Graduate
  1. Classical mechanics  1.1. Advanced Kinematics  1.1.1. Generalized coordinate systems  1.1.2. Parametric equations of motion  1.1.3. Non-inertial frames and fictitious forces  1.1.4. Covariant formulation of momentum  1.1.5. Action-angle variable  1.2. Lagrangian and Hamiltonian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Noether's theorem and conservation laws  1.2.4. Normalized Speed  1.2.5. Canonical conversion  1.2.6. Poisson bracket and Hamilton–Jacobi theory  1.2.7. Hamiltonian chaos and integrability  1.3. Rigid body mobility  1.3.1. Euler's equations of motion  1.3.2. Principal moments of inertia  1.3.3. Gyroscopic motion and precession  1.3.4. Inertia tensor  1.3.5. Stability of rotational speed  1.4. Nonlinear dynamics and chaos  1.4.1. Phase space and stability analysis  1.4.2. Poincaré sections and bifurcation theory  1.4.3. Strange Attractors and Fractals  1.4.4. Lyapunov exponent  1.4.5. KAM theorem and quasi-periodic motion
  2. Electromagnetism  2.1. Advanced Electrodynamics  2.1.1. Green's function and potential theory  2.1.2. Multipole expansion  2.1.3. Image charging method  2.1.4. Boundary conditions and uniqueness theorem  2.2. Electromagnetic wave propagation  2.2.1. Plane waves in dielectrics and conductors  2.2.2. Waveguides and cavity resonators  2.2.3. Radiation pressure and optical tweezers  2.2.4. Polarization and Jones calculus  2.3. Relativistic electrodynamics  2.3.1. Covariant formulation of electrodynamics  2.3.2. Lienard–Wiechert potentials  2.3.3. Synchrotron radiation and bremsstrahlung  2.3.4. Electromagnetic field tensor and Lorentz transformations  2.4. Plasma physics  2.4.1. Magnetohydrodynamics  2.4.2. Debye shielding and plasma oscillations  2.4.3. Alfvén waves and tokamak confinement  2.4.4. Plasma instabilities and turbulence
  3. Statistical mechanics and thermodynamics  3.1. Advanced Thermodynamics  3.1.1. Legendre transforms and thermodynamic potentials  3.1.2. Fluctuation–dissipation theorem  3.1.3. Onsager interpersonal relations  3.1.4. Critical events and phase transitions  3.2. Quantum statistical mechanics  3.2.1. Density Matrix and Ensemble Theory  3.2.2. Bose–Einstein condensates  3.2.3. Quantum phase transition  3.2.4. Fermi–Dirac and Bose–Einstein statistics  3.2.5. Partition functions and grand canonical ensembles
  4. Quantum mechanics  4.1. Advanced wave mechanics  4.1.1. WKB approximation  4.1.2. Path integral formulation  4.1.3. Quantum harmonic oscillator and coherent states  4.2. Angular momentum and spin  4.2.1. Spherical Harmonics  4.2.2. Clebsch–Gordan coefficient  4.2.3. Wigner–Eckart theorem  4.2.4. Spin–orbit coupling  4.3. Quantum scattering theory  4.3.1. Born approximation  4.3.2. Partial wave analysis  4.3.3. Optical theorem  4.3.4. S-matrix theory  4.4. Quantum field theory  4.4.1. Second Quantization  4.4.2. Feynman diagrams and propagators  4.4.3. Renormalization theory  4.4.4. Gauge theory and Yang–Mills fields  4.4.5. Spontaneous symmetry breaking and the Higgs mechanism
  5. General relativity and cosmology  5.1. Tensor calculus and differential geometry  5.1.1. Einstein field equations  5.1.2. Schwarzschild and Kerr metrics  5.1.3. Geodesics and Christoffel symbols  5.2. Cosmology and the Universe  5.2.1. The FLRW metric and cosmic inflation  5.2.2. Dark energy and structure formation  5.2.3. Cosmic microwave background radiation
  6. Condensed matter physics  6.1. Band structure and transport theory  6.1.1. Block theorem and the Kronig–Penney model  6.1.2. Fermi surface topology  6.1.3. Quantum Hall Effect  6.2. Superconductivity  6.2.1. BCS theory and Cooper pairs  6.2.2. Meissner effect and flux quantization  6.2.3. The Josephson Effect and SQUIDs  6.3. Topological phases of matter  6.3.1. Topological Insulators  6.3.2. Majorana fermions in topological phases of matter
  7. Nuclear and Particle Physics  7.1. Quantum Chromodynamics (QCD)  7.1.1. Quark–gluon plasma  7.1.2. Asymptotic freedom  7.1.3. Confinement and hadronization  7.2. Beyond the Standard Model  7.2.1. Grand Unified Theories  7.2.2. Supersymmetry and extra dimensions  7.2.3. Neutrino oscillations

Graduate → Electromagnetism → Electromagnetic wave propagation ↓


Radiation pressure and optical tweezers


The concepts of radiation pressure and optical tweezers are fascinating topics in the field of electromagnetism, which involves the manipulation and understanding of electromagnetic waves. These concepts have important applications in physics, biology, and engineering, especially in manipulating small particles such as atoms, molecules, and even cells.

Radiation pressure

Radiation pressure refers to the pressure exerted on a surface by electromagnetic radiation. The concept arises from the transfer of momentum from the fundamental particles of light, photons, to the surface they hit. When photons hit a surface, they can transfer momentum, exerting a small force. This effect is usually very weak, but is measurable and important in a variety of contexts, from solar sails to optical trapping in space exploration.

Understanding momentum transfer

Photons, despite being massless, have momentum, which is given by the following relation:

p = frac{E}{c}

where p is the momentum, E is the energy of the photon, and c is the speed of light in vacuum.

When photons are absorbed or reflected by a surface, the change in momentum appears as a force. For a perfectly reflective surface, the momentum change is twice that of an absorbent surface. The radiation pressure P is given by:

P = frac{I}{c}

For a perfectly absorbing surface, and

P = frac{2I}{c}

For a perfectly reflecting surface. Here, I is the intensity of the electromagnetic wave.

Solar sails and space exploration

An important application of radiation pressure is in solar sails used for space propulsion. By deploying large, reflective sails in space, spacecraft can use radiation pressure from sunlight to propel themselves without conventional fuel. This use of light pressure for propulsion demonstrates a new application in space exploration, providing a method for interstellar travel due to the constant push from sunlight.

sunlight

Optical tweezers

Optical tweezers are used to manipulate microscopic particles by applying very small forces to them using a highly focused laser beam. This technique was awarded the Nobel Prize in Physics in 2018, underlining its importance and diverse applications, especially in the biological sciences.

Modus operandi

The optical tweezer setup uses a highly focused laser beam, which creates a gradient in light intensity. This gradient generates a force that can trap and manipulate microscopic particles. The basic force balance can be divided into two components:

  • Gradient force: This force pulls the particle towards the region of highest light intensity, usually the center of the beam. It is mainly responsible for trapping the particle.
  • Scattering force: This force arises due to the transfer of momentum from the photon to the particle, pushing it in the direction of light propagation.

This trapping occurs when the gradient force is stronger than the scattering force, and successfully holds the particle in place.

laser beam Particle

Applications of optical tweezers

Optical tweezers are widely used in biological research, to manipulate and study cells, DNA, and other biomolecules without physical contact or damage. Some notable applications include:

  • To study the mechanical properties of DNA and other biomolecules.
  • Cell sorting and analysis, especially in the identification and separation of different cell types.
  • Monitoring biological processes, such as protein folding or cellular interactions.

Comparison and significance

Both radiation pressure and optical tweezers demonstrate the manipulation of matter through light. While radiation pressure involves a broadly uniform application of force, optical tweezers use precise and localized control to trap and manipulate particles. These concepts highlight the versatility of light in scientific applications.

The study of radiation pressure and optical tweezers emphasizes the fascinating interface between light and matter. Their theories make significant contributions to advancing technology and understanding in fields such as space exploration and biomedical research, expanding the realm of possibilities.

Understanding these concepts leads to a deeper understanding of the subtle and profound effects that electromagnetic waves have on the universe, and changes our approach to both exploration and subtle manipulation.


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Radiation pressure and optical tweezers

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