Acknowledgement:  This educational material was made possible by a grant from the National Science Foundation (Career Development Program Grant No. 1653270).

Below is a series of materials to help train new users (and hopefully, new builders) of time domain thermoreflectance (TDTR) systems.  Because the potential audience for this is quite diverse, information is given at wide range of detail-level that hopefully accommodates everyone from the complete newcomer to TDTR gurus; some of the information is generic but in many cases I’ve tried to include quantitative performance examples and give specific examples of model numbers/equipment.  Information is given about a wide variety of different TDTR systems/layouts in use, though most of my own experience is with two-tint TDTR a la David Cahill’s design at UIUC, so there is some bias in that direction.

Main Topics:

1. Course Introduction
2. TDTR Hardware
3. TDTR Theory
4. TDTR Data & Uncertainty Analysis
5. Advanced Topics

Introduction:

1. What to Expect:  Course Layout *clicking takes you to YouTube (slides)
2. What is TDTR? An Overview (slides)

TDTR Hardware:

1. Preliminary Concepts (optional)
   1. Polarization Optics
   2. Gaussian Beams
2. Common Variants of TDTR (two polarization vs. two color)
3. Quick Walkthrough of Two-Tint TDTR Hardware
4. Introduction to the TDTR Signal Anatomy
5. A more detailed look at Two-Tint TDTR Hardware
   1. Generating laser pulses / Ultrafast Oscillators
   2. Optical Isolator / Laser Power Tuning
   3. Dividing pulses into “Pump” and “Probe” / PBS
   4. Modulating the Pump pulses / Electro-Optic Modulation
   5. Advancing the Pump arrival time / Linear Stage/Retroreflector
   6. Recombining the Pump/Probe
      1. Part 1:  Combining the beams to be parallel to one another
      2. Part 2:  Focusing the beams onto the Sample
   7. Measuring the Change in Reflected Probe Beam / Photodiode circuitry
      1. Method 1:  Biased Photodiodes
         1. Part 1:  TDTR Signals from Biased Photodetectors
         2. Part 2:  Resonant Circuits for Low Noise Amplification
         3. Part 3:  Active Voltage Pre-amplifiers for TDTR
      2. Method 2:  Balanced Amplified Photodiodes
         1. Part 1:  Basic Principles
         2. Part 2:  Table Layout Strategy
         3. Part 3:  Calculating the Expected Signal
   8. Lockin Amplification of the Signal / RF-Lockin Amplifier
      1. “What is a Lockin Amplifier?”  (made by Zurich Instruments)
      2. More considerations
   9. Rejecting the Reflected Pump Beam / Two-tint filters & Mechanical Chopper
      1. Why is rejecting the pump beam big deal?
      2. The two-tint method of rejecting pump beam
      3. Rejecting false signals using an optical chopper / AF lockin amplifier
      4. Rejecting pump beam using an aperture

TDTR Theory

1. Introduction
2. A Primer on Fourier Transforms (optional)
3. The Nyquist Sampling Theorem
4. How TDTR and the Nyquist sampling theorem are related
5. A Primer on Hankel Transforms
6. Calculating the Fourier transform of average surface temperature
7. Calculating the Fourier(time)/Hankel(space) transform of the Pump beam.
   1. And plugging that in to find the avg surface temperature, T
      1. And plugging that in to find the avg sampled surface temperature, Ts
8. Mop-up work:
   1. Calculating the Hankel(space) transform of the Pump, Probe beams (P(k), S(k))
   2. Calculating the the point response function, g(r,t) -> G(k,f)
      1. What is a point response function, G, and why we need it.
      2. Hankel(space)/Fourier(time) transform for diffusion equation
      3. Matrix transformations for Multilayer system
9. Summary: How it All Works Together.
10. Additional Resources
    1. Papers
       1. DG Cahill, “Analysis of heat flow in layered structures for time-domain thermoreflectance,” Review of Scientific Instruments 75, 5119 (2004).
       2. A. Feldman, “Algorithm for solutions of the thermal diffusion equation in a stratified medium with a modulated heat source,” High Temp. – High Press. 31, 293 (1999)
       3. A.J. Schmidt, “Optical characterization of thermal transport from the nanoscale to the macroscale,” Dissertation, MIT (2008).
    2. Software

TDTR Data Analysis

1. Basic Idea of “Fitting Data”
2. “What can I fit for?” – Understanding Sensitivity
3. Typical TDTR Sensitivities
   1. “Low” thermal conductivity substrates, “Large” spot size
   2. “High” thermal conductivity substrates, “Large” spot size
   3. “Thin” Films
4. Estimating error bars using software

Advanced Topics

Preliminary Concepts

1. Intro to Polarization Optics (optional, but highly recommended)
   1. What is polarization? (slides/ video)
   2. Common polarization optics:
      1. Polarizing Beam Splitters (PBS)
      2. λ/2 (halfwave) plates
      3. λ/2-plate, PBS combo for power adjustment
      4. Faraday isolators
      5. Electro-optic modulation (EOM) systems
2. Gaussian Optics
   1. TDTR lasers are Gaussian beams.  What that means…