Electro-Optic Modulators

In this section, we discuss the operation and application of electro-optic devices that rely on the phenomenon of birefringence that is induced by application of voltage to a crystal. Let us first define birefringence. In certain crystalline materials, an incident light ray will separate into two rays that may travel in different directions. These crystals are called birefringent. The direction in which the light travels is dependent on its polarization. For each of the two different perpendicular states of polarization, the light will travel in a different direction. Birefringence is also called double refraction because when the light enters the crystal, it is refracted into two different directions.
Figure 1 shows the effect of birefringence when a beam of unpolarized light enters the surface of a birefringent material at an angle q to the normal to the surface. The two different components of polarization (horizontal and vertical) travel in two different directions. The material has two different indices of refraction, one for each of the two perpendicular components of polarization. In accordance with the laws of geometric optics, the two rays are refracted at different angles as they enter the crystal.

Fig. 1
Schematic diagram showing the separation of the two
components of polarization in a light beam traveling through a
birefringent material. The incident light is unpolarized.

Many crystalline materials exhibit birefringence naturally, without application of any voltage. The birefringence is present all the time. Examples of such crystals are quartz and calcite.
There are also a number of crystals that are not birefringent naturally but in which application of a voltage induces birefringence. This phenomenon is called the electro-optic effect. The electro-optic effect leads to the ability to control light beams in a variety of ways and is the basis of a number of applications, including light-beam modulators, Q-switches, and deflectors. Examples of crystals that exhibit the electro-optic effect are potassium dihydrogen phosphate (commonly called KDP), ammonium dihydrogen phosphate (ADP), potassium dideuterium phosphate (KD*P), lithium niobate, and barium sodium niobate.
The operation of an electro-optic device used as a light-beam modulator is shown schematically in Figure 2. Polarized light is incident on the modulator. The light may be polarized originally or a polarizer may be inserted, as shown. The analyzer, oriented at 90� to the polarizer, prevents any light from being transmitted when no voltage is applied to the electro-optic material. When the correct voltage is applied to the device, the direction of the polarization is rotated by 90� . Then the light will pass through the analyzer.

Fig. 2
Schematic diagram of the operation of a modulator based
on the electro-optic effect. In this configuration, the voltage is
applied parallel to the direction of light propagation.

Two types of electro-optic effect have been used: the Kerr electro-optic effect, which is shown by liquids such as nitrobenzene, and the Pockels electro-optic effect, shown by crystalline materials such as ammonium dihydrogen phosphate or lithium niobate. Some early electro-optic devices used nitrobenzene, but the liquid tends to polymerize in the presence of the intense laser light. Modern electro-optic modulators use the Pockels effect. The electro-optic modulators are often called Pockels cells.
The orientation of the polarizer and analyzer at 45� to the vertical, as shown in Figure 1, is a common configuration, used with many commercial modulators. But the orientation depends on the particular material used and on the direction in which the crystal has been cut. The manufacturer's instructions should be consulted to ensure proper orientation of the modulator and the directions of the pass axes for the polarizer and analyzer.
With the direction of polarization at 45� to the vertical direction, the polarization vector is composed of two perpendicular components of equal intensity, one vertical and one horizontal. The crystalline element is oriented with its axes in a specified orientation (which depends on the crystalline symmetry of the particular material). The applied voltage induces birefringence in the crystal, so that the two components of polarization travel with different velocities inside the crystal. This induced birefringence is the basis of the electro-optic effect.
The two components travel in the same direction through the crystal and do not become physically separated. But the two components, in phase as they enter the crystal, emerge with different phases. As they traverse the crystal, they accumulate a phase difference, which depends on the distance traveled and on the applied voltage. When the beams emerge from the crystal, the polarization of the combined single beam depends on the accumulated phase difference. If the phase difference is one-half wavelength, the polarization is rotated by 90� from its original direction. This by itself does not change the intensity of the beam. But, with the analyzer, the transmission of the entire system varies, according to

T = T₀ sin²(p D nL/l ) Equation 1

where T is the transmission, T₀ the intrinsic transmission of the assembly, taking into account all the losses, D n the birefringence (that is, the difference in refractive index for the two polarizations), L the length of the crystal, and l the wavelength of the light. The birefringence is an increasing function of the applied voltage, so that the transmission of the device will be an oscillatory function of applied voltage. The maximum transmission occurs when
D n = l /2L Equation 2
This occurs at a voltage called the half-wave voltage, denoted V_1/2. The half-wave voltage depends on the nature of the electro-optic material. The half-wave voltage for a particular material increases with the wavelength. Thus, in the infrared the required voltage is higher than in the visible. This factor can limit the application of electro-optic modulators in the infrared.
The transmission of an electro-optic device as a function of applied voltage is shown in Figure 3, indicating the maximum transmission at the half-wave voltage.

Fig. 3
Transmission of an electro-optic device as a function of applied voltage.
V_1/2 denotes the half-wave voltage.

In most crystals, each of the prominent crystalline faces belongs to one of three families of planes that intersect along what are called crystal axes. These axes can be designated as coordinate axes, even though they are not generally at right angles to each other. When one fabricates an electro-optic modulator, the crystal must be cut at certain specified angles to the crystalline axes. A full discussion of the different orientations and the reasons for them is beyond the scope of this module. We simply note that different crystalline symmetries require that specific relations be maintained between the crystalline axes and the faces of the electro-optic element.
One important performance parameter for electro-optic modulators is the extinction ratio, defined as the ratio of the transmission when the device is fully open, to the transmission when the device is fully closed. In practice there is always some light leakage, so the minimum transmission never reaches zero. A high value of the extinction ratio is desirable because it determines the maximum contrast that may be obtained in a system that uses the modulator. Commercial electro-optic modulators can have extinction ratios in excess of 1000.
Electro-optic modulators may be fabricated with different physical forms. In one form, voltage is applied parallel to the light propagation, as was shown in Figure 2. One uses transparent electrodes or electrodes with central apertures. This is called a longitudinal electro-optic modulator.
In another form, metal electrodes are on the sides of the crystal (which has a square cross section) and the voltage is perpendicular to the light propagation. This is called a transverse modulator. Two examples are shown in Figure 4. The top is a two-element configuration suitable for use with materials like ADP. The use of two crystals oriented as shown provides compensation for the natural birefringence of the material. The bottom portion of the figure shows a single-element configuration suitable for lithium tantalate-type materials. Both single- and dual-element configurations are in use in commercial modulators.

Fig. 4
Transverse electro-optic modulator configurations.
Top: Two-element configuration suitable for ADP-type materials.
Bottom: Single-element configuration suitable for lithium tantalate-type materials

Longitudinal and transverse modulators have different applications. Longitudinal modulators may have large apertures, but the half-wave voltage will be high, often in the kilovolt range. Longitudinal modulators are often used with conventional light sources. Because it is difficult to vary the required high voltages rapidly, the frequency response of longitudinal modulators tends to be low. Applications for which longitudinal modulators are suited include relatively low-frequency modulation of laser beams or use with non-laser sources.
In transverse modulators, the voltage is applied perpendicular to the light propagation. The phase retardation for a given applied voltage may be increased simply by making the crystal longer. The half-wave voltage thus may be much lower for transverse modulators, perhaps as low as 100 volts. It follows that the frequency response may be much higher. Transverse modulators are thus suited for fast, broadband applications. A problem with transverse modulators is the relatively small aperture that they permit, because the crystal may be a long, thin parallelepiped. This physical configuration means that transverse modulators are best suited for use with narrow, well-defined laser beams. In addition, the extinction ratios available with transverse modulators tend to be lower than for longitudinal modulators. Applications of transverse modulators include broadband optical communication, display and printing systems, and fast image and signal recorders.
Table 1 lists electro-optic materials and some of their characteristics. The table includes the names of a number of electro-optic materials, their common abbreviations, their chemical formulas, and the spectral range over which they are transmissive. The bandwidths quoted are for use of the materials in commercially available electro-optic light modulators. Most of the materials are suited for use in the visible and near-infrared portions of the spectrum, but cadmium telluride is useful as a modulator for CO₂ lasers in the long-wavelength infrared.
Of the materials in the table, ADP, AD*P, and KD*P are relatively older materials. They may be used as either longitudinal or transverse modulator materials, but have relatively high half-wave voltages.
Lithium niobate and lithium tantalate represent a relatively modern class of electro-optic materials, which have larger electro-optic effects and smaller half-wave voltages. They are hard to grow in large crystals of high quality but they are perhaps the best available modern electro-optic materials.


Ricardo Monroy  C.I. 17646658

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