# Conerefringent element

*also:* ** CRE**, *pl.* **CREs**

CRE is a crystal element cut along an optical axis of biaxial crystal. The two opposite sides of the cuts, named bases, are processed to admit the light to pass through.

It is convenient to describe the CRE by its Lambda-parameter and
stiff attached to it axis, denoted *Y*-axis.

Consider the unit eigenvectors associated with the eigenvalues of crystal dielectric tensor . Without loss of generality, suppose the CRE is cut along the optical axis with vector . Denote by the signs of the scalar products , , respectively. The two degrees of freedom for the directions of the vectors and generate four combinations , , and . The two combinations with determine uniquely the vector .

Define the
direction of the *Y*-axis along the unit
pseudovector .

Let is a laboratory Cartesian coordinate system, where the
components of above vectors are expressed. If we change the handedness of
the system to receive , by plane reflection or central inversion , then for
the primed system the direction of the *Y*-axis changes to the
opposite one.

To remove this ambiguity let us associate with CRE
right-hand coordinate system {X, Y, Z} . Now
we can even mark on each CRE the direction of the *Y*-axis, as
shown with red below. Define the coordinate
system in the next manner:

1) The Z-axes is always along the momentum p of the incident
photon. In the case of photon beam the *Z*-axis is
along the gravity center of the intensity cross sectional distribution of
the incident beam;

2) The X-axis is determined by the convention of the rifght handedness;

3) The plane {X, Y, 0} coincides with the isomomentum plane of the passed through CRE beam.

An experimental setup is presented in the figure for two cascaded CREs. In
the symbolic picture (in right) the arrows on both CREs show the orientations
of their *Y*-axes seen looking against the
beam propagation. For the picture above we can say that the second CRE is
rotated relative to the first CRE by angle in CCW direction. The term “CCW” is unambiguously
defined for the right-hand coordinate system.