Laser &
Fibre Optics
Interactive Study Guide · Animated Diagrams · Deep Explanations
Chapter 01
Laser Physics
① Spontaneous Emission
An atom has electrons that can exist in different energy levels. When an electron is in a higher (excited) energy state E₂ and no external trigger is needed, it randomly falls back to the lower ground state E₁.
While falling, it releases energy in the form of a photon. The energy of the photon equals exactly the difference between the two levels:
The key word is spontaneous — it happens on its own, at a random time and in a random direction. Photons emitted this way are incoherent (different phases, different directions). This is what happens in a normal light bulb or LED.
② Stimulated Emission
Now imagine an excited atom (electron in E₂) is hit by an incoming photon whose energy exactly matches E₂ − E₁.
This incoming photon stimulates the electron to drop down, releasing a second photon. The magic is that the emitted photon is identical to the incoming photon in: phase, frequency, direction, and polarization.
So one photon enters → two coherent photons leave. This is the fundamental mechanism of laser amplification — Light Amplification by Stimulated Emission of Radiation.
③ Population Inversion
In thermal equilibrium, most atoms are in the ground state (low energy). If a photon travels through, it's more likely to be absorbed than to cause stimulated emission. So no amplification happens!
For a laser to work, we need the opposite situation: more atoms in the excited state than in the ground state. This abnormal condition is called Population Inversion.
We achieve this by pumping energy into the medium (using light, electricity, or chemical reactions) to keep pushing atoms to higher levels faster than they fall back.
④ Metastable State
Atoms normally stay excited for only ~10⁻⁸ seconds before spontaneously emitting. But for population inversion, we need atoms to stay excited longer.
A metastable state is a special energy level where atoms remain for a relatively long time (~10⁻³ seconds — a million times longer!). Atoms are pumped to a higher short-lived level, quickly drop to the metastable state, and accumulate there.
This is what makes population inversion possible. The metastable state acts like a "waiting room" — atoms collect there until a photon stimulates them all to emit together.
⑤ Resonant Cavity (Optical Resonator)
A single pass of light through the gain medium isn't enough amplification. The resonant cavity solves this by bouncing light back and forth, amplifying it with each pass.
It consists of two mirrors: one fully reflective (100%) and one partially reflective (~95%). The partially reflective mirror lets a small fraction of the light out — this is the actual laser beam!
The cavity also acts as a frequency selector. Only wavelengths where an integer number of half-waves fit between the mirrors experience constructive interference and get amplified — others cancel out. This gives the laser its extremely narrow frequency.
⑥ Helium-Neon (He-Ne) Laser
The He-Ne laser is a classic gas laser that produces a bright red beam at 632.8 nm. It uses a mixture of He and Ne gases in a glass tube.
How it works (step-by-step):
1. An electrical discharge (high voltage) excites Helium atoms to metastable states (E₁* and E₂*).
2. Excited He atoms collide with Neon atoms and transfer their energy — this is called resonant energy transfer because He and Ne have nearly identical energy levels.
3. Neon atoms reach their metastable upper lasing levels and population inversion is achieved in Neon.
4. Stimulated emission occurs in Neon, producing the 632.8 nm laser light.
5. The resonant cavity amplifies this into a coherent beam.
⑦ LIDAR (Light Detection and Ranging)
LIDAR is the laser equivalent of RADAR. Instead of radio waves, it uses laser pulses to measure distances and create 3D maps of environments with incredible precision.
Working Principle:
A laser sends out a short pulse. The pulse hits an object and some light bounces back to a detector. By measuring the time of flight (time taken for the pulse to return), we calculate the exact distance:
By scanning millions of pulses in all directions, LIDAR builds a detailed 3D point cloud of the environment. Used in: autonomous cars, aircraft mapping, archaeology, meteorology (measuring cloud height), and even Mars rovers!
Chapter 02
Fibre Optics
① Total Internal Reflection (TIR)
When light travels from a denser medium (high refractive index n₁) to a rarer medium (low n₂), it bends away from the normal (Snell's Law). As the angle of incidence increases, the refracted ray bends more and more.
At a specific angle called the critical angle, the refracted ray travels along the interface (90° to normal). Beyond this angle — all light is reflected back into the denser medium. No light escapes. This is Total Internal Reflection.
Optical fibres exploit TIR to trap light inside the glass core and guide it over long distances.
② Critical Angle
The critical angle (θ_c) is the minimum angle of incidence (measured from the normal, inside the denser medium) at which Total Internal Reflection occurs.
Derived from Snell's Law: n₁·sin(θ₁) = n₂·sin(θ₂). At the critical angle, θ₂ = 90°, so sin(90°) = 1:
For glass (n₁ = 1.5) and air (n₂ = 1.0): θ_c = sin⁻¹(1/1.5) ≈ 41.8°
For a fibre core (n₁ = 1.48) and cladding (n₂ = 1.46): θ_c ≈ 80.6°
③ Acceptance Angle
Not all light entering a fibre will undergo TIR — only light entering within a cone of acceptance will be guided. The acceptance angle (θ_a) is the maximum angle to the fibre axis at which light can enter and still undergo TIR inside.
Light entering at an angle greater than θ_a will hit the core-cladding boundary at too shallow an angle and escape — it won't be guided.
④ Numerical Aperture (NA) — Full Derivation
The Numerical Aperture (NA) is the most important parameter of an optical fibre — it measures the fibre's ability to collect and guide light. It equals sin of the acceptance angle.
Step-by-step derivation for Step Index Fibre:
At the fibre entrance (in medium n₀), Snell's Law gives:
n₀ · sin(θ_a) = n₁ · sin(θ_r) …(1)
Inside the core, at the core-cladding boundary, for TIR we need the angle to be ≥ critical angle:
The ray hits the boundary at angle φ = (90° − θ_r)
For TIR: φ ≥ θ_c → (90° − θ_r) ≥ θ_c → θ_r ≤ (90° − θ_c)
At the limiting case (maximum acceptance): φ = θ_c
So: n₁ · sin(θ_c) = n₂ …(2) (from critical angle definition)
From (2): sin(θ_c) = n₂/n₁ → cos(θ_c) = √(1 − n₂²/n₁²)
At maximum acceptance: θ_r = 90° − θ_c
So: sin(θ_r) = sin(90° − θ_c) = cos(θ_c) = √(1 − n₂²/n₁²) = √(n₁² − n₂²)/n₁
Substituting back into (1):
n₀ · sin(θ_a) = n₁ · √(n₁² − n₂²)/n₁ = √(n₁² − n₂²)
Physical meaning: Higher NA → larger acceptance cone → easier to couple light → but more dispersion. Typical single-mode fibre: NA ≈ 0.1 to 0.2. Multimode: NA ≈ 0.2 to 0.5.
⑤ Step Index vs Graded Index Fibre
Optical fibres differ in how the refractive index varies across the cross-section of the core:
| Parameter | Step Index (Multimode) | Graded Index (Multimode) | Step Index (Single Mode) |
|---|---|---|---|
| RI Profile | Uniform core, sharp boundary | Gradually decreasing from axis | Uniform but very narrow core |
| Ray Path | Zigzag (bounces sharply) | Sinusoidal (curves smoothly) | Straight (only one mode) |
| Core Diameter | 50–200 μm | 50–100 μm | 8–10 μm |
| Bandwidth | Low (~20 MHz·km) | Medium (~500 MHz·km) | Very High (>10 GHz·km) |
| Modal Dispersion | High (different paths = diff. times) | Low (speed compensates path) | Zero (single mode) |
| Attenuation | High | Medium | Low |
| Cost | Cheapest | Medium | Most expensive |
| Applications | Short distance LAN | Campus networks | Long-haul telecom, internet backbone |
| NA | High (0.3–0.5) | Lower, varies with radius | Low (0.1–0.2) |
⑥ Attenuation in Optical Fibres
As light travels through an optical fibre, its power decreases with distance. This loss is called attenuation. It's measured in decibels per kilometre (dB/km).
Main causes of attenuation:
🔵 Rayleigh Scattering — Light scatters off microscopic density fluctuations in the glass. Dominant at short wavelengths. Follows λ⁻⁴ law — shorter λ = more scattering.
🔴 Absorption — Glass absorbs some photons due to impurities (OH⁻ ions, metal ions) or intrinsic glass absorption. Pure silica has very low absorption.
🟡 Micro/Macro-bending losses — Any bend in the fibre changes the angle of incidence at the core-cladding boundary. If the angle drops below critical angle, light escapes.
📡 The minimum attenuation window for silica fibre is at 1550 nm (~0.2 dB/km) — which is why all modern long-haul internet uses 1550 nm wavelength!