Optical Spectroscopy Lab Report: Lifetime Measurements in Physics 552 - Prof. Robert M. Cl, Lab Reports of Optics

Download Optical Spectroscopy Lab Report: Lifetime Measurements in Physics 552 - Prof. Robert M. Cl and more Lab Reports Optics in PDF only on Docsity! Physics 552 Optical Spectroscopy (Fall 08) - 1 - Lab 7 - Lifetime Measurements Report Questions Here are the report questions for your lab write-up. If you would like more background information than provided in the handouts, check the references below. References • Danielle E. Chandler, Zigurts K. Majumdar, Gregor J. Heiss and Robert M. Clegg, “Ruby Crystal for Demonstrating Time- and Frequency-Domain Methods of Fluorescence Lifetime Measurements.” J. Fluoresc. 2006 Nov; 16(6): 793-807. and its references: http://www.springerlink.com/content/t04m0j16235123v0/?p=f98161ded3054d27886aa663d23d3ac7&pi=0 • Lectures 19 and 20 • Valeur, Chapter 6. • Lakowicz, Chapter 4, 5. • For those of you who wanted more information about lock-in amplifiers, try the links on this site: http://www.cpm.uncc.edu/lock_in_1.htm Time Domain Measurements Q1) Time trace For both the rising and falling parts of the time trace you collected from the square wave, fit the data to find the lifetime. Show a plot of your fits with the data points and your measured lifetime for each fit. Q2) Pulse width variation Fit your data. Show a plot of your fit with the data points and your measured lifetime. Frequency Domain Measurements We present here again the formulae for the modulation and phase: 2 / 1 / 1 ( ) o o F FM E E ω ω ωτ ≡ = + )arctan( ωτ=φ where the excitation E and the emission F are given by ( ) cos( ) ( ) cos( ) o o E t E E t F t F F t ω ω ω ω φ = + = + + If there are two lifetimes, the equations become 2 2 2 211 ( ) 1 ( ) M α αωτα ωτ ωτ ⎛ ⎞ ⎛ ⎞ = + − +⎜ ⎟ ⎜ ⎟+ +⎝ ⎠ ⎝ ⎠ for 2 0τ ≈ (1) Physics 552 Optical Spectroscopy (Fall 08) - 2 - ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 2 1 2 2 2 01 2 1 22 2 11 2 1 1 1 1 arctan arctan 1 1 11 1 τ ωτ ωτ ωτα α α ωτ ωτ ωτ φ ααα α ωτωτ ωτ ≈ ⎛ ⎞ ⎛ ⎞+ −⎜ ⎟ ⎜ ⎟+ + +⎜ ⎟ ⎜ ⎟= ⎯⎯⎯→⎜ ⎟ ⎜ ⎟− + −+⎜ ⎟ ⎜ ⎟⎜ ⎟ ++ + ⎝ ⎠⎝ ⎠ (2) where α is the fractional intensity of the τ1 lifetime component. The R that you measured from the lock-in is the modulation depth of the fluorescence signal, F1, while the phase θ from the lock-in is φ plus some arbitrary shift which you’ll need to account for using the rhodamine measurement. Q3) M, φ vs. frequency a) Calculate MRuby (or MEuropium) for each of your data points. Plot MRuby vs. frequency and then fit to Eq. (1) to get a lifetime from the modulation data. Your plot should include your data points and your fit. Also include your fit parameters. b) Calculate φ for each of your data points. Plot φ vs. frequency and fit to Eq. (2). Your plot should include your data points and your fit. Also include your fit parameters. Do this for each of the following data sets: • Square wave at a single frequency, measuring harmonics (to determine the lifetime of ruby) • Square waves of different frequencies (to determine the lifetime of ruby) • Sine waves of different frequencies (to determine the lifetime of Europium) c) If you fit the europium data to a two-lifetime model without assuming the shorter lifetime is 0, you will get a lifetime in the nanosecond range. Now assume the short lifetime is 1 ns and the excitation light is driven at 500 MHz, what would the phase be? What would the modulation be? Q4) Make sure you understand what we are doing in the experiment with a square wave at a single frequency. a) Why is it that we can modulate the excitation light with a square wave at some frequency fo, then measure the modulation at the higher harmonics? (I.e., if we do a Fourier decomposition of the square wave, what frequencies of sine waves do we get?) b) Why was there no signal at even harmonics of the square wave frequency? Hint: think about the symmetry of the square wave (It starts at 1 at time t=0). Is it even or odd? Q5) Polar plot The polar plot has a coordinate system with cos( )x M φ= and sin( )y M φ= . M is the distance from the origin and φ is the angle, measured counter-clockwise from the x-axis. a) Show that the polar plot for any single lifetime is on a semicircle centered at (0.5, 0). In other words, it satisfies 2 2 21 1( ) 2 2 x y ⎛ ⎞− + = ⎜ ⎟ ⎝ ⎠ b) Make a polar plot for each of the following data sets: • Square wave at a single frequency, measuring harmonics (to determine the lifetime of ruby) • Square waves of different frequencies (to determine the lifetime of ruby) • Sine waves of different frequencies (to determine the lifetime of Europium) c) From your figures in b, can you tell if there is more than one lifetime?