PHYS 450 Fall semester Lecture 07: Spectroscopy and the Scanning Spectrometer. Ron Reifenberger Birck Nanotechnology Center Purdue University

Transcription

1 0/7/06 PHYS 450 Fall semester 06 Lecture 07: Spectroscopy and the Scanning Spectrometer Ron Reienberger Birck Nanotechnology Center Purdue University Lecture 07 Roadmap: Where We ve Been and Where We re Going Overview & History: Concept o OPL Mirrors OPL Intererence (-slits) Intererometers Lenses Reraction Prism; Dispersion Gratings Diraction Fourier Optics Optical Instruments Spectroscopy Polarization

2 0/7/06 Mapping Angles with a Lens + -s - or small +s s =-tan - + +s 3 Where the light ray hits the lens is not important CASE A: Ray, Ray, Ray 3, 3 Key Idea: Location in ocal plane maps incident angle CASE B: Ray, Ray 3, 3 Ray, 4

3 0/7/06 The Prism Spectrometer 5 Important Results Lecture 5 44 o isin sin n sin i cos sin i Interace Interace θ i δ θ t Light ray thru prism parallel to base 40 o incident ray air n θ t θ i prism B reracted ray 47 o t sin i n sin min sin sin 6 3

4 0/7/06 What determines n? Maxwell ' s Equations : B E t E B t Wave Equation : E E t 3 Simpliy to dimension : E E x t 4 Solution : x t E Eo sin T v T x vt E Eo sin E x vt E sin o x E v x vt E sin o t x vt v x vt Eosin Eosin Implication v In vacuum c o o c o o n v o o o v no magnetism Bottom Line: n depends on square root o dielectric constant o material 7 Bulk solid Simple Model What does the dielectric constant ε measure? EM wave Δt For a transparent material, individual atoms interact with EM radiation and cause the radiation to suer a short delay t with each interaction Delay aects the macroscopic (apparent) speed o EM radiation in the material The apparent speed o EM radiation is deined by v=c/n As v goes down, n must go up As the requency o EM radiation approaches internal "resonances" o the SYSTEM, the interactions become more pronounced and the dielectric constant can vary, sometimes wildly Beware: this intuitive model does injustice to more than one quantum mechanical concept! Quantum physics gives equations that provide more complete answers Beware o internal "resonances" Induced polarization Atom vibrations Induced atomic dipoles Electronic excitation atoms w electrons 8 4

5 0/7/06 How does ε vary qualitatively with wavelength (or requency)? electrical requency range optical requency range ε (real part) ε(0) ~ε o polar Orientation polarization Internal vibrations (phonons) Atomic polarizability (induced dipoles) Electronic excitations (core states) non-polar μ-wave Adsorption Band internal "resonances" IR/VIS Adsorption Band Cauchy s ormula Adsorption UV Band Frequency o EM radiation (Hz) 9 Representative values o low requency dielectric constant Material Dielectric Constant ((0)/ o ) Vacuum Glass 5-0 Mica 3-6 Mylar 3 Plexiglas 340 Telon Water 804 Benzene 84 Air( atm) Air(00 atm)

6 0/7/06 n vs wavelength (optical materials) visible n Prisms Lenses Cauchy Relationship 836: Augustin-Louis Cauchy suggests simple empirical ormula n B A Material A B (nm ) Fused silica Borosilicate glass BK Hard crown glass K Barium crown glass BaK Barium lint glass BaF Dense lint glass SF Dense lint glass SF* n - Index o reraction SF Glass Wavelength (nm) See * F El Ghussein, J M Wrobel, and M B Kruger, Am J Phys 74, 888 (006) 6

7 0/7/06 Simpliied Experimental Geometry 0 R re re Incident light rom slit and collimator Prism s Lens s Detector 3 Step : Measure i Step : Calculate n( re ) Basic Idea Calibrate to a standard n B re A re Computer Monitor α δ re Output θ i θ i re t Reerence Laser Reerence Laser: red HeNe re = 638 nm t = 0 Data Studio Interace Step 3: Calculate re ( re ) v o (sin re re i sin n re sin i sini cos ocal plane (FP) scanning photodiode x re = v o t 4 7

8 0/7/06 Measuring Wavelengths with a Prism Unknown wavelength α δ re δ(λ) s x' xre Measure n re θ i θ i Reerence Laser: HeNe 638 nm Reerence Laser δ t=0 Unknown wavelength v o x re =v o t x =v o t 5 Alignment Issues 3 00µm Focused laser beam ocal plane (FP) Diode Signal Simulated Scans Optimal Scan: Oset Scan: Tilted (thru FP): ,000 Diode Position 6 8

9 0/7/06 Asymmetry: Angled and O-Center 5 ocal plane (FP) Diode Signal Simulated Oset Scans IN FRONT: 4 BEHIND: ,000 Diode Location 4 00µm 7 V bias R00 k +5 V - I P OP-AMP + C Photodiode Light Detector -5 V V out /I P =R V out PASCO Si p-i-n photodiode spectral response P I N Light strikes photodiode and produces current I P Current proportional to light intensity OP-AMP conigured as a current to voltage converter V out is proportional to light striking photodiode 8 9

10 0/7/06 Measuring Wavelengths with a Prism Calibrate to a standard Measure α and θ i α δ re δ(λ) θ i θ i red Collimated light rom He discharge tube violet δ blue yellow green Reerence Laser Measure δ or each spectral line 9 Photodiode Signal (au) no laser with laser Raw data Time (seconds) HeNe laser A to D conversion rate = 00 Hz dc motor voltage = +3V No data points: ~ 3,000 Saturation Sweep direction? Forward or Backward 0 0

11 0/7/06 Raw data: Gain=00 and Gain=0 (Eliminate saturation) Photodiode Signal (au) 0 Gain=00 00 Gain= Time (seconds) Photodiode Signal (au) Set: A to D conversion rate (00 Hz) dc motor voltage ( 3V) Measure: i Speed o photodiode (m/s) Location o HeNe line Focal length o lens Know: Cauchy A, B HeNe wavelength Photdiode Signal (au) Enlarge! Processed Data He Spectrum w HeNe calibration line HeNe laser Wavelength (nm)

12 0/7/06 High Level Flow Chart Determine re or HeNe laser Measure location x or each 3 Calculate (): 4 Calculate n(): 5 Iner : n s x ' x re re sin n re i sin i i (sin sin cos ] B A n A B 3 Up Next Young s Double Slit 4