi:10.1364/AO.58.009240

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See also: Pockels effect, electro-optic modulators, phase modulators, intensity modulators, nonlinear crystal materials, Q switching
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