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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 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 k T = Temp. 4 L T in Kelvin T MAX Wavelength where flux is a maximum k = 2.898 x 10-3 m.K Wien’s Law Total energy emitted by an object (or Luminosity W/m2) = 5.7 x 10-8 W/(m2.K4) 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 Light is later emitted Light is perfectly absorbed Oscillators Matter at some temperature T A BLACKBODY • • • Problems with wave theory of light 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 F l u x F l u x Okay here Max Plank Solved the problem in 1900 Max Plank • 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 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 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= 6.626x10 -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/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. 2.5 eV and 2.5 x 10 21 photons / m 2 /s Shining light onto metals Light in Nothing happens METAL Shining light onto metals Different Energy Light in electrons come out 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 The Photoelectric Effect Kinetic Energy of electron Different metals fo Threshold frequency Frequency of Light 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) 400 500 600 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 -0.85 -1.51 -3.39 Balmer Visible Paschen IR n=4 n=3 n=2 -13.6 n=1 Lyman UV R =Rydberg 1 1 1 Constant = R( ) 1.09737x10 7m-1 nm2 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 wave picture (RayleighJeans) failed to explain the distribution of the energy versus wavelength. UV Catastrophe!!!! 6000K The RayleighJeans Observed 5000K 0 2 4 6 (10 -7 m) 8 10 Photoelectric Effect Light in e METAL 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 x x x fo = threshold freq below which no photoemission occurs. 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 1. If V is kept constant, the photoelectric current ip 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, Kmax, of the photoelectrons is independent of the light intensity I. 5. 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 Sound Track Phototube Light Source speaker Example: A GaN based UV detector This is a photoconductor 5m 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 PE effect e e Secondary electron emission e e e Electron multiplication Photomultiplier tube hf e Anode Dynode -V • 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 http://hea-www.harvard.edu/HRC/mcp/mcp.html http://hea-www.harvard.edu/HRC/mcp/mcp.html MCP array structure http://hea-www.harvard.edu/HRC/mcp/mcp.html 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 Evac Evac Ec Ef Ev Ef Metal Semiconductor Band gap: Eg=Ec-Ev Photoconductivity e To amplifier Ec Evac Ef Ev Semiconductor Photoconductors • Eg (~1 eV) can be made smaller than metal work functions (~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 Example: A GaN based UV detector This is a photoconductor 5m Lecture 13 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 1. If V is kept constant, the photoelectric current ip 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, Kmax, of the photoelectrons is independent of the light intensity I. 5. 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 Sound Track Phototube Light Source speaker Example: A GaN based UV detector This is a photoconductor 5m 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 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 Evac Evac Ec Ef Ev Ef Metal Semiconductor Band gap: Eg=Ec-Ev Photoconductivity e To amplifier Ec Evac Ef Ev Semiconductor 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 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 = 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: • 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 absorption Emission Absorption Einitial Efinal Efinal Einitial hf = Efinal - Einitial hf = Efinal - Einitial Explains Hydrogen spectra What happens when we have more than one electron? What happens when we have more than one electron? Apply rules: Empty • 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 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 spectrum 2. A series of sharp lines. 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 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 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 (Ztantalum =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 Ei= -13.6Z2/n2 = -(73)2(13.6 eV)/ 42 = -4529 eV Ef= -13.6(73)2/12 = -72464 eV hf = Ei- Ef= 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 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) Laser Globe 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 Energy N2 N1 Few atoms in this level Want N2 - N1 to be as large as possible Population Inversion (3 level System) E2 (pump state), t2 Pump light ts >t2 E1 (metastablestate), ts 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 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 Energy Classical Quantum E4 E3 E2 E1 E0 Molecular Energy Levels Increasing Energy Translation Electronic orbital Vibrational Rotational Nuclear Spin Electronic Spin Rotation Vibration etc. Electronic Orbital Etotal + Eorbital + Evibrational + Erotational +….. Molecular Vibrations • Longitudinal Vibrations along molecular axis • E=(n+1/2)hf where f is the classical frequency of the oscillator • 1 f 2 k 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 1.008 amu) r • 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 K m M = Mm/(M+m) K = f (r) Molecular Rotations • Molecule can also rotate about its centre of mass • v1 = wR1 ; v2 = wR2 M1 • L = M1v1R1+ M2v2R2 = (M1R12+ M2R22)w = Iw • EKE = 1/2M1v12+1/2M2v22 = 1/2Iw2 M2 R1 R2 Molecular Rotations • Hence, Erot= L2/2I • Now in fact L2 is quantized and L2=l(l+1)h2/42 • Hence Erot=l(l+1)(h2/42)/2I • Show that Erot=(l+1) h2/42/I. This is not equally spaced • Typically Erot=50meV (i.e for H2) Populations of Energy Levels ΔE<<kT ΔE=kT ΔE>kT ΔE (Virtually) all molecules in ground state States almost equally populated • Depends on the relative size of kT and E 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 Strong absorption hv Weak emission 2hv hv Transition saturated 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. r K m M f vib= (K/)1/2 = Mm/(M+m) K = f(r) 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 100 Detecting Art Forgery 80 YTI S NET NI • Ti-white became available only circa 1920. Pb white 60 40 • The Roberts painting shows clear evidence of Ti white but is dated 1899 20 Ti white 0 0 200 400 600 800 -1 WAVENUMBER (cm ) 200 150 YTI S NET NI 100 50 0 0 200 400 600 -1 WAVENUMBER (cm ) 800 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(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: n1sin1=n2sin2 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 – “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 (λb) which satisfies λb=2nD is reflected – Separation (D) of same order as than mode wavelength Phase modulated sensors 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 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 •Optical resolution determined by Bent NSOM/AFM Probe 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 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 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 k T = Temp. 4 L T in Kelvin T MAX Wavelength where flux is a maximum k = 2.898 x 10-3 m.K Wien’s Law Total energy emitted by an object (or Luminosity W/m2) = 5.7 x 10-8 W/(m2.K4) 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 Light is later emitted Light is perfectly absorbed Oscillators Matter at some temperature T A BLACKBODY • • • Problems with wave theory of light 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 F l u x F l u x Okay here Max Plank Solved the problem in 1900 Max Plank • 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 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 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= 6.626x10 -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/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. 2.5 eV and 2.5 x 10 21 photons / m 2 /s Shining light onto metals Light in Nothing happens METAL Shining light onto metals Different Energy Light in electrons come out 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 The Photoelectric Effect Kinetic Energy of electron Different metals fo Threshold frequency Frequency of Light 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) 400 500 600 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 -0.85 -1.51 -3.39 Balmer Visible Paschen IR n=4 n=3 n=2 -13.6 n=1 Lyman UV R =Rydberg 1 1 1 Constant = R( ) 1.09737x10 7m-1 nm2 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 wave picture (RayleighJeans) failed to explain the distribution of the energy versus wavelength. UV Catastrophe!!!! 6000K The RayleighJeans Observed 5000K 0 2 4 6 (10 -7 m) 8 10 Photoelectric Effect Light in e METAL 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 x x x fo = threshold freq below which no photoemission occurs. x f0 f, Hz Atomic Physics/The Photoelectric Effect-Application The sound on a movie film Sound Track Phototube Light Source speaker Lecture 13 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 1. If V is kept constant, the photoelectric current ip 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, Kmax, of the photoelectrons is independent of the light intensity I. 5. 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 Sound Track Phototube Light Source speaker Example: A GaN based UV detector This is a photoconductor 5m 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 PE effect e e Secondary electron emission e e e Electron multiplication Photomultiplier tube hf e Anode Dynode -V • 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 http://hea-www.harvard.edu/HRC/mcp/mcp.html http://hea-www.harvard.edu/HRC/mcp/mcp.html MCP array structure http://hea-www.harvard.edu/HRC/mcp/mcp.html 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 Evac Evac Ec Ef Ev Ef Metal Semiconductor Band gap: Eg=Ec-Ev Photoconductivity e To amplifier Ec Evac Ef Ev Semiconductor Photoconductors • Eg (~1 eV) can be made smaller than metal work functions (~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 Example: A GaN based UV detector This is a photoconductor 5m 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 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 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 Lecture 15 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 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 = 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: • 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 absorption Emission Absorption Einitial Efinal Efinal Einitial hf = Efinal - Einitial hf = Efinal - Einitial Explains Hydrogen spectra What happens when we have more than one electron? What happens when we have more than one electron? Apply rules: Empty • 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 What happens when we have more than one electron? Apply rules: Empty • 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 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 spectrum 2. A series of sharp lines. 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 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 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 (Ztantalum =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 Ei= -13.6Z2/n2 = -(73)2(13.6 eV)/ 42 = -4529 eV Ef= -13.6(73)2/12 = -72464 eV hf = Ei- Ef= 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 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) Laser Globe 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 Energy N2 N1 Few atoms in this level Want N2 - N1 to be as large as possible Population Inversion (3 level System) E2 (pump state), t2 Pump light ts >t2 E1 (metastablestate), ts 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 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 Energy Classical Quantum E4 E3 E2 E1 E0 Molecular Energy Levels Increasing Energy Translation Electronic orbital Vibrational Rotational Nuclear Spin Electronic Spin Rotation Vibration etc. Electronic Orbital Etotal + Eorbital + Evibrational + Erotational +….. Molecular Vibrations • Longitudinal Vibrations along molecular axis • E=(n+1/2)hf where f is the classical frequency of the oscillator • 1 f 2 k 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 1.008 amu) r • 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 K m M = Mm/(M+m) K = f (r) Molecular Rotations • Molecule can also rotate about its centre of mass • v1 = wR1 ; v2 = wR2 M1 • L = M1v1R1+ M2v2R2 = (M1R12+ M2R22)w = Iw • EKE = 1/2M1v12+1/2M2v22 = 1/2Iw2 M2 R1 R2 Molecular Rotations • Hence, Erot= L2/2I • Now in fact L2 is quantized and L2=l(l+1)h2/42 • Hence Erot=l(l+1)(h2/42)/2I • Show that Erot=(l+1) h2/42/I. This is not equally spaced • Typically Erot=50meV (i.e for H2) Populations of Energy Levels ΔE<<kT ΔE=kT ΔE>kT ΔE (Virtually) all molecules in ground state States almost equally populated • Depends on the relative size of kT and E 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 Strong absorption hv Weak emission 2hv hv Transition saturated 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. r K m M f vib= (K/)1/2 = Mm/(M+m) K = f(r) 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 100 Detecting Art Forgery 80 YTI S NET NI • Ti-white became available only circa 1920. Pb white 60 40 • The Roberts painting shows clear evidence of Ti white but is dated 1899 20 Ti white 0 0 200 400 600 800 -1 WAVENUMBER (cm ) 200 150 YTI S NET NI 100 50 0 0 200 400 600 -1 WAVENUMBER (cm ) 800 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(E/kT) Population inversion Lots of atoms in this level Energy N2 N1 Few atoms in this level Want N2 - N1 to be as large as possible Population Inversion (3 level System) E2 (pump state), t2 Pump light ts >t2 E1 (metastablestate), ts 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 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 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: n1sin1=n2sin2 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 – “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 (λb) which satisfies λb=2nD is reflected – Separation (D) of same order as than mode wavelength Phase modulated sensors 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 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 •Optical resolution determined by Bent NSOM/AFM Probe 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 18 • Not sure what goes here 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 spectrum 2. A series of sharp lines. 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 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 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 (Ztantalum =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 Ei= -13.6Z2/n2 = -(73)2(13.6 eV)/ 42 = -4529 eV Ef= -13.6(73)2/12 = -72464 eV hf = Ei- Ef= 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 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) Laser Globe 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 Energy N2 N1 Few atoms in this level Want N2 - N1 to be as large as possible Population Inversion (3 level System) E2 (pump state), t2 Pump light ts >t2 E1 (metastablestate), ts 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 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 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 Energy Classical Quantum E4 E3 E2 E1 E0 Molecular Energy Levels Increasing Energy Translation Electronic orbital Vibrational Rotational Nuclear Spin Electronic Spin Rotation Vibration etc. Electronic Orbital Etotal + Eorbital + Evibrational + Erotational +….. Molecular Vibrations • Longitudinal Vibrations along molecular axis • E=(n+1/2)hf where f is the classical frequency of the oscillator • 1 f 2 k 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 1.008 amu) r • 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 K m M = Mm/(M+m) K = f (r) Molecular Rotations • Molecule can also rotate about its centre of mass • v1 = wR1 ; v2 = wR2 M1 • L = M1v1R1+ M2v2R2 = (M1R12+ M2R22)w = Iw • EKE = 1/2M1v12+1/2M2v22 = 1/2Iw2 M2 R1 R2 Molecular Rotations • Hence, Erot= L2/2I • Now in fact L2 is quantized and L2=l(l+1)h2/42 • Hence Erot=l(l+1)(h2/42)/2I • Show that Erot=(l+1) h2/42/I. This is not equally spaced • Typically Erot=50meV (i.e for H2) Populations of Energy Levels ΔE<<kT ΔE=kT ΔE>kT ΔE (Virtually) all molecules in ground state States almost equally populated • Depends on the relative size of kT and E 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 Strong absorption hv Weak emission 2hv hv Transition saturated 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. r K m M f vib= (K/)1/2 = Mm/(M+m) K = f(r) 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 100 Detecting Art Forgery 80 YTI S NET NI • Ti-white became available only circa 1920. Pb white 60 40 • The Roberts painting shows clear evidence of Ti white but is dated 1899 20 Ti white 0 0 200 400 600 800 -1 WAVENUMBER (cm ) 200 150 YTI S NET NI 100 50 0 0 200 400 600 -1 WAVENUMBER (cm ) 800 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(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: n1sin1=n2sin2 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 – “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 (λb) which satisfies λb=2nD is reflected – Separation (D) of same order as than mode wavelength Phase modulated sensors 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 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 •Optical resolution determined by Bent NSOM/AFM Probe 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 18 • Not sure what goes here 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 spectrum 2. A series of sharp lines. 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 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 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 (Ztantalum =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 Ei= -13.6Z2/n2 = -(73)2(13.6 eV)/ 42 = -4529 eV Ef= -13.6(73)2/12 = -72464 eV hf = Ei- Ef= 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 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) Laser Globe 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 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 Energy Classical Quantum E4 E3 E2 E1 E0 Molecular Energy Levels Increasing Energy Translation Electronic orbital Vibrational Rotational Nuclear Spin Electronic Spin Rotation Vibration etc. Electronic Orbital Etotal + Eorbital + Evibrational + Erotational +….. Molecular Vibrations • Longitudinal Vibrations along molecular axis • E=(n+1/2)hf where f is the classical frequency of the oscillator • 1 f 2 k 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 1.008 amu) r • 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 K m M = Mm/(M+m) K = f (r) Molecular Rotations • Molecule can also rotate about its centre of mass • v1 = wR1 ; v2 = wR2 M1 • L = M1v1R1+ M2v2R2 = (M1R12+ M2R22)w = Iw • EKE = 1/2M1v12+1/2M2v22 = 1/2Iw2 M2 R1 R2 Molecular Rotations • Hence, Erot= L2/2I • Now in fact L2 is quantized and L2=l(l+1)h2/42 • Hence Erot=l(l+1)(h2/42)/2I • Show that Erot=(l+1) h2/42/I. This is not equally spaced • Typically Erot=50meV (i.e for H2) Populations of Energy Levels ΔE<<kT ΔE=kT ΔE>kT ΔE (Virtually) all molecules in ground state States almost equally populated • Depends on the relative size of kT and E 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 Strong absorption hv Weak emission 2hv hv Transition saturated 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. r K m M f vib= (K/)1/2 = Mm/(M+m) K = f(r) 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 100 Detecting Art Forgery 80 YTI S NET NI • Ti-white became available only circa 1920. Pb white 60 40 • The Roberts painting shows clear evidence of Ti white but is dated 1899 20 Ti white 0 0 200 400 600 800 -1 WAVENUMBER (cm ) 200 150 YTI S NET NI 100 50 0 0 200 400 600 -1 WAVENUMBER (cm ) 800 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(E/kT) 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 Energy Classical Quantum E4 E3 E2 E1 E0 Molecular Energy Levels Increasing Energy Translation Electronic orbital Vibrational Rotational Nuclear Spin Electronic Spin Rotation Vibration etc. Electronic Orbital Etotal + Eorbital + Evibrational + Erotational +….. Molecular Vibrations • Longitudinal Vibrations along molecular axis • E=(n+1/2)hf where f is the classical frequency of the oscillator • 1 f 2 k 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 1.008 amu) r • 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 K m M = Mm/(M+m) K = f (r) Molecular Rotations • Molecule can also rotate about its centre of mass • v1 = wR1 ; v2 = wR2 M1 • L = M1v1R1+ M2v2R2 = (M1R12+ M2R22)w = Iw • EKE = 1/2M1v12+1/2M2v22 = 1/2Iw2 M2 R1 R2 Molecular Rotations • Hence, Erot= L2/2I • Now in fact L2 is quantized and L2=l(l+1)h2/42 • Hence Erot=l(l+1)(h2/42)/2I • Show that Erot=(l+1) h2/42/I. This is not equally spaced • Typically Erot=50meV (i.e for H2) Populations of Energy Levels ΔE<<kT ΔE=kT ΔE>kT ΔE (Virtually) all molecules in ground state States almost equally populated • Depends on the relative size of kT and E 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 Strong absorption hv Weak emission 2hv hv Transition saturated 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. r K m M f vib= (K/)1/2 = Mm/(M+m) K = f(r) 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 100 Detecting Art Forgery 80 YTI S NET NI • Ti-white became available only circa 1920. Pb white 60 40 • The Roberts painting shows clear evidence of Ti white but is dated 1899 20 Ti white 0 0 200 400 600 800 -1 WAVENUMBER (cm ) 200 150 YTI S NET NI 100 50 0 0 200 400 600 -1 WAVENUMBER (cm ) 800 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(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: n1sin1=n2sin2 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 – “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 (λb) which satisfies λb=2nD is reflected – Separation (D) of same order as than mode wavelength Phase modulated sensors 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 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 •Optical resolution determined by Bent NSOM/AFM Probe 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 18 • Not sure what goes here