1. Group Velocity and Ultrafast Optics
James Hendrie

2. Velocities Associated with Light Pulses
Phase
Ray
Group
Envelope

3. Derivation of Group Velocityz
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
Describe the standard path pulses take through an IPI cavity
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. Normalized Pulse Energy
Bunch Generation
Time (nano-sec)
Normalized Pulse Energy t

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

19. Gaussian in the Steady State Regime
500 Laser Cavity Round Trips
Fabry-Perot Cavity Round Trips 30 40 50 20 60
Normalized Pulse Energy
0.05
0.1
0.15 20 40 60 80
100 15 10 5
1000
900
800
700
600
500
400
300
200
Center of Gravity
Number of Pulses
Laser 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 Group indices must be constant at each point
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
Side View
Cap View x y z

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
Gyro Effect aka Sagnac effect
two beams in the same cavity see different path lengths is cavity is rotated.
The different paths cause a phase shift that can be seen in frequency

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!!
In an absolute reference frame, consider the observer in the laboratory frame that sees the successive nodes/antinodes of the standing wave pattern
2) In an absolute reference frame, consider the observer in the laboratory frame that sees the clockwise wave Doppler upshifted, counterclockwise down.
In the laboratory frame, the clockwise wave sees a longer perimeter than the counter-clockwise wave, hence different cavity modes for the two directions.
The Gyro effect is inherently due to phase velocity!!

39. Standing Wave DescriptionR

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??