1 P1X: Optics, Waves and Lasers Lectures, Lasers and their Applications i) to understand what is meant by coherent and incoherent light sources; ii) to understand the terms spontaneous and stimulated emission and population inversion and to be able to describe the requirements for laser action; iii) to understand the operation of simple 3 and 4 level lasers; iv) to be able to describe the main properties of some commonly used lasers, and some of their many applications such as in precision measurement, medical physics and optical communications. Objectives:

2 P1X: Optics, Waves and Lasers Lectures, Lecture 6: Lasers and their applications (I) o Coherence: A monochromatic source of light (with the same frequency and wavelength) and with a constant phase between two points on the wave front at a given time is said to be coherent. Two conditions for coherence: Temporal: longitudinal space coherence is a measure of how well points A and B remain in phase (eg. A continuous sine wave is perfectly coherent). Coherent and incoherent light sources (Y&F 35.1): y t

3 P1X: Optics, Waves and Lasers Lectures, Spatial: the lateral displacement coherence is a measure of the phase relationship between two points A and B equidistant from the source (e.g: a point source has perfect spatial coherence) A B

4 P1X: Optics, Waves and Lasers Lectures, o Light sources: bursts of waves Thermal: filament is heated and radiated energy can give light (eg. Electric light bulb). Characteristics: * Wide range of wavelengths and frequencies. (ie. wide bandwidth) * Produces short wave-packets of different and phase --> short coherence time * Normally incoherent light, white in colour (a mixture of wavelengths).

5 P1X: Optics, Waves and Lasers Lectures, Gas discharge: gas excited by electric discharge with electrons jumping to outer levels and then de-exciting to give off photons. Light observed has different colours e.g: sodium (orange), neon (red), spectral lines of helium and mercury, each corresponding to transitions from different energy levels More monochromatic means more coherence and longer wavepackets emitted Why do some materials glow under ultraviolet light? Three level system absorbs UV, emits visible + - E1E1 E2E2 PHOTON E2E2 E1E1 Excitation De-excitation Photon emitted with frequency f: h= Planck’s constant=6.63x J s VIS E1E1 E3E3 E2E2 UV

6 P1X: Optics, Waves and Lasers Lectures, Example: The first three energy levels of a hydrogen atom are: E 1 =-13.6 eV, E 2 =-3.4 eV, E 3 = -1.5 eV. The Balmer series of spectral lines are the lines emitted when electrons jump from levels n=3,4,5, … down to level n=2. What is the wavelength of light emitted when an electron jumps from n=3 to n=2? And from n=2 to n=1? Unit of energy: electronvolt (eV) Energy required to accelerate one electron by a potential difference of 1V 1 eV = 1.6x Cx1V= 1.6x J h= Planck’s constant=6.63x J s c= 3x10 8 ms -1 For E 2 -E 1 =10.2eV and wavelength is =121.9 nm (ultraviolet). (red) Energy (eV) E1E1 E3E3 E2E2 0

7 P1X: Optics, Waves and Lasers Lectures, Lasers: very monochromatic, highly coherent light with long wavepackets LASER: Light Amplification by Stimulated Emission of Radiation Characteristics: * Radiation coherent in space (across wavefront and in time (along wavefront) * Very monochromatic: * Very bright: e.g. CO 2 laser can have power >100 kW in continuous light; pulsed laser ~2.5x10 13 W over s. * High power density (intensity): >10 17 W/cm 2 * Can have very short pulses (~10 fs = s) * Collimated beam ---> very directional LASER action produced by absorption and emission processes, especially stimulated emission

8 P1X: Optics, Waves and Lasers Lectures, Spontaneous and stimulated emission, population inversion (Y&F 38.6): o Atom populations: absorption, emission and stimulated emission Einstein (1917) was the first to fully explain the absorption and emission processes in atoms when light radiation interacts with them. Consider a gas of atoms with 2 possible energy states E 1 and E 2 with populations of N 1 and N 2 atoms/cm 3. If gas in thermal equilibrium, N 1 and N 2 depend on temperature T: with k= Boltzmann’s constant = 1.38x JK -1 o Example: If E 2 -E 1 = 2 eV = 3.2x J, with temperature of filament T=3000 K, then: Many more atoms in state 1 than 2 (N 2 <<N 1 )

9 P1X: Optics, Waves and Lasers Lectures, o Possible transitions from one state to another: a) Absorption (resonant absorption of photons): An atom with an electron in the lower of the two states can absorb radiation of a certain frequency f and jump to the higher state. hf E 2, N 2 E 1, N 1 b) Spontaneous emission of photons: If an electron of an atom is in a higher state and there is a lower available state the the electron can spontaneously jump to the lower state emitting a photon of energy: Note: it can only absorb radiation of that frequency. hf E 2, N 2 E 1, N 1

10 P1X: Optics, Waves and Lasers Lectures, Two photons are emitted from the stimulated transition and they have the same energy, direction, phase and polarization, the two photons are coherent. c) Stimulated emission of photons: This effect was predicted by Einstein. He realised that there exists another type of emission that can be stimulated by radiation of frequency f, causing a jump from a higher level to a lower level only if: E 2, N 2 E 1, N 1 hf Summary:

11 P1X: Optics, Waves and Lasers Lectures, o Light amplification: The two photons emitted by stimulated emission can further stimulate emission from state 2 to state 1 so a large number of photons of the same wavelength can be emitted by this mechanism If N 1 >N 2 : there are more electrons in the lower state so there is more absorption than emission (light attenuation). If N 2 >N 1 : there is more emission than absorption, causing a chain reaction (light amplification). o Population inversion: Since the normal population condition is that N 1 <N 2, one needs to achieve a non-equilibrium situation where there are more states in the higher level than the lower level (population inversion). Population inversion can only be achieved if there are more than two states available and if we can pump electrons to higher energy levels (e.g. optical pumping, electric discharge, injection of electrons). E 2, N 2 E 1, N 1 hf