1. Pulse train in a tunable cavity
Xiwen Zhang
PHYS presentation

2. Continuous wave in a tunable cavity
Pulse train in a tunable cavity
Example for application
Summary
Supplement

3. Continuous wave in a tunable cavity: Model

4. Cavity field Transmission coefficient Reflection
Slow varying amplitude: E0
Round-trip phase
v: speed of the movement of the mirror
n: number of round-trips
K. An, C. Yang, R.R. Dasari and M.S. Feld, Optics Lett. 20, (1995)

5. Cavity field Assume that at t=0, the cavity becomes resonant:
Discretize time by round-trip time 2L0/c:
Round-trip phase becomes:
verified numerically
K. An, C. Yang, R.R. Dasari and M.S. Feld, Optics Lett. 20, (1995)

6. Intensity of cavity field: fast scan
Intensity of the cavity field:
R = r2, reflectance
When >>1 at l = n
Fast scan of the cavity:
1 - R << 1

7. Intensity of cavity field: slow scan
Intensity of the cavity field:
R = r2, reflectance
Slow scan of the cavity:
Number of oscillations:
K. An, C. Yang, R.R. Dasari and M.S. Feld, Optics Lett. 20, (1995)

8. Experimental result Probe laser: 791 nm; Mirror spacing L0 ~ 1 mm,
varied by a piezoelectric transducer.
Cavity decay time Tcav = 1.14 μs;
Cavity finesse: 1.03 × 106;
Mirror speed v = 32 μm/s;
Τ12 ~ 170 ns.
Cavity decay time Tcav = 1.14 μs;
Cavity finesse: 1.03 × 106;
Mirror speed v = 6.4 μm/s;
Τ12 ~ 380 ns.
K. An, C. Yang, R.R. Dasari and M.S. Feld, Optics Lett. 20, (1995)

9. Preliminary experimental result
From Aysenur Bicer

10. Pulse train in a tunable cavity: Model

11. Interference and resonance condition
Interference condition:
Resonance condition:
p0 -1 pulses,
not 2L/cT pulses
Size of the resonant cavity:
Resonant wavelength:

12. Time discretization
Round-trip time level
Pulse separation level

13. Cavity field
t = lT

14. Preliminary numerical result

15. An example for application of frequency comb laser in a cavity: The measurement of group delay dispersion and cavity loss factor
Usually, a frequency comb laser has optical frequency ωn = n ωr+ ωCE, with ωCE = ΦCE/T, where ΦCE is the pulse-to-pulse phase shift, and ωr = 2π/T.
Notation:
T: pulse duration separation
T’: round-trip time in a cavity
A. Schliesser, C. Gohle, T. Udem and T.W. Hänsch, Optics Express 14, 5975 (2006)

16. Cavity field
In the vacuum with ideal mirror, the cavity round-trip phase is φ(ω) = kL = Lω/c.
In general case, there is dispersion due to intracavity elements and mirror coatings:
In the resonant case, φ(ω) = 2 π.
The steady-state electric field inside a resonator can be expressed as
A. Schliesser, C. Gohle, T. Udem and T.W. Hänsch, Optics Express 14, 5975 (2006)

17. Measurement of the group delay dispersion(GDD) and cavity loss factor
Replace φ by Δφ = φ – 2 π n. This is done by setting Δφ = (2) – (1):
const
const
A. Schliesser, C. Gohle, T. Udem and T.W. Hänsch, Optics Express 14, 5975 (2006)

18. Summary
For continuous wave inside a tunable cavity, if the cavity is scanned very fast, one observed the usual cavity field decay
If the cavity is scanned slowly, interference happens along with the cavity decay, which can be used to measure slow velocity
The same effect should be observed for a pulse train in a tunable cavity

19. Thank You!
11/30/2012

20. Justification of the Discretization of the time by round-trip time 2L0/c
With continuous time t
With discretized time t

21. Sample of the numerical result of the pulse train in a tunable cavity