How to phase modulate a laser: the Pockels effect


As discussed in a previous article, the phase modulation of a laser is used in ICF (Inertial Confinement Fusion) in order to prevent any damage to the system. The goal of this article is to present how this phase modulation is usually carried out.

The phase modulation is accomplished using the Pockels effect created in the so-called Pockels cells. These cells are electro-optic crystals through which the light can propagate and the phase delay is modulated by the electric voltage applied on it. These cells are made of a non centro-symetrical crystal so that the refractive index of this type of crystal is modified in proportion to the applied electric field strength.

Mathematically the Pockels effect is best described via the induced deformation of the index ellipsoid, defined by:

Equation 1

Where n is the media’s refractive index.

Since in a Cartesian coordinate system, an electric field changes the coefficient according to the following law:

Equation 2

and since 

Equation 3


Equation 4

The largest coefficient of the tensor being the r33, by applying a transverse electric field to the crystal, the optical index change will be:

Equation 5

Generally, the Pockels cell efficiency is characterized by its half-wave voltage Vπ, which is the voltage required to introduce a phase change of π. The typical value of the half-wave voltage is in the order of several 100’s or 1000’s volts, which implies the use of a high voltage amplifier. To get rid of this hassle, highly nonlinear crystals such as LiNbO3 (so with high r33 coefficients) integrated into an electro-optic system can be used to reduce the half-wave voltage to only a few volts. However these devices have limited power handling capabilities.

It exists two main types of Pockels cells which have different behaviors: the transverse and the longitudinal cells.

The transverse Pockels cell has an electric field perpendicular to the light beam. In this configuration the half-wave voltage depends on the crystal material, the electrode separation and the length of the crystal. However, in the case of large aperture, the electrode separation, thus the half-wave voltage, needs to be large. To overcome this issue, longitudinal cells are being used.

Figure 1

Transverse Pockels Cells

For a longitudinal Pockels cell length such as the one showed below, the light passes through holes in the electrode. In this case, for any aperture, the drive voltage remains constant since a shorter length also increases the electric field strength. Larger apertures are possible without increasing the half-wave voltage.

Figure 2

Longitudinal Pockels Cells

In addition to the phase modulation in ICF, the Pockels cells are also a basic component of the electro-optic modulators. They are for instance used in Q-switching lasers, or used in combination with a polarizer to create really fast optical shutters.

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