Lasers and Quanta

Light and matter, the laser, fibres, quantum optics.

What the course covers

A first course in photonics, built in five parts. Atoms hold quantized energy levels, and Einstein’s three processes govern the radiation between them, chained by $A/B = 8\pi h\nu^3/c^3$ . Invert the populations and absorption becomes gain; add a cavity and you have a laser. The same optics explains polarizers, the blue sky, and the fibres carrying this sentence. It closes on quantum light, where $g^{(2)}(0)$ separates a laser from a single photon.

Light and matter

The photon. Light arrives in countable lumps.
Waves that add. Superposition builds and destroys light.
The uncertainty principle. Blur is built into the universe.
Why atoms emit light. Line spectra are atomic fingerprints.
Why lines have width. No spectral line is perfectly sharp.
Light from solids. Levels melt into bands in crystals.
Gain media you can hold. Ruby, Nd:YAG and Ti:sapphire compared.
Einstein’s three processes. Three routes between two levels.
Planck and the black body. Counting light modes broke physics.
Relating A and B. Equilibrium chains emission to absorption.
Rate equations. Bookkeeping for atomic populations.
Saturation of absorption. Bright light turns absorbers transparent.
Beer’s law. Each slice takes the same cut.
From absorption to gain. Flip the populations, flip the sign.
Origin of refractive index. Slow light is really interference.
Light and matter review. From photon to gain in one thread.

Polarization

The dance of the field. What the field vector actually does.
Malus’ law. Cosine squared rules every polarizer.
Polarization by scattering. Why the blue sky is polarized.
Brewster’s angle. One angle deletes a polarization.
Dichroic polarizers. Materials that eat one polarization.
Birefringent crystals. Two speeds of light in one crystal.
Optical activity. Chiral stuff twists the light.
Polarization review. Every way to sort a wobbling field.

The laser

Gifts of stimulated emission. Perfect copies, on demand.
Amplifier into oscillator. Add mirrors, get feedback.
Modes and the gain curve. Only certain colours may compete.
How lasing switches on. From random sparks to one voice.
Equilibrium never lases. Boltzmann forbids inversion at any T.
Pumping schemes. Three ways to cheat Boltzmann.
How bright is light. The sun outshines a laser. Barely.
Laser threshold. The pump level where lasing ignites.
Gain clamping. Why gain freezes at the loss line.
Two kinds of broadening. Homogeneous versus inhomogeneous blur.
Coherence and speckle. Light that keeps its promises.
Directionality and divergence. The cavity carves the beam.
The laser review. Gain, feedback and one bright rule.

Fibre optics

Total internal reflection. Where else could the light go?
The quickest path. All paths vote; the fastest wins.
The evanescent wave. The field that leaks but never leaves.
Anatomy of a fibre. Core, cladding and an acceptance cone.
Waveguide modes. Only self-agreeing angles survive.
Single-mode fibre. Shrink the core till one mode fits.
Why fibres lose light. Hunting photons lost in the glass.
Modal dispersion. Different paths, different arrival times.
Material dispersion. Every pulse contains its own rivals.
Drawing glass into fibre. Ten kilometres of perfection from a rod.
Fibre amplifiers. A laser without mirrors, spliced in line.
Fibre optics review. From perfect mirror to global net.

Quantum light

What a photon is. Not a little wavepacket after all.
Fingerprinting light. Two detectors expose photon statistics.
Thermal and coherent light. The laser is classical after all.
Light beyond classical. Antibunching and squeezed light.
Single-photon sources. Four platforms, no free lunch.
Single-photon detectors. From vacuum tubes to nanowires.
Why quantum light matters. Simulation, secrecy and sharper rulers.
Quantum light review. Three families and their uses.

One lesson in full

Planck and the black body. Counting light modes broke physics.

Warm up an empty box and light fills it, like sound filling an organ pipe. Ask an innocent question: how much light energy is in there? Around 1900, the honest answer broke physics.

The disaster

The light in the box lives as standing waves, and shorter wavelengths fit in ever more ways. Classical physics hands every one of those waves the same thermal pocket money, an energy $kT$ , where $T$ is temperature and $k$ is Boltzmann’s constant. Infinitely many waves, each paid $kT$ : infinite energy in a warm oven. Absurd.

Planck’s fix

Planck’s escape: energy is only sold in whole lumps of size $h\nu$ . A fast-wiggling wave demands a big lump. If the lump costs more than the thermal budget $kT$ , that wave never wakes up. The short waves fall silent and the infinity vanishes.

The formula that worked

Do the bookkeeping and you get the light energy per unit volume, per slice of frequency, written $\rho(\nu)$ . It matches the measured glow of hot things perfectly.

\rho(\nu) = \frac{8\pi h\nu^3}{c^3}\,\frac{1}{e^{h\nu/kT} - 1}

Keep this crowbar

This looks like a formula about ovens. It is not. In the next lesson we will use it to pry open a hidden connection between Einstein’s three processes.

A question to try

A blackbody is heated to a higher temperature. What happens to the radiation it emits at long wavelengths?

It is unchanged, since only the peak moves
It decreases at first and then increases
It increases, as it does at every wavelength
It decreases, because the peak has moved to shorter wavelengths

The answer, and why

The answer: It increases, as it does at every wavelength.

Two things happen at once and only one of them is a shift: the peak moves to shorter wavelengths, and the whole curve rises. Reading Wien displacement as a redistribution rather than an addition is the usual error.

It is unchanged, since only the peak moves. Wien displacement describes where the maximum sits, not what the rest of the curve does. The total emission also rises as the fourth power of temperature.
It decreases at first and then increases. There is no such turnover. Emission at every single wavelength increases monotonically with temperature.
It decreases, because the peak has moved to shorter wavelengths. This is the trap, and it comes from picturing a fixed amount of radiation being shifted around. Planck curves for different temperatures never cross: the hotter one lies above the cooler one everywhere.

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