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Pockels cells are divided into two configurations depending on the crystals' electro-optic properties: longitudinal and transverse. Longitudinal Pockels cells operate with electric field applied along the crystal optic axis or along incident beam propagation. Such crystals include KDP, KD*P, and ADP.
The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...
Figure 1 shows a light beam that propagates in the direction, while and are the transverse directions. If we assume that the electric field as (,,,), where denotes time, is linearly polarized and therefore can be treated as a scalar, we can express it in terms of the slowly varying normalized complex envelope (,,,) in this way
The geometrical definition of longitudinal emittance is more complex than that of transverse emittance. While the x {\displaystyle x} and y {\displaystyle y} coordinates represent deviation from a reference trajectory which remains static, the z {\displaystyle z} coordinate represents deviation from a reference particle, which is itself moving ...
Relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each other, is often derived as if it were the classical phenomenon, but modified by the addition of a time dilation term.
In hadron collider physics, the rapidity (or pseudorapidity) is preferred over the polar angle because, loosely speaking, particle production is constant as a function of rapidity, and because differences in rapidity are Lorentz invariant under boosts along the longitudinal axis: they transform additively, similar to velocities in Galilean ...
The first six longitudinal modes of a plane-parallel cavity. A longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting ...
In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration [8] or transverse acceleration [9] is an acceleration that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axis. This article ...