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Agenda

Agenda. Last class review Lorentzian atoms in a cavity: getting close to a laser. Oscillator strength Microscopic origins of “friction term” ASIDE: Problem set #4 second half now available. Due November 10 th. M.E.: pp 80-83. M.E.: pp 88-90. M.E.: pp 93-98.

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Agenda

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  1. Agenda • Last class review • Lorentzian atoms in a cavity: getting close to a laser. • Oscillator strength • Microscopic origins of “friction term” ASIDE: Problem set #4 second half now available. Due November 10th. M.E.: pp 80-83 M.E.: pp 88-90 M.E.: pp 93-98 Note: questions boxed by a dashed line are meant to help you understand the material. I strongly recommend that you consider them. Laser Optics – Phys460

  2. nR, nI real n imag n Frequency (THz) 1. Last class review • System with more than one resonance Gallium Arsenide - GaAs Laser Optics – Phys460

  3. real imag 1. Last class review: Cavity modes Check for consistency! Induced polarization in the cavity We have used: n =ckn Laser Optics – Phys460

  4. 2. Lorentz atoms in a lossy cavity Define: Real part Imaginary part Explore this expression first! This is impossible!! Laser Optics – Phys460

  5. 2. Real cavity, cont. If g is positive: frequency n  0 frequency 0 n  Redraw these illustrations for g negative. (This is known “frequency pushing”.) This is known as FREQUENCY PULLING. Laser Optics – Phys460

  6. 2. Real cavity, cont. for steady-state, but Lorentzian atoms cannot support a steady-state E in a cavity with any loss. Actually this result should not be surprising: • no matter how hard you drive them, Lorentzian atoms cannot even be saturated! • model has no coupling between different “springs” Name three ways that the Lorentzian model does not match real atoms? Laser Optics – Phys460

  7. Linear with driving field? Is this amplitude correct? What is this “friction”? 2. Real cavity, cont. Something is wrong in the model. The suspects: Laser Optics – Phys460

  8. 3. Start with “oscillator strength” Absorption was measured for atomic hydrogen. Let’s compare it to model predictions: Lecture 20: Absorption coefficient Absorption for one “atom” [S.I. units: (s·m)-1] 2.6510-6m2s-1 Laser Optics – Phys460

  9. 2.6510-6m2s-1 3. “oscillator strength”, cont. Experimental results for atomic hydrogen: 1.1010-6m2s-1 Absorption observed at 121.6nm (2465THz) f - “oscillator strength” cannot be explained by classical theory Other wavelengths were also observed to absorb: Absorption wavelengthoscillator strength 121.6nm (2465THz) f=0.416 102.6nm (2922THz) f=0.079 97.3nm (3081THz) f=0.029 95.0nm (3156THz) f=0.014 93.8nm (3196THz) f=0.0078 …. Laser Optics – Phys460

  10. 4. Origin of “friction”-  • Microscopic origin dependent on the system. • We will pick a particular system : a gas of atoms No collisions P p With collisions Laser Optics – Phys460

  11. Average time between collisions= 4. Origin of “”, cont. • How do collisions change P Time <t1 Time t1 Time >t1 For those atoms that collide at t=t1, Boundary conditions! Solution is a combination of homogeneous and inhomogenous solutions! Average over all atoms no matter when their last collision was. Details: M.E.94-95 Laser Optics – Phys460

  12. 4. Origin of , cont. Solution: Recall: Set =1/  term can be completely explained by collisions! This is not to say there are not many other microscopic processes contributing to . Now we see why  cannot be negative – negative collision time is meaningless. Randomizing dipole amplitude and velocity also known as “dephasing”. Examples of ensemble dephasing: • gas: collisions (even elastic) • condensed matter: lattice vibrations (phonons) Laser Optics – Phys460

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