Optics: Polarisation of Light - State of Polarisation (SOP)

  • Introduction to Polarisation of Light
  • Definition of State of Polarisation (SOP)
  • Importance of SOP in Optics
  • Various methods of Polarisation
  • Comparison of Unpolarised, Partially Polarised, and Fully Polarised Light

Introduction to Polarisation of Light

  • Definition: Polarisation is a property of transverse waves that can oscillate in more than one direction.
  • Polarisation of light refers to the orientation of its transverse electric field.
  • Key concept in understanding the behavior of light in optical systems.

Definition of State of Polarisation (SOP)

  • State of Polarisation (SOP) describes the polarisation characteristics of a light wave.
  • It specifies the direction, amplitude, and phase of the oscillating electric vector of the light wave.
  • SOP can be linear, circular, elliptical, or unpolarised.

Importance of SOP in Optics

  • SOP is crucial in many optical phenomena, such as interference, diffraction, and scattering.
  • Determining the SOP helps in understanding the behavior of light in polarisers, retarders, and other optical devices.
  • SOP also plays a significant role in applications like 3D cinema, LCD displays, and communication systems.

Various methods of Polarisation

  1. Natural Polarisation: Light from the sun or other natural sources is typically unpolarised.
  1. Polarisation by Reflection: Light reflected from a non-metallic surface can become partially polarised.
  1. Polarisation by Refraction: Light transmitted through a transparent medium can experience polarisation.
  1. Polarisation by Scattering: In scattering processes such as Rayleigh scattering, light is partially polarised.

Comparison of Unpolarised, Partially Polarised, and Fully Polarised Light

  • Unpolarised Light:
    • Randomly oriented electric field vectors.
    • No preferred direction of polarisation.
  • Partially Polarised Light:
    • Contains a mixture of polarised and unpolarised light.
    • Preferred direction of polarisation, but not fully aligned.
  • Fully Polarised Light:
    • All electric field vectors are aligned in one direction.
    • Specific direction of polarisation. …Continued on the next slide

Comparison of Unpolarised, Partially Polarised, and Fully Polarised Light (Continued)

  • Example: Sunlight
    • Unpolarised: Electric field vectors have random orientations.
    • Partially Polarised: After scattering in the Earth’s atmosphere, the light becomes partially polarised.
    • Fully Polarised: The polarising sunglasses filter out unwanted light, leaving only polarised light from a single direction.
  • Applications:
    • Unpolarised: General illumination, thermal radiation.
    • Partially Polarised: LCD monitors, optical fibers.
    • Fully Polarised: Polaroid lenses, optical experiments.

Example of Polarised Light

  • Experiment with Polaroid Filters:
    • Two Polaroid filters (polarisers) are placed in succession.
    • The first filter allows only vertically polarised light to pass through.
    • The second filter can be rotated to control the intensity of light transmitted.
  • Result:
    • When the two filters are aligned with the same SOP, maximum intensity is observed.
    • When the second filter is rotated perpendicular to the first, minimum intensity (or complete darkness) is observed.

Equation for Electric Field Vector of Polarised Light

  • Electric field vector of linearly polarised light:

    • E = E₀ * cos(ωt + φ₀)
    • E₀: Amplitude of the electric field
    • ω: Angular frequency of the light wave
    • t: Time
    • φ₀: Phase constant
  • For circularly or elliptically polarised light, the equation is more complex.

  • The SOP can be mathematically described using Stokes parameters or Jones vectors.

Summary

  • Polarisation of light refers to the orientation of its transverse electric field.
  • The State of Polarisation (SOP) describes the polarisation characteristics of a light wave.
  • SOP is important for understanding optical phenomena and designing optical devices.
  • Various methods of polarisation include reflection, refraction, and scattering.
  • Unpolarised, partially polarised, and fully polarised light have different characteristics.
  • The behaviour of polarised light can be studied using experiments and mathematical equations.

Optics: Polarisation of Light - State of Polarisation (SOP)

  • Unpolarised light can be polarised by passing it through a polarising filter.
  • The intensity of polarised light depends on the angle between the filter and the initial orientation of the electric field.
  • Polarised light can be used to selectively transmit or block specific orientations of the electric field.
  • Polarisation of light is widely used in applications like photography, optical microscopy, and polarised sunglasses.
  • The study of polarisation is an essential aspect of understanding the behavior of light in various optical systems.

Polarisation by Reflection

  • When light is incident on a non-metallic surface at a certain angle called the Brewster’s angle, the reflected light becomes polarised.
  • The reflected light is completely polarised perpendicular to the plane of incidence.
  • This phenomenon is used in the construction of polarisers and anti-reflection coatings for optical devices.
  • Example: Polaroid sunglasses exploit polarisation by reflection to reduce glare from reflected light.

Polarisation by Refraction

  • Light can also become polarised when it is transmitted through a transparent medium, such as glass or water.
  • The refracted light is partially polarised, with the electric field vector oriented parallel to the surface of the medium.
  • The extent of polarisation depends on the angle of incidence and the refractive indices of the media.
  • Example: Glare on water surfaces can be reduced by using polarised sunglasses that selectively block the polarised light.

Polarisation by Scattering

  • Scattering of light by small particles or impurities in a medium can cause the light to become partially polarised.
  • Rayleigh scattering, which explains the blue color of the sky, is an example of polarisation by scattering.
  • The scattered light becomes polarised with the electric field vector perpendicular to the direction of propagation.
  • Polarisation by scattering is commonly observed in atmospheric phenomena like rainbows and halos.

Malus’ Law

  • Malus’ Law relates the intensity of polarised light after passing through a polariser to the angle between the polariser and the initial polarisation direction.
  • Mathematically, I = I₀ * cos²(θ), where I is the transmitted intensity, I₀ is the initial intensity, and θ is the angle between the polariser and the initial polarisation direction.
  • Malus’ Law can be used to calculate the intensity of transmitted light in various polarisation configurations.

Circular Polarisation

  • Circular polarisation occurs when the electric field vector of a light wave rotates in a circular manner as it propagates.
  • Circularly polarised light can be left-handed (counterclockwise rotation) or right-handed (clockwise rotation).
  • It can be obtained by passing unpolarised light through a quarter-wave plate or by using specialized optical devices.
  • Applications of circular polarisation include 3D cinema, optical communication, and circular dichroism spectroscopy.

Elliptical Polarisation

  • Elliptical polarisation is a general case of polarisation where the electric field vector traces an ellipse as the light wave propagates.
  • It is a combination of linear and circular polarisations with different amplitudes and phases.
  • Elliptical polarisation can be obtained by passing unpolarised light through a birefringent material or using specific optical devices.
  • Example: Elliptical polarisation is commonly observed in cases where the incident light interacts with anisotropic materials.

Stokes Parameters

  • Stokes parameters are a set of four numbers used to fully describe the polarisation state of light.
  • They provide a quantitative description of the intensity, polarisation direction, and ellipticity of the light wave.
  • Stokes parameters can be measured experimentally using polarimeters or derived from the measured intensity of light in different polarisation configurations.
  • The analysis of Stokes parameters is essential in polarimetry, remote sensing, and characterising polarised light sources.

Jones Vectors

  • Jones vectors are a mathematical representation commonly used to describe the polarisation state of light.
  • They are two-dimensional complex vectors that represent the amplitude and phase of the electric field components.
  • Jones vectors are used in the Jones calculus, which allows the analysis of the transformation of polarised light by optical devices.
  • The Jones matrix is a 2x2 matrix that represents the effect of an optical device on the polarisation state of incident light.

Summary

  • Polarisation of light can be achieved through various methods like reflection, refraction, and scattering.
  • Polarised light is widely used in applications such as photography, LCD displays, and optical communication.
  • Malus’ Law relates the intensity of transmitted polarised light to the angle between the polariser and the initial polarisation direction.
  • Circular and elliptical polarisations are specific cases of polarisation, with unique characteristics and applications.
  • The polarisation state of light can be thoroughly described using Stokes parameters or Jones vectors.

Applications of Polarisation

  • Photography: Polarising filters can enhance the colors and reduce reflections in photographs.
  • LCD Displays: Liquid crystal displays (LCDs) use polarisers to control the passage of light and create images.
  • Optical Microscopy: Polarised light is used in microscopy to enhance contrast and reveal specific features.
  • Polarised Sunglasses: They reduce glare and improve visibility by selectively blocking polarised light.
  • Optical Communication: Polarisation of light is utilized for signal transmission in optical fibers.

Polarisation in Optical Instruments

  • Polarising Microscopes: Used to observe and analyze the polarisation characteristics of materials.
  • Polarimeters: Instruments used to measure the polarisation state of light.
  • Wave Plates: Also known as retarders, they introduce a phase shift between the two orthogonal components of polarised light.
  • Beam Splitters: Divide incoming light into two components with different polarisations.
  • Polarisation Modulators: Devices that manipulate the polarisation state of light for various applications.

Examples of Polarisation Phenomena

  • Double Refraction: Certain crystals exhibit birefringence, causing light to split into two polarised beams.
  • Polarised Reflection: When polarised light reflects off a surface, the reflected light becomes partially polarised.
  • Optical Activity: Some materials rotate the plane of polarisation of incident light.
  • Photoluminescence Polarisation: Fluorescent materials emit polarised light due to the orientation of their emitting dipoles.
  • Polarised Emission and Absorption: Atomic systems exhibit specific polarisation characteristics during emission and absorption processes.

Stokes Parameters Examples

  • Linearly Polarised Light: Stokes parameters (S₀, S₁, S₂, S₃) for linear polarisation are (I, I, 0, 0).
  • Circularly Polarised Light: Stokes parameters for right-handed and left-handed circular polarisation are (I, -I, 0, 0) and (I, I, 0, 0), respectively.
  • Unpolarised Light: For completely unpolarised light, Stokes parameters are (I, 0, 0, 0).
  • Partially Polarised Light: Stokes parameters vary based on the degree of polarisation and the orientation of the polarisation axis.

Jones Vectors Examples

  • Linear Polarisation: Jones vectors for horizontal and vertical linear polarisation are [1, 0] and [0, 1], respectively.
  • Circular Polarisation: Jones vectors for right-handed and left-handed circular polarisation are [(1+i)/√2, (1-i)/√2] and [(1-i)/√2, (1+i)/√2], respectively.
  • Unpolarised Light: Jones vectors can represent unpolarised light as a balanced superposition of horizontal and vertical components.
  • Elliptical Polarisation: Jones vectors can describe the amplitude and phase relationship of the two orthogonal components in an elliptically polarised light wave.

Applications of Polarisation in Medicine

  • Polarised Light Imaging: Used in medical imaging techniques such as polarised light dermoscopy for skin cancer diagnosis.
  • Optic Nerve Imaging: Polarisation-sensitive optical coherence tomography (PS-OCT) provides information on the nerve fiber layer.
  • Cataract Surgery: Polarisation can be used to assess the tissue properties of the lens during cataract surgery.
  • Retinal Imaging: Polarimetry can detect changes in retinal structures, aiding diagnosis and monitoring of diseases like glaucoma.

Quantum Aspects of Polarisation

  • Photon Polarisation: Photons can be described by their polarisation states, such as horizontal, vertical, or circular polarisation.
  • Quantum Entanglement: Two or more particles can become entangled, sharing a common polarisation state regardless of their separation distance.
  • Quantum Teleportation: The entanglement of polarised photons enables the transfer of quantum information between distant locations.
  • Quantum Cryptography: Polarisation states of photons can be used to securely transmit information with fundamental quantum security.

Polarisation-Selective Materials

  • Polarisation Filters: These materials transmit light with a specific polarisation while blocking others.
  • Retarders (Phase Shifters): Materials that introduce a controlled phase shift between two orthogonal components of polarised light.
  • Dichroic Materials: Differentially absorb light based on its polarisation state.
  • Birefringent Crystals: Crystals that have two different refractive indices for orthogonal polarisation states.
  • Metamaterials: Engineered materials with unique polarisation properties not found in natural materials.

Importance of Understanding Polarisation

  • Optical Design: Knowledge of polarisation enables the design of optical systems that manipulate light effectively.
  • Imaging Techniques: Polarisation information can enhance the contrast, resolution, and information content in imaging techniques.
  • Material and Surface Analysis: Polarisation analysis can provide insights into the properties of materials and surfaces.
  • Quantum Technologies: The understanding of polarisation is critical for the development of quantum communication and computing technologies.
  • Fundamental Physics: The study of polarisation helps deepen our understanding of the nature of light and its interaction with matter.

Summary

  • Polarisation of light refers to the orientation of its electric field vector.
  • The State of Polarisation (SOP) describes the polarisation characteristics of a light wave.
  • Polarisation can be achieved through reflection, refraction, and scattering processes.
  • Malus’ Law relates the intensity of transmitted polarised light to the angle between the polariser and the initial polarisation direction.
  • Circular and elliptical polarisations have unique characteristics and applications.
  • Stokes parameters and Jones vectors are mathematical tools to describe and analyze polarisation.
  • Polarisation has various applications in optics, medicine, quantum technologies, and material science.