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Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 15 — Jul. 25, 2005
  • pp: 5662–5668
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Circumvention of noise contributions in fiber laser based frequency combs

Erik Benkler, Harald R. Telle, Armin Zach, and Florian Tauser  »View Author Affiliations


Optics Express, Vol. 13, Issue 15, pp. 5662-5668 (2005)
http://dx.doi.org/10.1364/OPEX.13.005662


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Abstract

We investigate the performance of an Er:fiber laser based femtosecond frequency comb for precision metrological applications. Instead of an active stabilization of the comb, the fluctuations of the carrier-envelope offset phase, the repetition phase, and the phase of the beat from a comb line with an optical reference are synchronously detected. We show that these fluctuations can be effectively eliminated by exploiting their known correlation. In our experimental scheme, we utilize two identically constructed frequency combs for the measurement of the fluctuations, rejecting the influence of a shared optical reference. From measuring a white frequency noise level, we demonstrate that a fractional frequency instability better than 1.4 × 10-14 for 1 s averaging time can be achieved in frequency metrology applications using the Er:fiber based frequency comb.

© 2005 Optical Society of America

1. Introduction

However, heading for frequency combs as a general, user-friendly laboratory tool, it is desirable to use mode-locked Er:fiber lasers instead of free-space Ti:sapphire systems due to their convenience of operation, superior long-term stability, compactness and lower cost. On the other hand, CEO beat signals generated from fiber lasers are known to exhibit more high frequency noise [5–9

5. F.-L. Hong, H. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, “Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser,” Opt. Lett. 28, 1516–1518, (2003). [CrossRef] [PubMed]

]. Prior to this work, it has therefore been unclear whether a level of short-term instability better than several times 10-13 in one second can be achieved by use of such systems [9

9. F. Adler, K. Moutzouris, A. Leitenstorfer, H. Schnatz, B. Lipphardt, G. Grosche, and F. Tauser, “Phase-locked two-branch erbium-doped fiber laser system for long-term precision measurement of optical frequencies,” Opt. Express 12, 5872 (2004). [CrossRef] [PubMed]

]. Extremely fast servo elements acting on the CEO frequency with impractical bandwidths of at least several 100 kHz would be required in order to achieve a tight phase-lock for an Er:fiber based frequency comb. It should be noted that, in contrast to Ti:sapphire lasers, the CEO frequency is not amenable to changes of the pump power faster than approx. 10 kHz, owing to the long fluorescence lifetime of Erbium ions. If, however, the frequency and phase fluctuations of all comb lines are sufficiently correlated and can be described within an elastic tape model, the so-called transfer oscillator concept can be employed instead of the stabilization of the comb [10

10. H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002). [CrossRef]

, 11

11. J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002). [CrossRef] [PubMed]

]. Within this concept, noise contributions are eliminated by exploiting the correlations between the characteristic signals in a comb-based measurement, relying solely on relations which are known a priori. The aim of this paper is to investigate the impact of noise contributions violating the elastic tape model in a fiber-generated frequency comb. Such contributions, if present, would ultimately limit the achievable stability for high-precision metrology applications for both phase-locked frequency combs as well as transfer oscillator measurements.

2. Elastic tape model

The frequency vm of a line in a notionally perfect frequency comb of a mode-locked laser is given by

vm(t)=vCEO(t)+mfrep(t),
(1)

where m is the integer order number of the comb line. Since fluctuating quantities in eq. (1) can be visualized by stretching and translating an elastic tape labeled with the equidistant comb lines, we will refer to Eq. (1) as elastic tape model. We first consider only fluctuations caused by noise processes compliant with the elastic tape model. For the special case of a single noise process, a correlation between the dilations and translations of the elastic tape exists, such that they cancel out against each other at a particular fixed point frequency v fix [10

10. H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002). [CrossRef]

].

In a real-world system, fluctuations resulting from, e.g., technical noise processes or quantum noise not necessarily in accordance with the elastic tape model may be present. For this reason, we add the residual term δv res to Eq. (1), which accounts for these non-compliant fluctuations:

vm(t)=vCEO(t)+mfrep(t)+δvres(m,t).
(2)

The main goal of this paper is to investigate the properties of the residual term to estimate the quantitative impact of noise contributions not compliant with the elastic tape model, which ultimately limits the performance of the frequency comb in precision frequency metrological applications. Due to the lack of any a priori information about δv res (m, t), the non-compliant fluctuations cannot be corrected for using the transfer oscillator principle. Neither would a stabilization of the comb by phase-locking two of the quantities, vm v CEO and f rep eliminate the fluctuations not in compliance with the elastic tape model. Integration of Eq. (2) yields the corresponding equation for the instantaneous phases:

φm(t)=φCEO(t)+mφrep(t)+φres(m,t),
(3)

where φm , φ CEO, φ repand φ res are the phases of vm , v CEO, f rep and δv res, respectively. The value of φ res contains quantitative information about the impact of noise contributions not compliant with the elastic tape model. We will refer to φ res as residual phase throughout this work.

The rigorous validity of Eq. (1), or a sufficiently small residual phase in Eq. (3) would open up novel possibilities for the application of fiber lasers in high precision frequency metrology by use of the transfer oscillator concept. Therefore, the purpose of this study is to determine φ res (m, t) experimentally for a single order number m by measurement of, φm φ CEO and φ repand application of Eq. (3). This method yields an estimate for the uncorrelated phase noise contributions violating the elastic tape model.

3. Experimental setup and data analysis

According to Eq. (3), the determination of φ res (m, t) requires knowledge of the instantaneous phases φm , φ CEO and φ rep. These quantities are numerically derived from the corresponding temporal signals, which are detected with a sufficient signal to noise ratio (S/N). The phase φm is obtained from the beat signal between the field of a stable cw reference laser and the nearest comb line with order number m. The phase φ CEO is obtained from the CEO beat signal measured by the f-2f self referencing technique [12

12. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999). [CrossRef]

, 13

13. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000). [CrossRef] [PubMed]

], and the repetition phase φ rep is derived from a measurement of a high harmonic signal of the repetition rate. In a measurement with a single frequency comb, φm would contain noise of the optical reference and φ repwould contain noise of a microwave local oscillator (LO) used in the detection electronics. To avoid these problems, we performed the measurement using two identically constructed frequency comb generators sharing the same optical reference laser and a common LO. Fluctuations of the reference laser and of the LO thus do not enter the final expression for the residual phase φ res (m, t).

The experimental setup is shown in Fig. 1. We employed two identical passively modelocked Er:fiber lasers (TOPTICA FFS F-C SYS) as frequency comb generators. The repetition rate of the Er:fiber oscillators is tuned to approximately 107 MHz in our experiments. Since the setup is symmetric, the elements are described for one branch only in the following. The output of the fiber oscillator is split into three parts: One part is amplified in an Er:fiber amplifier, allowing for the generation of sub-100 fs pulses with 200 mW average power. An octave-spanning comb spectrum is generated by coupling this high power output into a highly nonlinear, dispersion shifted specialty fiber.

Fig. 1. Schematic drawing of the experimental setup. Red lines: optical signals, blue dashed lines: electrical signals. Details are described in the text.

This supercontinuum output ① of the laser is fed into an f-2f interferometer stage, which provides the CEO beat signal v CEO1 (v CEO2), detected with a Si avalanche photodiode. Part ② of the oscillator output is used for the generation of the beat note with cw light from a DFB fiber laser (KOHERAS ADJUSTIK) common to both branches of the setup. The wavelength of the DFB laser is λ = 1.5426μm, corresponding to an order number m ≈ 19312×94 of the nearest comb line. The beat signal v x1 v x2 is detected with InGaAs photodiode PD1 (PD2). At oscillator output ③, the h = 94 -th harmonic of the repetition rate near 10 GHz is detected with the fast InGaAs photodiode PD3 (PD4). In order to improve the dynamic range of the photodiode, an etalon with free spectral range of approximately 10 GHz (1 cm thick fused silica plate) is placed in front of it. The microwave signals obtained from PD3 and PD4 are amplified and down-converted to intermediate frequencies (IF) of 37.9 MHz and 43.6 MHz using a joint local oscillator LO (Agilent E8257D microwave synthesizer) and doublebalanced mixers. The repetition rates of laser 1 and laser 2 are deliberately detuned by a small frequency such that the intermediate frequencies differ by 5.7 MHz. The IF signals are bandpass filtered (BPF) and then mixed in a third double-balanced mixer. The output signal Δf rep is low-pass filtered to obtain the signal at the difference frequency of 5.7 MHz, which is free of noise contributions from the LO [14

14. R. Paschotta, B. Rudin, A. Schlatter, G.J. Spühler, L. Krainer, S.C. Zeller, N. Haverkamp, H.R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005). [CrossRef]

].

Time series of the signals v x1 , v x2, v CEO1, v CEO2 and Δf rep are recorded with a multichannel electronic sampling oscilloscope. The instantaneous phase angles φ x1, φ x2, φ CEO1, φ CEO2 and Δφ rep are derived from these five signals by a numerical phase-retrieval algorithm. Unwanted noise contributions of the common optical reference are eliminated by subtraction of the phases for branches 1 and 2 as in the case of the repetition rate signals. Using Eq. (3) and considering that Δφ rep is referred to the h = 94 -th harmonic of the repetition rate, one arrives at the expression for the difference between the residual phases of the two combs:

Δφres(t)=(φCEO1(t)φCEO2(t))+(φx1(t)φx2(t))mhΔφrep(t),
(4)

In order to demonstrate the enhancement due to application of the transfer oscillator concept, we compare the spectral noise density of the residual phase to the noise densities of the individual phases. All single-sided phase noise spectral densities shown in the following refer to a single laser and 10 GHz carrier frequency. Hence, the spectral densities of phase differences between the two branches of the setup must be divided by a factor of two, because the noise of the two lasers is not correlated. Referring to 10 GHz carrier frequency requires that all phases or phase differences except for Δφ rep must be divided by the ratio m/h between the order number and the order of repetition rate harmonic before determination of the spectral density. Please notice that due to the slight detuning of the repetition rates, the order numbers are slightly different in the two branches, i.e. m 1/h= 19317, m 2/h 19307. The spectral densities are determined by a fast Fourier transform method using Hann windowing.

4. Experimental results

Figure 2 shows the experimentally determined spectral noise densities of φ CEO, φx and φ rep. In order to obtain better visibility of details at high Fourier frequencies, a frequency-adaptive moving average over N=f312.5kHz+1 data points was applied for Fourier frequencies f > 625 kHz before transformation of the noise densities to the logarithmic dB scale.

Fig. 2. Spectral noise densities of the repetition phase (black solid line), of the phase of the beat between comb and optical reference (blue dotted), and of the CEO phase (red dashed).

The repetition phase noise density Sφrep is limited above f ≈ 40 kHz to the noise floor of ≈ - 120 dBrad2/Hz caused by the S/N of the photodiodes PD3 (PD4) and associated electronics like amplifiers and mixers. Furthermore, the noise floor due to digitization noise of the oscilloscope is - 125 dBrad2/Hz. This digitization noise floor is, however, not reached in our measurements. In the case of the phases φ CEO and φx, the noise floor is much lower and likewise not reached in our measurements, because these phases were determined in the optical domain, but are referred to a 10 GHz carrier, pushing the noise floor down by the factor (m/h)2, i.e. by 86 dB.

It can be seen that the spectral noise densities follow a similar frequency dependence. The CEO phase noise density SφCEO and repetition phase noise density Sφrepare of the same order of magnitude while the phase noise density Sφx of the beat with the optical reference is about 20 dB lower. From this observation, we can infer that there is a dominant technical noise contribution with a fixed point frequency v fix near the optical carrier. It is known that the fixed point frequency of pump laser current fluctuations typically shows such behavior [15

15. 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, 321–324 (2004). [CrossRef]

] and one might argue that the origin of the main technical noise contribution are pump current fluctuations or mode-hops of the pump laser diode. By use of a scanning Fabry-Perot interferometer, we found that although the wavelength of all pump diodes is stabilized by fiber Bragg gratings, their emission does not occur in a single longitudinal mode.

If the noise contributions of φ CEO, φx and φ rep are treated as uncorrelated, the spectral noise density of the residual phase is given by the sum Sφ=Sφrep+SφCEO+Sφx. This spectral density is shown as red dotted line in Fig. 3. In contrast to a picture of uncorrelated phase fluctuations within the optical frequency comb, we find that correlated fluctuations are strongly suppressed in the actual spectral noise density of the residual phase Sφres (black solid line in Fig. 3), when φ res is calculated according to Eq. (4), i.e. the elastic tape model is applied. At 100 Hz, the lowest frequency measured here due to memory size limitations of the oscilloscope, an enhancement of about 55 dB due to common mode rejection of correlated noise of the comb lines is demonstrated.

Fig. 3. Comparison between the experimentally determined spectral densities of the residual phase, treating comb fluctuations as correlated (black solid line) or uncorrelated (red dotted). The blue dashed line shows the noise floor of the measurement due to the phase noise of the oscilloscope time base.

It is important to notice that the experimentally determined residual phase noise spectral density Sφres is limited by the noise floor of the detection system in this first proof of principle and an actual enhancement due to the transfer oscillator principle even larger than 55 dB can be expected over the entire frequency spectrum. For Fourier frequencies below f ≈ 20 kHz, the noise floor is given by the phase noise of the sampling oscilloscope time base, which is shown as a blue dashed line in Fig. 3. The noise floor above 20 kHz is caused by the S/N of the photodiodes PD3/4 due to AM-PM conversion and noise in associated amplifiers and mixers. In principle, this noise floor could be reduced by correlation-based phase noise measurements [16

16. E.N. Ivanov, S.A. Diddams, and L. Hollberg, “Experimental Study of Noise Properties of a Ti:Sapphire Femtosecond Laser,” IEEE Trans. Ultrason. Ferroel. Freq. Contr. 50, 355–360 (2003). [CrossRef]

], in which the entire detection system is duplicated and the two identical systems share the same optical signal under test. The uncorrelated noise contributions of the detection systems can then be drastically reduced by measuring the temporally averaged cross-spectrum between the signals detected by the two systems.

With knowledge of Sφres, the resulting fractional frequency instability of the frequency comb in conjunction with a use of the transfer oscillator principle can now be estimated. The phase noise density Sφ shows a 1/f 2 - frequency dependence between 100 Hz and 10 kHz, and the roll-off becomes steeper at frequencies above 10 kHz. It is reasonable to assume that the enhancement of at least 55 dB observed at low Fourier frequencies is also valid at higher frequencies, where it is only hidden under the noise floor of the detection system. Hence, essentially the same frequency dependence for Sφres can be assumed as for Sφ, resulting in a white frequency noise level of Sv = f 2 Sφres(f) = 4 × 10-8 Hz2/Hz between 100 Hz and 10 kHz referred to a carrier frequency of v 0 = 10 GHz. Since fluctuations in the fiber laser based frequency comb arise from a piece of fiber with finite length, the value of the residual phase φ res is bounded. Therefore, the phase noise density does not diverge at low Fourier frequencies. However, assuming as a conservative estimate that the frequency noise remains white below 100 Hz, the Allan standard deviation is given by [17

17. NIST technical note 1337: Characterization of clocks and oscillators, D.B. Sullivan, D.W. Allan, D.A. Howe, and F.L. Walls, eds. (U.S. Government printing office, Washington, 1990), table I, p. TN-341.

]:

σy=1v0Sv2τ=1.4×1014[τHz]12,
(5)

where τ is the averaging time. Hence, a fractional frequency instability of 1.4 × 10-14 in 1 s averaging time results. It should be noted that this is rather a conservative estimate, mainly because the measured 55 dB enhancement due to application of the transfer oscillator principle is limited by the noise floor of the detection system. In principle, this result could also be obtained by frequency counting, which would, however, require counters with impracticable interpolation capabilities of 10-4 of a period, i.e. a timing resolution of 10 fs at v 0 = 10 GHz.

5. Conclusions

Acknowledgments

The authors thank G. Grosche for the loan of the DFB optical reference laser.

References and Links

1.

S.T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003). [CrossRef]

2.

A. Bartels, S.A. Diddams, C.W. Oates, G. Wilpers, J.C. Bergquist, W.H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005). [CrossRef] [PubMed]

3.

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004). [CrossRef] [PubMed]

4.

P. Baum, E. Riedle, M. Greve, and H. Telle, “Phase-locked ultrashort pulse trains at separate and independently tunable wavelengths,” Opt. Lett., (to be published). [PubMed]

5.

F.-L. Hong, H. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, “Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser,” Opt. Lett. 28, 1516–1518, (2003). [CrossRef] [PubMed]

6.

B.R. Washburn, S.A. Diddams, N.R. Newbury, J.W. Nicholson, M.F. Yan, and C.G. Jorgensen, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett. 29, 250–252 (2004). [CrossRef] [PubMed]

7.

B.R. Washburn, S.A. Diddams, N.R. Newbury, J.W. Nicholson, M.F. Yan, and C.G. Jorgensen, “A phase locked, fiber laser-based frequency comb: limit on optical linewidth,” CLEO/IQEC and PhAST Technical Digest on CD-ROM (The Optical Society of America, Washington, DC, 2004), CMO3.

8.

T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inabe, A. Onae, H. Matsumoto, I. Hartl, and M. Fermann, “Frequency metrology with a turnkey all-fiber system,” Opt. Lett. 29, 2467–2469 (2004). [CrossRef] [PubMed]

9.

F. Adler, K. Moutzouris, A. Leitenstorfer, H. Schnatz, B. Lipphardt, G. Grosche, and F. Tauser, “Phase-locked two-branch erbium-doped fiber laser system for long-term precision measurement of optical frequencies,” Opt. Express 12, 5872 (2004). [CrossRef] [PubMed]

10.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002). [CrossRef]

11.

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88, 073601 (2002). [CrossRef] [PubMed]

12.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999). [CrossRef]

13.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000). [CrossRef] [PubMed]

14.

R. Paschotta, B. Rudin, A. Schlatter, G.J. Spühler, L. Krainer, S.C. Zeller, N. Haverkamp, H.R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005). [CrossRef]

15.

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, 321–324 (2004). [CrossRef]

16.

E.N. Ivanov, S.A. Diddams, and L. Hollberg, “Experimental Study of Noise Properties of a Ti:Sapphire Femtosecond Laser,” IEEE Trans. Ultrason. Ferroel. Freq. Contr. 50, 355–360 (2003). [CrossRef]

17.

NIST technical note 1337: Characterization of clocks and oscillators, D.B. Sullivan, D.W. Allan, D.A. Howe, and F.L. Walls, eds. (U.S. Government printing office, Washington, 1990), table I, p. TN-341.

OCIS Codes
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(140.3510) Lasers and laser optics : Lasers, fiber
(320.7160) Ultrafast optics : Ultrafast technology

ToC Category:
Research Papers

History
Original Manuscript: June 3, 2005
Revised Manuscript: July 7, 2005
Published: July 25, 2005

Citation
Erik Benkler, Harald Telle, Armin Zach, and Florian Tauser, "Circumvention of noise contributions in fiber laser based frequency combs," Opt. Express 13, 5662-5668 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-15-5662


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References

  1. S.T. Cundiff and J. Ye, "Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003). [CrossRef]
  2. A. Bartels, S.A. Diddams, C.W. Oates, G. Wilpers, J.C. Bergquist, W.H. Oskay, and L. Hollberg, "Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005). [CrossRef] [PubMed]
  3. F. Keilmann, C. Gohle, and R. Holzwarth, "Time-domain mid-infrared frequency-comb spectrometer," Opt. Lett. 29, 1542-1544 (2004). [CrossRef] [PubMed]
  4. P. Baum, E. Riedle, M. Greve, and H. Telle, "Phase-locked ultrashort pulse trains at separate and independently tunable wavelengths," Opt. Lett., (to be published). [PubMed]
  5. F.-L. Hong, H. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, "Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser," Opt. Lett. 28, 1516-1518, (2003). [CrossRef] [PubMed]
  6. B.R. Washburn, S.A. Diddams, N.R. Newbury, J.W. Nicholson, M.F. Yan, and C.G. Jorgensen, "Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared," Opt. Lett. 29, 250-252 (2004). [CrossRef] [PubMed]
  7. B.R. Washburn, S.A. Diddams, N.R. Newbury, J.W. Nicholson, M.F. Yan, and C.G. Jorgensen, "A phase locked, fiber laser-based frequency comb: limit on optical linewidth," CLEO/IQEC and PhAST Technical Digest on CD-ROM (The Optical Society of America, Washington, DC, 2004), CMO3.
  8. T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inabe, A. Onae, H. Matsumoto, I. Hartl, and M. Fermann, "Frequency metrology with a turnkey all-fiber system," Opt. Lett. 29, 2467-2469 (2004). [CrossRef] [PubMed]
  9. F. Adler, K. Moutzouris, A. Leitenstorfer, H. Schnatz, B. Lipphardt, G. Grosche, and F. Tauser, "Phase-locked two-branch erbium-doped fiber laser system for long-term precision measurement of optical frequencies," Opt. Express 12, 5872 (2004). [CrossRef] [PubMed]
  10. H. R. Telle, B. Lipphardt, and J. Stenger, "Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements," Appl. Phys. B 74, 1-6 (2002). [CrossRef]
  11. J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, "Ultraprecise measurement of optical frequency ratios," Phys. Rev. Lett. 88, 073601 (2002). [CrossRef] [PubMed]
  12. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999). [CrossRef]
  13. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000). [CrossRef] [PubMed]
  14. R. Paschotta, B. Rudin, A. Schlatter, G.J. Spühler, L. Krainer, S.C. Zeller, N. Haverkamp, H.R. Telle, and U. Keller, "Relative timing jitter measurements with an indirect phase comparison method," Appl. Phys. B 80, 185 - 192 (2005). [CrossRef]
  15. 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, 321-324 (2004). [CrossRef]
  16. E.N. Ivanov, S.A. Diddams, and L. Hollberg, "Experimental Study of Noise Properties of a Ti:Sapphire Femtosecond Laser," IEEE Trans. Ultrason. Ferroel. Freq. Contr. 50, 355-360 (2003). [CrossRef]
  17. NIST technical note 1337: Characterization of clocks and oscillators, D.B. Sullivan, D.W. Allan, D.A. Howe, and F.L. Walls, eds. (U.S. Government printing office, Washington, 1990), table I, p. TN-341.

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