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🔬Modern Optics

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4.2 Polarization devices: polarizers, waveplates, and retarders

4 min readLast Updated on July 22, 2024

Polarization devices are essential tools in optics, manipulating light's electric field oscillations. From linear polarizers to wave plates, these components control light's intensity, phase, and polarization state, enabling various applications in imaging and communication.

Understanding polarization devices involves key principles like Malus' law and birefringence. Calculations using Jones calculus and Stokes parameters help predict how light behaves through these devices, allowing precise control of polarization for specific optical systems and experiments.

Polarization Devices

Principles of polarization devices

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  • Linear polarizers transmit light with electric field oscillations aligned with the polarizer's transmission axis while blocking light with electric field oscillations perpendicular to the transmission axis
  • Malus' law describes the transmitted intensity through a linear polarizer as I=I0cos2θI = I_0 \cos^2 \theta, where I0I_0 is the incident intensity and θ\theta is the angle between the incident polarization and the transmission axis
  • Quarter-wave plates introduce a phase shift of π/2\pi/2 between the fast and slow axes, converting linearly polarized light to circularly polarized light and vice versa (right-handed or left-handed circular polarization)
  • Quarter-wave plates are made of birefringent materials (calcite, quartz) with a specific thickness to achieve the desired phase shift
  • Half-wave plates introduce a phase shift of π\pi between the fast and slow axes, rotating the plane of polarization by an angle 2θ2\theta, where θ\theta is the angle between the incident polarization and the fast axis
  • Half-wave plates are also made of birefringent materials with a specific thickness to achieve the desired phase shift

Calculation of output polarization states

  • Jones calculus represents polarization states using Jones vectors and polarization devices using Jones matrices
  • Output polarization state is calculated by multiplying the input Jones vector by the Jones matrices of the devices in the order they are encountered
  • Stokes parameters represent polarization states using Stokes vectors (S0, S1, S2, S3) and polarization devices using Mueller matrices
  • Output Stokes vector is calculated by multiplying the input Stokes vector by the Mueller matrices of the devices in the order they are encountered
  • Stokes parameters provide a complete description of the polarization state, including the degree of polarization and the relative phase between orthogonal components

Design for polarization transformations

  • Combination of linear polarizers and wave plates can be used to achieve desired polarization states or transformations
  1. Use a linear polarizer to set the initial polarization state (horizontal, vertical, or at a specific angle)
  2. Use a quarter-wave plate to convert between linear and circular polarization (right-handed or left-handed)
  3. Use a half-wave plate to rotate the plane of polarization to the desired angle
  • Liquid crystal devices exhibit electrically controllable birefringence, allowing them to function as variable wave plates and polarization rotators
  • Polarizing beam splitters separate orthogonal polarization components (s-polarized and p-polarized) and can be used to create and analyze polarization states

Effects on light intensity and phase

  • Linear polarizers reduce intensity according to Malus' law, with the transmitted intensity depending on the angle between the incident polarization and the transmission axis
  • Wave plates (quarter-wave and half-wave) do not change the intensity of light but introduce a phase shift between the fast and slow axes
  • Polarizing beam splitters divide the intensity between the transmitted and reflected components based on their polarization (s-polarized or p-polarized)
  • Quarter-wave plates introduce a π/2\pi/2 phase shift between the fast and slow axes, while half-wave plates introduce a π\pi phase shift
  • Combinations of wave plates can introduce arbitrary phase shifts between orthogonal polarization components, enabling the creation of various polarization states (elliptical, circular)

Applications and Effects

Principles of polarization devices

  • Polarization state control is achieved using linear polarizers to set the polarization state to linear, quarter-wave plates to convert between linear and circular polarization, and half-wave plates to rotate the plane of polarization
  • Birefringence is a key property of wave plates, which are made of materials (calcite, quartz) with different refractive indices for different polarization directions, introducing a phase shift between orthogonal polarization components

Calculation of output polarization states

  • Matrix multiplication is used in Jones calculus and Mueller calculus to calculate the output polarization state through multiple devices
  • Polarization state evolution occurs as light passes through each device, with the final polarization state depending on the order and orientation of the devices
  • Multiplying the input polarization state (Jones vector or Stokes vector) by the matrices representing the polarization devices yields the output polarization state

Design for polarization transformations

  • Polarization state generation is achieved using combinations of linear polarizers and wave plates to produce specific polarization states (linear, circular, elliptical)
  • Polarization state analysis is performed using polarizing beam splitters and linear polarizers to separate and measure the intensity of orthogonal polarization components, allowing for the determination of the Stokes parameters
  • Polarization state manipulation is achieved using wave plates and liquid crystal devices, with dynamic control of the polarization state possible by rotating wave plates or applying electric fields to liquid crystal devices

Effects on light intensity and phase

  • Polarization-dependent loss occurs in linear polarizers, which reduce the intensity of light based on the angle between the incident polarization and the transmission axis, and in polarizing beam splitters, which divide the intensity between the transmitted and reflected components based on their polarization
  • Polarization-dependent phase shift is introduced by wave plates, with the amount of phase shift depending on the type of wave plate (quarter-wave or half-wave) and its orientation relative to the incident polarization
  • Interference effects can arise when light with polarization-dependent phase shifts is recombined, leading to constructive or destructive interference based on the relative phase of the polarization components
  • Polarization-dependent effects can be exploited in various applications (liquid crystal displays, polarization microscopy) to control the intensity, phase, and propagation of light


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.