Abstract

We measure the frequency noise across a Cr:forsterite infrared frequency comb through the optical heterodyne beat of different comb teeth against stable continuous wave (CW) lasers. This sensitive measurement shows strong correlations of the frequency noise between spectral components of the comb, relative to a fixed optical frequency near the 1.3 micron carrier of the Cr:forsterite laser. The correlated frequency fluctuations are shown to arise from amplitude noise on the pump laser. We also report a preliminary comparison of excess noise that occurs during supercontinuum generation in both highly nonlinear fiber and an extruded glass microstructured fiber.

©2007 Optical Society of America

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References

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  1. J. L. Hall, “Nobel Lecture: Defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279 (2006).
    [Crossref]
  2. T. W. Hänsch, “Nobel Lecture: Passions for precision,” Rev. Mod. Phys. 78, 1297 (2006).
    [Crossref]
  3. John M. Dudley, Goëry Genty, and Stèphane Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
    [Crossref]
  4. Nathan R. Newbury and William C. Swann, “Low-noise fiber-laser frequency combs,” J. Opt. Soc. Am. B,  24, 1756 (2007).
    [Crossref]
  5. J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Elimination of pump-induced frequency jitter on fiber-laser frequency combs,” Opt. Lett. 31, 1997 (2006).
    [Crossref] [PubMed]
  6. J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219 (2007).
    [Crossref]
  7. H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1 (2002).
    [Crossref]
  8. N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321 (2004).
    [Crossref]
  9. D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
    [Crossref]
  10. I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “420-MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1–2-µm range,” Opt. Lett. 28, 1368 (2003).
    [Crossref] [PubMed]
  11. K. Kim, B. R. Washburn, G. Wilpers, C.W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J.W. Nicholson, and M. F. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932 (2005).
    [Crossref] [PubMed]
  12. K. Kim, S. A. Diddams, P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Improved stabilization of a 1.3µm femtosecond optical frequency comb by use of a spectrally tailored continuum from a nonlinear fiber grating,” Opt. Lett. 31, 277 (2006).
    [Crossref] [PubMed]
  13. J. W. Nicholson, M. F. Yan, P. Wisk, J. Fleming, F. DiMarcello, E. Monberg, A. Yablon, C. Jørgensen, and T. Veng, “All-fiber, octave-spanning supercontinuum,” Opt. Lett. 28, 643 (2003).
    [Crossref] [PubMed]
  14. V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).
  15. A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, “Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers,” Opt. Lett. 29, 403 (2004).
    [Crossref] [PubMed]
  16. B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond fiber laser,” Opt. Express 13, 10622 (2005).
    [Crossref] [PubMed]

2007 (3)

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219 (2007).
[Crossref]

D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
[Crossref]

Nathan R. Newbury and William C. Swann, “Low-noise fiber-laser frequency combs,” J. Opt. Soc. Am. B,  24, 1756 (2007).
[Crossref]

2006 (5)

K. Kim, S. A. Diddams, P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Improved stabilization of a 1.3µm femtosecond optical frequency comb by use of a spectrally tailored continuum from a nonlinear fiber grating,” Opt. Lett. 31, 277 (2006).
[Crossref] [PubMed]

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Elimination of pump-induced frequency jitter on fiber-laser frequency combs,” Opt. Lett. 31, 1997 (2006).
[Crossref] [PubMed]

J. L. Hall, “Nobel Lecture: Defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279 (2006).
[Crossref]

T. W. Hänsch, “Nobel Lecture: Passions for precision,” Rev. Mod. Phys. 78, 1297 (2006).
[Crossref]

John M. Dudley, Goëry Genty, and Stèphane Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

2005 (2)

2004 (2)

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321 (2004).
[Crossref]

A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, “Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers,” Opt. Lett. 29, 403 (2004).
[Crossref] [PubMed]

2003 (2)

2002 (2)

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1 (2002).
[Crossref]

Bartels, A.

Coen, Stèphane

John M. Dudley, Goëry Genty, and Stèphane Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Corwin, K. L.

Diddams, S. A.

DiMarcello, F.

Dudley, John M.

John M. Dudley, Goëry Genty, and Stèphane Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Fallnich, C.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321 (2004).
[Crossref]

Feder, K. S.

Fleming, J.

Genty, Goëry

John M. Dudley, Goëry Genty, and Stèphane Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

George, A. K.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Gohle, Ch.

D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
[Crossref]

Hall, J. L.

J. L. Hall, “Nobel Lecture: Defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279 (2006).
[Crossref]

Hänsch, T. W.

T. W. Hänsch, “Nobel Lecture: Passions for precision,” Rev. Mod. Phys. 78, 1297 (2006).
[Crossref]

Hänsch, T.W.

D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
[Crossref]

Haverkamp, N.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321 (2004).
[Crossref]

Hollberg, L.

Hundertmark, H.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321 (2004).
[Crossref]

Jørgensen, C.

Kim, K.

Knight, J. C.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Lipphardt, B.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1 (2002).
[Crossref]

McFerran, J. J.

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219 (2007).
[Crossref]

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Elimination of pump-induced frequency jitter on fiber-laser frequency combs,” Opt. Lett. 31, 1997 (2006).
[Crossref] [PubMed]

Monberg, E.

Newbury, N. R.

Newbury, Nathan R.

Nicholson, J. W.

Nicholson, J.W.

Oates, C.W.

Omenetto, F. G.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Ravi Kanth Kumar, V. V.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Reeves, W. H.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Russell, P. St. J.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Stein, B.

D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
[Crossref]

Stenger, J.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1 (2002).
[Crossref]

Swann, W. C.

Swann, William C.

Taylor, A. J.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Telle, H. R.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321 (2004).
[Crossref]

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1 (2002).
[Crossref]

Thomann, I.

Udem, Th.

D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
[Crossref]

Veng, T.

Walker, D.R.

D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
[Crossref]

Washburn, B. R.

Westbrook, P. S.

Wilpers, G.

Wisk, P.

Yablon, A.

Yan, M. F.

Appl. Phys. B (4)

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219 (2007).
[Crossref]

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1 (2002).
[Crossref]

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321 (2004).
[Crossref]

D.R. Walker, Th. Udem, Ch. Gohle, B. Stein, and T.W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535 (2007).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Express. (1)

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation,” Opt. Express. 10, 1520 (2002).

Opt. Lett. (6)

Rev. Mod. Phys. (3)

J. L. Hall, “Nobel Lecture: Defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279 (2006).
[Crossref]

T. W. Hänsch, “Nobel Lecture: Passions for precision,” Rev. Mod. Phys. 78, 1297 (2006).
[Crossref]

John M. Dudley, Goëry Genty, and Stèphane Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. The supercontinuum spectra generated with femtosecond Cr:forsterite laser pulses after (a) 2-m HNLF and (b) 3-cm PCF. The arrows indicate the wavelengths of available stable CW lasers for heterodyne measurements.

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Fig. 2.
Fig. 2. The changes of f0 and fr with pump power modulation, measured at different modulation depths. The solid line is a linear fit to the data.

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Fig. 3.
Fig. 3. Scheme of frequency mixing between the optical heterodyne RF beat notes at two different wavelengths from 1064nm, 1112nm, and 1550nm.

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Fig. 4.
Fig. 4. The RF spectra of the two mixing products of optical beats between modes from the supercontinuum and stable CW lasers. See text for details. (a) 1064 nm, 1550 nm and (b) 1064 nm, 1112 nm. The resolution bandwidth was 10 kHz. The various RF beats are offset from their nominal center frequencies fcenter and also vertically offset for clarity and ease of comparison.

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Fig. 5.
Fig. 5. For the optical beat notes heterodyned with stable CW lasers at 1064 nm, 1319 nm, and 1550 nm, a delay-line discriminator was used to measure the (a) amplitude and (b) phase of the frequency comb response to modulation of the pump laser power. That is, we measure and plot the complex transfer coefficient between amplitude modulation on the pump and frequency modulation on specific comb lines. (c) The difference of the measured phase of beats at 1064 nm and 1550 nm. (d) The frequency shift of the beats at 1064 nm and 1550 nm in the time domain while the pump power was modulated at 200 kHz.

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Fig. 6.
Fig. 6. The frequency noise (at a Fourier frequency of 100 kHz) was measured at different wavelengths of the comb at both the Cr:forsterite laser output and after supercontinuum generation in HNLF and PCF. The error bars on each point are representative of the uncertainty in the measurements and calibration of the delay-line frequency discriminator

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Equations (3)

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f n = n f r − f 0 ,
df n dP = n df r dP − df 0 dP
df n dP ≈ ( f n − f fix ) df r dP .

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