Pockels Cells

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 and regenerative amplifiers. 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.

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.

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.

Note that the choice of material may be influenced by a wide range of aspects to consider. For example, desirable properties can be:

• a high electro-optic coefficient for reducing the required drive voltage
• transparency in the required spectral region
• low residual absorption, a high damage threshold and low optical nonlinearities for operation at high intensity levels
• availability of large enough crystals with high quality and at reasonable prices
• a low dielectric susceptibility for minimizing the electrical capacitance
• a low tendency for ringing effects (see below)

Often, one needs to carefully consider the trade-off between different aspects in the light of a particular application.

Half-wave Voltage

An important property of a Pockels cell is the half-wave voltage <$U_{\pi }$> (also called <$U_{\lambda /2}$> or <$V_{\lambda /2}$>). This is the voltage required for inducing a phase change of <$\pi$>, 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 <$U_{\pi }$>. 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 <$\Delta \varphi = \pi \: U / U_{\pi }$>. The total transmitted amplitude is then proportional to <$0.5 \cdot (1 + \exp i\Delta \varphi )$>, and we obtain the following result for the power transmission:

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 <$-U_{\pi } / 2$> and <$+U_{\pi } / 2$>.

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 <$\epsilon_\textrm{r}$>. 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 pulse 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.

Details to Consider

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

Large Crystals for High-Power Lasers

Particularly for application in Q-switched lasers with high pulse energies, one is forced to operate Pockels cells with a relatively large beam radius in order to avoid laser-induced damage. Unfortunately, the required nonlinear crystal is then quite large and correspondingly expensive. Depending on the used crystal material, large enough crystals may not be available because they are difficult to make with sufficiently high quality.

Another consequence is that the capacitance will be larger (due to the increased electrode area), which means additional demands on the used Pockels cell driver.

It can also be important to optimize the 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.

Residual Absorption

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.

End Reflectivities

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].

Temperature Dependence

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.

Optical Nonlinearities and Chromatic Dispersion

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.

Also, the chromatic dispersion of the crystal can be detrimental, particularly for devices operating with ultrashort pulses, such as regenerative amplifiers.

Piezoelectric Ringing

Nonlinear crystals often exhibit substantial piezo-electric and elasto-optic effects, which can have substantial influences on the performance at high modulation frequencies [1, 12]. It is common to observe “ringing” effects, which can substantially degrade the performance e.g. of Q-switched lasers or optical modulators; this often implies a limit for the usable modulation bandwidth. To some extent, such problems may be mitigated with sophisticated driver electronics.

More to Learn

Encyclopedia articles:

• Pockels effect
• electro-optic modulators
• phase modulators
• intensity modulators
• nonlinear crystal materials