A λ/ 6 plate is introduced in between the two crossed...

A $\lambda / 6$ plate is introduced in between the two crossed polarizers in such a way that the optic axis of the $\lambda / 6$ plate makes an angle of $45^{\circ}$ with the pass axis of the first polarizer (see Fig. 22.45). Consider an unpolarized beam of intensity $I_{0}$ to be incident normally on the polarizer. Assume the optic axis to be along the $x$ -axis and the propagation along the $z$ -axis. Write the $x$ and $y$ components of the electric fields (and the corresponding total intensities) after passing through (i) $P_{1}$ (ii) $\lambda / 6$ plate and (iii) $P_{2}$

A $\lambda / 6$ plate is introduced in between the two crossed polarizers in such a way that the optic axis of the $\lambda / 6$ plate makes an angle of $45^{\circ}$ with the pass axis of the first polarizer (see Fig. 22.45). Consider an unpolarized beam of intensity $I_{0}$ to be incident normally on the polarizer. Assume the optic axis to be along the $x$ -axis and the propagation along the $z$ -axis. Write the $x$ and $y$ components of the electric fields
(and the corresponding total intensities) after passing through (i) $P_{1}$ (ii) $\lambda / 6$ plate and (iii) $P_{2}$

Key Concepts

Polarization

Polarization refers to the orientation and phase of the electric field oscillations in a light wave. It is a fundamental property of light that describes how the electric field vectors are distributed in different directions. Understanding polarization is essential for analyzing how light interacts with optical elements that are sensitive to its directional properties.

Polarizer

A polarizer is an optical element that transmits light with a specific polarization orientation while absorbing or reflecting components of the electric field in the orthogonal direction. It is used to convert unpolarized light into linearly polarized light and to analyze the state of polarization after the light passes through various optical components.

Wave Plate

A wave plate (or retarder) is an optical device made from a birefringent material that introduces a specific phase difference between the orthogonal components of an incident wave. This phase shift alters the overall polarization state of the light, transforming it from linear to elliptical or circular polarization, depending on the retardance and the orientation of the incoming polarization.

Phase Retardation

Phase retardation is the measure of the phase difference introduced between two orthogonal components of the electric field as light passes through a birefringent material. The specific retardance (for instance, ?/6 in this case) is critical in determining how the relative phases of the electric field components change, thereby modifying the polarization state.

Jones Calculus

Jones calculus is a mathematical framework used to analyze the polarization of light and its transformation by optical systems. It represents the polarization state of light as a vector (Jones vector) and optical components as matrices (Jones matrices), allowing for systematic calculation of the changes in amplitude and phase of the field components as light propagates through optical elements.

Intensity and Electric Field Amplitude

The intensity of a light beam is directly proportional to the square of the amplitude of its electric field. This relationship is fundamental in optics, as it connects the measurable quantity of light intensity with the underlying electric field components, which are modified by elements like polarizers and wave plates.

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