Unit 2: Lasers and Applications

1. Fundamentals of Laser

The term LASER stands for Light Amplification by Stimulated Emission of Radiation. To understand lasers, one must first understand the quantum mechanical interaction between light and matter.

1.1 Energy Levels in Atoms

• Discrete States: According to quantum mechanics, electrons in an atom can only exist in specific, discrete energy levels ().
• Ground State (): The lowest energy state where electrons reside naturally. It is stable.
• Excited State (): Higher energy states. Electrons in these states are generally unstable and tend to return to the ground state.

1.2 Radiation-Matter Interaction

There are three distinct processes through which radiation (photons) interacts with matter:

A. Induced Absorption

• Process: An atom in the ground state () absorbs a photon of energy and transitions to an excited state ().
• Condition: The energy of the incident photon must exactly equal the energy difference between the two levels.
  
• Result: Atom gains energy; photon disappears.

B. Spontaneous Emission

• Process: An atom in an excited state () naturally decays back to the ground state () without external influence.
• Lifetime: This happens after a short duration called the lifetime of the excited state (typically seconds).
• Result: Emission of a photon with energy .
• Characteristics: The emitted light is incoherent (random phase) and polychromatic (random direction). This is how standard light bulbs work.

C. Stimulated Emission (The Principle of Laser)

• Process: An atom is already in an excited state (). An incident photon with energy passes by the atom. This photon "stimulates" or triggers the atom to drop to immediately.
• Result: Two photons are released: the incident photon and the emitted photon.
• Characteristics: The two photons are:
  1. Identical in energy (frequency).
  2. Traveling in the same direction.
  3. In phase (Coherent).
• This leads to light amplification ( photons).

2. Einstein’s Coefficients

Einstein derived the mathematical relationship between the probabilities of absorption, spontaneous emission, and stimulated emission.

Let be the number of atoms in ground state and be the number of atoms in excited state . Let be the energy density of the incident radiation.

1. Rate of Induced Absorption ():
   

   
   Where is the Einstein coefficient for absorption.

2. Rate of Spontaneous Emission ():
   

   
   Where is the Einstein coefficient for spontaneous emission (independent of ).

3. Rate of Stimulated Emission ():
   

   
   Where is the Einstein coefficient for stimulated emission.

Relationship between A and B Coefficients

At thermal equilibrium, the rate of upward transitions equals the rate of downward transitions:

Using Boltzmann’s distribution law () and Planck’s radiation law, Einstein deduced two important relations:

1. Equality of Stimulation Probabilities:
   

   
   (The probability of induced absorption equals the probability of stimulated emission).

2. Ratio of Spontaneous to Stimulated Emission:
   

   • Significance: The ratio is proportional to . At high frequencies (like X-rays), spontaneous emission dominates, making it very difficult to build lasers. At lower frequencies (optical/microwave), stimulated emission is easier to achieve.

3. Requirements for Lasing Action

To achieve laser output, specific conditions must be met to ensure stimulated emission dominates over absorption and spontaneous emission.

3.1 Population of Energy Levels & Population Inversion

• Normal Population: Under thermal equilibrium, lower energy levels have more atoms than higher levels (). This leads to net absorption of light.
• Population Inversion: A non-equilibrium state where the number of atoms in the excited state is greater than in the ground state ().
• Necessity: Inversion is required so that incoming photons are more likely to cause stimulated emission (amplification) than to be absorbed.

3.2 Metastable State

• A normal excited state has a lifetime of seconds. Atoms drop too fast to build up a population.
• A Metastable State is a semi-stable excited state with a much longer lifetime (approx. seconds).
• Atoms "pile up" in this state, allowing population inversion to occur.

3.3 Excitation Mechanisms (Pumping)

Pumping is the process of supplying energy to the medium to transfer atoms from lower to higher energy levels to achieve population inversion.

• Optical Pumping: Using a light source (flash lamp) (e.g., Ruby Laser, Nd:YAG).
• Electrical Discharge: Passing electric current through a gas (e.g., He-Ne Laser).
• Direct Conversion: Forward biasing a junction (e.g., Semiconductor Laser).

3.4 Resonant Cavity (Optical Resonator)

• The active medium is placed between two mirrors:
  1. High Reflector: 100% reflective.
  2. Partial Reflector: ~90-99% reflective (Output Coupler).
• Function: Photons bounce back and forth, passing through the medium repeatedly. Every pass stimulates more emissions (Positive Feedback), causing a cascade of amplification. A small percentage of light escapes through the partial reflector as the laser beam.

4. Properties of Laser

1. Monochromaticity: Laser light consists of a single wavelength (color). The spectral width is extremely narrow.
2. Coherence:
   • Temporal Coherence: Phase correlation at a single point over time.
   • Spatial Coherence: Phase correlation across different points in the beam cross-section.
3. Directionality: The beam travels in a straight line with very little divergence (spreading).
4. High Intensity: High energy is concentrated in a small area.

5. Types of Lasers

5.1 Nd:YAG Laser (Solid State Laser)

• Active Medium: Yttrium Aluminum Garnet (YAG) crystal doped with Neodymium () ions. The ions are responsible for lasing.
• Type: 4-Level Laser System (More efficient than 3-level systems like Ruby).
• Pumping: Optical Pumping (Krypton flash tube or Diode laser).
• Working:
  1. ions are pumped from ground state () to absorption bands ().
  2. Ions decay rapidly (non-radiative) to the metastable state ().
  3. Population Inversion occurs at .
  4. Lasing transition occurs from (Stimulated emission).
  5. Ions decay rapidly from back to .
• Output Wavelength: (Infrared - invisible to human eye).
• Applications: Cutting, drilling, welding, medical surgery (cataract), range finders.

5.2 He-Ne Laser (Gas Laser)

• Active Medium: A mixture of Helium (He) and Neon (Ne) gases in a ratio of 10:1. Neon is the active lasing element; Helium assists in pumping.
• Type: 4-Level System.
• Pumping: Electrical Discharge.
• Working:
  1. High voltage ionizes the gas mixture. Electrons collide with He atoms, exciting them to metastable states and .
  2. Resonant Energy Transfer: The excited He levels act as a perfect energy match for Ne excited levels ( and ). Through collisions, He transfers energy to Ne, exciting Ne atoms.
  3. Population inversion is achieved in Ne levels.
  4. Lasing transition occurs between Ne levels (typically ).
  5. Neon atoms decay back to ground state through spontaneous emission and collision with tube walls.
• Output Wavelength: (Continuous Wave - Red light).
• Applications: Barcode scanners, alignment in construction, interferometry, holography.

5.3 Semiconductor Laser (Diode Laser)

• Active Medium: A P-N junction diode made of direct bandgap semiconductors (e.g., Gallium Arsenide - GaAs).
• Pumping: Direct conversion (Forward bias current).
• Construction: The sides of the crystal are polished to form the resonant cavity faces.
• Working:
  1. When forward biased, electrons are injected into the conduction band (n-region) and holes into the valence band (p-region).
  2. At the junction (depletion region), high concentrations of electrons and holes overlap.
  3. Recombination: Electrons fall into holes, releasing energy as photons (, where is bandgap).
  4. At low current, this is an LED (Spontaneous emission). At high current (Threshold current), the photon density increases, triggering stimulated emission.
• Output: Depends on bandgap material. GaAs produces IR; GaAlAs produces red.
• Advantages: Compact size, high efficiency, low cost, easy modulation.
• Applications: Fiber optic communication, CD/DVD players, laser pointers, laser printers.

6. Applications of Laser: Holography

Holography (Greek Holos = whole, Grapho = writing) is the science of producing 3D images. Unlike photography, which records only intensity (amplitude), holography records both the amplitude and the phase of the light waves.

6.1 Basic Principle

Holography is based on Interference and Diffraction.

6.2 Construction (Recording) of a Hologram

1. Coherent Source: A laser beam is split into two parts by a beam splitter.
2. Reference Beam: One part travels directly to the photographic plate (holographic film).
3. Object Beam: The second part illuminates the object. Light reflects off the object and travels to the photographic plate.
4. Interference: The Reference Beam and the Object Beam overlap on the film. Since they are coherent, they create a complex interference pattern (fingerprint of the object).
5. Hologram: The developed film, containing the interference pattern, is called a Hologram. It looks like random noise to the naked eye.

6.3 Reconstruction of the Image

1. The developed hologram is illuminated by the Reference Beam only (at the same angle used during recording).
2. Diffraction: The hologram acts as a diffraction grating.
3. The light diffracts and recreates the wavefronts that originally came from the object.
4. Result: The observer sees a virtual, 3D image of the object behind the film. If the observer moves their head, they can see around the object (parallax), exactly as if the real object were there.

6.4 Applications of Holography

• Data Storage: Holographic memory stores data in 3D volume, offering immense density.
• Security: Holograms on credit cards and currency to prevent counterfeiting.
• Interferometry: Detecting microscopic stress or fractures in materials (Non-destructive testing).
• Art and Displays: 3D visualization.