# Absorption and emission processes

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Absorption and emission processes
2 1 absorption spontaneous emission stimulated emission Absorption Molecule absorbs a quantum of radiation (a photon) and is excited from 1 to 2. M + h  M* (state 1) (state 2) Spontaneous emission M* (in state 2) spontaneously emits a photon of radiation. M *  M + h Stimulated emission A quantum of radiation is required to stimulate M* to go from 2 to 1. M * + h  M + 2h

Lecture 1 - Basics of laser systems
LASER SPECTROSCOPY Lecture 1 - Basics of laser systems Absorption and Emission processes. Conditions for laser action. Properties of laser radiation. Real Laser Systems. Recommended reading - not buying! High Resolution Spectroscopy/Modern Spectroscopy by J.M.Hollas. An Introduction to Lasers and their Applications by O’Shea, Callen and Rhodes. Laser Electronics by Verdeyen.

Rates of absorption and emission processes
Rates are determined by the Einstein coefficients for each process Absorption () is the energy density of the incident radiation and N1 and N2 are the populations of states 1 and 2 respectively. Stimulated emission Spontaneous emission Under thermal conditions the population of two states 1 and 2, is determined by the Boltzman distribution. Where E is the energy difference between the two states, T is the temperature and k is Boltzmans constant.

Stimulated and spontaneous emission
Photons emitted in all directions and on a random time scale. The emitted photons are INCOHERENT Stimulated emission Emitted and stimulating photons have the same : Frequency Direction Phase The emitted and incident photons are COHERENT

First condition for laser action
If N1 > N2 If most molecules in state 1, then incoming radiation is mainly absorbed. Incident radiation is attenuated (reduced). If N2 > N1 If most molecules are in state 2, absorption of incoming radiation is hindered. The result is stimulated emission. Incident radiation is amplified. Thus for laser action require a population inversion, N2 > N1

How to obtain a population inversion
Consider the Boltzman equation. When kT is large, the ratio of N2/N11, equal numbers of molecules in state 1 and state 2. When kT is small the ratio of N2/N1  0 and all molecules are in state 1. Cannot obtain a population inversion using thermal methods in a 2 level system. Multi-level systems must be employed. Molecules need to be pumped into a higher energy state. Various methods : electrical discharge, flashlamp excitation. Continuous pumping gives a Continuous Wave (CW) Laser. Pulsed pumping gives a Pulsed Laser (PL) output.

Population Inversion E3 E2 E1 Example of a 3 level system LASING
Rapid decay E2 LASING E1 13 transition is pumped. Rapid decay from 3 2. State 2 is metastable, excited molecules can remain in state 2 for an extended time period, population of state 2 builds up. Decay from state 3 means absorption from 1 3 is favoured, creating population inversion between 2 and 1. Laser action is possible between states 2 and 1.

Population Inversion E4 E3 E2 E1 Example of a 4 level system LASING
Rapid decay LASING E1 E4 E3 E2 14 transition is pumped. Rapid decay from 4 3. A population inversion is produced between states 3 and 2. Laser action is therefore possible between 3 2. Molecules decay rapidly from 2 1, replenishing population of 1.

Laser Gain The amount of amplification of the incident beam in a single pass is small, a fraction of a percent/centimetre of travel. To increase the path length through the sample could use either: A very long laser/gain medium. Mirrors to reflect the beam back into the sample. mirror gain medium The gain medium is the substance which can support the population inversion, can be solid, liquid or gas. The combination of the gain medium and the mirrors is called the laser cavity or the optical resonator.

Basics of a complete laser system
The gain medium is pumped by some method. Some of the atoms/molecules are excited. Spontaneous emission occurs, in all directions. Emission along long axis of cavity is reflected back through the gain medium. The spontaneously emitted photons stimulate further emission from the medium. A large radiation density quickly builds up. mirror gain medium LASING mirror gain medium mirror mirror One of the mirrors is usually partially transmitting to allow some of the laser radiation to escape.

Summary of requirements for laser action
GAIN MEDIUM EXCITER energy LASER OUTPUT OPTICAL RESONATOR The three components required for laser action are: A gain medium which can support a population inversion. An external exciter to create the population inversion in the gain medium. An optical resonator or cavity to create a high radiation density. The various types of lasers differ in the types of gain medium, external exciter and size and type of cavity employed.

Ruby Laser Invented in the 60’s, was the first proper laser.
The gain medium is a crystal of Ruby, which is an aluminium oxide crystal with some of the aluminium atoms replaced with chromium. The excitation of the ruby crystal is obtained by a flashlamp spiralled around the crystal. Mirrors at each end of the crystal form the cavity.

Ruby Laser The lasing constituents of the Ruby crystal are the Cr3+ ions, present in low concentration. The laser action follows that of a 3 level system. Pump either the 4T1 or 4T2 states, use nm or nm radiation respectively. Each decays to the metastable 2E state. Laser action occurs from 2E to 4A2,with a frequency of 694 nm. Energy 4A2 4T2 4T1 2T2 2E LASING rapid decay

Gain Media Can be a solid, liquid or gas.

Properties of laser output
Output is intense and coherent. The linewidth (spread of frequencies) of the laser beam is determined by several factors: Doppler broadening (gases, liquids). Collisional broadening (gases, liquids, also solid state,due to crystal interactions). Natural linewidth of the lasing transition (uncertainty principle). Number of modes active in the cavity. The linewidth of most lasers is still of the order of a wavenumber or less, sufficient for most spectroscopic applications. To achieve very narrow line widths (for rotational spectroscopy) optical components can be inserted into the cavity to narrow the number of modes which are active, or to favour a single mode.

The Optical resonator The size and quality of the cavity are crucial for successful laser action. To support lasing the length of the cavity (L) must be and integral (n) number of half wavelengths (/2). (This is the condition for constructive interference.) For each cavity, many modes can satisfy this resonance condition. Laser output is, therefore, composed of a spread of frequencies.

The Optical resonator The Quality or Q-factor of a laser cavity is essentially a measures the ability of a laser cavity to store energy. The Q factor can be related to the energy stored in the cavity Ec, and the amount lost, Et, by the following equation. Every laser cavity must have some loses due to the partially reflective nature of the cavity mirrors. Q-switching is a method of producing short pulses of very high energy in pulsed laser systems. Q-switching is often achieved by having shutters or a saturatable absorber in the cavity.

Tunablity of wavelength.
Most lasers emit a single, or several discrete frequencies of radiation. However, for many spectroscopic applications wavelength tunability is necessary. Solution is to use a dye laser pumped by a fixed frequency laser. The gain medium is an organic dye, which has a broad emission and absorption profile. LASING Population inversion occurs between v`=0 in S1 and v``=n in S0. Emission frequency selected by a diffraction grating. Used to stimulate further emission from amplifier dye cells.

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