text: The main component of a VIPA is a glass plate whose normal is slightly tilted with respect to the input light. One side (light input side) of the glass plate is coated with a 100% reflective mirror and the other side (light output side) is coated with a highly reflective but partially transmissive mirror. The side with the 100% reflective mirror has an anti-reflection coated light entrance area, through which a light beam enters the glass plate. The input light is line-focused to a line (focal line) on the partially transmissive mirror on the light output side. A typical line-focusing lens is a cylindrical lens, which is also part of the VIPA. The light beam is diverging after the beam waist located at the line-focused position.
  After the light enters the glass plate through the light entrance area, the light is reflected at the partially transmissive mirror and the 100% reflective mirror, and thus the light travels back and forth between the partially transmissive mirror and the 100% reflective mirror.
  It is noted that the glass plate is tilted as a result of its slight rotation where the axis of rotation is the focal line. This rotation/tilt prevents the light from leaving the glass plate out of the light entrance area. Therefore, in order for the optical system to work as a VIPA, there is a critical minimum angle of tilt that allows the light entering through the light entrance area to return only to the 100% reflective mirror. Below this angle, the function of the VIPA is severely impaired. If the tilting angle were zero, the reflected light from the partially transmissive mirror would travel exactly in reverse and exit the glass plate through the light entrance area without being reflected by the 100% reflective mirror. In the figure, refraction at the surfaces of the glass plate was ignored for simplicity.
  When the light beam is reflected each time at the partially transmissive mirror, a small portion of the light power passes through the mirror and travels away from the glass plate. For a light beam passing through the mirror after multiple reflections, the position of the line-focus can be seen in the virtual image when observed from the light output side. Therefore, this light beam travels as if it originated at a virtual light source located at the position of the line-focus and diverged from the virtual light source. The positions of the virtual light sources for all the transmitted light beams automatically align along the normal to the glass plate with a constant spacing, that is, a number of virtual light sources are superimposed to create an optical phased array. Due to the interference of all the light beams, the phased array emits a collimated light beam in one direction, which is at a wavelength dependent angle, and therefore, an angular dispersion is produced.