THE ORIGINS OF LIGHT

1. THE ORIGINS OF LIGHT Prof. John Watson EG 40GC Optical Engineering LECTURE NOTES

2. The Character of Light • To understand the operation of the laser and other light sources • need to appreciate the unique character of light emitted from gases and solids. • All radiating bodies when viewed by the naked eye possess a characteristic colour. • Sunlight is white, a piece of hot iron is orange-red, a sodium lamp is yellow. • If the light from any of these sources is passed through a prism • it spreads out in a series of component colours known as a spectrum. • Sunlight appears as a continuous band of colours ranging from red through to violet • The piece of iron also shows a continuum but only from dull red to orange • The sodium lamp displays a series of bright, sharp, narrow lines • Whether the spectral distribution is continuous or is in discrete lines depends on the nature and temperature of the source. • In this lecture we will discuss thermal light sources • Those whose spectral output is related to their temperature Prof John Watson

3. Spectral Emission Prof John Watson

4. Light originates from excitation and de-excitation of atoms between various energy states • Atoms consist of nucleus surrounded by “orbiting” electrons in different states of excitation Prof John Watson

5. W u D W W l Absorption W u D W W l Spontaneous Emission Absorption & Emission of Energy in Isolated Atoms • Atoms can be excited into higher energy states • Absorbed energy moves electron/s into vacant shell/s • Absorbed energy corresponds to difference between shells • W = |Wu-Wl| Absorbed energy • Excited atom can spontaneously de-excite to a lower level • Average lifetime of atom in excited state is nanoseconds • Electron/s randomly drop to vacant level/s • Corresponding emission of energy • W = |Wu-Wl|Emitted energy Prof John Watson

6. Absorption & Emission of Energy • Absorbed in discrete amounts: a quantum of energy • absorbed/emitted in many forms: e.g. heat, light, collisions • if absorbed or emitted as light – photon • Energy emitted (the energy of each photon) is • Wph = W = |Wu – Wl| • Wph = h = hc/ • Planck's constant h = 6.63x10-36 J s • velocity of light c = 300x106 m/s • An energy diagram shows the range of possible optical transitions • Spectral emission is in discrete (almost monochromatic) lines • Line spectrum Prof John Watson

7. Prof John Watson

8. Worked Example - 1 • Calculate the wavelength of emission when an atom de-excites from an energy state at 12.09 eV to one at 10.2 eV above the ground state. • Solution • The emission energy is • W = Wu - Wl = 12.09 eV - 10.2 eV = 1.89 eV • The photon energy is • Wph = W = 1.89 eV • The wavelength of emission is thus • l = hc/Wph • = 6.63x10-34 J s x 3x108 m/s / (1.89 eV x 1.6x10-19 J/eV) • = 657.7x10-9 m • = 657.7 nm Prof John Watson

9. Worked Example - 2 • How much energy does a hydrogen atom need to absorb to be raised from its lowest (ground) state to its first excited state? Also, what is the wavelength of the photon emitted when the atom drops back to its ground state? • Solution: • When the atom is in its ground state it possesses -13.6 eV of energy, in the first excited state it possesses -3.4 eV of energy. • The electron is less strongly bound. • The energy required to lift the atom into the higher level is just the difference in energy between the two. • Hence the absorption energy. • W = Wu – Wl = 13.6 eV – 3.4 eV = 10.2 eV Prof John Watson

10. Worked Example – 2: Contd • The energy emitted as a photon when the electron falls back to ground must also equal the difference between the two levels, • Wph = W = 10.2 eV. • Hence wavelength of the emitted photon is • l = hc/Wph • 663x10-36 J s x 300x106 m s-1 • = --------------------------------------- • (10.2 eV x 160x10-21 J eV-1) • = 121 x 10-9 m • = 121 nm Prof John Watson

11. Atomic Gases • Energy structure described earlier describes a single atom • When vast numbers of atoms collect or combine to form an atomic gas • the atoms are so far away from each other • The spectral behaviour of the gas is the same as that of a single atom • If gas is excited by addition of energy (e.g. thermal, collisions) • The atoms will be spread amongst different states of excitation • some in ground state, some in excited states Prof John Watson

12. Distribution of Atoms in Thermal Equilibrium • At a given temperature, • atoms distributed amongst all available levels • Ground state will always contain the bulk of the atoms • other levels will contain exponentially less • Maxwell-Boltzmann distribution • describes the population of atoms in a given energy level at a given temp. • N2/N1 = exp(-DW/kT) Prof John Watson

13. Spectral Line Sources - 1 • The processes we have just described form the basis of light emission from gases which are in thermal equilibrium with their surroundings. • If a low pressure gas, such as hydrogen, is enclosed in an evacuated glass tube and excited by the passage of an electric current through it, • the constituent atoms and molecules continually absorb energy by collisions with electrons and also with each other. • no sooner do the atoms gain energy than they lose it again by a mixture of spontaneous emission of photons, heat and collisional de-excitation. • In such a dynamic situation, • the energy level populations are governed by the Boltzmann relationship at the specific temperature of the gas. Prof John Watson

14. Spectral line sources - 2 • The light emitted from such a source covers a wide range of wavelengths, • the photons have different amplitudes, • are emitted at different times and directions • have no constant phase relationship with each other. • The emitted spectrum is composed of discrete well-defined wavelengths of varying intensities • Such sources of light are known as gas discharge sources and are widely used as reference sources in spectroscopy. • They are said to be incoherent in time and space. • Typical examples are sodium & mercury vapour street lamps Prof John Watson

15. Dense Gases & Solids • When atoms are closer together, • as in a dense gas like the sun or a solid such as a piece of hot iron, • the energy structures associated with individual atoms influence one another. • This is the collective behaviour of many interacting atoms of different species, • rather than characteristic behaviour of individual atoms of a particular element. • The isolated energy levels shift slightly in energy • overlap in relation to each other to accommodate all the available electrons. • Instead of individual, discrete energy levels as for isolated atom, • bands of closely spaced energy levels develop. • In between these bands are forbidden zones of energy, energy gaps, which atoms cannot possess. • The nature of light emission from such materials • Depends on the formation and occupation of these bands Prof John Watson

16. Overlapping Energy levels Prof John Watson

17. Energy Bands in Solids • 3-d array of vast numbers of atoms or ions linked in crystalline structure • Valence electrons are far from nucleus • can be detached from the atom if enough energy supplied • free to move through crystal • Properties depend on how tightly bound electrons are in crystal • As for a gas, at a given temperature, the lowest available energy levels are filled with electrons • these are known as the valence bands. • above the VB are a range of mainly empty bands - the conduction bands. • Occupation of these bands with electrons determines the electrical, thermal and optical properties of the material Prof John Watson

18. Absorption & Emission from Solids • In some materials e.g metals and other hot solids • The VB and CB actually overlap • Electrons very loosely bound to host ions • very easy to break free from ions • free to "wander" around crystal  large numbers of free electrons • Emission and absorption of light occurs over very broad energy ranges • Spectral emission is in form of broadband continuum • Characterised by “black-body” radiation • Semiconductors • Electrons have moderate binding energies • Energy gap (between VB and CB) is of order of 1 eV • at absolute zero, all electrons are tightly bound • at high temps electrons can be excited from VB to CB • By thermal excitation, collisions or irradiation with light • relatively easy for electrons to absorb energy - be excited to CB • Also easy for electrons to de-excite to VB –emission of photons Prof John Watson

19. Excitation of electrons in solids takes place between VB and CB If the energy is supplied in form of light, the minimum photon energy required must equal the band gap energy WG Wph = h≥ WG The corresponding photon wavelength must be less than lG hc / WG Light of a longer wavelength has insufficient energy to excite the electrons This represents the long wavelength cut-off Absorption of Light in a Semiconductor Prof John Watson

20. Emission of Light from Semiconductors • Emission of a photon occurs when • an electron in a conduction band relaxes to a valence band • releases the corresponding amount of energy. • Emitted energy • Wph = h = hc/≥ WG • Since photons will be emitted from a range of energies in the CB to a range of energies in the VB • The photons will cover a widespread of wavelengths from the cut-off down • Because the energy states within each band are closely spaced • emitted spectrum will resemble a continuum below this cut-off Prof John Watson

21. Black Body Radiation - 1 • The radiation profile emitted from an ideal hot body can be described in terms of an ideal thermal radiator: the black body. • An ideal radiator is one that emits as much energy as it absorbs. • The overall spectral distribution is given by the Planckblack-body relationship which relates the radiant energy emitted by an ideal radiator to its temperature, • Spectral Radiant Emittance • Me() = (2hc2/5)/{exp(hc/kBT) - 1}[W nm-1 m-2] • The above relationships describes the radiant flux emitted per unit surface area per unit wavelength interval from a the surface of a source into a 2 solid angle. • The equation as it stands applies to unpolarised light, for linearly polarised light we should divide by 2. • Spectral Radiation Density • () = (82n3/c3)h/[exp(h/kBT)-1][J Hz-1 m-3] Prof John Watson

22. Spectral-emittance of a BB • Some important points: • Total radiant emittance at a given T equals area under the curve • Emitted flux increases as the temperature of the body increases, • that is, as the body gets hotter it emits more energy, and, • Peak of the curve shifts to lower wavelengths, (higher frequencies) as the T increases. • e.g. as a piece of steel is heated up its colour changes from dull red through orange to white-hot • A family of spectral radiant emittance curves for a BB as a function of emitted wavelength and temperature. Prof John Watson

23. Radiant Emittance • The total flux emitted from the source is obtained by integrating Me() over all wavelengths up to max • Me = eT4 •  is the Stefan constant  = 56.7 nW m-2 K-4] • e is a factor, called the emissivity of the surface, • varies between zero for no radiant emission and unity for a black body. • This is the maximum radiant power which can be emitted from any source at a given temperature • The radiant emittance from a line source at the same temperature can never be greater than the ideal BB radiant emission. Prof John Watson

24. Black Body Radiation - 3 • Finally, for each constant temperature curve, known as an isotherm, • the peak wavelength is obtained by differentiating with respect to  and equating to zero. • pkT = hc/4.97kB • In developing the black-body relationship, • Planck had to assume that the energy distribution within the source, was not a continuous function of frequency as assumed up until then • but existed in discrete quanta of energy known as photons. • On this basis, the energy is distributed amongst permitted modes of oscillation within the source volume. • The existence of these modes is analogous to the permitted modes of vibration on a stretched string or the modes of oscillation within an optical cavity Prof John Watson

25. Black-body Radiation - 4 • Exercise • Estimate the radiant emittance of a black body at a temperature of 300 K. • [460 W m-2] • Exercise • By making sensible assumptions about the surface area of a human body and its radiant temperature, calculate the total flux emitted. • [ 500 - 1000 W] • Exercise • If you wanted to take thermal pictures of the human body in the previous example, at what wavelength should the thermal camera have its peak sensitivity? • [10 µm] Prof John Watson

26. Thermal Sources - Summary • In summary, thermal light sources produce opticalradiation as a result of a dynamic process of excitation and spontaneous de-excitation of valence electrons. • Because excitation occurs to a number of different energy levels the radiation is composed of a wide range of wavelengths, emitted at random times and in random directions: • the light is said to be incoherent. • This behaviour is in stark contrast to that pertaining to a laser • the light emitted is almost monochromatic, in phase and unidirectional: • this light is said to be coherent. Prof John Watson