Electro – Optic Pockels Cells
There are some particular crystals showing change in refractive indices directly
proportional to applied electric field. The phenomenon is called linear electro
– optic (EO) effect or Pockels effect. Electrically induced birefringence causes
plane polarized light propagating through the crystal to be resolved into two
orthogonal vectors with change in retardation between them proportional to
the magnitude of electric field (applied voltage). In general case this is
described by tensor of EO coefficient and leads to rather complicated expressions.
However, in many cases calculations are simplified due to crystal symmetry
and special configurations between electric field and light propagation referring
to crystal axes. There are two practically useful cases.
In longitudinal configuration light beam and electric field
are parallel. For example, in the KDP crystal for propagation along Z–axis
be defined as Ã = pno3r63 E
• L /λ, where r63 is appropriate EO
coefficient, E – electric field, L – crystal length. Apparently,
phase retardation Ã is
proportional to voltage U = E • L applied to crystal. This is called phase
we place the crystal between two crossed polarizers, output intensity will
obey Malu’s law: I = Io • sin2(Ã/2) i.e. output intensity
can be modulated by applied
voltage and this is called amplitude modulation. Max output
intensity is achieved when phase retardation is equal to p (or
half–wave). It can be seen that appropriate
voltage Up = λ/2no3r63 i.e.
is defined only by wavelength and material constants. So Up or half–wave voltage is
often used as parameter characterizing the efficiency of material as electro–optic
Longitudinal configuration is particularly useful for modulation of large aperture
light beams and it is still widely used for KDP crystal and it’s isomorphs although
there are disadvantages related to rather high applied voltages (usually 3 –
10 kV) and technical problems of making transparent electrodes or special ring
electrodes for generation of longitudinal electric field.
In the transverse configuration electric
field is perpendicular to light beam which is achieved by placing electrodes
directly on two side
faces of crystal.
In this case phase retardation depends not only on the applied voltage but
also on geometry of crystal. In addition to simple design of electrodes transverse
configuration allows to reduce applied voltage by factor d/L, where d is distance
between electrodes. So transverse modulation is widely used with LiNbO3,
some other crystals (BBO, KTP).
EO crystal cut , polished , with proper coatings and electrodes, usually mounted
in some kind of holder, sometimes with additional polarizing elements ( Glan
prism or waveplate ) is usually called Pockels cell by the name of effect. There
are many parameters that define final choice of EO crystal for some definite
application: transparency range, optical damage threshold, EO coefficients or
half–wave voltage, dielectric properties, etc.
Crystals of LiNbO3 and LiTaO3 are non-hygroscopic,
mechanically and chemically stable and available in large sizes with high internal
perfection at moderate
cost. These properties, combined with wide transparency range and high EO coefficients
lead to wide use of LiNbO3 and LiTaO3 for development of Pockels
cells with compact and rugged design for environmental, military, R&D and other applications.
Such cells are often used as intra-cavity electro-optic Q-switches.