Atomic Physics and Lasers The idea of a photon –Black body radiation –Photoelectric Effect The structure of the atom How does a Laser work? Interaction.

Atomic Physics and Lasers The idea of a photon –Black body radiation –Photoelectric Effect The structure of the atom How does a Laser work? Interaction of lasers with matter –Laser safety Applications –Spectroscopy, detection of art forgery, flow cytometry, eye surgery.

The idea of a photon What is light? A wave? Well yes, but…. The wave picture failed to explain physical phenomena including : the spectrum of a blackbody the photoelectric effect line spectra emitted by atoms

Light from a hot object... Vibrational motion of particles produces light (we call the light “Thermal Radiation”)

The first clue that something was very, very wrong…Blackbody radiation What is a blackbody? What is a blackbody? An object which emits or absorbs all the radiation incident on it. An object which emits or absorbs all the radiation incident on it. Typical black bodiesTypical black bodies A light globeA light globe A box with a small hole in it.A box with a small hole in it.

Example of a Blackbody A BLACKBODY

We measure radiation as a function of frequency (wavelength) Example of a Blackbody

A Thermal Spectrum How does a thermal spectrum change when you change T?

Thermal Radiation Wavelength where flux is a maximum Total energy emitted by an object (or Luminosity W/m 2 ) T = Temp. in Kelvin k = 2.898 x 10 -3 m.K  = 5.7 x 10 -8 W/(m 2.K 4 ) Stefan’s Law Wien’s Law

The spectra we have looked at are for ideal objects that are perfect absorbers and emitters of light Matter at some temperature T Light and matter interact Light is perfectly absorbed Light is later emitted A BLACKBODY Oscillators

Problems with wave theory of light Take a Blackbody with a temperature, T Calculate how the spectrum would look if light behaved like a wave (Lord Rayleigh) Compare with what is actually observed FluxFlux FluxFlux Okay here Not so good here

Max Plank Max Plank Solved the problem in 1900 Oscillators cannot have any energy! They can be in states with fixed amounts of energy. The oscillators change state by emitting/absorbing packets with a fixed amounts of energy

Atomic Physics/Blackbody Max Planck (1858-1947) was impressed by the fact Max Planck (1858-1947) was impressed by the fact spectrum of a black body was a universal property. spectrum of a black body was a universal property. To get agreement between the experiment and the theory, Planck proposed a radical idea: Light comes in packets of energy called photons, and the energy is given by E= nhf To get agreement between the experiment and the theory, Planck proposed a radical idea: Light comes in packets of energy called photons, and the energy is given by E= nhf E =nhf The birth of the quantum theory = Planck’s hypothesis

The birth of the Photon In 1906, Einstein proved that Planck’s radiation law could be derived only if the energy of each oscillator is quantized. E n = nhf ; n = 0, 1, 2, 3, 4,... h=Planck’s constant= 6.626x10 -34 J.s f=frequency in Hz; E=energy in Joules (J). Einstein introduced the idea that radiation Einstein introduced the idea that radiation equals a collection of discrete energy quanta. equals a collection of discrete energy quanta. G.N. Lewis in 1926 named quanta “Photons”. G.N. Lewis in 1926 named quanta “Photons”.

Atomic Physics/Photon The energy of each photon: E = hf h=Planck’s constant f=frequency Ex. 1. Yellow light has a frequency of 6.0 x 10 14 Hz. Determine the energy carried by a quantum of this light. If the energy flux of sunlight reaching the earth’s surface is 1000 Watts per square meter, find the number of photons in sunlight that reach the earth’s surface per square meter per second. Ans. 2.5 eV and 2.5 x 10 21 photons / m 2 /s

Lecture 12

Shining light onto metals METAL Light in Nothing happens

Shining light onto metals METAL Different Energy Light in electrons come out

The Photoelectric Effect When light is incident on certain metallic surfaces, electrons are emitted = the Photoelectric Effect (Serway and Jewett 28.2) Einstein: A single photon gives up all its energy to a single electron E Photon = E Free + E Kinetic Need at least this much energy to free the electron Whatever is left makes it move

The Photoelectric Effect Frequency of Light Kinetic Energy of electron fofo Threshold frequency Different metals

Application of Photoelectric Effect Soundtrack on Celluloid film To speaker Metal plate

Another Blow for classical physics: Line Spectra The emission spectrum from a rarefied gas through which an electrical discharge passes consists of sharp spectral lines. Each atom has its own characteristic spectrum. Hydrogen has four spectral lines in the visible region and many UV and IR lines not visible to the human eye. The wave picture failed to explain these lines.

Atomic Physics/Line spectra 400 500 600 400 500 600 (nm) (nm) H The absorption spectrum for hydrogen; dark absorption lines occur at the same wavelengths as emission lines. Emission spectrum for hydrogen

Atomic Physics/Line Spectra 1 1 1 1 1  R (   n  m 2 ) R =Rydberg Constant = 1.09737x10 7 m -1 Lyman UV -13.6n=1 BalmerVisible -3.39 n=2 Paschen IR IR n=3-1.51 -0.85 n=4

So what is light? Both a wave and a particle. It can be both, but in any experiment only its wave or its particle nature is manifested. (Go figure!)

Two revolutions: The Nature of light and the nature of matter Light has both a particle and wave nature: Wave nature: –Diffraction, interference Particle nature –Black body radiation, photoelectric effect, line spectra Need to revise the nature of matter (it turns out that matter also has both a particle and wave nature

The spectrum from a blackbody 0 2 4 6 8 10 (10 -7 m) (10 -7 m) Relative Intensity 5000K 6000K Rayleigh- Jeans Jeans Observed Empirically:Empirically:  max)T = constant, Hotter = whiter l The wave picture (Rayleigh- Jeans) failed to explain the distribution of the energy versus wavelength. UV Catastrophe!!!!

Photoelectric Effect METAL Light in e Electron out

The Photoelectric Effect Photoelectric effect=When light is incident on certain metallic surfaces, photoelectrons are emitted. Einstein applied the idea of light quanta: In a photoemission process, a single photon gives up all its energy to a single electron. Energy of photon = Energy to free electron + KE of emitted electron

Atomic Physics/Photoelectric Effect hf = KE +   =work function; minimum energy needed to extract an electron. KE f, Hz f0f0f0f0 x x x x fo = threshold freq below which no photoemission occurs.

Atomic Physics/The Photoelectric Effect-Application Light Source Sound Track  speaker Phototube The sound on a movie film

incident.Photoelectric effect=When light is incident on certain metallic surfaces, photoelectrons are emitted. Einstein applied the idea of light quanta: In a photoemission process, a single photon gives up all its energy to a single electron. Energy of photon = Energy to free electron + KE of emitted electron The photoelectric effect

The Photoelectric Effect experiment Metal surfaces in a vacuum eject electrons when irradiated by UV light.

PE effect: 5 Experimental observations 1. If V is kept constant, the photoelectric current i p increases with increasing UV intensity. 2. Photoelectrons are emitted less than 1 nS after surface illumination 3. For a given surface material, electrons are emitted only if the incident radiation is at or above a certain frequency, independent of intensity. 4. The maximum kinetic energy, K max, of the photoelectrons is independent of the light intensity I. 5. The maximum kinetic energy, K max of the photoelectrons depends on the frequency of the incident radiation.

Failure of Classcial Theory Observation 1: is in perfect agreement with classical expectations Observation 2: Cannot explain this. Very weak intensity should take longer to accumulate energy to eject electrons Observation 3: Cannot explain this either. Classically no relation between frequency and energy. Observations 4 and 5: Cannot be explained at all by classical E/M waves.. Bottom line: Classical explanation fails badly.

Quantum Explanation. Einstein expanded Planck’s hypothesis and applied it directly to EM radiation EM radiation consists of bundles of energy (photons) These photons have energy E = hf φ, If an electron absorbs a photon of energy E = hf in order to escape the surface it uses up energy φ, called the work function of the metal φ φ is the binding energy of the electron to the surface This satisfies all 5 experimental observations.

hf = KE + φ hf = KE + φ ( φ =work function; minimum energy needed to extract an electron.) ( φ =work function; minimum energy needed to extract an electron.) fo = threshold freq, below which no photoemission occurs fo = threshold freq, below which no photoemission occurs KE f (Hz) f0f0f0f0 x x x x. Photoelectric effect

Light Source Sound Track  speaker Phototube Application: Film soundtracks

Example: A GaN based UV detector 5m5m This is a photoconductor

Response Function of UV detector

Choose the material for the photon energy required. Band-Gap adjustable by adding Al from 3.4 to 6.2 eV Band gap is direct (= efficient) Material is robust

The structure of a LED/Photodiode

Characterization of Detectors NEP= noise equivalent power = noise current (A/  Hz)/Radiant sensitivity (A/W) D = detectivity =  area/NEP IR cut-off maximum current maximum reverse voltage Field of view Junction capacitance

Photomultipliers hf e e e e e e PE effect Secondary electron emission Electron multiplication

Photomultiplier tube Combines PE effect with electron multiplication to provide very high detection sensitivity Can detect single photons. -V hf e Anode Dynode

Microchannel plates The principle of the photomultiplier tube can be extended to an array of photomultipliers This way one can obtain spatial resolution Biggest application is in night vision goggles for military and civilian use

http://hea-www.harvard.edu/HRC/mcp/mcp.html MCPs consist of arrays of tiny tubes Each tube is coated with a photomultiplying film The tubes are about 10 microns wide Microchannel plates

MCP array structure http://hea-www.harvard.edu/HRC/mcp/mcp.html

MCP fabrication http://hea-www.harvard.edu/HRC/mcp/mcp.html

Disadvantages of Photomultiplers as sensors Need expensive and fiddly high vacuum equipment Expensive Fragile Bulky

Photoconductors As well as liberating electrons from the surface of materials, we can excite mobile electrons inside materials The most useful class of materials to do this are semiconductors The mobile electrons can be measured as a current proportional to the intensity of the incident radiation Need to understand semiconductors….

Photoelecric effect with Energy Bands EfEf E vac Semiconductor Band gap: E g =E c -E v Metal EfEf E vac EcEc EvEv

Photoconductivity Semiconductor Ef Evac Ec Ev e To amplifier

Photoconductors E g (~1 eV) can be made smaller than metal work functions  (~5 eV) Only photons with Energy E=hf>E g are detected This puts a lower limit on the frequency detected Broadly speaking, metals work with UV, semiconductors with optical

Band gap Engineering Semiconductors can be made with a band gap tailored for a particular frequency, depending on the application. Wide band gap semiconductors good for UV light III-V semiconductors promising new materials

Lecture 13

Photodiodes Photoconductors are not always sensitive enough Use a sandwich of doped semiconductors to create a “depletion region” with an intrinsic electric field We will return to these once we know more about atomic structure

Orientation Previously, we considered detection of photons. Next, we develop our understanding of photon generation We need to consider atomic structure of atoms and molecules

Line Emission Spectra The emission spectrum from an exited material (flame, electric discharge) consists of sharp spectral lines Each atom has its own characteristic spectrum. Hydrogen has four spectral lines in the visible region and many UV and IR lines not visible to the human eye The wave picture of electromagnetic radiation completely fails to explain these lines (!)

Atomic Physics/Line Spectra The absorption spectrum for hydrogen: dark absorption lines occur at the same wavelengths as emission lines.

Atomic Physics/Line Spectra

Rutherford’s Model

Problem 1: From the Classical Maxwell’s Equation, an accelerating electron emits radiation, losing energy. This radiation covers a continuous range in frequency, contradicting observed line spectra. Problem 2: Rutherford’s model failed to account for the stability of the atom. +Ze Fatal problems !

Bohr’s Model Assumptions: Electrons can exist only in stationary states Dynamical equilibrium governed by Newtonian Mechanics Transitions between different stationary states are accompanied by emission or absorption of radiation with frequency  E = hf

Transitions between states hf E3 E1 E2 E 3 - E 2 = hf Nucleus

How big is the Bohr Hydrogen Atom? R n =a 0 n 2 /Z 2 R n =radius of atomic orbit number n a 0 =Bohr radius = 0.0629 nm Z=atomic numner of element Exercise: What is the diameter of the hydrogen atom?

What energy Levels are allowed?

Exercise A hydrogen atom makes a transition between the n=2 state and the n=1 state. What is the wavelength of the light emitted? Step1: Find out the energy of the photon: E 1 =13.6 eV E 2 =13.6/4=3.4 eV hence the energy of the emitted photon is 10.2 eV Step 2: Convert energy into wavelength. E=hf, hence f=E/h =10.2*1.6x10 -19 /6.63x10 -34 = 2.46x10 15 Hz Step 3: Convert from frequency into wavelength: =c/f =3x10 8 /2.46x10 15 = 121.5 nm

Emission versus absorption E initial E final Emission hf = E final - E initial E final E initial Absorption hf = E final - E initial Explains Hydrogen spectra

What happens when we have more than one electron?

Apply rules: Pauli principle: only two electrons per energy level Fill the lowest energy levels first In real atoms the energy levels are more complicated than suggested by the Bohr theory Empty

Atomic Physics – X-rays How are X-rays produced? High energy electrons are fired at high atomic number targets. Electrons will be decelerated emitting X-rays. Energy of electron given by the applied potential (E=qV)

The X-ray spectrum consists of two parts: 1. A continuous spectrum 2. A series of sharp lines. 0.5 A 0 Intensity X-rays

The continuous spectrum depends on the voltage across the tube and does not depend on the target material. The continuous spectrum depends on the voltage across the tube and does not depend on the target material. This continuous spectrum is explained by the decelerating electron as it enters the metal This continuous spectrum is explained by the decelerating electron as it enters the metal 15 keV 25 keV 0.83 A 0 0.5 A 0 Intensity X-rays

Atomic Physics/X-rays The characteristic spectral lines depend on the target material. These Provides a unique signature of the target’s atomic structure Bohr’s theory was used to understand the origin of these lines

Atomic Physics – X-rays The K-shell corresponds to n=1 The L-shell corresponds to n=2 M is n=2, and so on

Atomic Spectra – X-rays Example: Estimate the wavelength of the X-ray emitted from a tantalum target when an electron from an n=4 state makes a transition to an empty n=1 state (Z tantalum =73)

Emission from tantalum

Atomic Physics – X-rays The X-ray is emitted when an e from an n=4 states falls into the empty n=1 state E i = -13.6Z 2 /n 2 = -(73) 2 (13.6 eV)/ 4 2 = -4529 eV E f = -13.6(73) 2 /1 2 = -72464 eV hf = E i - E f = 72474-4529= 67945 eV = 67.9 keV What is the wavelength? Ans = 0.18 Å

Using X-rays to probe structure X-rays have wavelengths of the order of 0.1 nm. Therefore we expect a grating with a periodicity of this magnitude to strongly diffract X-rays. Crystals have such a spacing! Indeed they do diffract X-rays according to Bragg’s law 2dsin  = n We will return to this later in the course when we discuss sensors of structure

Line Width Real materials emit or absorb light over a small range of wavelengths Example here is Neon

Stimulated emission E2E2 E1E1 E 2 - E 1 = hf Two identical photons Same - frequency - direction - phase - polarisation

Lasers LASER - acronym for –Light Amplification by Stimulated Emission of Radiation –produce high intensity power at a single frequency (i.e. monochromatic)

Principles of Lasers Usually have more atoms in low(est) energy levels Atomic systems can be pumped so that more atoms are in a higher energy level. Requires input of energy Called Population Inversion: achieved via Electric discharge Optically Direct current

Population inversion N2N2 N1N1 Energy Lots of atoms in this level Few atoms in this level Want N 2 - N 1 to be as large as possible

Population Inversion (3 level System) E2 (pump state), t 2 E1 (metastable- state), t s E1 (Ground state) Laser output hf Pump light hf o t s >t 2

Light Amplification Light amplified by passing light through a medium with a population inversion. Leads to stimulated emission

Requires a cavity enclosed by two mirrors. Provides amplification Improves spectral purity Initiated by “spontaneous emission”

Laser Cavity Cavity possess modes Analagous to standing waves on a string Correspond to specific wavelengths/frequencies These are amplified

Spectral output

Properties of Laser Light. Can be monochromatic Coherent Very intense Short pulses can be produced

Types of Lasers Large range of wavelengths available: Ammonia (microwave) MASER CO 2 (far infrared) Semiconductor (near-infrared, visible) Helium-Neon (visible) ArF – excimer (ultraviolet) Soft x-ray (free-electron, experimental)

Lecture 16

Molecular Spectroscopy Molecular Energy Levels –Vibrational Levels –Rotational levels Population of levels Intensities of transitions General features of spectroscopy An example: Raman Microscopy –Detection of art forgery –Local measurement of temperature

Molecular Energies Classical Quantum Energy E0E0 E4E4 E3E3 E2E2 E1E1

Molecular Energy Levels Translation Nuclear Spin Electronic Spin Rotation Vibration Electronic Orbital Increasing Energy etc. Electronic orbital Vibrational E total + E orbital + E vibrational + E rotational +….. Rotational

Molecular Vibrations Longitudinal Vibrations along molecular axis E=(n+1/2)hf where f is the classical frequency of the oscillator where k is the ‘spring constant Energy Levels equally spaced How can we estimate the spring constant? m M r k k = f (r)  = Mm/(M+m) Atomic mass concentrated at nucleus

Molecular Vibrations E vib =(n+1/2)hf  f =0.273eV/(1/2(h)) = 2.07x10 13 Hz To determine k we need μ μ=(Mm)/(M+m) =(1.008) 2 /2(1.008) amu =(0.504)1.66x10 -27 kg =0.837x10 -27 kg k= μ(2πf) 2 =576 N/m m M r K K = f (r)  = Mm/(M+m) Hydrogen molecules, H 2, have ground state vibrational energy of 0.273eV. Calculate force constant for the H 2 molecule ( mass of H is 1.008 amu)

Molecular Rotations Molecule can also rotate about its centre of mass v 1 =  R 1 ; v 2 =  R 2 L = M 1 v 1 R 1 + M 2 v 2 R 2 = (M 1 R 1 2 + M 2 R 2 2 )  = I  E KE = 1/2M 1 v 1 2 +1/2M 2 v 2 2 = 1/2I  2 R1R1 R2R2 M1M1 M2M2

Molecular Rotations Hence, E rot = L 2 /2I Now in fact L 2 is quantized and L 2 =l(l+1)h 2 /4  2 Hence E rot =l(l+1)(h 2 /4  2 )/2I Show that  E rot =(l+1) h 2 /4  2 /I. This is not equally spaced Typically  E rot =50meV (i.e for H 2 )

Populations of Energy Levels Depends on the relative size of kT and  E ΔE<<kT ΔE=kT ΔE>kT ΔEΔE (Virtually) all molecules in ground state States almost equally populated

Intensities of Transitions Quantum Mechanics predicts the degree to which any particular transition is allowed. Intensity also depends on the relative population of levels Strong absorption Weak emission Transition saturated hv 2hv hv

General Features of Spectroscopy Peak Height or intensity Frequency Lineshape or linewidth

Raman Spectroscopy Raman measures the vibrational modes of a solid The frequency of vibration depends on the atom masses and the forces between them. Shorter bond lengths mean stronger forces. m M r K f vib = (K/  ) 1/2 K = f(r)  = Mm/(M+m)

Raman Spectroscopy Cont... Laser In Sample Lens Monochromator CCD array Incident photons typically undergo elastic scattering. Small fraction undergo inelastic  energy transferred to molecule. Raman detects change in vibrational energy of a molecule.

Raman Microscope

Pb white Ti white Tom Roberts, ‘Track To The Harbour’ dated 1899 Detecting Art Forgery Ti-white became available only circa 1920. The Roberts painting shows clear evidence of Ti white but is dated 1899

Raman Spectroscopy and the Optical Measurement of Temperature Probability that a level is occupied is proportional to exp(  E/kT)

Lecture 17

Optical Fibre Sensors Non-Electrical Explosion-Proof (Often) Non-contact Light, small, snakey => “Remotable” Easy(ish) to install Immune to most EM noise Solid-State (no moving parts) Multiplexing/distributed sensors.

Applications Lots of Temp, Pressure, Chemistry Automated production lines/processes Automotive (T,P,Ch,Flow) Avionic (T,P,Disp,rotn,strain,liquid level) Climate control (T,P,Flow) Appliances (T,P) Environmental (Disp, T,P)

Optical Fibre Principles Cladding: glass or Polymer Core: glass, silica, sapphire TIR keeps light in fibre Different sorts of cladding: graded index, single index, step index.

Optical Fibre Principles Snell’s Law: n 1 sin  1 =n 2 sin  2  crit = arcsin(n 2 /n 1 ) Cladding reduces entry angle Only some angles (modes) allowed

Optical Fibre Modes

Phase and Intensity Modulation methods Optical fibre sensors fall into two types: –Intensity modulation uses the change in the amount of light that reaches a detector, say by breaking a fibre. –Phase Modulation uses the interference between two beams to detect tiny differences in path length, e.g. by thermal expansion.

Intensity modulated sensors: Axial displacement: 1/r 2 sensitivity Radial Displacement

Microbending (1) Microbending –Bent fibers lose energy –(Incident angle changes to less than critical angle)

Microbending (2): Microbending –“Jaws” close a bit, less transmission – Give jaws period of light to enhance effect Applications: – Strain gauge – Traffic counting

More Intensity modulated sensors Frustrated Total Internal Reflection: –Evanescent wave bridges small gap and so light propagates –As the fibers move (say car passes), the gap increases and light is reflected Evanescent Field Decay @514nm

More Intensity modulated sensors Frustrated Total Internal Reflection: Chemical sensing –Evanescent wave extends into cladding –Change in refractive index of cladding will modify output intensity

Disadvantages of intensity modulated sensors Light losses can be interpreted as change in measured property −Bends in fibres −Connecting fibres −Couplers Variation in source power

Phase modulated sensors Bragg modulators: –Periodic changes in refractive index –Bragg wavelenght (λ b ) which satisfies λ b =2nD is reflected –Separation (D) of same order as than mode wavelength

Phase modulated sensors Multimode fibre with broad input spectrum Strain or heating changes n so reflected wavelength changes Suitable for distributed sensing λ b =2nD Period,D

Phase modulated sensors – distributed sensors

Temperature Sensors Reflected phosphorescent signal depends on Temperature Can use BBR, but need sapphire waveguides since silica/glass absorbs IR

Phase modulated sensors Fabry-Perot etalons: –Two reflecting surfaces separated by a few wavelengths –Air gap forms part of etalon –Gap fills with hydrogen, changing refractive index of etalon and changing allowed transmitted frequencies.

Digital switches and counters Measure number of air particles in air or water gap by drop in intensity –Environmental monitoring Detect thin film thickness in manufacturing –Quality control Counting things –Production line, traffic.

NSOM/AFM Combined SEM - 70nm aperture Bent NSOM/AFM Probe Optical resolution determined by diffraction limit (~λ) Illuminating a sample with the "near-field" of a small light source. Can construct optical images with resolution well beyond usual "diffraction limit", (typically ~50 nm.)

NSOM Setup Ideal for thin films or coatings which are several hundred nm thick on transparent substrates (e.g., a round, glass cover slip).