Electro-optic Modulators

The simplest type of electro-optic modulator is a phase modulator containing only a Pockels cell, where an electric field (applied to the crystal via electrodes) changes the phase delay of a laser beam sent through the crystal. The polarization of the input beam often has to be aligned with one of the optical axes of the crystal, so that the polarization state is not changed.

Many applications require only a small (periodic or nonperiodic) phase modulation. For example, this is often the case when one uses an EOM for monitoring and stabilizing a resonance frequency of an optical resonator. Resonant modulators (see below) are often used when a periodic modulation is sufficient, and make possible a large modulation depth with a moderate drive voltage. The modulation depth can in some cases be so high that dozens of sidebands are generated in the optical spectrum (comb generators, frequency combs).

Note that an electro-optic modulator is not suitable for frequency modulation, or precisely speaking only for limited short-term frequency changes. For example, it could not be used to generate a constant change of optical frequency of an optical signal, since that would imply a linearly increasing phase delay (without any limit to the phase excursion).

Depending on the type and orientation of the nonlinear crystal, and on the direction of the applied electric field, the phase delay can depend on the polarization direction. A Pockels cell can thus be seen as a voltage-controlled waveplate, and it can be used for modulating the polarization state. For a linear input polarization (often oriented at 45° to the crystal axes), the output polarization will in general be elliptical, rather than simply a linear polarization state with a rotated direction.

Combined with other optical elements, in particular with polarizers, Pockels cells can be used for other kinds of modulation. In particular, an amplitude modulator (Figure 2) is based on a Pockels cell for modifying the polarization state and a polarizer for subsequently converting this into a change in transmitted optical amplitude and power.

An alternative technical approach is to use an electro-optic phase modulator in one arm of a Mach–Zehnder interferometer in order to obtain amplitude modulation. This principle is often used in integrated optics (for photonic integrated circuits), where the required phase stability is much more easily achieved than with bulk optical elements.

Optical switches are modulators where the transmission is either switched on or off, rather than varied gradually. Such a switch can be used, e.g., as a pulse picker, selecting certain pulses from a train of ultrashort pulses, or in cavity-dumped lasers (with an EOM as cavity dumper) and regenerative amplifiers.

In configurations where the induced relative phase change between two polarization directions is used, thermal influences can be disturbing. They result in a drift of the operation point, which may have to be compensated with an automatically adjusted bias voltage. Additional electronics may be used for such purposes, deriving the required bias voltage from some optical signals.

Some electro-optic modulators contain two matched Pockels cells in an athermal configuration where the temperature dependence of the relative phase shift is largely canceled. There are also configurations with four crystals of exactly the same length, canceling both birefringence effects and spatial walk-off. Various types of multi-crystal designs are used, depending on the material and the exact requirements.

For some applications, a purely sinusoidal modulation with constant frequency is required. In that case, it is often beneficial to use an electrically (not mechanically) resonant electro-optic modulator, containing a resonant LC circuit. The input voltage of the device can then be substantially lower than the voltage across the electrodes of the Pockels cell. A high ratio of these voltages requires a high Q factor of the LC circuit and reduces the bandwidth in which strong resonant enhancement can be achieved. The disadvantage of using a resonant device is that one loses flexibility: changing the resonance frequency requires the exchange of at least one electric component.

Broadband modulators are optimized for operation in a wide frequency range, which typically starts at zero frequency. A high modulation bandwidth typically requires a Pockels cell with a small electric capacitance, and excludes the exploitation of a resonance.

For particularly high modulation bandwidths e.g. in the gigahertz region, integrated optical traveling-wave modulators are often used. Here, the electric drive signal generates an electromagnetic wave (microwave) propagating along the electrodes in the direction of the optical beam. Ideally, the phase velocities of both waves are matched so that efficient modulation is possible even for frequencies which are so high that the electrode length corresponds to several wavelengths of the microwave.

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