Unit 4 | Engineering Physics Notes | AKTU Notes

UNIT 4: Fiber Optics and Laser

PART A: FIBER OPTICS

4.1 Principle and Construction of Optical Fiber

An optical fiber is a thin, flexible, transparent thread made of glass or plastic that transmits light from one end to the other using the principle of Total Internal Reflection (TIR).

Principle — Total Internal Reflection:

• When light travels from a denser medium (high refractive index) to a rarer medium (low refractive index), and the angle of incidence exceeds the critical angle, the light is completely reflected back into the denser medium.
• No light escapes — 100% reflection. This is Total Internal Reflection.
• Critical angle: sinC = n₂/n₁ where n₁ = refractive index of core, n₂ = refractive index of cladding, n₁ > n₂.

Construction of Optical Fiber:

• Core: The central part through which light travels. Made of glass or plastic with high refractive index (n₁).
• Cladding: A layer surrounding the core with lower refractive index (n₂). Keeps light inside core by TIR.
• Buffer/Jacket: Outer protective plastic coating. Provides mechanical strength and protection.

4.2 Acceptance Angle and Numerical Aperture

Acceptance Angle (θₐ):

• The maximum angle at which light can enter the fiber and still undergo total internal reflection inside.
• If light enters at an angle greater than θₐ, it escapes through the cladding and is lost.
• The cone defined by the acceptance angle is called the acceptance cone.

Numerical Aperture (NA):

• NA is a measure of the light-gathering ability of the fiber.
• Formula: NA = sinθₐ = √(n₁² − n₂²)
• Higher NA → fiber accepts light from a wider range of angles → more light is collected.
• Typical values: NA = 0.1 to 0.5 for different fibers.

Acceptance Cone:

• The cone of light rays that can enter the fiber and be guided by TIR.
• Half-angle of acceptance cone = acceptance angle θₐ.
• Rays inside the cone → guided. Rays outside the cone → lost through cladding.

4.3 Step Index and Graded Index Fibers

Step Index Fiber:

• The refractive index of the core is uniform throughout and changes abruptly at the core-cladding boundary.
• Like a step function — hence the name.
• Two types: Single mode and multimode step index.
• Light travels in a zigzag path (bouncing off the cladding).
• Problem: Different rays travel different path lengths → they arrive at different times → modal dispersion → signal is spread out.

Graded Index Fiber (GRIN Fiber):

• The refractive index of the core gradually decreases from the center to the edge (highest at center, lowest near cladding).
• Light rays are continuously bent (refracted) toward the axis — they travel in curved sinusoidal paths.
• Advantage: Rays that travel longer paths (near the edge) travel faster (lower refractive index) — so all rays arrive at nearly the same time.
• Result: Much less modal dispersion — better signal quality over longer distances.

Parameter	Step Index Fiber	Graded Index Fiber
Refractive Index	Uniform in core, abrupt change	Gradually decreasing from center
Light Path	Zigzag (bouncing)	Curved (sinusoidal)
Modal Dispersion	High	Low
Bandwidth	Lower	Higher
Cost	Lower	Higher

4.4 Fiber Optic Communication Principle

How fiber optic communication works:

• Step 1 — Transmitter: The electrical signal (voice, data, video) is converted into a light signal using an LED or Laser diode.
• Step 2 — Optical Fiber: The light signal travels through the optical fiber (guided by TIR) over long distances.
• Step 3 — Receiver: At the other end, a photodetector (photodiode) converts the light signal back into an electrical signal.
• Step 4 — Repeaters: For very long distances, repeaters or amplifiers (EDFA — Erbium Doped Fiber Amplifiers) boost the signal at regular intervals.

Advantages over copper cables:

• Much higher bandwidth (more data per second).
• No electromagnetic interference.
• Lighter and thinner.
• More secure (light cannot be tapped easily).
• Very low signal loss over long distances.

4.5 Attenuation in Optical Fiber

Attenuation is the loss of signal power (light intensity) as it travels through the fiber.

Causes of Attenuation:

• Absorption losses: Material absorbs some light (impurities in glass absorb certain wavelengths).
• Scattering losses (Rayleigh scattering): Microscopic variations in the glass cause light to scatter in all directions. Dominant at shorter wavelengths.
• Bending losses: When fiber is bent sharply, some light escapes through the cladding.

Attenuation Coefficient (α):

• α = (10/L) × log₁₀(Pᵢₙ/Pₒᵤₜ) dB/km
• Modern fibers: α ≈ 0.2 dB/km at 1550 nm wavelength (very low loss window).

4.6 Dispersion in Optical Fiber

Dispersion is the spreading of a light pulse as it travels through the fiber, which limits the data rate.

Types of Dispersion:

• Modal Dispersion: Different modes (paths of light) travel at different speeds — arrive at different times. Eliminated in single-mode fiber.
• Material Dispersion: Different wavelengths travel at different speeds in glass (refractive index depends on wavelength).
• Waveguide Dispersion: Depends on the fiber geometry (core size and profile).
• Chromatic Dispersion: Total of material + waveguide dispersion.

4.7 Applications of Optical Fiber

• Telecommunications: Internet cables, telephone networks (submarine cables carry internet across oceans).
• Medical: Endoscopes — fiber bundles carry light and images inside the human body for diagnosis and surgery.
• Sensors: Temperature, pressure, and strain sensors using fiber optic sensing.
• Military: Secure communication, guidance systems.
• Cable TV: High quality video transmission.
• Decorative lighting: Fiber optic lamps and decorations.

PART B: LASER

4.8 Absorption of Radiation

When light (photon) of appropriate energy falls on an atom in the ground state (lowest energy level), the atom absorbs the photon and jumps to a higher energy level (excited state).

• Energy of absorbed photon: E = hν = E₂ − E₁
• Where E₁ = ground state energy, E₂ = excited state energy, ν = frequency of photon.
• The atom stays in the excited state for a very short time (~10⁻⁸ seconds) before releasing the energy.

4.9 Spontaneous and Stimulated Emission of Radiation

Spontaneous Emission:

• An atom in the excited state spontaneously (on its own, without any external trigger) falls back to the ground state and emits a photon.
• The emitted photon has random direction and random phase.
• This is ordinary light emission — like from a light bulb or LED.
• Rate of spontaneous emission is random and cannot be controlled.

Stimulated Emission:

• An incoming photon of the right energy triggers an excited atom to emit a photon and fall to the ground state.
• The emitted photon is an exact copy of the triggering photon — same frequency, same direction, same phase.
• This produces coherent light.
• One photon triggers emission of another → now we have 2 identical photons → these trigger 2 more → 4 photons → chain reaction → amplification of light.
• This is the basis of LASER action.

Property	Spontaneous Emission	Stimulated Emission
Trigger	No external trigger	Triggered by incoming photon
Direction	Random	Same as triggering photon
Phase	Random	Same as triggering photon
Coherence	Incoherent	Coherent
Example	Ordinary light bulb	LASER

4.10 Population Inversion

Normally, most atoms are in the ground state and very few are in the excited state. For stimulated emission to dominate over absorption, we need more atoms in the excited state than in the ground state.

Population Inversion = condition where the number of atoms in the excited state is greater than in the ground state.

• This is a non-equilibrium condition — not naturally found.
• It is achieved by pumping — supplying energy (optical, electrical, or chemical) to push atoms to higher energy levels.
• A metastable state (a long-lived excited state, lifetime ~10⁻³ s instead of 10⁻⁸ s) is needed so atoms can accumulate there.
• Once population inversion is achieved → stimulated emission dominates → laser action occurs.

4.11 Einstein's Coefficients

Einstein related the three processes (absorption, spontaneous emission, stimulated emission) using coefficients.

• A₂₁ = Einstein's A coefficient = probability of spontaneous emission per unit time.
• B₁₂ = Einstein's B coefficient for absorption = probability of absorption per unit time per unit radiation density.
• B₂₁ = Einstein's B coefficient for stimulated emission = probability of stimulated emission per unit time per unit radiation density.

Important Relations:

• B₁₂ = B₂₁ (absorption and stimulated emission have equal probability).
• A₂₁/B₂₁ = 8πhν³/c³ (ratio of spontaneous to stimulated emission probability).
• At high frequencies, spontaneous emission dominates (hard to make X-ray lasers).
• At low frequencies (radio waves), stimulated emission dominates.

4.12 Principles of Laser Action

LASER = Light Amplification by Stimulated Emission of Radiation

Three essential requirements for a laser:

• 1. Active Medium: The material (solid, liquid, gas) that amplifies light through stimulated emission. Examples: Ruby crystal, Helium-Neon gas, CO₂ gas, semiconductor.
• 2. Pumping Mechanism: External energy source to achieve population inversion. Types: optical pumping (flash lamp), electrical discharge, chemical reaction.
• 3. Optical Resonator (Cavity): Two mirrors at both ends of the active medium. One mirror is 100% reflective, the other is partially transparent (~95%). Light bounces back and forth, getting amplified with each pass. The partially transparent mirror lets some light out — this is the laser beam.

Properties of Laser Light:

• Monochromaticity: Very pure single wavelength (color).
• Coherence: All photons have same phase and frequency.
• Directionality: Very narrow beam — does not spread out like ordinary light.
• High Intensity: Extremely concentrated energy.

4.13 Solid State Laser — Ruby Laser

The Ruby laser was the first laser ever built (by Theodore Maiman in 1960).

Active Medium: Ruby crystal (Al₂O₃ with 0.05% Cr³⁺ chromium ions — the chromium ions are responsible for laser action).

Pumping: Optical pumping using a helical xenon flash lamp wrapped around the ruby rod.

Construction:

• Ruby rod (cylindrical) with both ends polished flat and parallel.
• One end is fully silvered (100% reflective), other end is partially silvered.
• Flash lamp surrounds the ruby rod.

Working (Three-Level System):

• Flash lamp pumps Cr³⁺ ions from ground state (E₁) to excited band (E₃).
• Ions quickly fall to metastable state (E₂) — non-radiatively (releasing heat, not light).
• Ions accumulate in E₂ → Population inversion achieved between E₂ and E₁.
• Stimulated emission occurs from E₂ to E₁ → Red laser light at λ = 694.3 nm.

Limitations:

• Operates in pulses (not continuous) — the flash lamp pumps in pulses.
• Low efficiency (~0.1%).
• Requires cooling.

4.14 Gas Laser — He-Ne Laser

The He-Ne laser is the most common laser used in laboratories.

Active Medium: Mixture of Helium and Neon gases in ratio 10:1 (He:Ne). Neon is the lasing medium; Helium is the helper.

Pumping: Electrical discharge (high voltage applied to gas tube).

Construction:

• A glass tube filled with He-Ne gas mixture.
• Two electrodes for electrical discharge.
• Two mirrors at both ends (optical resonator).

Working (Four-Level System):

• Electrical discharge excites He atoms to excited states F₂ and F₃.
• He atoms collide with Ne atoms and transfer their energy (resonance transfer) — He returns to ground state, Ne atoms get excited to levels E₆ and E₄.
• Population inversion achieved in Ne between E₆ and E₃.
• Stimulated emission from E₆ to E₃ → Red laser light at λ = 632.8 nm (most common).
• Also produces infrared wavelengths at 1150 nm and 3390 nm.

Advantages:

• Continuous wave (CW) output — not pulsed.
• Very stable, highly coherent beam.
• Low cost, long life.

4.15 Applications of Laser

• Medical: Laser surgery (eye surgery — LASIK), tumor removal, dental procedures, kidney stone breaking (lithotripsy).
• Communication: Fiber optic communication uses laser as light source.
• Industry: Laser cutting, welding, drilling of hard materials.
• Defense: Laser range finders, target designators, laser weapons research.
• Scientific Research: Spectroscopy, holography, nuclear fusion research.
• Consumer: Barcode scanners, laser printers, CD/DVD players, laser pointers.
• Measurement: Laser interferometry for precision measurements, LIDAR for distance measurement and mapping.