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.