E-O Crystals Principle

When an electric field (E) is applied to an electro-optic (E-O) crystal, the refractive index of E-O crystal will change linearly to electric field. The phenomenon is called linear electro-optic effect. For KD*P crystal, for example, the change of the refractive index (Dn) is Dn = 0.5n3or63E if both the directions of light propagation and electric field are along the z-axis, where no is refractive index without electric field and r63 is electro-optic coefficient of KD*P.

If a linearly polarized light passes through an E-O crystal, the phase retardation (G) will be induced by Dn to G = 2pDnL, where L is crystal length, for KD*P, again as an example, G = pLn3or63E/l. It is clear that the phase of light will change together with electric field (E). This is called electro-optic phase modulation. If two crossed polarizers are placed at input and output ends of E-O crystal separately, the output intensity of light will be I = I0sin2(G/2), where I0 is input intensity. That means the intensity or amplitude of light can also be modulated by electric field. This is called amplitude modulation.

longitudinal E-O modulation	transverse E-O modulation

There are two kinds of E-O modulations. One is longitudinal E-O modulation if the directions of electric field and light propagation are the same. The KDP isomorphic crystals are normally used in this scheme. If the directions of electric field and light propagation are perpendicular, it is called transverse E-O modulation. The LiNbO3, MgO:LiNbO3, ZnO:LiNbO3, BBO and KTP crystals are usually employed in this scheme.

The half-wave voltage (Vp) is defined as the voltage at G = p, for example, Vp=l/(2no3r63) for KD*P and Vp=ld/(2no3r22L) for LiNbO3, where l is light wavelength and d is the distance between the electrodes.

Electro-Optic Modulator Materials

KD*P Crystals

KD*P crystal is widely applied for electro-optic application as Q-switch and Pockels cells. KD*P is routinely used for Q-switching applications from the uv out to about 1.1 µm where absorption limits its use in active cavities, although it can be useful at longer wavelengths when a few percent of absorption can be tolerated. KD*P has high optical uniformity and is useful for large aperature applications.

RTP Crystals

The new crystal RTP is an isomorph of KTP. However, it has higher damage threshold (about 1.8 times KTP), higher resistivity, and no sign of electro- chromism.These are Biaxial crystals and natural Birefringence needs to be compensated by use of two crystal rods specially oriented so that beam passes along the X-direction. The Q-switch is built using two RTP elements in a temperature compensating design. Input beam is polarized along the diagonal of the input face and Z and Y axis are perpendicular to the two side faces. Y and Z faces are rotated by 90° in the second crystal for thermal compensation. The ‘o' ray in the first crystal becomes the ‘e' ray in the second crystal and vice versa, so that the thermal birefringence is compensated. Matched pairs (equal lengths polished together) are required for effective compensation.

The effective E-O constant r c1 (light propagating along the Y axis) is 23.6 pm/V and E-O constant r c2 (light propagating along the X axis) is 20.3 pm/V. The contrast ratio is better for r c2 constant. At repetition rates of 50KHz, the noise due to piezo-electric ringing is less than 3% while that in BBO it is 10% when operated at 30KHz. However in RTP Pockels cells, the half-wave voltage is about 40% and the hold-off is about 25% of that of BBO pockels cell.

These are transverse Pockels devices and the voltage increases linearly with wavelength for a given aspect ratio. BBO is slightly hygroscopic while RTP is not, so hermetical sealed housing is not required. Water cooled BBO Q switches are tested for average powers up to 150W, and RTP may be usable up to these levels at 1064nm. BBO optical bandwidth is 200nm to 2000nm while that of RTP is 400nm to 2500nm.

BBO Crystals

BBO is the electro-optic material of choice for high average power Pockels cell applications at the wavelength range from 200nm to 2500nm. BBO has a high damage threshold and a low dielectric constant and is useful in high repetetion rate, high average power (up to 150W) diode pumped solid state lasers (DPSS lasers). BBO has significant advantages over other materials in terms of laser power handling abilities, temperature stability, and substantial freedom from piezoelectric ringing. Because it relies on the electro optic effect, switching time — aided by the low capacitance of the Pockels cell — is very fast. The wide transparency range of BBO allows it to be used in diverse applications

Electro-optic Pockels cells are used in applications that require fast switching of the polarization direction of a beam of light. These uses include Q-switching of laser cavities, coupling light into and out from regenerative amplifiers, and, when used in conjunction with a pair of polarizers, light intensity modulation. Pockels cells are characterized by fast response, since the Pockels Effect is largely an electronic effect that produces a linear change in refractive index when an electric field is applied, and are much faster in response than devices based on acoustic changes in a material, for example.

Because of crystal symmetry and the desire for the light beam to experience no birefringence in the absence of an electric field, BBO Pockels cells are transverse-field devices.

It has electro-optic coefficients g11=2.7pm/V and g22, g31<0.1 g11. It can be used for Q-Switching a cw diode pumped Nd:YAG laser with average power>50W.

LiNBO3

Crystal Lithium Niobate (LN) has higher transmission, and high contrast ratio at average powers in the KW range. Applications that utilize the large electro-optic coefficients of lithium niobate are optical modulation and Q-switching of infrared wavelengths. Because the crystal is nonhygroscopic and has a low half-wave voltage, it is often the material of choice for Q-switches in military applications. The crystal can be operated in a Q-switch configuration with zero residual birefringence and with an electric field that is transverse to the direction of light propagation. Because piezoelectric ringing can be severe, piezoelectrically damped designs can be very useful. The damage threshold of the intrinsic material at 1.06 microns with a 10 nsec pulse is approximately 3 J/cm2. With appropriate AR coatings, a surface damage threshold of 300-500 MW/cm2 can be achieved for the same conditions.

The light propagates in z-axis and electric field applies to x-axis, the refractive retardation will be G = pLnr22V/ld. The electro-optic coefficients of LiNbO3 are: r33 = 32 pm/V, r31 = 10 pm/V, r22 = 6.8 pm/V at low frequency and r33 = 31 pm/V, r31 = 8.6 pm/V, r22 = 3.4 pm/V at high electric frequency.

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