1. ECE-1466 Modern Optics Course Notes Part 10
Prof. Charles A. DiMarzio
Northeastern University
Spring 2002
May 02002
Chuck DiMarzio, Northeastern University

2. Chuck DiMarzio, Northeastern University
Lecture Overview
Two-Photon Mathematical Analysis
Classical
“Electron on a Spring”
Non-Linear Response
Quantum
Second-Order Perturbation
“Virtual State”
Spatial and Temporal Issues
May 02002
Chuck DiMarzio, Northeastern University

3. Classical Description
(Electron as a Mass on a Spring) a x v v x
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Chuck DiMarzio, Northeastern University

4. Chuck DiMarzio, Northeastern University
Energy Level Diagrams
Fluorescence
2-photon
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Chuck DiMarzio, Northeastern University

5. Chuck DiMarzio, Northeastern University
Mathematical Model
Oversimplification, but useful for understanding
Poisson Distribution
Mean Number
Probability of a Pair
Time Interval
Virtual State Lifetime
May 02002
Chuck DiMarzio, Northeastern University

6. Chuck DiMarzio, Northeastern University
Calculations
Mean Number of Fluorescence Photons
Mean Rate
Defines d = 2-Photon cross-section in m4sec
Typical Value
For 1/10 Photon per 100fs (laser pulse interval)
May 02002
Chuck DiMarzio, Northeastern University

7. Chuck DiMarzio, Northeastern University
Power Requirement
Photon Irradiance
Irradance
Diffraction-Limited Area (1 square micrometer)
Average Power at 100MHz, 100 fs width
May 02002
Chuck DiMarzio, Northeastern University

8. Spatial and Temporal Issues
Focus the Light
High Irradiance
Depth-Slicing
Resolution Sharpening
Make the Pulse Short
Low Duty Cycle
Less Damage
High Peak Power
Stronger Signals E2 E
E2A
P=EA
May 02002
Chuck DiMarzio, Northeastern University

9. Chuck DiMarzio, Northeastern University
Course Summary
Radiometry
Diffraction F F’
Object
Image
Polarization
Geometric Optics
NL Optics
Interference
Applications
May 02002
Chuck DiMarzio, Northeastern University