LASERS and OPTICAL FIBERS Notes

LASERS & OPTICAL FIBERS

Laser History

• 1917: Einstein - Stimulated absorption and emission of light.
• 1954: Charles Townes and Schawlow - Maser, prediction of the optical laser.
• 1960: Theodore Maiman - First demonstration of a laser: Ruby laser.

Introduction to Lasers

• LASER stands for Light Amplification by Stimulated Emission of Radiation.
• Laser light differs from conventional light.
• Applications include:
  • Cutting, drilling, and welding metals (Industrial processing).
  • Surgery (Medical).
  • Light shows.
  • Security and Defense.
  • Barcode readers.
  • Color printers.

Characteristics of Laser Light

• Ordinary Light vs. Laser.
• Unique characteristics of Lasers:
  • Monochromaticity.
  • Coherence.
  • Directionality.
  • High Intensity.
• Other properties:
  • Pulsed or continuous operation.
  • Tunable operation.

Monochromaticity

• Laser beam is more strictly monochromatic (single frequency) than conventional sources.
• Laser beam has a narrow bandwidth, unlike ordinary light which spreads over a wide range of frequencies.
• Obtaining absolute monochromaticity is difficult, but lasers achieve a high degree of monochromaticity with a very small bandwidth.

Coherence

• Ordinary light (e.g., incandescent bulb) produces incoherent light.
• Incoherent light waves move randomly with no common phase relationship.
• Laser light waves are in the same phase and of the same frequency.
• Laser light is highly coherent.
• Two independent concepts of coherence:
  • Temporal coherence.
  • Spatial coherence.

Directionality

• Laser beam is highly directional; emits light in one direction.
• Can travel long distances without divergence.
• Directionality is expressed in terms of divergence (angular spread).
• Conventional light sources (e.g., torchlight) emit light in all directions.

Intensity

• Laser beam is narrow, concentrating energy into a small region.
• Number of photons emitted contributes to increased intensity.
• Intensity of conventional light decreases rapidly with distance.
• Power range of laser: $10^3$W for a CW Laser and $10^9$W for a pulsed laser.

Principle of Laser

• Consider an atom with two energy levels, $E<em>1$ and $E</em>2$.
• When exposed to radiation (photons with energy $h u$), three processes can occur:
  • Absorption.
  • Spontaneous emission.
  • Stimulated emission.

Absorption

• Atom in the ground state $E<em>1$ absorbs a photon of energy $h u$ and transitions to the higher energy state $E</em>2$.

Spontaneous Emission

• Atoms in the excited state remain for a short time ($10^{-8}$ seconds), known as the lifetime of the excited state.
• Spontaneous emission: atom returns from the excited state to the ground state by itself after its lifetime, emitting a photon.
• Photons emitted are in different directions, different wavelengths, and are out of phase (incoherent).
• Example: Light from an electric bulb.
• Rate of spontaneous emission is directly proportional to the population of energy level $E_2$.

Stimulated Emission

• A photon with energy $h<br /> u<em>{12} (= E</em>2 - E<em>1)$ impinges on an atom in the excited state, stimulating it to transition to the ground state and emit a photon of energy $h u</em>{12}$.
• Emitted photon is in phase with the incident photon.
• The two photons travel in the same direction, possess same energy and frequency (coherent).

Population Inversion

• Energy state of an atom results from individual electron energy levels.

• At thermal equilibrium, the number of atoms $N<em>1$ in the lower energy state $E</em>1$ relates to the number of atoms $N_2$ in the higher energy state, given by the Boltzmann relation:

  • $\frac{N<em>2}{N</em>1} = e^{-\frac{E<em>2 - E</em>1}{K<em>B T}} = e^{-\frac{h\nu}{K</em>B T}}$, where $N<em>1$ and $N</em>2$ are populations of energy levels $E<em>1$ and $E</em>2$, respectively, $K_B$ is Boltzmann's constant.

• To produce a laser beam, stimulated emission is required.

• Stimulated emission occurs only if the number of atoms in the higher energy level is greater than the number of atoms in the lower energy level ($N<em>2 > N</em>1$).

• Population Inversion Condition:

  • Normal Condition: $N<em>1 > N</em>2$
  • Population Inversion Condition: $N<em>2 > N</em>1$

Einstein Coefficients and Relations

• Distribution of atoms in the two energy levels changes by absorption or emission of radiation.
• Einstein introduced three empirical coefficients to quantify the change of population of the two levels.

Absorption of Radiation

• Process: $A + h\nu \rightarrow A^*$ (excited state)
• Rate of absorption $= B<em>{12}U</em>{\nu}N_1$, where
  • $N_1$ = Number of atoms in the ground state.
  • $U_{\nu}$ = Energy density of the incident radiation.
  • $B_{12}$ = Einstein coefficient of absorption.
• $\frac{\partial N<em>2}{\partial t} = B</em>{12}U<em>{\nu}N</em>1$

Spontaneous Emission

• Process: $A^* \rightarrow A + h\nu$
• Rate of spontaneous emission $= A<em>{21}N</em>2$, where
  • $N_2$ = Number of atoms in the excited state.
  • $A_{21}$ = Einstein coefficient of spontaneous emission.
• $\frac{\partial N<em>2}{\partial t} = A</em>{21}N_2$

Stimulated Emission

• Process: $A^* + h\nu \rightarrow A + 2h\nu$
• Rate of stimulated emission $= B<em>{21}U</em>{\nu}N_2$
  • $N_2$ = Number of atoms in the higher energy state.
  • $U_{\nu}$ = Energy density of the incident radiation.
  • $B_{21}$ = Einstein coefficient of induced (stimulated) emission.
• $\frac{\partial N<em>2}{\partial t} = B</em>{21}U<em>{\nu}N</em>2$

Metastable States

• Normally, an excited atom drops to the ground state in $10^{-8}$ seconds (life time).
• Key to laser action: Atoms remain in energy levels longer, with life times of $10^{-3}$ seconds or more.
• These long-lived excited states are called metastable states.

Energy Density of Incident Radiation in Terms of Einstein Coefficients

• At thermal equilibrium, Rate of absorption = Rate of spontaneous emission + Rate of stimulated emission
• $B<em>{12}U</em>{\nu}N<em>1 = A</em>{21}N<em>2 + B</em>{21}U<em>{\nu}N</em>2$
• $U<em>{\nu} = \frac{A</em>{21}N<em>2}{B</em>{12}N<em>1 - B</em>{21}N<em>2} = \frac{A</em>{21}}{B<em>{21}} \frac{1}{\frac{B</em>{12}N<em>1}{B</em>{21}N_2} - 1}$
• The populations of energy levels $E<em>1$ and $E</em>2$ are given by the Boltzmann factor: $\frac{N<em>2}{N</em>1} = e^{-\frac{h\nu}{kT}}$, thus $\frac{N<em>1}{N</em>2} = e^{\frac{h\nu}{kT}}$
  • The energy density can be expressed using Planck's law:
    • $U_{\nu} = \frac{8\pi h\nu^3}{c^3} \frac{1}{e^{\frac{h\nu}{kT}} - 1}$
• Comparing equations, we find
  • $\frac{A<em>{21}}{B</em>{21}} = \frac{8\pi h\nu^3}{c^3}$
  • $\frac{B<em>{12}}{B</em>{21}} = 1 \implies B<em>{12} = B</em>{21}$
  • Implies, probability of induced absorption($B<em>{12}$) is equal to the probability of stimulated emission($B</em>{21}$). The subscripts can be dropped from above identity.

Conditions for Light Amplification

• At thermal equilibrium, ratio of stimulated to spontaneous emission:
  • $\frac{\text{Stimulated Emission}}{\text{Spontaneous Emission}} = \frac{B<em>{21}U</em>{\nu}N<em>2}{A</em>{21}N<em>2} = \frac{B</em>{21}U<em>{\nu}}{A</em>{21}}$
• To enhance the number of stimulated transitions, the radiation density $U_{\nu}$ should be high.
• Ratio of stimulated emission to absorption:
  • $\frac{\text{Stimulated Emission}}{\text{Absorption}} = \frac{B<em>{21}U</em>{\nu}N<em>2}{B</em>{12}U<em>{\nu}N</em>1} = \frac{B<em>{21}N</em>2}{B<em>{12}N</em>1}$
• If $B<em>{12} = B</em>{21}$, the stimulated emission is greater than the absorption only when $N<em>2 > N</em>1$.
• The condition $N<em>2 > N</em>1$ is known as "population inversion".

Requisites of a Laser System

• Three essential components:
  • An active medium: to support population inversion.
  • Pumping mechanism: to excite atoms to higher energy levels.
  • An optical cavity or optical resonator: to generate intense and coherent laser beams.

Active Medium

• The material medium (solid, liquid, or gas) where laser action occurs.
• Only a few atoms contribute to stimulated emission (active centers).
• Remaining medium supports the active centers.
• In thermal equilibrium, populations of energy levels $E<em>2$ and $E</em>1$ are given by Boltzmann factor:
  • $N<em>2 = N</em>1e^{-\frac{(E<em>2 - E</em>1)}{kT}}$. The negative component indicates that $N<em>2 << N</em>1$ under thermal equilibrium.

Resonant Cavity

• Diagram including:
  • 100% reflecting mirror.
  • Partially reflecting mirror.
  • Active medium.
  • Pump.
  • Laser beam.

Pumping Mechanism

• Energy is supplied to achieve population inversion.
• Pumping: process of supplying energy to transfer the medium into population inversion.
• Important pumping mechanisms:
  • Optical pumping: Suitable light source for excitation. Used in solid-state lasers (e.g., Ruby laser).
  • Electric discharge: Electric field causes ionization, raising to excited state. Used in gas lasers (e.g., Ar+ laser).
  • Inelastic atom-atom collision: Combination of two gases (A and B). Electric discharge excites A atoms, which collide with B atoms, causing B to transition to excited state. Used in gas lasers (e.g., He-Ne laser).
  • Direct conversion: Electrical energy directly converted into light energy. Used in semiconductor lasers.

Three-Level System

• Energy levels: $E<em>0$, $E</em>1$, $E_2$.
• Pumping: $h\nu = (E<em>2 - E</em>0)$.
• Non-radiative transition from $E<em>2$ to metastable state $E</em>1$.
• Lasing transition: $h\nu = (E<em>1 - E</em>0)$.

Four-Level System

• Energy levels: $E<em>0$, $E</em>1$, $E<em>2$, $E</em>3$.
• Pumping: $h\nu = (E<em>3 - E</em>0)$
• Rapid decay (non-radiative) from pumping level $E<em>3$ to metastable state $E</em>2$.
• Laser emission: $h\nu = (E<em>2 - E</em>1)$.
• Non-radiative transition from lower energy level $E<em>1$ to ground level $E</em>0$.

Ruby Laser

• Based on three-level concept, solid-state laser device.
• Essential components:
  • Active working material: Ruby crystal rod.
  • Resonant cavity: Two optically plane mirrors (one fully reflecting, one partially reflecting).
  • Exciting system: Helical-shaped xenon flash tube.
• Ruby: Single crystal of $Al<em>2O</em>3$ with ~0.05% chromium atoms. $Cr^{3+}$ ions are active centers.

Construction

• Three-level solid-state laser constructed by T. Maiman.
• Ruby $(Al<em>2O</em>3 + Cr<em>2O</em>3)$: Aluminum oxide crystal doped with 0.05% chromium oxide. Active medium is $Cr^{3+}$ ions.
• Cylindrical shape, pink color, 4cm length, 5mm diameter.
• Ends polished, flat, parallel, and coated with silver (one fully reflecting, one partially reflecting).
• Ruby rod placed in glass tube with provision for cooling.
• Xenon flash lamp spirally wound around the tube, connected to a power supply.
• Emitted wavelength: 6943$\text{A}^0$

Pumping Mechanism

• Chromium ions are responsible for stimulated emission; Aluminum and Oxygen ions are passive.
• $Cr^{3+}$ ions absorb two wavelengths (5500 $\text{A}^0$ and 4000 $\text{A}^0$) and get excited to $E_3$ energy levels.
• $Cr^{3+}$ undergo non-radiative transitions to level $E_2$.
• Metastable state $E<em>2$ has a lifetime approximately 1000 times more than $E</em>3$ levels.

Drawbacks

• Requires high pumping power.
• Low efficiency.
• Pulsed laser.

Uses

• Optical photography.
• Removal of skin melanin.
• Recording of holograms.

Carbon Dioxide Laser ($CO_2$)

• First molecular laser; four-level laser.
• Recall rotational and vibrational spectrum of $CO_2$ molecules.
• Three atoms in a ring over a straight line, O-C-O.

Construction

• Radiation power (output power) depends on tube diameter.
• Output power can be raised by increasing tube diameter.

Pumping Mechanism and Lasing Action

• Generally uses two additional gases, $N_2$ and He.
• When current passes through the gas mixture, $N_2$ molecules go into an excited state.
• $N<em>2$ molecules undergo inelastic collisions with $CO</em>2$ molecules and transfer energy.
• Population of $CO_2$ molecules builds up in higher energy levels.
• Random photons are emitted spontaneously.
• Spontaneous photons travel through the mixture and cause stimulated emission.
• Laser transition between $E<em>5 \rightarrow E</em>4$ levels produces a wavelength of 10.6 $\,\mu m$ and $E<em>5 \rightarrow E</em>3$ levels produces a wavelength of 9.6 $\,\mu m$.

Important Features

• Uses four-level system.
• Active centers are $CO_2$ molecules.
• Electrical discharge pumping.
• High efficiency and high output power (kilowatts).

Nd:YAG Laser

• Optically pumped solid-state laser.
• Produces very high power emission.
• YAG: yttrium aluminum garnet ($Y<em>3Al</em>5O_{12}$); Nd: neodymium.
• YAG is doped with neodymium ($Nd^{3+}$) resulting in a crystalline structure.
• Four-level laser, more gain, low threshold pump power.

Resonating Cavity

• Rod of 5-10 cm length and 6-9 mm diameter.
• Neodymium (active center) mixed in yttrium-aluminum garnet (active medium).
• Ends polished, optically flat and parallel.
• One end 100% reflecting mirror, other end partially reflecting mirror.

Pumping Mechanism

• Optical pumping.
• Population inversion achieved by xenon or krypton flash tube.
• Nd:YAG absorbs mostly in the bands between 730-760 nm and 790-820 nm.
• Krypton flash lamps more efficient due to high output at these bands.
• $Nd^{3+}$ ions transported into excited energy levels.
• Laser transition from metastable state to ground state emits a laser beam in the infrared region, wavelength 1064 nm.
• Rod and flash tube kept inside reflecting elliptical cavity.

Working Method

• Laser action achieved by optical pumping using a flash lamp.
• Small fraction of emitted energy used for excitation, rest heats the apparatus.
• Neodymium ions absorb radiations at ~730 nm ($E<em>1$) and ~800 nm ($E</em>2$) and go to excited states.
• Atoms decay by rapid non-radiative transition to the metastable level ($E_4$), achieving population inversion.
• Laser output at 1064 nm obtained corresponding to the transition between levels $E<em>4$ and $E</em>1$.

Advantages

• High output and repetition rate.
• Easier to achieve population inversion.
• Small line width due to crystalline structure, lower thresholds.
• Can be used in lasers utilizing frequency doubling/tripling and high energy Q-switching.
• Better thermal conductivity and longer fluorescence lifetime than Nd:YVO4.
• Operated on power levels up to kilowatts; can be directly Q-switched with $Cr^{4+}$ -YAG.

Applications

• Most widely used active laser medium in solid-state lasers.
• Transmitting signals over longer distances, long-haul communication systems, remote sensing.
• Medical field: endoscopic applications, correcting posterior capsular opacification.
• Manufacturing: engraving, etching, marking metals and plastics.
• Cerium-doped YAG (YAG-Ce) as a phosphor in applications ranging from cathode ray tubes to white LEDs.
• Cutting, welding, and marking metals, spectroscopy, pumping dye lasers.

OPTICAL FIBERS

• Optical frequencies are extremely high (~$10^{15}$Hz) compared to radio waves or microwaves.
• Light beam as a carrier wave can carry far more information.
• Optical fibers are waveguides carrying light through long distances with low losses.
• Signal transmission through metallic wires is electronic; in optical fibers, it is optical.
• Using optical fibers, speed, information density, and transmission density have increased with decreased error rate.
• Inexpensive, lightweight, high reliability, exceedingly small attenuation, immune to electromagnetic radiation.

Fiber Structure

• Core: Cylindrical central part; made of pure silica; diameter of a few mm.
• Cladding: Cylindrical coating over the core; diameter of 100–400 mm; made of silica doped with germanium and fluorine to control refractive index.
• Refractive index of cladding is less than that of the core, enabling internal reflection.
• Jacket: Outermost coating (60 mm thick); made of polymeric material; protects core and cladding from external damage.

Waveguides (Propagation Mechanism)

• Tubular structure guiding EM radiation in the form of waves; optical fibers known as light guides.
• Works on total internal reflection (TIR).
• Refractive Index $(RI)<em>{Cladding} < (RI)</em>{Core}$.
• Light signal entering the core strikes the core-cladding interface at angles greater than the critical angle for TIR.
• Light signal propagates in the core by undergoing multiple TIRs.

Principle of Optical Fiber

• Refractive index (n): ratio of the velocity of light in vacuum (c) to the velocity of light in a medium (v): $n = \frac{c}{v}$.
• Light undergoes refraction and reflection when there is a change of refractive index.
• If light propagates at angle $\theta<em>1$ (\theta1 < \thetac) from a high refractive index medium ($n</em>1$) to a low refractive medium ($n<em>2$), a portion is reflected back to $n</em>1$, and another part is refracted into $n_2$.
• From Snell’s law, $n<em>1 sin\theta</em>1 = n<em>2 sin\theta</em>2$.
• As the angle of incidence increases, the ray refracts away from the normal. If angle $\theta_1$ is further increased, the refracted ray travels along the interface.
• If the angle is above the critical angle, $\theta<em>3 > \theta</em>c$, the ray is totally reflected back into the higher refractive index medium $n_1$.

Acceptance Angle and Numerical Aperture

• $sin\theta<em>{max} = \frac{n</em>1}{n<em>0} \sqrt{1 - \frac{n</em>2^2}{n<em>1^2}} = \frac{1}{n</em>0} \sqrt{n<em>1^2 - n</em>2^2}$,
  where $n<em>0, n</em>1, n_2$ are the refractive indices of air, core and cladding, respectively.
• The maximum angle of incidence $\theta<em>{max}$ is known as acceptance angle: $\theta</em>{max} = sin^{-1} \sqrt{n<em>1^2 - n</em>2^2}$ (for $n_0 = 1$).
• Numerical aperture (NA) measures the light-gathering ability of an optical fiber.

Modes of Propagation

• Number of paths available for light beam determines number of modes.
• Single-mode fiber: supports only one signal.
• Multimode fiber: supports many rays.
• Number of modes determined by V-number:
  • $V = \frac{\pi d}{\lambda} \sqrt{n<em>1^2 - n</em>2^2}$
• where d is the core diameter, $n<em>1$ is the refractive index of core, $n</em>2$ is the refractive index of the cladding and $\lambda$ is the wavelength of the light propagating through the fiber.
• If fiber is surrounded by a medium of refractive index $n<em>0$, then $V = \frac{\pi d}{\lambda n</em>0} \sqrt{n<em>1^2 - n</em>2^2} = (\frac{\pi d}{\lambda}) NA$

Classification of Optical Fibers

• Based on variation of refractive index of the core and number of modes:
  • Based on refractive index of the core: step index fiber and graded index fiber.
  • Based on modes: single-mode fiber and multimode fiber.

Step Index Fiber

• Refractive index of the core is constant throughout.
• Sudden step-wise change in refractive index at the core-cladding interface.

Step Index (Single Mode Fiber)

• Core and cladding have uniform refractive index values.
• Sudden increase in refractive index from cladding to core.
• Core diameter: 8 to 10 $\,\mu m$, cladding diameter: 60 to 70 $\,\mu m$.
• Guides only a single beam of laser.
• Requires lasers as source.
• Hard to splice.
• Application: Underwater cable system.

Step Index (Multi-mode Fiber)

• Core and cladding have uniform refractive index values.
• Sudden increase in refractive index from cladding to core.
• Core diameter: 50 to 100 $\,\mu m$, cladding diameter: 100 to 250 $\,\mu m$.
• Guides multiple beams of laser.
• Laser and LED can be used as source.
• Least expensive.
• Application: Lower bandwidth requirements.

Graded Index (Multi-mode Fiber)

• Refractive index varies within the core; cladding has uniform refractive index.
• Refractive index decreases gradually in the radially outward direction.
• Core diameter: 50 to 100 $\,\mu m$, cladding diameter: 100 to 250 $\,\mu m$.
• Guides multiple beams of laser.
• Laser and LED can be used as source.
• Very expensive.
• Application: Large bandwidth requirements.

Applications of Optical Fibers

Communication Applications

• Point-to-Point (P-P) communication.
• Local Area Network (LAN) communication.
• Community Antenna Television (CATV).
• System includes:
  • Information input (voice or video).
  • Coder or Converter.
  • Light source transmitter (pulses light on/off at rapid rate).
  • Fiber optic cables.
  • Receiver (photo cell or light detector).

Features (or) Advantages of Optical Fibers in Communication

• Extreme Bandwidth: Transmission bandwidth is large as $10^5$GHz.
• Small size and weight: Fibers are small in diameter and light in weight.
• Lack of cross-talk: Negligible even when many fibers are cabled together.
• Low transmission loss: 0.2 dB/Km compared to copper cables.
• Low cost: Made of silica which is available in Earth’s crust.
• Longer life span: 20 to 30 years compared to 15 to 20 years for copper cables.
• Much safer: Uses light, not electricity.
• Ruggedness and Flexibility: Can be bent/twisted without damage.

Other Applications

• Domestic:
  • Illumination.
  • Decoration and ceremonies.
  • Entertainment.
• Telecommunication: more channels, less energy loss.
• Sensors: measure displacement, pressure, temperature, liquid level, chemical composition.
• Communications: telephone companies, cable television companies, networking (LAN).
• Medical Field: Endoscope applications (view internal parts of body without surgery), laser guided by fibers to correct vision.
• Material processing: carry high power laser beams for cutting, drilling, and welding.