Optics Lecture 4. Quantum Optics Part 2

Recommended Article : 【Physics】 Physics Table of Contents

1. Interference

2. Scattering

3. Absorption

4. Relaxation

5. Generation

a. Quantum Optics Part 1

1. Interference

⑴ Overview

① Phenomenon in which photons are generally generated in a medium larger than the wavelength of light

② Constructive interference and destructive interference

⑵ Type 1. Straightness of Light : A type of interference of light

⑶ Type 2. Reflection of Light : A type of interference of light

⑷ Type 3. Refraction of Light : A type of interference of light

⑸ Type 4. Polarization of Light

① Overview

○ Definition : Light vibrating in only one direction

○ (Note) Natural light vibrates in all directions perpendicular to the direction of propagation

○ Polarization is important evidence that light exhibits wave characteristics

② Application 1. Malus’s Law

③ Application 2. Brewster’s Law

○ Definition : Reflection and refraction rays become polarized when the angle between them is 90 degrees

④ Application 3. Birefringence

○ Two refracted lights are called ordinary ray and extraordinary ray, respectively

○ Ordinary ray and extraordinary ray are both polarized light

⑤ Application 4. Scattering

○ Scattered light consists of two types of polarized light vibrating perpendicular to each other

2. Scattering

⑴ Overview

① Definition : Phenomenon where light deviates from its original direction and moves in a different direction when passing through a medium with particles smaller than the wavelength of light

② Can be understood as the collision between photons and particles

③ Scattered light consists of two types of polarized light vibrating perpendicular to each other

⑵ Type 1. Elastic Scattering

① Definition : Scattering without energy change. Incident wavelength and scattered wavelength are the same

② 1-1. Rayleigh Scattering : When the wavelength is much larger than the particle size

○ Intensity of scattering, wavelength λ for Rayleigh scattering can be expressed as follows

○ Short atmospheric layer (daytime)

○ Red, yellow, and orange light are mostly transmitted

○ Violet light scatters a lot and does not reach the eyes

○ Blue light scatters moderately, giving the sky a blue color

○ Thick atmospheric layer (evening)

○ Must pass through about 40 times the thickness of the daytime atmosphere

○ Only long-wavelength red, orange, and yellow light reaches the eyes

○ Blue and violet light scatter a lot and do not reach the eyes

○ Outer space : Appears black because there are no gas particles to scatter

○ Sunset on Mars : Blue sunset is observed due to the sparse gas

Figure 1. Sunset on Mars1]

③ 1-2. Mie Scattering

○ Scattering when the wavelength is similar to the particle size

○ Scatters all wavelength ranges, resulting in white scattered light

④ 1-3. Tyndall Phenomenon

○ Definition : The path of incident light is visible due to the particles in the colloid

○ Similar to Rayleigh scattering but different conditions and paths of scattering

○ There is currently no mathematical formula that precisely describes Tyndall phenomenon

⑶ Type 2. Inelastic Scattering

① Definition : Scattering with energy change. Incident wavelength and scattered wavelength are different

② 2-1. Raman Scattering

○ Represented by Raman shift depending on how much it shifted from Rayleigh scattering

○ Cannot directly measure vibrational energy, similar to infrared spectroscopy

○ Raman shift is measured in cm-1

○ Quantum mechanical understanding : Energy difference before and after Raman scattering corresponds to molecular vibrational energy

○ Called Stokes scattering when the material gains energy

○ Called anti-Stokes scattering when the material loses energy

○ Since there are more molecules in the ground state than in the vibrational excited state, Stokes scattering is more common than anti-Stokes scattering

○ Application : Raman Spectroscopy

③ 2-2. Compton Scattering(Compton scattering)

④ 2-3. Bragg Scattering

⑤ 2-4. Inelastic X-ray Scattering

3. Absorption

⑴ Definition : The phenomenon in which light is absorbed and disappears in a material

⑵ Type 1. Absorption according to the type of material : Spectroscopy

⑶ Type 2. Absorption according to the concentration of the material : Lambert-Beer’s Law

① I : Intensity of light

② d : Length of the path that light penetrates

③ a : Absorption coefficient depending on the medium

④ T : Transmittance

⑤ A : Absorbance (unit : OD(optical density))

⑥ c : Molar concentration

⑦ ε : Molar absorptivity coefficient

⑷ Color

① Definition : The characteristic of selectively absorbing visible light by a substance, resulting in different visual perceptions

② Color Optics

4. Relaxation

⑴ Definition: The conversion of light energy into other forms of energy.

⑵ Type 1. Photothermal Effect:

① Definition: The absorbed energy is emitted as heat energy.

○ Molecules in an electric field of electromagnetic waves undergo polarization, rotation, vibration, and friction, generating heat (temperature increase).

② Used for food heating in the range of 13.56 to 24.125 GHz.

○ Mainly 2.45 GHz is used.

○ Depending on the wavelength used, it can be categorized as microwave heating and radiofrequency heating.

③ Heat energy generated per unit volume of genome.

○ f : Frequency (Hz)

○ E : Electric field magnitude

○ ε” = ε tan δ, tan δ : Probably the loss coefficient (could be something else)

④ Applications: Heating of food, enhancement of seed germination rate, drying, pest eradication.

⑶ Type 2. Fluorescence:

① Definition: Absorbed energy is emitted as light energy.

② Resonance Fluorescence: The emission of radiation with the same frequency as the absorbed radiation.

③ FRAP and FLIP experiments:

○ FRAP experiment: Used to evaluate the recovery of bleached fluorescent membrane proteins.

○ FLIP experiment: Used to evaluate the mobility of fluorescent membrane proteins.

⑷ Type 3. Photoelectric Effect:

① Definition: Light energy releases photoelectrons.

② Principle of X-ray Photoelectron Spectroscopy (XPS).

5. Generation

⑴ Black Body Radiation:

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 modes of vibration:

○ Based on Standing Wave at nodes.

○ 1D Standing Wave: With a length L, different normal modes of vibration exist depending on the natural number n.

○ 3D Standing Wave: Different waves (light) exist according to the state vector (l, m, n) of the wave modes.

○ Number of modes: If there are N*(p) grid points within 1/8 of a sphere with radius p from the origin,

○ Relationship between the number of modes (N*) and frequency (ν).

○ The formula does not consider two waves with the same state number but opposite phases.

○ Conclusion: Volume V = L3, Number of modes N = N* / V.

⑴ Rayleigh-Jeans Law:

○ Overview: For the analysis of black body radiation, UV catastrophe should be observed.

○ Average vibrational energy per unit volume for a given frequency ν.

○ UV Catastrophe: Black bodies radiate infinite energy for wavelengths approaching zero.

○ In reality, near-zero wavelength light converges to zero intensity.

⑤ Planck’s Law:

○ Max Planck introduced quantization, successfully explaining the energy of a single photon.

○ Energy of a single photon.

○ Probability of having n photons with frequency ν.

○ Average energy of the system.

○ Average radiated energy per unit volume at frequency ν.

○ Planck’s curve: Distribution of emitted energy according to wavelength, dependent solely on temperature.

Figure 2: Planck’s curve.

⑥ Stefan-Boltzmann Law: The energy radiated per unit area per unit time by a black body is proportional to the fourth power of the body’s absolute temperature T(K).

○ For real objects, the formula is sometimes multiplied by the reflectivity ε.

○ Here, σ : Stefan-Boltzmann constant, 8.22 × 10^-11.

⑦ Wien’s Displacement Law: The wavelength λmax (μm) at which maximum radiant energy is emitted is inversely proportional to the absolute temperature T(K) of the black body.