LASERS

Normal and Inverse Population

• Normal population refers to the typical distribution of particles across energy levels at thermal equilibrium, with more particles in lower energy states.
• Inverse population is a non-equilibrium condition where a higher number of particles occupy higher energy levels compared to lower ones.

Fundamental Concepts of Laser Operation

• Spontaneous Emission: Light emitted from atoms in an excited state without external influence, incoherent.
• Stimulated Emission: Emission of light where an incoming photon stimulates excited atoms, producing coherent light.
• Absorption: The process where photons are absorbed by atoms, transitioning atoms from a lower energy level to a higher one.

Idealized Model of an Atom

• Atoms modeled with two energy levels, E1 (lower) and E2 (higher).
• Transitions between these levels can happen spontaneously or through forced absorption/emission.

Optical Transitions

• There are three types of optical transitions:
  • Spontaneous Emission: Involuntary emission of light by excited atoms.
  • Forced Absorption Transition: Atom goes from E1 to E2 by absorbing a photon.
  • Forced Emission Transition: Atom shifts back from E2 to E1, emitting a photon of the same energy as the stimulating photon.

Forced (Induced) Transition with Absorption

• Transition probability for E1 → E2 is given by P{12} = B{12} ho( u) dt where:
  • $B_{12}$: Einstein's coefficient for emission in the ground state
  • 
    ho(
    u): Spectral density of the incident radiation
• Number of atoms transitioning from E1 to E2 is given by:
  • dN{12}= B{12} N_1
    ho(
    u) dt
    where N1 is the number of atoms in the lower state.

Spontaneous Emission of Light

• Common radiation mechanism (e.g., thermal radiation).
• Results in incoherent light due to randomized emission of photons.
• Rate of spontaneous emission can be modeled by:
  • $-dN<em>{21} = A</em>{21} N_2 dt$ where:
  • $A_{21}$: Einstein’s coefficient for spontaneous emission.

Radiated Energy in Spontaneous Transition

• Energy radiated during spontaneous transition: $dW = \bar{<br />\nu} dN<em>{21} = A</em>{21} N_2 \bar{<br />\nu} dt$
• Average lifetime of excited state $au_{2}$, until population decreases by a factor of e:
  • $N(t) = N<em>0 e^{-t/ au</em>{2}}$
• Relate $A<em>{21}$ to $au</em>{2}$ using:
  • $au<em>{2} = \frac{1}{A</em>{21}}$.

Lifetime of Energy Levels

• Short-lived levels: $au_n ≈ 10^{-8} s$.
• Metastable levels: $au_n ≈ 10^{-3} ext{ to } 10^{-6} s$.
• Metastable states are crucial for lasers as they enable longer particle confinement.

Stimulated Emission of Light

• Occurs when an atom in an excited state interacts with an electromagnetic field.
• The emitted photon has the same energy, phase, and direction as the stimulating photon, resulting in coherent light.
• Invoked in devices such as lasers for amplification.

Einstein's Principles on Transition Probabilities

• Derived mathematical probabilities for stimulated emission matching absorption transition probabilities:
  • $P<em>{21} = P</em>{12}$
• Stated that:
  • $B<em>{21} = B</em>{12}$,
• Emphasized need for equilibrium between the rates of spontaneous and stimulated transitions.

Thermodynamic Equilibrium

• At equilibrium, B{12} ho( u) N1 = A{21} N2 + B{21} ho( u) N2
• Predicts that the population of the lower energy state exceeds that of the higher.
• Concept linked to Boltzmann's law of statistical distribution which describes particle distribution in thermal systems.

Inverse Population & Laser Gain

• Inverse population defined as: $N<em>2 > N</em>1$ for gain.
• Conditions lead to a negative absolute temperature state, influencing emission probabilities.
• Gain coefficients required for laser operation, defining the fractional change in intensity per unit propagation distance.

Types of Lasers

• Classifications based on working medium and operational modes:
  • By Medium:
  • Solid-State Lasers
  • Gas Lasers
  • Semiconductor Lasers
  • Dye Lasers
  • Free Electron Lasers
  • By Operation Modes:
  • Continuous
  • Pulse: Single, Repetitive, Frequency, Quasi-Continuous

Ruby Laser

• First successful laser using synthetic ruby as the medium (λ = 694.3 nm).
• Key specifications:
  • Work in continuous/pulsed modes,
  • Output linewidth $Δλ ≈ 0.01 ext{ to } 0.1 nm$.
  • Requires a pumping power exceeding a threshold of 10-20%.

Working Substance in Lasers

• Refers to materials achieving population inversion, termed as laser gain medium, can be:
  • Solid, Gas, Semiconductor, or Liquid.
  • Required to have efficient energy level structuring to maintain population inversion.

Pumping Source

• Mechanisms providing energy to the working material for achieving particle inversion:
  1. Optical Excitation: Using light sources (e.g., lasers, lamps).
  2. Gas Discharge Excitation: Utilizing electric arcs.
  3. Chemical Excitation: Energy from chemical reactions.
  4. Nuclear Energy Excitation: Using nuclear fission products for excitation.

Optical Resonator Definition

• Composed of two mirrors, enhancing light travel distance and facilitating resonant conditions for laser emission:
  • Provides feedback allowing oscillation formation.
  • Selectively filters out non-useful wavelengths.

Resonator Stability

• A resonator is defined as stable or unstable based on the ability of the beam path to remain within certain boundaries after multiple reflections.

Laser Generation Conditions

• Achieving effective generation requires appropriate gain exceeding losses.
• Total loss $α<em>{Σ} = 2α</em>{l<em>a} + α</em>{m}$ must be compensated by gain $g$.

Laser Characteristics

• High temporal/spatial coherence.
• Strict monochromaticity with varying spectral output.
• High energy density and small angular divergence.
• Polarization properties depending on the construction of the optical system.

Laser Effects on Biological Tissues

• Impact of laser light varies significantly among wavelengths:
  • Absorption characteristics differ leading to varying tissue interactions and precision of treatment.
• Selective photothermolysis in medical applications helps minimize damage to surrounding tissues while targeting treatment areas.

Conclusion

• Lasers represent a critical technology in numerous fields, particularly medical, through their unique and controlled light emission properties. The understanding of their operation principles, types, and biological effects is foundational for their application in diagnostics and therapy.