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Group Velocity and Ultrafast Optics

Explore the dynamics of group velocities associated with light pulses and the manipulation of light speed in dispersive media for fast light effects. Learn about phase sensitivity amplification, group delay, and applications in mode-locked lasers.

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Group Velocity and Ultrafast Optics

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  1. Group Velocity and Ultrafast Optics Ultrafast 2016 James Hendrie

  2. Velocities Associated with Light Pulses Phase Ray Group Envelope

  3. Derivation of Group Velocity t z z = ct z = vt

  4. Slow/Fast Light Manipulation of the Group Velocity within a dispersive medium

  5. (dk/dΩ) ≡ Group Delay/L • Choosing materials that manipulate the speed at which light propagates Small (dk/dΩ) ≡ “Fast Light” • The idea that light travels much faster in materials with these small values of dk/dΩ “Fast Light”≡ Phase Sensitivity is Amplified • Large group delays amount to additional phase shift as light travels through the material.

  6. Group Delay NOT GROUP VELOCITY!!!

  7. Carrier Envelope Offset Beat Note

  8. IPI Schematic Beat Note Measurement Phase Alteration D

  9. Derivation of Envelope Velocity

  10. Group Velocity Dynamics within Gain/Saturable Absorber

  11. Fabry-Perot Etalon Inside a Mode-Locked Cavity

  12. Nested Fabry-Perot in Mode-Locked Lasers to Monitor Minute Changes of Index James Hendrie, Koji Masuda, Adam Hecht, Jean-Claude Diels, and Ladan Arissian CLEO 2015 Ultrafast Class 2016

  13. Motivation • Mode-locked lasers generate frequency combs which are sensitive to their parent cavities. • Inserting an etalon into the cavity generates a nested comb comprised of two repetition rates. • The ratio of these repetition rates can be used as an accurate measure of the optical path within the etalon.

  14. Theory

  15. Bunch Generation Pics from pics from latest paper

  16. Bunch Generation t

  17. Bunch Generation Normalized Pulse Energy Time (nano-sec) t

  18. Bunch Generation 0 Center of Gravity Shift (s) • Pulse bunch reaches steady state condition after many roundtrips Number of Pulses 0 100 200 300 400 500 600 700 800 900 1000 Number of Round Trips NRT = 1000 a = 0.0002 R = 0.05

  19. Gaussian in the Steady State Regime 0.15 20 100 500 Laser Cavity Round Trips 80 15 0.1 60 Normalized Pulse Energy 10 Center of Gravity Number of Pulses 40 0.05 5 20 0 0 200 300 400 500 600 700 800 900 1000 100 20 30 40 50 60 Laser Cavity Round Trips Fabry-Perot Cavity Round Trips Koji Masuda, James Hendrie, Jean Claude Diels and Ladan Arissian; Envelope, Group and Phase velocities in a nested frequency comb, Under Review.

  20. Fourier Transformation 146 ps 6.4 ns 1 ns Time 155 MHz 6.8 GHz 1 GHZ Frequency

  21. Nested Comb Characterization

  22. Nested Comb Characterization

  23. The Real Thing

  24. Pump Power Effect on Repetition Rate ML Cavity FP Cavity

  25. Resonant Frequencies The central optical frequency, is resonant with both cavities Cavity and FP frequencies are defined via group indices

  26. Frequency Ratio Want to measure this!! Group indices must be constant at each point

  27. Three Experiments Temperature Radiation Ring Laser Gyroscope

  28. Temperature By changing the applied temperature of an intra-cavity Fabry-Perot etalon, one observes a change in frequency ratio.

  29. Experimental Example SMALL Index changes due to applied heat SMALL

  30. Experimental Setup

  31. Temperature Diffusion in Glass Cap View Side View x z y

  32. Center Line • Temperature change in the center of the etalon is very small

  33. Fabry-Perot Angle Scan Internal Angle (milli radians)

  34. Cavity Length Scan

  35. Radiation K. Masuda, E. I. Vaughan, L. Arissian, J. P. Hendrie, J. Cole, J. -C. Diels, and A. A. Hecht, Novel techniques for high precision refractive index measurements, and application to assessing neutron damage and dose in crystals, Nuclear Instruments and Methods A (2014).

  36. Ring Laser Gyroscope with Group Velocity Enhancement

  37. Gyro Explanation • Counter propagating beams sharing a single cavity see equal and opposite phase shifts throughout the duration of any applied rotation to that cavity

  38. Three Descriptions • Standing wave created by counter propagating beams • Doppler Shift • Counter propagating beams see different perimeters These descriptions hold true in both cw and pulsed operations!! The Gyro effect is inherently due to phase velocity!!

  39. Standing Wave Description R

  40. Doppler

  41. Perimeter Change

  42. Enhanced Gyro Derivation Taylor Expansion

  43. Current Results Blue -> With FP Red -> Without FP

  44. Current Results

  45. Questions??

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