Unit2 - Subjective Questions

The interaction of radiation with matter involves three fundamental processes:

1. Stimulated Absorption:

• An atom in the lower energy state () absorbs an incident photon of energy $h
  u = E_2 - E_1E_2$).
• Rate: Rate of absorption Energy density of radiation $\rho(
  u)N_1$.
• $R{abs} = B{12} \rho(
  u) N1B{12}$ is the Einstein coefficient for induced absorption.

2. Spontaneous Emission:

• An atom in the excited state () is unstable and transitions to the ground state () voluntarily without any external inducement, releasing a photon of energy $h
  u$.
• The emitted photons are random in phase and direction (incoherent).
• Rate: , where is the Einstein coefficient for spontaneous emission.

3. Stimulated Emission:

• An atom in the excited state () is triggered by an external photon of energy $h
  u = E_2 - E_1E_1$).
• This results in the emission of two photons (incident + emitted) that are coherent (same frequency, phase, and direction).
• Rate: $R{st} = B{21} \rho(
  u) N2B{21}$ is the Einstein coefficient for stimulated emission.

Consider an assembly of atoms in thermal equilibrium at temperature . Let and be the number of atoms in energy levels and respectively.

1. Rate Equations:

• Rate of Absorption: $R{abs} = B{12} N_1 \rho(
  u)$
• Rate of Spontaneous Emission:
• Rate of Stimulated Emission: $R{st} = B{21} N_2 \rho(
  u)$

2. At Thermal Equilibrium:
Rate of Absorption = Rate of Emission (Spontaneous + Stimulated)

Rearranging for $\rho(
u)$:

Dividing numerator and denominator by :

3. Using Boltzmann's Distribution Law:

4. Comparison with Planck's Law:
Planck's radiation law is given by:

Comparing (1) and (2):

1. (Probability of absorption equals stimulated emission).
2. $\frac{A{21}}{B{21}} = \frac{8\pi h
   u^3}{c^3}$

Conclusion: The ratio of spontaneous to stimulated emission coefficients is directly proportional to the cube of the frequency ($
u^3$).

Definition:
Population Inversion is a non-equilibrium state in which the number of atoms in a higher energy excited state () is greater than the number of atoms in a lower energy ground state (). That is, .

Necessity for Laser Action:

• Under normal conditions (thermal equilibrium), according to Boltzmann's law. In this state, absorption dominates over stimulated emission.
• For Lasing Action (Light Amplification), stimulated emission must dominate over absorption.
• Since the rate of stimulated emission is proportional to and absorption is proportional to , we require .
• If population inversion is achieved, an incident photon is more likely to cause stimulated emission (generating a second photon) than be absorbed, leading to the amplification of light.

Metastable State:
A metastable state is an excited energy state where atoms stay for a relatively longer time (approx. s) compared to ordinary excited states (approx. s).

Role in Population Inversion:

• In a typical 3-level or 4-level laser system, atoms are pumped to a short-lived high energy state.
• They rapidly decay to the metastable state via non-radiative transitions.
• Because the lifetime of the metastable state is long, atoms 'accumulate' there, creating a bottleneck.
• This accumulation allows the population of the metastable state () to exceed the population of the lower state (), thereby achieving population inversion, which is the prerequisite for stimulated emission and laser operation.

The four characteristic properties of laser light are:

1. Coherence:
   • Laser waves are coherent in both space and time. This means the light waves maintain a fixed phase relationship with each other over time and distance. This property allows lasers to be focused to very small spots and used in holography.
2. Monochromaticity:
   • Laser light usually consists of a single wavelength (or a very narrow band of wavelengths). The spectral width is extremely small compared to ordinary light sources.
3. Directionality:
   • Lasers emit light in a highly directional beam with very low divergence. The beam spreads very little even after traveling long distances.
4. High Intensity (Brightness):
   • Since the energy is concentrated in a very narrow beam with a specific wavelength, the intensity (power per unit area) of laser light is extremely high.

Construction:

• Active Medium: A mixture of Helium and Neon gases (ratio approx 10:1) enclosed in a quartz tube.
• Resonator: Two mirrors, one fully reflecting and one partially reflecting, forming a resonant cavity.
• Excitation: Electric discharge (RF generator) is used to pump Helium atoms.

Working Principle (Energy Level Diagram):

1. Pumping: High voltage electrical discharge excites Helium atoms from ground state to metastable states and .
2. Energy Transfer: Excited He atoms collide inelastically with Neon atoms. Since He states () are resonant with Ne excited states (), energy is transferred to Neon, exciting Ne atoms to and .
3. Population Inversion: Ne atoms accumulate in and , creating a population inversion relative to lower states and .
4. Lasing Transition:
   • The transition from gives the standard red laser light at 632.8 nm.
   • Other transitions (IR) are also possible ( and ).
5. De-excitation: Ne atoms drop from to via spontaneous emission (giving incoherent light) and finally from to ground state via wall collisions (non-radiative).

Role of Helium: Helium acts as the pumping agent to transfer energy to Neon atoms effectively.

A laser system consists of three main components:

1. Active Medium:

   • It is the material (solid, liquid, or gas) in which population inversion can be achieved.
   • It contains the atoms, molecules, or ions that undergo the specific electronic transitions to emit laser light (e.g., Ne in He-Ne laser, ions in Nd-YAG).

2. Pumping Source (Excitation Mechanism):

   • An external source of energy is required to raise atoms from the lower energy state to the higher energy state to achieve population inversion.
   • Methods include Optical Pumping (flash lamps), Electrical Discharge, Chemical pumping, etc.

3. Optical Resonator (Resonant Cavity):

   • It consists of a pair of mirrors (one 100% reflecting, one partially reflecting) placed at the ends of the active medium.
   • It provides feedback by reflecting photons back and forth through the medium, stimulating further emission.
   • It selects the direction of the beam and amplifies the light to produce a high-intensity coherent beam.

Type: Solid-state, 4-level laser.

Construction:

• Active Medium: Yttrium Aluminum Garnet () rod doped with Neodymium () ions.
• Pumping Source: Krypton arc lamp or Xenon flash lamp (Optical Pumping).
• Resonator: The ends of the rod are polished and silvered, or external mirrors are used to form the cavity.

Working:

1. Pumping: The flash lamp emits light which is absorbed by ions, exciting them from the ground state () to multiple absorption bands ().
2. Non-radiative Decay: Ions in decay rapidly to the metastable state via non-radiative transitions, losing energy as heat.
3. Population Inversion: Ions accumulate in the metastable state , establishing population inversion with respect to the lower active level .
4. Lasing: Stimulated emission occurs from , producing a laser beam at 1.064 (IR region).
5. Return to Ground: Ions in rapidly decay to the ground state via non-radiative transitions, readying them for the next cycle.

Advantages: High power output, robust construction, operates in both pulsed and CW modes.

Definition:
An optical resonator is an arrangement of mirrors (usually two) placed at the ends of the active medium, forming a cavity.

Function:

1. Feedback: It reflects the photons emitted along the axis back into the active medium. These reflected photons stimulate more excited atoms to emit photons, creating a cascade effect (amplification).
2. Directionality: Only photons traveling parallel to the axis of the cavity are sustained; off-axis photons escape the system. This ensures the output beam is highly directional.
3. Wavelength Selection: The cavity supports standing waves only for specific frequencies satisfying (where is cavity length). This helps in narrowing the spectral output.

Structure: Typically consists of one high-reflectivity mirror () and one output coupler () through which the laser beam emerges.

Principle:
It works on the principle of stimulated recombination of electron-hole pairs in a direct bandgap semiconductor (Forward Biased p-n junction).

Construction:

• Made of Gallium Arsenide (GaAs) heavily doped p-n junction.
• The crystal faces perpendicular to the junction are polished to act as a resonator (Fabry-Perot cavity).

Working:

1. Forward Bias: When a sufficiently large forward voltage is applied, electrons are injected from the n-side and holes from the p-side into the junction (depletion) region.
2. Population Inversion: At high current density, the concentration of electrons in the Conduction Band and holes in the Valence Band within the active region becomes very high, creating a population inversion.
3. Recombination: Electrons recombine with holes. In direct bandgap materials like GaAs, this energy is released as photons ($E_g = h
   u$).
4. Stimulated Emission: The photons traveling along the junction plane stimulate further recombination, generating coherent radiation.
5. Output: The laser beam is emitted from the junction edge. For GaAs, (Infrared).

Heterojunction Lasers: Modern semiconductor lasers use heterojunctions (layers of different bandgaps) to confine carriers and light better, reducing threshold current.

Excitation or pumping is the process of supplying energy to the active medium to achieve population inversion. Common mechanisms include:

1. Optical Pumping:
   • Uses a light source (flash lamp, arc lamp, or another laser) to excite atoms.
   • Used in solid-state lasers (e.g., Nd-YAG, Ruby).
2. Electrical Discharge:
   • A high-voltage electric field accelerates electrons, which collide with gas atoms to excite them.
   • Used in gas lasers (e.g., He-Ne, lasers).
3. Direct Conversion (Injection Current):
   • Current is passed through a p-n junction diode, causing electron-hole injection.
   • Used in Semiconductor diode lasers.
4. Chemical Pumping:
   • Energy released from an exothermic chemical reaction excites the atoms.
   • Used in Chemical lasers.
5. Inelastic Atom-Atom Collisions:
   • Energy is transferred from one type of atom (auxiliary) to the active atom via collision (e.g., He transferring energy to Ne in He-Ne laser).

Holography:
Holography is the science and practice of making holograms. It is a technique of recording and reconstructing the complete amplitude and phase information of the light waves reflected from an object to produce a 3D image. (Greek: holos = whole, graph = writing).

Differences from Photography:

1. Information Recorded:
   • Photography: Records only the intensity (amplitude squared) of light. Phase information is lost, resulting in a 2D image.
   • Holography: Records both amplitude and phase of the light wave. This creates a 3D image.
2. Method:
   • Photography: Uses a lens to form an image on film.
   • Holography: Does not use a lens. It uses the interference pattern created by the reference beam and the object beam.
3. Visibility:
   • Photography: The negative shows a recognizable image of the object.
   • Holography: The hologram (plate) looks like a random pattern of whirls and specks; the image appears only upon reconstruction.

1. Recording (Construction):

• Principle: Based on Interference.
• Setup: A laser beam is split into two: a Reference Beam (goes directly to the photographic plate) and an Object Beam (illuminates the object and scatters onto the plate).
• Process: The light scattered from the object interferes with the reference beam on the photographic plate. This interference pattern, containing both amplitude and phase information of the object, is recorded. The developed plate is called a Hologram.

2. Reconstruction:

• Principle: Based on Diffraction.
• Process: The hologram is illuminated by a beam of light identical to the original reference beam (same wavelength and angle).
• Result: The hologram acts as a diffraction grating. The light is diffracted to produce two images:
  • Virtual Image: Appears behind the hologram (true 3D representation).
  • Real Image: Forms in front of the hologram (pseudoscopic).
• The observer looking through the hologram sees the 3D virtual image of the object.

From the derivation of Einstein's coefficients, we know:

Also, the ratio of the rate of stimulated emission () to spontaneous emission () is:

Substituting $\frac{B{21}}{A{21}} = \frac{c^3}{8\pi h
u^3}\rho(
u) = \frac{8\pi h
u^3}{c^3} \frac{1}{e^{h
u/k_BT} - 1}$:

Significance:
For optical frequencies ($h
u \gg k_BTe^{h
u/k_BT}R$ large), we need a massive photon density or non-equilibrium conditions (Population Inversion).

The main applications of Holography include:

1. Holographic Interferometry: Used for non-destructive testing (NDT) to detect stress, strain, and minute deformations in materials.
2. Data Storage: Holographic memories can store vast amounts of data in a small volume (3D storage).
3. Security: Holograms are used on credit cards, currency notes, and product labels to prevent counterfeiting.
4. Medical Imaging: Generating 3D images of internal organs for diagnostics and surgical planning.
5. Microscopy: Holographic microscopy allows viewing specimens at different depths without refocusing.
6. Art and Entertainment: Creating 3D visual displays and art pieces.

Role of Active Medium:

1. Source of Transitions: The active medium contains the specific atoms, ions, or molecules that possess the energy levels suitable for the desired laser transition. For example, ions in Nd-YAG or Neon atoms in He-Ne.
2. Amplification: It is the material wherein 'Population Inversion' is established. When light passes through this inverted medium, it undergoes stimulated emission, resulting in optical amplification (Gain).
3. Determination of Wavelength: The energy gap () of the lasing transition within the active medium determines the wavelength (color) of the laser light produced ().

Three-Level System:

• The laser transition terminates at the Ground State ().
• To achieve population inversion (), more than 50% of all atoms must be pumped from the ground state to the excited state.
• This requires very high pumping power.

Four-Level System:

• The laser transition terminates at an intermediate state () which is above the ground state ().
• The population of is negligible at thermal equilibrium (atoms rapidly decay to ).
• Therefore, even a small number of atoms pumped to the upper laser level () creates a population inversion relative to empty .
• Conclusion: Population inversion is much easier to achieve and sustain in a 4-level system, making it more efficient with a lower lasing threshold.

1. Temporal Coherence (Longitudinal):

• Refers to the correlation between the phase of a light wave at one point in time and its phase at a later time.
• It is related to the monochromaticity of the source. A strictly monochromatic wave has infinite temporal coherence.
• The time interval over which phase remains predictable is called Coherence Time ().

2. Spatial Coherence (Transverse):

• Refers to the correlation between the phases of two different points in space on the wave front at the same time.
• If two points on a wavefront always maintain a constant phase difference, the wave is spatially coherent.
• Lasers exhibit high spatial coherence, allowing them to travel long distances with minimal spreading (high directionality).