atomic physics and lasers

Atomic Physics and LasersThe idea of a photon Black body radiation Photoelectric Effect The structure of the atomHow does a Laser work? Interaction of lasers with matterLaser safetyApplicationsSpectroscopy, detection of art forgery, flow cytometry, eye surgery.

The idea of a photonWhat 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 wrongBlackbody radiation

What is a blackbody? An object which emits or absorbs all the radiation incident on it.Typical black bodiesA light globe A box with a small hole in it.

Example of a BlackbodyA BLACKBODY

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

A Thermal SpectrumHow does a thermal spectrum change when you change T?

Thermal RadiationWavelength where flux is a maximumTotal energy emittedby an object (or Luminosity W/m2)T = Temp.in Kelvink = 2.898 x 10-3 m.Ks = 5.7 x 10-8 W/(m2.K4)Stefans LawWiens Law

Light and matter interactThe spectra we have looked at are for ideal objects that are perfect absorbers and emitters of lightLight is perfectlyabsorbedLight is lateremittedA BLACKBODY

Problems with wave theory of lightTake 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

Max PlankMax Plank Solved the problem in 1900Oscillators 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 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= nhfE =nhfThe birth of the quantumtheory = Plancks hypothesis

The birth of the PhotonIn 1906, Einstein proved that Plancks radiation law could be derived only if the energy of each oscillator is quantized. En = nhf ; n = 0, 1, 2, 3, 4,... h=Plancks constant= 6.626x10 -34 J.s f=frequency in Hz; E=energy in Joules (J).

Einstein introduced the idea that radiation equals a collection of discrete energy quanta. G.N. Lewis in 1926 named quanta Photons.

Atomic Physics/PhotonThe energy of each photon: E = hf h=Plancks constant f=frequency Ex. 1. Yellow light has a frequency of 6.0 x 1014 Hz. Determine the energy carried by a quantum of thislight. If the energy flux of sunlight reaching the earthssurface is 1000 Watts per square meter, find the number of photons in sunlight that reach the earths surfaceper square meter per second. Ans. 2.5 eV and 2.5 x 10 21 photons / m 2 /s

Shining light onto metalsMETALLight inNothing happens

Shining light onto metalsMETAL

The Photoelectric EffectWhen 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 electronEPhoton = EFree + EKineticNeed at least this much energy to free the electronWhatever is leftmakes it move

The Photoelectric Effect

Application of Photoelectric EffectSoundtrack on Celluloid filmTo speaker

Another Blow for classical physics: Line SpectraThe 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 (nm)HThe absorption spectrum for hydrogen; dark absorptionlines occur at the same wavelengths as emission lines.Emission spectrum for hydrogen

Atomic Physics/Line Spectra

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 matterLight has both a particle and wave nature:Wave nature:Diffraction, interferenceParticle natureBlack body radiation, photoelectric effect, line spectraNeed to revise the nature of matter (it turns out that matter also has both a particle and wave nature

The spectrum from a blackbody0 2 4 6 8 10 (10 -7 m)

Relative Intensity

5000K6000KRayleigh- JeansObservedEmpirically:(max)T = constant, Hotter = whiter

The wave picture (Rayleigh-Jeans) failed to explain the distribution of the energy versus wavelength. UV Catastrophe!!!!

Photoelectric EffectMETALLight ineElectron out

The Photoelectric EffectPhotoelectric 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 ofphoton=Energy to freeelectron+KE of emittedelectron

Atomic Physics/Photoelectric Effect hf = KE + =work function; minimum energy needed to extract an electron.KEf, Hzf0xxxxfo = threshold freqbelow which no photoemission occurs.

Atomic Physics/The Photoelectric Effect-Application Light SourceSound TrackspeakerPhototubeThe sound on amovie film

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 ofphoton=Energy to freeelectron+KE of emittedelectron

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

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

Failure of Classcial TheoryObservation 1: is in perfect agreement with classical expectations Observation 2: Cannot explain this. Very weak intensity should take longer to accumulate energy to eject electronsObservation 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 Plancks hypothesis and applied it directly to EM radiation EM radiation consists of bundles of energy (photons) These photons have energy E = hf If an electron absorbs a photon of energy E = hf in order to escape the surface it uses up energy , called the work function of the metal is the binding energy of the electron to the surface This satisfies all 5 experimental observations.

Photoelectric effect hf = KE + ( =work function; minimum energy needed to extract an electron.) fo = threshold freq, below which no photoemission occursKEf (Hz)f0xxxx.

Application: Film soundtracks Light SourceSound TrackspeakerPhototube

Example: A GaN based UV detectorThis 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 eVBand gap is direct (= efficient)Material is robust

The structure of a LED/Photodiode

Characterization of DetectorsNEP= noise equivalent power = noise current (A/Hz)/Radiant sensitivity (A/W)D = detectivity = area/NEPIR cut-offmaximum currentmaximum reverse voltageField of viewJunction capacitance

PhotomultipliershfeeeeeePE effectSecondary electron emissionElectron multiplication

Photomultiplier tubeCombines PE effect with electron multiplication to provide very high detection sensitivityCan detect single photons.

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

Microchannel plateshttp://hea-www.harvard.edu/HRC/mcp/mcp.htmlMCPs consist of arrays of tiny tubesEach tube is coated with a photomultiplying filmThe tubes are about 10 microns wide

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

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

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

PhotoconductorsAs 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 radiationNeed to understand semiconductors.

Photoelecric effect with Energy BandsEfEvacSemiconductorBand gap: Eg=Ec-Ev

Photoconductivity

PhotoconductorsEg (~1 eV) can be made smaller than metal work functions f (~5 eV)Only photons with Energy E=hf>Eg are detectedThis puts a lower limit on the frequency detectedBroadly speaking, metals work with UV, semiconductors with optical

Band gap EngineeringSemiconductors 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

Photoconductivity

PhotodiodesPhotoconductors 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 SpectraThe absorption spectrum for hydrogen: dark absorption lines occur at the same wavelengths as emission lines.

Rutherfords Model

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

Bohrs ModelAssumptions:Electrons can exist only in stationary statesDynamical equilibrium governed by Newtonian MechanicsTransitions between different stationary states are accompanied by emission or absorption of radiation with frequency E = hf

Transitions between stateshfE3E1E2E3 - E2 = hfNucleus

How big is the Bohr Hydrogen Atom?Rn=a0n2/Z2Rn=radius of atomic orbit number na0=Bohr radius = 0.0629 nmZ=atomic numner of elementExercise: 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: E1=13.6 eV E2=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 = 2.46x1015 Hz Step 3: Convert from frequency into wavelength: =c/f =3x108/2.46x1015 = 121.5 nm

Emission versus absorptionEinitialEfinalEmissionhf = Efinal - EinitialEfinalEinitialAbsorptionhf = Efinal - EinitialExplains Hydrogen spectra

What happens when we have more than one electron?

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 theoryEmpty

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)

X-raysThe X-ray spectrum consists of two parts:1. A continuous spectrum2. A series of sharp lines.0.5 A0Intensity

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 metal15 keV25 keV0.83 A00.5 A0IntensityX-rays

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

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

Atomic Spectra X-raysExample: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 (Ztantalum =73)

Emission from tantalum

Atomic Physics X-raysThe X-ray is emitted when an e from an n=4 states falls into the empty n=1 stateEi= -13.6Z2/n2 = -(73)2(13.6 eV)/ 42 = -4529 eVEf= -13.6(73)2/12 = -72464 eVhf = Ei- Ef= 72474-4529= 67945 eV = 67.9 keVWhat is the wavelength?Ans = 0.18

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 Braggs law2dsin = 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 emissionE2E1E2 - E1 = hfTwo identical photonsSame- frequency - direction- phase- polarisation

LasersLASER - acronym forLight Amplification by Stimulated Emission of Radiationproduce high intensity power at a single frequency (i.e. monochromatic)

Principles of LasersUsually have more atoms in low(est) energy levelsAtomic 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 inversionN2N1EnergyLots of atoms in this levelFew atoms in this levelWant N2 - N1 to be as large as possible

Population Inversion (3 level System)E2 (pump state), t2E1 (metastable- state), tsE1 (Ground state)Laser outputhf

Pump lighthfots >t2

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

LaserRequires a cavity enclosed by two mirrors. Provides amplification Improves spectral purity Initiated by spontaneous emission

Laser CavityCavity 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 CoherentVery intenseShort pulses can be produced

Types of LasersLarge range of wavelengths available: Ammonia (microwave) MASER CO2 (far infrared) Semiconductor (near-infrared, visible) Helium-Neon (visible) ArF excimer (ultraviolet) Soft x-ray (free-electron, experimental)

Lecture 16

Molecular SpectroscopyMolecular Energy LevelsVibrational LevelsRotational levelsPopulation of levelsIntensities of transitionsGeneral features of spectroscopyAn example: Raman MicroscopyDetection of art forgeryLocal measurement of temperature

Molecular EnergiesClassicalQuantumEnergyE0E4E3E2E1

Molecular Energy LevelsTranslationNuclear SpinElectronic SpinRotation Vibration Electronic OrbitalIncreasing Energyetc.Electronic orbitalVibrationalEtotal + Eorbital + Evibrational + Erotational +..

Rotational

Molecular VibrationsLongitudinal Vibrations along molecular axisE=(n+1/2)hf where f is the classical frequency of the oscillator

where k is the spring constantEnergy Levels equally spacedHow can we estimate the spring constant?mMrkk = f (r) = Mm/(M+m)Atomic mass concentrated at nucleus

Molecular Vibrations

Evib=(n+1/2)hf f =0.273eV/(1/2(h)) = 2.07x1013 Hz

To determine k we need =(Mm)/(M+m) =(1.008)2/2(1.008) amu =(0.504)1.66x10-27kg =0.837x10-27kg

k= (2f)2 =576 N/m Hydrogen molecules, H2, have ground state vibrational energy of 0.273eV. Calculate force constant for the H2 molecule (mass of H is 1.008 amu)

Molecular RotationsMolecule can also rotate about its centre of massv1 = wR1 ; v2 = wR2L = M1v1R1+ M2v2R2 = (M1R12+ M2R22)w = IwEKE = 1/2M1v12+1/2M2v22 = 1/2Iw2R1R2M1M2

Molecular RotationsHence, Erot= L2/2INow in fact L2 is quantized and L2=l(l+1)h2/4p2Hence Erot=l(l+1)(h2/4p2)/2IShow that DErot=(l+1) h2/4p2/I. This is not equally spacedTypically DErot=50meV (i.e for H2)

Populations of Energy LevelsDepends on the relative size of kT and DEE

Intensities of TransitionsQuantum Mechanics predicts the degree to which any particular transition is allowed. Intensity also depends on the relative population of levelsStrong absorptionWeak emissionTransition saturatedhv2hvhvhvhv

General Features of SpectroscopyPeak Height or intensityFrequencyLineshape or linewidth

Raman SpectroscopyRaman measures the vibrational modes of a solidThe frequency of vibration depends on the atom masses and the forces between them.Shorter bond lengths mean stronger forces.

Raman Spectroscopy Cont...Laser InSampleLensMonochromatorCCD arrayIncident 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 whiteTi white Tom Roberts, Track To The Harbour dated 1899Detecting 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 TemperatureProbability that a level is occupied is proportional to exp(DE/kT)

Lecture 17

Optical Fibre SensorsNon-ElectricalExplosion-Proof(Often) Non-contactLight, small, snakey => RemotableEasy(ish) to installImmune to most EM noiseSolid-State (no moving parts)Multiplexing/distributed sensors.

ApplicationsLots of Temp, Pressure, Chemistry Automated production lines/processesAutomotive (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 PrinciplesCladding: glass or PolymerCore: glass, silica, sapphireTIR keeps light in fibreDifferent sorts of cladding: graded index, single index, step index.

Optical Fibre PrinciplesSnells Law: n1sin1=n2sin2 crit = arcsin(n2/n1)Cladding reduces entry angleOnly some angles (modes) allowed

Optical Fibre Modes

Phase and Intensity Modulation methodsOptical 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/r2 sensitivityRadial Displacement

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

Microbending (2):MicrobendingJaws close a bit, less transmission Give jaws period of light to enhance effectApplications: Strain gauge Traffic counting

More Intensity modulated sensorsFrustrated Total Internal Reflection:Evanescent wave bridges small gap and so light propagatesAs the fibers move (say car passes), the gap increases and light is reflectedEvanescent Field Decay @514nm

More Intensity modulated sensors Frustrated Total Internal Reflection: Chemical sensingEvanescent wave extends into claddingChange in refractive index of cladding will modify output intensity

Disadvantages of intensity modulated sensorsLight losses can be interpreted as change in measured propertyBends in fibresConnecting fibresCouplers

Variation in source power

Phase modulated sensorsBragg modulators:Periodic changes in refractive indexBragg wavelenght (b) which satisfies b=2nD is reflectedSeparation (D) of same order as than mode wavelength

Phase modulated sensorsMultimode fibre with broad input spectrumStrain or heating changes n so reflected wavelength changesSuitable for distributed sensing b=2nDPeriod,D

Phase modulated sensors distributed sensors

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

Phase modulated sensorsFabry-Perot etalons:Two reflecting surfaces separated by a few wavelengthsAir gap forms part of etalonGap fills with hydrogen, changing refractive index of etalon and changing allowed transmitted frequencies.

Digital switches and countersMeasure number of air particles in air or water gap by drop in intensityEnvironmental monitoring Detect thin film thickness in manufacturingQuality controlCounting thingsProduction line, traffic.

NSOM/AFM CombinedSEM - 70nm apertureBent NSOM/AFM ProbeOptical resolution determined by diffraction limit (~) Illuminating a sample with the "near-field" of a small light source. Can construct optical images with resolution well beyond usual "diffraction limit", (typically ~50nm.)

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

Lecture 12