1. All-Fiber, Phase-Locked Supercontinuum Source for Frequency Metrology and Molecular Spectroscopy
Brian R. Washburn
National Institute of Standards and Technology
Optoelectronics Division
325 Broadway
Boulder, CO 80305

2. Acknowledgments S. A. Diddams, N. R. Newbury, S. L. Gilbert, W. Swann
National Institute of Standards and Technology
J. W. Nicholson and M. F. Yan
OFS Laboratories, USA
C. G. Jørgensen
OFS Fitel Denmark I/S, Denmark

3. Introduction: Output of a Mode-Locked Laser
10 ns
Time
Domain
Power
10 fs
time
0.1 THz
10 MHz
Frequency Domain
Power
Frequency
Small Dt => Broad Spectral Coverage

4. Supercontinuum
Ti:sapphire Laser
Microstructure
Fiber

5. Optical Frequency Metrology
Mode-Locked
Lasers
Nonlinear
Optical Fibers
Radio Frequency
Standards
Optical Frequency Metrology
Molecular
Spectroscopy

6. Part One: Mode-locked Fiber Lasers
Outline
Part One: Mode-locked Fiber Lasers
Compare/contrast fiber lasers to free-space lasers
Fiber Dispersion and Nonlinearities
Mode-locking in fiber lasers
Part Two: Optical Frequency Metrology
Components of the all-fiber supercontinuum source
Phase-locking a fiber laser
System performance
Part Three: Molecular Spectroscopy

7. Passively Mode-locked Lasers
Elements of mode-locked lasers
Pump source
Gain element
Saturable absorber for mode-locking
Dispersion compensation for shortest pulses

8. Fiber Lasers: Advantages and Disadvantages
Easy to align fiber laser cavity
Less sensitive to misalignment
Passive optical elements are inexpensive
Uses less power than Ti:sapphire laser
More compact
Disadvantages
More sensitive to environment (polarization)
Optical fiber limits total laser power
All fiber cavity limits ability to easily experiment with laser design
Careful dispersion and nonlinearity management is needed for proper laser design

9. Gain Medium: Erbium-Doped Fiber (EDF)
EDF Gain Bandwidth
Use a fiber that is highly doped with Er as the gain element of the laser
This fiber exhibits normal dispersion : D=-70 ps/nm-km

10. Saturable Absorber for Mode-Locking
A saturable allows the laser cavity to “favor” high peak power, ultrashort pulses
An absorber created by Kerr lensing is typically used in solid state lasers
Fiber nonlinearities are used in fiber lasers
Need a complete understanding of fiber dispersion and nonlinearities

12. Fiber Dispersion and Nonlinearities
Group Velocity Dispersion (GVD)
Fiber

13. Fiber Dispersion and Nonlinearities
Self Phase Modulation (SPM)
Fiber

14. Characterizing Dispersion and Nonlinearity in an Optical Fiber
Assume single mode and no birefringence
Concerned with phase matched nonlinearities
Assumptions leads to SPM and GVD only

15. Characterizing Dispersion and Nonlinearity in an Optical Fiber
The dispersion length (LD) is the length of fiber where a Gaussian pulse to temporally broadens by Sqrt(2)
The nonlinear length (LNL) is the length of fiber for which a pulse gains a phase of 1 radian

16. The Nonlinear Schrödinger Equation
A beautiful equation which accurately describes a highly nonlinear optical system
An understanding of this equation provides the ability to design and predict the behavior of active fiber devices
Fiber lasers
Erbium doped fiber amplifiers
Nonlinear loop mirrors/switches
TOADs

17. Mode-locking in Fiber Lasers
Active Mode-locking
Typically use AOM or Mach Zehnder to achieve mode locking
Sigma laser (Duling et al, Opt Lett Vol 21, )
Advantage: Can achieve high repetition rates (10 GHz)
Passive Mode-locking
Interferometric designs based on gain and saturable absorber sections
Figure eight lasers (Sacnac switch)
Stretched Pulse Lasers
Advantage: sub-picosecond, high energy pulses

18. Figure Eight Laser
Output

19. Nonlinear Loop Mirror: Linear Operation
No phase shift between interferometer arms

20. Nonlinear Loop Mirror: Nonlinear Operation

21. Figure Eight Laser Performance
AMP
Temporal FWHM <100 fs
Average Power= 100 mW
Center Wavelength= 1560 nm

22. Stretched Pulse Laser
Normal Dispersion
Anomalous
Dispersion

23. Nonlinear Polarization RotationEy Ex

24. Nonlinear Polarization RotationEy Ex

25. Nonlinear Polarization RotationEy Ex

26. Nonlinear Polarization RotationEy Ex

27. Nonlinear Polarization RotationEy Ex

28. Stretched-Pulse Operation
intensity
time

29. Stretched-Pulse Fiber Laser
Isolator
Polarizer
Polarization
Controllers
EDF
980 nm
Pump
WDM
90/10
Splitter
Output

30. Stretched-Pulse Laser Performance
Temporal FWHM <100 fs
Average Power= 100 mW
Center Wavelength= 1560 nm
AMP

31. Part Two: Optical Frequency Metrology
Mode-Locked
Lasers
Nonlinear
Optical Fibers
Radio Frequency
Standards
Optical Frequency Metrology
New way to connect microwave and optical frequencies

32. Electric Field from a Mode-locked Laser
Time domain (Pulses in time)
Time domain (Pulses in time)
E(t)
E(t) Df Df
2Df
2Df
Carrier-envelope phase slip from pulse to pulse because group and phase velocities differ
Carrier-envelope phase slip from pulse to pulse because group and phase velocities differ t t
repetition
rate
repetition
rate
Frequency domain (Comb of lines)
fn = nfr + fo
I(f) f
fo = fr Df/2p
repetition
frequency fr
Stable frequency comb if
Repetition rate (fr) locked
Offset frequency (f0) (phase slip) locked

33. Acoustic Frequency Metrology: Guitar Tuning
Known Frequency, fk
Unknown Frequency, fun
Df=0.5 Hz
Df=0.01 Hz

34. Optical Frequency Metrology
fun
fn = nfr + fo
I(f) f
fo = fr Df/2p
repetition
frequency fr
RF Beat
1550 nm
193,548,387,096,774.2 Hz
10,000,000.0 Hz
Locking
Electronics
Stability and accuracy of RF standard passed to optical frequencies
Cesium Time
Standard
~9 GHz
Hydrogen
Maser
10 MHz

35. Stabilize frequency comb by Self-reference frequency lockingfo
I(f) f
fn = n fr + fo x2
f2n = 2nfr + fo
Measure offset frequency fo as shown and lock to zero
Phase-lock fr directly to an rf synthesizer
To Lock comb to an RF oscillator

36. Supercontinuum Frequency Comb

37. A Fiber Laser-Based Frequency Comb Translate Ti:Sapphire results to Fiber-based system
Most existing frequency combs limited to Ti:Sapphire laser-based systems
No self-referenced frequency combs from a mode-locked fiber laser in use
Locking of a fiber laser to other stabilized sources have been achieved*
Until recently a full octave from fiber laser not available*
A fiber-based frequency comb can provide
Compact, inexpensive design
Potential for stable “hands-free” operation
Optical frequency metrology in the IR
* References
F. Tauser et al, Opt. Express 11, 594 (2003)
F.-L. Hong et al, Opt. Lett. 28, 1 (2003)
J. Rauschenberger et al., Opt. Express 10, 1404 (2002)

38. All-Fiber Supercontinuum Source
HNLF
1480 nm pump
1480 nm pump
Er fiber
SMF
pigtail
980 nm pump
Er fiber
isolator
Continuum after 20 cm
DF - HNLF

39. Highly Nonlinear Fiber (HNLF)
nonlinearity : 8 to 15 1/W-km
Effective Area : 13 mm2
loss : 0.7 to 1 dB/km
dispersion (1550 nm) :
-10 to +10 ps/nm-km
dispersion slope (1550 nm) :
0.024 ps/nm2-km
splice loss (to SMF) :0.18 dB
splice loss (to HNLF) :0.02 dB

40. f-to-2f Interferometer
An octave of supercontinuum allow the generation of CEO beat frequencies with a SNR of 30 dB

41. Phase-locked Frequency Comb
f-to-2f Interferometer
Supercontinuum generation in highly nonlinear fiber (HNLF), 23 cm of length
Amplifier: 100 mW output, FWHM < 100 fs
Oscillator: 20 nm FWHM pulses, 50 MHz rep rate

42. Fiber Laser-Based Frequency Comb
f-to-2f interferometer
Supercontinuum Source
(all fiber)

43. Frequency Stability
- Optical comb phase locked to RF source - Any optical comb line known absolutely by fn = nfr + fo

44. Phase Noise Measurements
CEO frequency lock : integrated phase error for 2.07 MHz signal (DC to 25 MHz) was ~10 mrad
Repetition rate lock : integrated phase error (DC to 25 MHz) was <1 mrad

45. Optical Frequency Metrology
Mode-Locked
Lasers
Nonlinear
Optical Fibers
Radio Frequency
Standards
Optical Frequency Metrology
Molecular
Spectroscopy

46. Standard Reference Materials
Standards for
Wavelength Division Multiplexing

47. Spectroscopy of Acetylene
Wavemeter Frequency
Uncertainty: ~1.8 MHz
Typical wavemeters:
~20 MHz
(0.15 pm at 1550 nm)
Reference:
Swann and Gilbert,
JOSA B Vol. 17,7, (2000)

48. Metrology with Supercontinuum Comb
fn = nfr + fo
I(f) f
fo = fr Df/2p
repetition
frequency fr
RF Beat
fun fr
2fr
Fiber-based
Frequency Comb
Tunable CW
Laser
12C2H2
ESA
Computer

49. Conclusions
Stabilized frequency combs have revolutionized optical clocks
Previous systems limited to 400 nm to 1300 nm
Fiber laser-based frequency comb demonstrated
Potentially more robust than Ti:sapphire laser based frequency comb
Extend phase-lock frequency combs into the IR
Permit unprecedented accuracy in IR frequency metrology
Can lock frequency comb to Cesium time standard or other atomic standard

50. Thank you for your time! Brian R. Washburn
National Institute of Standards and Technology
Optoelectronics Division

51. EXTRA SLIDES

52. Four-Wave Mixing and Self-Phase Modulation
Nonlinear effects in fused-silica are due to the c(3) susceptibility
Four-Wave Mixing is the result of the instantaneous component of c(3) (Kerr effect)
Four Wave Mixing (FWM)
- Specific conditions needed to
assure phase matching
Self-Phase Modulation (SPM)
- Completely degenerate FWM
- Automatically phase-matched
Intensity dependent
Index

53. Solitons
Soliton Propagation
GVD
Only
SPM
Only

54. Stimulated Raman Scattering (SRS)
SRS is from the non-instantaneous component of the c(3) susceptibility
SRS typically leads to a frequency downshift of the incident light
The Raman gain curve (gR) characterizes the frequency downshift (Dn) acquired by the incident light

55. The NLSE
Assumptions
1) The nonlinear polarization PNL(r,t) can be treated as a small perturbation to PL(r,t).
2 The linear response is instantaneous.
3) The optical field maintains its polarization along the fiber length so a scalar approach is valid
4) E(r,t) is quasi-monochromatic.
5) The slowly varying envelope approximation (SVEA)
6) The mode profile is single mode, specifically LP01

56. Including SRS
To include the effect of SRS, the c(3) susceptibility was broken into fast (SPM) and slow (SRS) portions
The measured Raman gain curve (gR) can be implemented using

57. Extended NLSE for Including SRS
Describes spectral features developed over a frequency range of up to a third of the carrier frequency .
Uses the experimental nonlinear Raman response of fused-silica

58. Soliton Propagation Solitons are formed after a balance of GVD and SPM
Higher order dispersion and nonlinearities cause soliton breakup

59. Pulse Propagation Regimes
N=1 Soliton
Axis of Evil

60. How to Choose Fiber Lengths?
Need enough EDF to provide sufficient gain in the laser cavity
Need enough SMF to provide adequate nonlinear polarization
Net cavity dispersion is anomalous:
Soliton Regime
Net cavity dispersion is slightly normal
Stretched-pulse Regime
Net cavity dispersion is strongly normal
No mode-locking

61. Soliton vs. Nonsoliton Regime
Sidebands (Kelly sidebands) indicative of soliton propagation
Inhibiting soliton formation increases spectral bandwidth

62. Femtosecond-Laser-Based Optical Synthesizer
reference
m-wave
m-wave out
optical out
fn = nfr + fo
I(f) f fo fr
Sounds great, but can you do it?
Ti:Sapphire femtosecond laser + novel nonlinear fiber (‘00)
D. J. Jones et al. Science 288, 635 (2000)
Broadband Ti:Sapphire femtosecond laser (‘01/’02)
Morgner et al., PRL, 86, 5462,’01, T. Ramond et al., Opt. Lett 27, 1842
Femtosecond Er Fiber laser + novel nonlinear fiber (‘03)
Washburn et al., accepted to Opt. Lett, Oct. ‘03

63. Details on Locking Electronics
CEO Frequency Locking Electronics
Repetition Rate Locking Electronics

64. Frequency Stability verses Gate Time
Normalized Frequency Uncertainty (/favg)
Normalized Frequency Uncertainty (/favg)
Gate Time (ms)
Uncertainty on locked repetition rate (Frep) is near the system floor
Uncertainty on counted CEO beat (f0) is larger due to linewidth of the beat
Gate Time (ms)

65. Spectrum of Figure-Eight Laser

66. Spectrum of Stretched-Pulse Laser