Atomic Physics and Lasers

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? An object which emits or absorbs all the radiation incident on it. Typical black bodies A light globe 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 We measure radiation as a function of frequency (wavelength)

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

Thermal Radiation T = Temp. Wien’s Law Stefan’s Law in Kelvin
Total energy emitted by an object (or Luminosity W/m2) Wavelength where flux is a maximum s = 5.7 x 10-8 W/(m2.K4) k = x 10-3 m.K Wien’s Law Stefan’s Law

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

Problems with wave theory of light
u x Not so good here 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 Okay here F l u x

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 Max Plank

Atomic Physics/Blackbody
Max Planck ( ) was impressed by the fact spectrum of a black body was a universal property. 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 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. En = nhf ; n = 0, 1, 2, 3, 4,... h=Planck’s constant= 6.626x 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/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 1014 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 eV and x photons / m 2 /s

Shining light onto metals
Light in Nothing happens METAL

electrons come out Different Energy Light in METAL

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 EPhoton = EFree + EKinetic Need at least this much energy to free the electron Whatever is left makes it move

Frequency of Light Kinetic Energy of electron Different metals fo Threshold frequency

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

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
(nm) H Emission spectrum for hydrogen The absorption spectrum for hydrogen; dark absorption lines occur at the same wavelengths as emission lines.

Atomic Physics/Line Spectra
Lyman UV -13.6 n=1 Balmer Visible -3.39 n=2 Paschen IR n=3 -1.51 -0.85 n=4 R ( nm2 ) R =Rydberg Constant = x10 7m-1

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
Empirically: (max)T = constant, Hotter = whiter The wave picture (Rayleigh-Jeans) failed to explain the distribution of the energy versus wavelength. UV Catastrophe!!!! 6000K Rayleigh- Jeans Relative Intensity Observed 5000K  ( m)

Photoelectric Effect Light in e Electron out METAL

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
=work function; minimum energy needed to extract an electron. hf = KE +  KE x fo = threshold freq below which no photoemission occurs. x x x f0 f, Hz

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

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 = +

The Photoelectric Effect experiment
Metal 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 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 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 is the binding energy of the electron to the surface This satisfies all 5 experimental observations .

Photoelectric effect hf = KE + φ
( φ =work function; minimum energy needed to extract an electron.) fo = threshold freq, below which no photoemission occurs KE x . x x x f0 f (Hz)

Application: Film soundtracks
Phototube Light Source speaker

Example: A GaN based UV detector
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 PE effect Secondary electron Electron multiplication
hf e e e PE effect Secondary electron emission Electron multiplication

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

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

Microchannel plates MCPs consist of arrays of tiny tubes
Each tube is coated with a photomultiplying film The tubes are about 10 microns wide

MCP array structure

MCP fabrication

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
Metal Evac Ef Evac Ec Ev Ef Semiconductor Band gap: Eg=Ec-Ev

Photoconductivity Semiconductor Ef Evac Ec Ev e To amplifier

Photoconductors Eg (~1 eV) can be made smaller than metal work functions f (~5 eV) Only photons with Energy E=hf>Eg 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 (!)

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

Rutherford’s Model

Fatal problems ! 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

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 E3 - E2 = hf E2 E1 Nucleus

How big is the Bohr Hydrogen Atom?
Rn=a0n2/Z2 Rn=radius of atomic orbit number n a0=Bohr radius = 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: 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 = nm

Emission versus absorption
Efinal Einitial Efinal Einitial hf = Efinal - Einitial hf = Efinal - Einitial 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)

X-rays The X-ray spectrum consists of two parts: 1. A continuous
2. A series of sharp lines. Intensity 0.5 A0 

X-rays 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 Intensity 25 keV 15 keV 0.5 A0 0.83 A0 

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

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 (Ztantalum =73)

Emission from tantalum

The X-ray is emitted when an e from an n=4 states falls into the empty n=1 state Ei= -13.6Z2/n2 = -(73)2(13.6 eV)/ 42 = eV Ef= -13.6(73)2/12 = eV hf = Ei- Ef= = 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 E2 - E1 = hf E2 E1 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 Lots of atoms in this level N2 Energy N1
Few atoms in this level Want N2 - N1 to be as large as possible

Population Inversion (3 level System)
E2 (pump state), t2 ts >t2 E1 (metastable- state), ts Pump light hfo Laser output hf E1 (Ground state)

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

Laser 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 CO2 (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 E4 E3 Energy E2 E1 E0

Molecular Energy Levels
Electronic orbital Vibrational Translation Nuclear Spin Electronic Spin Rotation Vibration Electronic Orbital Rotational Increasing Energy etc. Etotal Eorbital Evibrational Erotational +…..

Atomic mass concentrated at nucleus
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? r k m M  = Mm/(M+m) Atomic mass concentrated at nucleus k = f (r)

Molecular Vibrations Hydrogen molecules, H2, have ground state vibrational energy of 0.273eV. Calculate force constant for the H2 molecule (mass of H is amu) Evib=(n+1/2)hf  f =0.273eV/(1/2(h)) = 2.07x1013 Hz To determine k we need μ μ=(Mm)/(M+m) =(1.008)2/2(1.008) amu =(0.504)1.66x10-27kg =0.837x10-27kg k= μ(2πf)2 =576 N/m m M r K K = f (r)  = Mm/(M+m)

Molecular Rotations Molecule can also rotate about its centre of mass
v1 = wR1 ; v2 = wR2 L = M1v1R1+ M2v2R2 = (M1R12+ M2R22)w = Iw EKE = 1/2M1v12+1/2M2v22 = 1/2Iw2 M2 M1 R1 R2

Molecular Rotations Hence, Erot= L2/2I
Now in fact L2 is quantized and L2=l(l+1)h2/4p2 Hence Erot=l(l+1)(h2/4p2)/2I Show that DErot=(l+1) h2/4p2/I. This is not equally spaced Typically DErot=50meV (i.e for H2)

Populations of Energy Levels
Depends on the relative size of kT and DE ΔE<<kT ΔE=kT ΔE>kT ΔE (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 hv 2hv hv hv hv Strong absorption Weak emission Transition saturated

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

Raman Microscope

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

Raman Spectroscopy and the Optical Measurement of Temperature
Probability that a level is occupied is proportional to exp(DE/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.

Snell’s Law: n1sin1=n2sin2 crit = arcsin(n2/n1) 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/r2 sensitivity Radial Displacement

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

Microbending (2): Microbending Applications:
“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

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 (λb) which satisfies λb=2nD is reflected Separation (D) of same order as than mode wavelength

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

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

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 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.) SEM - 70nm aperture

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

Lecture 12