Optics Chapter 3. Quantum Optics Part 1
Recommended Article : 【Physics】 Physics Table of Contents
3. Comparison with Other Optics
1. History of Light
⑴ Overview
① Wave Theory: Light is described as a wave.
② Corpuscular Theory: Light is described as particles.
③ The history of light research can be seen as the history of determining whether light is a wave or a particle.
⑵ History up to Modern Times
① Aristotle (BC. 384-322): When we see something in the world, what comes out of our eyes is something that is reflected from objects.
② Hasan Ibn al Haytham (965-1040): Claimed similarities between the anatomy of the eye and the pinhole camera.
③ Francesco Maria Grimaldi (Bologna): Explained diffraction of light as particle theory in 1660.
④ Huygens: Advocated the wave theory of light. Effectively explained reflection and refraction.
○ Treatise on light (1690)
○ Thought light is waves that move through a medium called “aether.”
⑤ Newton: Claimed light consists of particles called corpuscles.
○ Opticks (1704)
⑥ Diffraction Experiment
⑦ Scattering Experiment
⑧ Thomas Young (1773-1829)
○ Double-slit interference experiment (1801-1803)
○ Measurement of light wavelengths
⑨ Augustine Fresnel (1788-1827)
○ Advocated the wave nature of light
○ Developed methodology for diffraction from Huygens’ principles (1818)
⑩ James Clerk Maxwell (1831-1879)
○ Formulated mathematical theories of electricity and magnetism into 4 Maxwell’s equations
○ Presented a theory of electromagnetic wave propagation (1873)
○ Calculated the speed of electromagnetic waves and found it equal to the speed of light
⑪ Heinrich Hertz (1857-1894): Produced and detected electromagnetic waves predicted by Maxwell (1887)
⑶ Photoelectric Effect: Adopted as evidence for the particle nature of light through Einstein’s interpretation.
① Overview
○ Definition: Phenomenon where incident light collides with a metal plate, emitting photoelectrons.
○ Work Function: Minimum energy required for the photoelectric effect, equivalent to ionization energy.
○ Threshold Frequency: Minimum frequency of light for the photoelectric effect. h × threshold frequency = work function.
○ Maximum Kinetic Energy of Photons: Incident light energy - work function
Figure 1. Relationship between voltage, photoelectric current, and light intensity.
② Interaction between Matter and Light
Figure 2. Energy levels and the photoelectric effect.
○ X = a, Y = b, Z = c
○ No photoelectrons are emitted when X and Z are illuminated separately. Photoelectrons are emitted when Y is illuminated.
○ Energy of photon Y is equal to the sum of energies of photons X and Z.
○ No photoelectrons are emitted when X and Z are illuminated simultaneously at point P.
○ Reason: A photon interacting with a single atom can only interact once.
③ Applications
○ Charge-Coupled Devices (CCD)
○ X-ray Photoelectron Spectroscopy (XPS)
① Definition: Phenomenon where all objects with energy emit light.
② Blackbody: An object that absorbs all incident energy and emits all absorbed energy.
③ Number of Wave Modes
○ Based on Steady Waves, assigned according to direction.
○ 1D Steady Waves: Depending on state number n (natural number), various steady waves of different frequencies exist for length L.
○ 3D Steady Waves: Various waves (in this case, light) exist depending on the state vector (l, m, n) of the wave.
○ State vectors can be correlated to orthogonal coordinates: Consider 1/8 octant due to positive integers l, m, n.
○ Number of wave modes: For a distance from origin p and radius p within 1/8 octant lattice points, N*(p),
○ Relationship between mode number (N*) and frequency (ν)
○ The formula does not account for the possibility of two waves with the same state number but opposite phases.
○ Conclusion: For volume V = L^3, with state number per unit volume N = N* / V,
④ Rayleigh-Jeans Law
○ Overview: To analyze blackbody radiation as waves, ultraviolet catastrophe should be observed.
○ Thermodynamics: Average vibrational energy in addition to translational and rotational motion, assigned a degree of freedom of 2.
○ Average radiant energy per unit volume at frequency ν
○ Ultraviolet Catastrophe (UV catastrophe): Blackbody radiates infinitely close light with wavelengths near 0.
○ In reality, light with wavelengths near 0 converges to zero intensity.
⑤ Planck’s Law
○ Max Planck introduced particles and assumed E = hν to successfully explain it in 1900.
○ Energy of a single photon
○ Probability of having n photons with frequency ν: Probability of particles with a specific energy follows Maxwell-Boltzmann distribution).
○ Average energy of the system
○ Average radiant energy per unit volume at frequency ν
Figure 3. Planck’s curve.
○ Total energy per unit volume of the system
○ Photon flux
⑥ Stefan-Boltzmann Law: Energy emitted by a unit area per unit time by a blackbody is proportional to the fourth power of the blackbody’s absolute temperature T(K).
○ Real objects sometimes account for reflectivity ε in the equation
○ σ: Stefan-Boltzmann constant, 8.22 × 10^-11
⑦ Wien’s Displacement Law: Wavelength λmax (µm) at which maximum radiative energy is emitted is inversely proportional to the blackbody’s absolute temperature T(K).
○ α: Wien’s constant, 2.89 × 10^3
⑧ Pauli Exclusion Principle
○ Definition: No two quantum numbers for an electron in the same orbit can be identical.
○ Why Planck’s curve appears as a continuous graph
○ As atoms aggregate, energy levels slightly shift, and energy levels appear continuously.
Figure 4. Splitting of energy levels due to orbital overlap.
Figure 5. Formation of energy bands due to orbital overlap.
⑸ Compton Scattering
① Phenomenon where light is incident on a stationary electron, and photon and electron undergo elastic collision.
② Evidence of the particle nature of light
⑹ Wave Nature of Electrons
① Davisson-Germer Experiment: Demonstrated diffraction when electron beam is incident on a nickel crystal.
② Thomson’s Electron Scattering Experiment (1925)
○ Obtained electron diffraction pattern similar to X-ray diffraction by illuminating electron beam onto metal foil
Figure 6. Thomson’s electron scattering experiment.
Left: X-ray diffraction pattern, Right: Electron scattering pattern
○ Conclusion: Experimentally demonstrated that electrons, conventionally known as particles, can undergo diffraction.
○ Inference: If electrons have wave-like properties, their precise orbits cannot be determined.
2. Nature of Light
⑴ Light is an electromagnetic wave that conveys electromagnetism.
⑵ Invariant Speed of Light Law
⑶ Rest Mass = 0
m0 = 0
⑷ Vector particle with spin 1
⑸ Charge is 0
3. Comparison with Other Optics
⑴ Geometric Optics ⊂ Wave Optics ⊂ Quantum Optics
⑵ Geometric Optics: Considers light as rays
⑶ Wave Optics: Considers light as waves
⑷ Quantum Optics: Considers light as particles. Utilizes Feynman diagrams. Energy of a photon with 500 nm wavelength: E = hf = hc / λ = 3.98 × 10^-19 J
Input : 2020-03-23 23:03
Modified : 2022-09-12 19:42