Group Velocity and Ultrafast Optics James Hendrie

Velocities Associated with Light Pulses Phase Ray Group Envelope

Derivation of Group Velocity z z = ct z = vt

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

(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.

Group Delay NOT GROUP VELOCITY!!!

Carrier Envelope Offset Beat Note

IPI Schematic Beat Note Measurement Phase Alteration D Describe the standard path pulses take through an IPI cavity Beat Note Measurement Phase Alteration D

Derivation of Envelope Velocity

Group Velocity Dynamics within Gain/Saturable Absorber

Fabry-Perot Etalon Inside a Mode-Locked Cavity

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

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.

Theory

Bunch Generation Pics from pics from latest paper

Bunch Generation t

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

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 = 0.0002 R = 0.05

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.

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

Nested Comb Characterization                

Nested Comb Characterization                  

The Real Thing

Pump Power Effect on Repetition Rate ML Cavity FP Cavity

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

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

Three Experiments Temperature Radiation Ring Laser Gyroscope

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

Experimental Example SMALL Index changes due to applied heat SMALL    

Experimental Setup

Temperature Diffusion in Glass Side View Cap View x y z    

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

Fabry-Perot Angle Scan Internal Angle (milli radians)

Cavity Length Scan  

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).

Ring Laser Gyroscope with Group Velocity Enhancement

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

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!!

Standing Wave Description     R

Doppler        

Perimeter Change          

Enhanced Gyro Derivation Taylor Expansion

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

Current Results

Questions??