Pockels Cells

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, which passes through holes in the 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.

• 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).

An important property of a Pockels cell is the half-wave voltage U_π (also called U_λ/2 or V_λ/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 this 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. 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.

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_π. 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 = π U / U_π. The total transmitted amplitude is then proportional to 0.5 · (1 + exp iΔφ), 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_π / 2 and +U_π / 2.

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 ε_r. Besides, the chosen electrode geometry can play a role, and that may also be influenced e.g. by requirements concerning the open aperture.

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