PH481/581-VTA (Mirov)
Spontaneous and Stimulated Transitions
Lectures 1-2
Fall 2017 C. Davis, “Lasers and Electro-optics”
6 A laser is an oscillator of optical frequencies that concentrates light energy in spatial, spectral and temporal domains.
Excited state LOSER – Truthful Acronym- Light Oscillation by Stimulated Emission of Radiation. Inappropriate!!! LASER - Light Amplification by Stimulated Emission of Radiation Stimulated emission - Stimulated emission Ground state occurs when a traveling photon interacts with an exited atom. During the interaction, the atom will become de-excited and release a photon of the same frequency and 100% Mirror 75 % Mirror direction of the incident photon.
Gain medium Lasers have 3 parts: 1. Gain medium – a place for stimulated emmision to occur (crystal, gas, etc.) 2. Positive feedback – means for oscillation (mirrors, diffraction grating, etc.) 3. Source of energy – an incoming energy source which keeps more atoms in the excited state than in the ground state. First Solid State Ruby Laser (Dr. Ted Maiman, Hughes Aircraft 1960) A laser is an oscillator that operates at optical frequencies. These frequencies of operation lie within a spectral region that extends from the very far infrared to the vacuum ultraviolet (VUV) or soft-X-ray region. At the lowest frequencies at which they operate, lasers overlap with the frequency coverage of masers (mm scale).
Ti:S/Cr:LiSAF Co:MgF2 Cr:Zn/CdSe Fe:ZnSe/ CdZnTe Athmospheric transmission
0.2 0.5 1 2 5 10 20 µm
Cr:YAG Tm:laser Molecular frequencies
UV –Middle infrared part of electromagnetic spectrum and tuning ranges of the most common solid state lasers
9 HISTORY
A laser is an oscillator of optical frequencies that concentrates light energy in spatial, spectral and temporal domains.
In 1917 Albert Einstein, in his paper On the Quantum Theory of Radiation, laid the foundation for the invention of the laser and its predecessor, the maser, by introducing the concepts of probability coefficients (later to be termed 'Einstein coefficients') for the absorption, spontaneous emission, and stimulated emission of electromagnetic radiation. A little bit of history
1917 Albert Einstein. Basic physics of light emission and absorption by atoms and molecules 1928 Rudolph Walther Landenburg confirmed the existence of stimulated emission and negative absorption. 1939, Valentin Fabrikant predicted the actual use of stimulated emission in gas discharges to amplify light. Observation and patenting of negative absorption in 1944. 1954 James Gordon, Herbert Zeigel and Charles Townes proposed and developed maser, a microwave amplifier using stimulated emission. 1954 Aleksandr Prokhorov and Nikolai Basov independently proposed and developed maser. 1960 Theodore H. Maiman –first Ruby laser.
1964, Nikolai Basov, Charles Townes, and Aleksandr Prokhorov received the Nobel Prize for "fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based 11 on the maser-laser principle. Academician T. Basiev
ZrO2
Lebedev Physics Institute
Academician A. Prokhorov explains how laser works
Academician V. Osiko inventor of CubicCubic Zirconia Zirconia Gems Gems Light and Electromagnetic Waves
Light is one form of electromagnetic radiation. Electromagnetic radiation, which transports energy from point to point at the velocity of light, can be described in terms of both wave and particle "pictures" or "models." This is the famous "wave-particle" duality of all fields or particles in our model of the Universe. In the electromagnetic-wave picture, waves are characterized by their frequency , wavelength , and the velocity of light c, which are inter-related by c = . A propagating electromagnetic wave is characterized by a number of field vectors, which vary in time and space. These include the electric field E (volts/m), the magnetic field H (amps/m), the displacement vector D (coulombs/m2), and the magnetic flux density B (tesla). For a complete description the polarization state of the wave must also be specified. Linearly polarized waves have fixed directions for their field vectors, which do not re-orient themselves as the wave propagates. Circularly or elliptically polarized waves have field vectors that trace out circular, or elliptical, helical paths as the wave travels along.
13 Particle Picture of Light
ln the particle picture, electromagnetic energy is carried from point to point as quantized packets of energy called photons. The energy of a photon of frequency is h , where h is Planck's constant, namely 6.626 x10-34 J s. Photons have zero mass, and travel at the velocity of light, but carry both linear and angular momentum. The linear momentum of a photon of wavelength is p = h /, and the angular momentum depends on the equivalent polarization state of the corresponding wave. Circularly polarized photons have angular momentum h /(2 ) =
Our everyday experience of "light" generally encompasses only the small part of the electromagnetic spectrum to which the human eye is sensitive, a wavelength range running roughly from 400 nm to 700 nm. The full electromagnetic spectrum, going from low to high frequencies, is divided into radiowaves (0-1 GHz), microwaves (1-300 GHz), infrared waves (of wavelength = 0.7-1000 m; 300 GHz to 430 THz), visible light (= 400- 700 nm), ultraviolet light (= 10-400 nm), X-rays (= 0.1-10 nm), and - rays (< 0.1 nm). 14 Some basic electromagnetic theory
15 16 The polarization state of an electromagnetic wave
17 18 19 20 21 22 23 Bands in crystalline solids
24 Bands in crystalline solids
25 Basic laser structure
26 Amplifier of optical frequencies
27 Spontaneous Emission
28 29 The lineshape function, g()
30 Lineshape function. Example
Hz s 31 32 Stimulated Emission
33 The relation between energy density and intensity
34 35 36 37 38 Intensity of a Beam of Electromagnetic Radiation in Terms of Photon Flux
40 Blackbody Radiation
Incident radiation is completely absorpbed after successive reflections. The radiation emitted by the hole will have a blackbody spectrum
41 Blackbody Radiation – experimental results 1899 first accurate measurements by Lummer and Pringsheim
Spectral radiancy ܴ ் ሺߥ ሻ : The spectral distribution of blackbody radiation.
்ܴሺߥሻ݀ߥ represents the emitted energy from a unit area per unit time between ߥ and ߥ݀ߥ from a unit area of the surface at absolute temperature T.
The total energy emitted per unit time per unit area is called Radiancy RRvdv TT0
Figure of spectral distribution of blackbody radiation 42 The spectral radiancy of blackbody radiation shows that:
(1) little power radiation at very low frequency (2) the power radiation increases rapidly as ν increases from very small value.
(3) the power radiation is most intense at certain v max for particular temperature.
(4)vv max , RvT drops slowly, but continuously as ν increases,
and Rv T 0.
(5)vmax increases linearly with increasing temperature. (6) the total radiation for all ν ( radiancy RRvdv ) TT0 increases more rapidly than linearly with increasing temperature. 43 Stefan’s and Wien’s Laws
44 Stars as black bodies
45 Classical theory of cavity radiation. Rayleigh-Jeans calculations
R-J took as a blackbody the cavity shown in the figure and calculated the energy density inside.
The energy density T v is defined as the energy contained in a unit volume of the cavity at temperature T in the frequency interval vvdv to , and is related to the spectral radiancy by the relationship:
c Rv v TT4 Rayleigh and Jeans (1900): (1) standing wave with nodes at the metallic surface (2) geometrical arguments count the number of standing waves (3) average total energy depends only on the temperature
46 Rayleigh-Jeans calculations For simplicity, we assume a metallic cubic cavity filled with electromagnetic radiation. The incident and reflected waves combine to form standing waves. one-dimensional cavity: one-dimensional electromagnetic standing wave 2x Ext(,) E0 sin( )sin(2 t ) for all time t, nodes at 2x / n , n 0,1,2,3...... x 0 x a 2 a n 2a / n nc / 2a
standing wave N ( )d : the number of allowed standing wave between ν and ν+dν n (2a / c ) dn (2a / c )d N ( )d 2 dn (4a / c )d
two polarization states
d (2a / c )( d ) d (2a / c ) 47 0 n Rayleigh-Jeans calculations
Three dimensional cavity: we follow the same procedure counting the number of points within a shell of radius r and thickness dr
r (2a / c) dr (2a / c)d the volume of concentric shell r r dr 2 2a 2 2 2a 2a 3 2 4 r dr 4 ( ) v ( )d 4 ( ) d c c c 1 8 a 3 8 V N ( )d 2 4 r 2dr 2d 2d 8 c 3 c 3
48 Rayleigh-Jeans calculations: classical kinetic theory
the final stage will be to evaluate the average energy contained on each standing wave of frequency v apply classical statistical physics and the law of equipartition energy: For a system of gas molecules in thermal equilibrium at temperature T, the average kinetic energy of a molecules per degree of freedom is kT/2, k 1.38 10 23 joule / oK is Boltzmann constant.
average total energy of each standing wave : 2 KT / 2 KT the energy density between ν and ν+dν: 8 2 ( )d kTd Rayleigh-Jeans blackbody radiation T c 3
ultraviolet catastrophe Thermal radiation and Planck’s postulate The real problem in classical derivation of the radiancy spectrum is in the kT assumption. Planck’s theory of cavity radiation Planck’s assumption: ( T , ) and kT, 0 0 the origin of equipartition law kT . Boltzmann distribution P( ) e / kT / kT When we have a large number of entities in thermal equilibrium at temperature T, the probability of finding a system with energy between ε and ε+dε Pd() P( )d 0 P( )d 0 / kT e 1 P( )d d (kT )e / kT | 1 0 0 kT kT 0 / kT e P( )d d 00 kT 1 / kT / kT [ (kT )e |0 (kT )e ] kT kT 0 kT Planck’s discretization hypothesis
51 Planck’s discretization hypothesis
52 Planck’s formula for the average energy
53 Planck’s formula for the average energy
54 Planck’s blackbody spectrum
55 Planck’s postulate: physical implications
56 Macroscopic systems
57 Energy density of radiation within the cavity
58 Relation Between the Einstein A and B Coefficients
59 Einstein relations
60 The effect of level degeneracy
61 Ratio of Spontaneous and Stimulated Transitions
62 63