## Generation of ultrahigh and tunable repetition rates in CW injection-seeded frequency-shifted feedback lasers |

Optics Express, Vol. 21, Issue 13, pp. 15065-15074 (2013)

http://dx.doi.org/10.1364/OE.21.015065

Acrobat PDF (1773 KB)

### Abstract

We show both theoretically and experimentally that frequency-shifted feedback (FSF) lasers seeded with a single frequency laser can generate Fourier transform-limited pulses with a repetition rate tunable and limited by the spectral bandwidth of the laser. We demonstrate experimentally in a FSF laser with a 150 GHz spectral bandwidth, the generation of 6 ps-duration pulses at repetition rates tunable over more than two orders of magnitude between 0.24 and 37 GHz, by steps of 80 MHz. A simple linear analytical model *i.e.* ignoring both dynamic and non-linear effects, is sufficient to account for the experimental results. This possibility opens new perspectives for various applications where lasers with ultra-high repetition rates are required, from THz generation to ultrafast data processing systems.

© 2013 OSA

## 1. Introduction

1. M. Stellpflug, G. Bonnet, B. W. Shore, and K. Bergmann, “Dynamics of frequency shifted feedback lasers: simulation studies,” Opt. Express **11**, 2060–2080 (2003) [CrossRef] [PubMed] .

2. F. V. Kowalski, C. Ndiaye, K. Nakamura, and H. Ito, “Noise waveforms with repetitive phase and nonrepetitive amplitude,” Opt. Lett. **27**, 1965–1967 (2002) [CrossRef] .

4. H. Guillet de Chatellus and J.-P. Pique, “Statistical properties of frequency shifted feedback lasers,” Opt. Commun. **283**, 71–77 (2010) [CrossRef] .

5. F. V. Kowalski, C. Ndiaye, K. Nakamura, and H. Ito, “Noise waveforms generated by frequency shifted feedback lasers: application to multiple access communications,” Opt. Commun. **231**, 149–164 (2004) [CrossRef] .

6. H. Guillet de Chatellus and J.-P. Pique, “*λ*/2 fringe spacing interferometer,” Opt. Lett. **34**, 755–757 (2009) [CrossRef] .

7. K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, and H. Ito, “Optical frequency domain ranging by a frequency-shifted feedback laser,” IEEE J. Quantum Electron. **36**, 305–316 (2000) [CrossRef] .

8. V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “High accuracy ranging with Yb3+-doped fiber-ring frequency-shifted feedback laser with phase-modulated seed,” Opt. Commun. **266**, 266–273 (2006) [CrossRef] .

3. L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Coherence in the output spectrum of frequency shifted feedback lasers,” Opt. Commun. **282**, 300–309 (2009) [CrossRef] .

9. H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “The hypothesis of the moving comb in frequency shifted feedback lasers,” Opt. Commun. **284**, 4965–4970 (2011) [CrossRef] .

10. H. Guillet de Chatellus, E. Lacot, O. Jacquin, W. Glastre, and O. Hugon, “Heterodyne beatings between frequency-shifted feedback lasers,” Opt. Lett. **37**, 791–793 (2012) [CrossRef] .

11. S. Balle, I. C. Littler, K. Bergmann, and F. V. Kowalski, “Frequency shifted feedback dye laser operating at a small shift frequency,” Opt. Commun. **102**, 166–173 (1993) [CrossRef] .

12. F. V. Kowalski, S. J. Shattil, and P. D. Hale, “Optical pulse generation with a frequency shifted feedback laser,” Appl. Phys. Lett. **53**(9), 734–736 (1988) [CrossRef] .

13. H. Sabert and E. Brinkmeyer, “Pulse generation in fiber lasers with frequency shifted feedback,” J. Lightwave. Technol. **12**, 1360–1368 (1994) [CrossRef] .

18. A. M. Heidt, J. P. Burger, J.-N. Maran, and N. Traynor, “High power and high energy ultrashort pulse generation with a frequency shifted feedback fiber laser,” Opt Express **15**, 15892–15897 (2007) [CrossRef] [PubMed] .

*f*was equal to the cavity free spectral range

_{s}*f*[19

_{c}19. F. V. Kowalski, J. A. Squier, and J. T. Pinckney, “Pulse generation with an acousto-optic frequency shifter in a passive cavity,” Appl. Phys. Lett. **50**, 711–713, 1987 [CrossRef] .

*f*/

_{s}*f*=

_{c}*p/q*(

*p*and

*q*being coprime integers) the laser generates pulses at repetition rate

*qf*[20

_{s}20. P. D. Hale and F. V. Kowalski, “Output characterization of a frequency shifted laser: Theory and experiment,” IEEE J. Quantum Electron. **26**, 1845–1851 (1990) [CrossRef] .

*f*/

_{s}*f*= 2 [21

_{c}21. M. W. Phillips, G. Y. Liang, and J. R. M. Barr, “Frequency comb generation and pulsed operation in a Nd:YLF laser with frequency-shifted feedback,” Opt. Commun. **100**, 473–478 (1993) [CrossRef] .

22. P. Coppin and T. G. Hodgkinson, “Novel optical frequency comb synthesis using optical feedback,” Electron. Lett. **26**, 28–30 (1990) [CrossRef] .

*et al.*developed a numerical model of a FSF laser where the gain and losses of the cavity were taken into account, which proved numerically the possibility of increasing the repetition rate by adjusting the frequency shift

*f*and the cavity free spectral range

_{s}*f*as the ratio of two integers [23

_{c}23. L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. **236**, 183–202 (2004) [CrossRef] .

*f*/

_{s}*f*=

_{c}*p/q*, the repetition rate is equal to

*qf*=

_{s}*pf*. Since then however, despite recent experimental investigations of seeded FSF lasers for frequency combs and metrology applications [24

_{c}24. V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental Characterization of an Yb3+-doped Fiber Ring Laser with Frequency-shifted Feedback,” Opt. Commun. **266**, 627–637 (2006) [CrossRef] .

26. M. Nikodem and K. Abramski, “Controlling the frequency of the frequency shifted feedback fiber laser using injection-seeding technique,” Opt. Commun. **283**, 2202–2205 (2010) [CrossRef] .

*f*/

_{s}*f*= 2.

_{c}*p*and

*q*as large as 183 and 586 respectively. Indeed we prove the generation of 6 ps Fourier-transform limited pulses with a repetition rate tunable by steps of

*f*= 80 MHz between 3 ×

_{s}*f*(240 MHz) and 458 ×

_{s}*f*(37 GHz), with an average power larger than 100 mW. We provide a simple (linear) model based on the interference of the optical modes of the frequency comb generated at the output of the CW injection-seeded FSF laser, and attribute this behavior to the fact that the phase of the

_{s}*n*

^{th}mode has a quadratic dependence with

*n*.

## 2. Theoretical description

### 2.1. Expression of the electric field

3. L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Coherence in the output spectrum of frequency shifted feedback lasers,” Opt. Commun. **282**, 300–309 (2009) [CrossRef] .

*τ*= 1/

_{c}*f*= 2

_{c}*π*/

*ω*and the frequency shift per roundtrip

_{c}*f*=

_{s}*ω*/2

_{s}*π*(Fig. 1). The cavity is seeded continuously with a monochromatic field

*E*

_{0}

*e*

^{−iω0t}: at each roundtrip in the cavity the angular frequency is shifted by

*ω*. A slightly transmitting mirror enables to extract a fraction of the intracavity field. The output optical spectrum consists in a comb of optical modes separated by the frequency

_{s}*f*. The influence of the gain and losses of the FSF cavity is modeled by a real and positive function

_{s}*g*, where

*E*

_{0}

*g*(

*n*) is the amplitude of the mode of angular frequency

*ω*

_{0}+

*nω*. One sets

_{s}*g*(

*n*) = 0 when

*n*< 0 and

*n*>

*N*, the cutoff limit of

*g*(Fig. 1). Calling Δ

*ω*the spectral bandwidth of the FSF laser,

*N*= Δ

*ω*/

*ω*. The electric field at the output of the cavity is, following [19

_{s}19. F. V. Kowalski, J. A. Squier, and J. T. Pinckney, “Pulse generation with an acousto-optic frequency shifter in a passive cavity,” Appl. Phys. Lett. **50**, 711–713, 1987 [CrossRef] .

20. P. D. Hale and F. V. Kowalski, “Output characterization of a frequency shifted laser: Theory and experiment,” IEEE J. Quantum Electron. **26**, 1845–1851 (1990) [CrossRef] .

23. L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. **236**, 183–202 (2004) [CrossRef] .

*ϕ*

_{1}= (

*ω*

_{0}+

*ω*)

_{s}*τ*,

_{c}*ϕ*

_{2}=

*ϕ*

_{1}+(

*ω*

_{0}+ 2

*ω*)

_{s}*τ*,

_{c}*ϕ*

_{3}=

*ϕ*

_{2}+(

*ω*

_{0}+ 3

*ω*)

_{s}*τ*... Finally the phase of the n

_{c}*mode is:*

^{th}*ϕ*=

_{n}*nω*

_{0}

*τ*+

_{c}*n*(

*n*+ 1)

*ω*/2 and the resulting electric field is: where

_{s}τ_{c}*ϕ*=

*ω*= 2

_{s}τ_{c}*πf*/

_{s}*f*. Note that

_{c}*E*(

*t*) appears as a Fourier series with phase terms quadratic in

*n*: the same kind of expression was previously shown as playing a fundamental role in the time-spectrum description of modeless FSF lasers [9

9. H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “The hypothesis of the moving comb in frequency shifted feedback lasers,” Opt. Commun. **284**, 4965–4970 (2011) [CrossRef] .

10. H. Guillet de Chatellus, E. Lacot, O. Jacquin, W. Glastre, and O. Hugon, “Heterodyne beatings between frequency-shifted feedback lasers,” Opt. Lett. **37**, 791–793 (2012) [CrossRef] .

### 2.2. Expression of the intensity

*I*(

*t*) =

*E*(

*t*)

*E*

^{*}(

*t*). Writing

*I*

_{0}= |

*E*

_{0}|

^{2}leads to: which can be rewritten as (introducing

*k*=

*n*−

*m*):

*(*

_{m}g*k*+

*m*)

*g*(

*m*)

*e*

^{−ikmϕ}is a direct consequence of the quadratic phases in Eq. (2): it ensures a selection of specific values of

*k*based on the comparison between the width of the function

*m*↦

*g*(

*k*+

*m*)

*g*(

*m*) and the period of

*m*↦

*e*

^{−ikmϕ}. For simplicity reasons it is assumed

*g*(

*m*) is a Gaussian function of characteristic width

*N*/2. Then the width of

*g*(

*k*+

*m*)

*g*(

*m*) is

*k*satisfying: the term ∑

*(*

_{m}g*k*+

*m*)

*g*(

*m*)

*e*

^{−ikmϕ}is a sum of positive terms whereas for other values of

*k*, both positive and negative terms appear in the sum and limit its amplitude. Therefore only integers satisfying Eq. (5) contribute significantly to the sum over

*k*arising in Eq. (4). We consider the case

*ϕ*= 2

*πp/q*where

*p*and

*q*are coprime integers and

*q*<

*N*. Then the previous condition reduces to:

*pk*is an integer and

*k*= 0 [

*q*]. Then the intensity rewrites: where

*G*(

*λ*) = ∑

*(*

_{m}g*λ*+

*m*)

*g*(

*m*) is the discrete autocorrelation function of

*g*.

*p*is even or

*q*is odd: whereas when

*p*is odd and

*q*is even,

*G*(

*λ*) is real this Fourier series describes Fourier transform-limited pulses at the repetition rate

*qf*=

_{s}*pf*, according to

_{c}*ϕ*= 2

*πf*/

_{s}*f*= 2

_{c}*πp/q*[23

23. L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. **236**, 183–202 (2004) [CrossRef] .

*π*/(

*Nω*) = 2

_{s}*π*/Δ

*ω*. The average intensity is constant and equal to

*Ī*=

*I*

_{0}

*G*(0) whereas the peak intensity is equal to

*I*=

_{peak}*I*

_{0}∑

*(*

_{k}G*kq*). The conservation of energy leads to

*I*≈

_{peak}*I*

_{0}

*G*(0)

*Nf*/

_{s}*q*. Note that the maximal repetition rate is limited by the number of modes and therefore by the spectral bandwidth of the laser: when

*q*becomes comparable to

*N*, the pulses begin to overlap.

### 2.3. Intensity fluctuations

*ϕ*= 2

*πp/q*, the laser emits pulses at the repetition rate

*q f*and a signature of this appears in the variation with

_{s}*ϕ*of the relative intensity fluctuations of the laser defined by: where <> denotes the average over time. When

*ϕ*= 2

*πp/q*with

*q*<<

*N*, the laser emits q pulses per period 2

*π*/

*ω*. The average intensity does not depend on the repetition rate and a simple calculation leads to:

_{s}*W*(2

*πp/q*) ∼ 1/

*q*. The intensity fluctuations of the injected FSF laser tend therefore to the self-similar so-called ”Thomae’s function” defined on [0, 1] by:

*T*(

*p/q*) = 1/

*q*when

*p*and

*q*are coprimes, and

*T*(

*η*) = 0 when

*η*is irrational.

## 3. Experimental validation

### 3.1. Experimental setup

*f*= 80 MHz. The output coupler of the FSF laser is mounted on a translation stage (TS1) enabling to scan the cavity length over more than 7 cm and consequently the cavity free spectral range

_{s}*f*between 240 and 280 MHz. The typical output beam power is 100 mW and the spectral bandwidth is 150 GHz. The latter can be reduced down to about 3 GHz by the insertion in the FSF cavity of a Fabry-Perot etalon. A fraction of the output beam is directed onto a fast photodiode (100 ps resp. time) and the signal is acquired by a fast digital oscilloscope (5 GHz BW). The other part of the beam is sent into a Michelson interferometer whose moving mirror is mounted on a second translation stage (TS2). The output of the interferometer is focused onto a BBO crystal tuned for second harmonic generation (SHG) at 580 nm. The UV signal is filtered out by a prism and a color glass plate and detected by a photomultiplier tube (PMT).

_{c}### 3.2. Experimental results

*ϕ*= 2

*πp/q*, that is

*f*/

_{s}*f*is a rational quantity.

_{c}*f*is kept constant while

_{s}*f*is adjusted by tuning the cavity length with TS1. First the cavity length is adjusted to relatively low values of

_{c}*q*(

*q*< 30) and the intensity spectrum of the FSF laser is recorded for different values of the cavity free spectral range. Results are plotted on Fig. 4 and demonstrate the decimation in the intensity spectrum predicted theoretically: beside additional beat notes of smaller amplitude, only RF frequencies corresponding to common multiples of

*f*and

_{s}*f*appear in the intensity spectrum, in accordance to Eq. (6). This also corresponds to the fact that the repetition rate of the laser is the least common multiple of

_{c}*f*and

_{s}*f*.

_{c}*q*(which corresponds to repetition rates out of reach of our electronic detection system) we record the interferometric autocorrelation trace < |

*E*(

*t*) +

*E*(

*t*+

*τ*)|

^{4}> by measuring the time-averaged SHG signal at the output of the interferometer (

*τ*is the time delay of the interferometer). The cavity length is adjusted to a given value

*f*= (

_{c}*q/p*)

*f*and the mobile arm in the Michelson interferometer is scanned around null delay by TS2. A central fringe pattern is recorded in all cases, independently from the cavity length and represents the autocorrelation of a single pulse (Fig. 5). Note that the width of this trace is independent from the cavity length and simply proportional to the inverse of the spectral bandwidth of the laser, that is the coherence time of the source. In the case of a pulsed source the theoretical ratio between the baseline and the top of the fringes is equal to 1:8. A slightly lower value is obtained in our case due to an average over the fringes caused by the excessive scan speed of TS2. The appearance of additional peaks in the autocorrelation trace for path delays much smaller than the cavity length is the signature of the multiplication of the repetition rate and corresponds to the overlap of successive light pulses at the output of the interferometer. It could be shown theoretically that the lack of fringe pattern in the satellite peaks is due to the absence of average coherence between consecutive pulses, which results in the 1:2 ratio between the baseline and the height of the secondary peak. The repetition rate can be deduced from the time delay between consecutive peaks on the autocorrelation trace while the pulse duration corresponds to the widths of the peaks. According to the theoretical description, Fig. 5(b) evidences the generation of 6 ps duration Fourier-transform limited pulses at a repetition rate as high as 37 GHz, which is close to the ultimate limit set by the bandwidth of the laser (150 GHz in this case).

_{s}*W*(

*ϕ*). The experimental results are shown on Fig. 6. When the spectral bandwidth of the laser is increased from 3 to 150 GHz, the intensity fluctuations tend to the self-similar Thomae’s function and reveal self-similarity.

## 4. Conclusion

*i.e.*by the spectral bandwidth of the laser. We have given a brief analytical description of this phenomenon, based on a linear approach,

*i.e.*a pure interference phenomenon between waves with quadratic phases, ignoring both dynamic or non-linear effects. This simple approach is sufficient however to account for the experimental results. In the present study the repetition rate is a multiple of

*f*= 80 MHz and tunable over two orders of magnitude between 3 ×

_{s}*f*and 458 ×

_{s}*f*. Note that we have neglected so far the role of the coherence of the seed laser since our theoretical description involves a pure monochromatic wave. In fact to ensure Fourier transform-limited pulses, the coherence time of the seed laser needs to be longer than the photon cavity lifetime in the cavity, that is

_{s}*Nτ*. In the current experiment the coherence time of the seed laser (1

_{c}*μ*s) is of the same order of magnitude (although smaller) as the photon cavity lifetime (about 4

*μ*s). To demonstrate ultrahigh repetition rates (100 GHz to THz), seed lasers with longer coherence time will be required, such as extended-cavity diode lasers or distributed feedback lasers (with 10

*μ*s up to 1 ms respective coherence times). Finally an additional advantage of this scheme for high repetition rates is the fact that the repetition rate is derived from the electronic frequency driving the AOFS, and not only from the cavity free spectral range, like in conventional passive mode-locking.

## 5. Acknowledgments

## References and links

1. | M. Stellpflug, G. Bonnet, B. W. Shore, and K. Bergmann, “Dynamics of frequency shifted feedback lasers: simulation studies,” Opt. Express |

2. | F. V. Kowalski, C. Ndiaye, K. Nakamura, and H. Ito, “Noise waveforms with repetitive phase and nonrepetitive amplitude,” Opt. Lett. |

3. | L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Coherence in the output spectrum of frequency shifted feedback lasers,” Opt. Commun. |

4. | H. Guillet de Chatellus and J.-P. Pique, “Statistical properties of frequency shifted feedback lasers,” Opt. Commun. |

5. | F. V. Kowalski, C. Ndiaye, K. Nakamura, and H. Ito, “Noise waveforms generated by frequency shifted feedback lasers: application to multiple access communications,” Opt. Commun. |

6. | H. Guillet de Chatellus and J.-P. Pique, “ |

7. | K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, and H. Ito, “Optical frequency domain ranging by a frequency-shifted feedback laser,” IEEE J. Quantum Electron. |

8. | V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “High accuracy ranging with Yb3+-doped fiber-ring frequency-shifted feedback laser with phase-modulated seed,” Opt. Commun. |

9. | H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “The hypothesis of the moving comb in frequency shifted feedback lasers,” Opt. Commun. |

10. | H. Guillet de Chatellus, E. Lacot, O. Jacquin, W. Glastre, and O. Hugon, “Heterodyne beatings between frequency-shifted feedback lasers,” Opt. Lett. |

11. | S. Balle, I. C. Littler, K. Bergmann, and F. V. Kowalski, “Frequency shifted feedback dye laser operating at a small shift frequency,” Opt. Commun. |

12. | F. V. Kowalski, S. J. Shattil, and P. D. Hale, “Optical pulse generation with a frequency shifted feedback laser,” Appl. Phys. Lett. |

13. | H. Sabert and E. Brinkmeyer, “Pulse generation in fiber lasers with frequency shifted feedback,” J. Lightwave. Technol. |

14. | G. Bonnet, S. Balle, T. Kraft, and K. Bergmann, “Dynamics and self-modelocking of a titanium-sapphire laser with intracavity frequency shifted feedback,” Opt. Commun. |

15. | J. M. Sousa and O. G. Okhotnikov, “Short pulse generation and control in Er-doped frequency-shifted-feedback fiber lasers,” Opt. Commun. |

16. | M. P. Nikodem, H. Sergeant, P. Kaczmarek, and K. M. Abramski, “Actively mode-locked fiber laser using acousto-optic modulator,” Proc. SPIE |

17. | M. P. Nikodem, E. Kluzniak, and K. Abramski, “Wavelength tunability and pulse duration control in frequency shifted feedback Er-doped fiber lasers,” Opt. Express |

18. | A. M. Heidt, J. P. Burger, J.-N. Maran, and N. Traynor, “High power and high energy ultrashort pulse generation with a frequency shifted feedback fiber laser,” Opt Express |

19. | F. V. Kowalski, J. A. Squier, and J. T. Pinckney, “Pulse generation with an acousto-optic frequency shifter in a passive cavity,” Appl. Phys. Lett. |

20. | P. D. Hale and F. V. Kowalski, “Output characterization of a frequency shifted laser: Theory and experiment,” IEEE J. Quantum Electron. |

21. | M. W. Phillips, G. Y. Liang, and J. R. M. Barr, “Frequency comb generation and pulsed operation in a Nd:YLF laser with frequency-shifted feedback,” Opt. Commun. |

22. | P. Coppin and T. G. Hodgkinson, “Novel optical frequency comb synthesis using optical feedback,” Electron. Lett. |

23. | L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Theory of a frequency-shifted feedback laser,” Opt. Commun. |

24. | V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “Experimental Characterization of an Yb3+-doped Fiber Ring Laser with Frequency-shifted Feedback,” Opt. Commun. |

25. | H. Y Ryu, H. S. Moon, and H. S. Suh, “Optical frequency comb generator based on actively mode-locked fiber ring laser using an acousto-optic modulator with injection-seeding,” Opt. Express |

26. | M. Nikodem and K. Abramski, “Controlling the frequency of the frequency shifted feedback fiber laser using injection-seeding technique,” Opt. Commun. |

27. | M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. |

**OCIS Codes**

(030.4070) Coherence and statistical optics : Modes

(140.4050) Lasers and laser optics : Mode-locked lasers

(140.3538) Lasers and laser optics : Lasers, pulsed

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: February 6, 2013

Revised Manuscript: April 18, 2013

Manuscript Accepted: May 6, 2013

Published: June 17, 2013

**Citation**

H. Guillet de Chatellus, O. Jacquin, O. Hugon, W. Glastre, E. Lacot, and J. Marklof, "Generation of ultrahigh and tunable repetition rates in CW injection-seeded frequency-shifted feedback lasers," Opt. Express **21**, 15065-15074 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15065

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### References

- M. Stellpflug, G. Bonnet, B. W. Shore, and K. Bergmann, “Dynamics of frequency shifted feedback lasers: simulation studies,” Opt. Express11, 2060–2080 (2003). [CrossRef] [PubMed]
- F. V. Kowalski, C. Ndiaye, K. Nakamura, and H. Ito, “Noise waveforms with repetitive phase and nonrepetitive amplitude,” Opt. Lett.27, 1965–1967 (2002). [CrossRef]
- L. P. Yatsenko, B. W. Shore, and K. Bergmann, “Coherence in the output spectrum of frequency shifted feedback lasers,” Opt. Commun.282, 300–309 (2009). [CrossRef]
- H. Guillet de Chatellus and J.-P. Pique, “Statistical properties of frequency shifted feedback lasers,” Opt. Commun.283, 71–77 (2010). [CrossRef]
- F. V. Kowalski, C. Ndiaye, K. Nakamura, and H. Ito, “Noise waveforms generated by frequency shifted feedback lasers: application to multiple access communications,” Opt. Commun.231, 149–164 (2004). [CrossRef]
- H. Guillet de Chatellus and J.-P. Pique, “λ/2 fringe spacing interferometer,” Opt. Lett.34, 755–757 (2009). [CrossRef]
- K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, and H. Ito, “Optical frequency domain ranging by a frequency-shifted feedback laser,” IEEE J. Quantum Electron.36, 305–316 (2000). [CrossRef]
- V. V. Ogurtsov, L. P. Yatsenko, V. M. Khodakovskyy, B. W. Shore, G. Bonnet, and K. Bergmann, “High accuracy ranging with Yb3+-doped fiber-ring frequency-shifted feedback laser with phase-modulated seed,” Opt. Commun.266, 266–273 (2006). [CrossRef]
- H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “The hypothesis of the moving comb in frequency shifted feedback lasers,” Opt. Commun.284, 4965–4970 (2011). [CrossRef]
- H. Guillet de Chatellus, E. Lacot, O. Jacquin, W. Glastre, and O. Hugon, “Heterodyne beatings between frequency-shifted feedback lasers,” Opt. Lett.37, 791–793 (2012). [CrossRef]
- S. Balle, I. C. Littler, K. Bergmann, and F. V. Kowalski, “Frequency shifted feedback dye laser operating at a small shift frequency,” Opt. Commun.102, 166–173 (1993). [CrossRef]
- F. V. Kowalski, S. J. Shattil, and P. D. Hale, “Optical pulse generation with a frequency shifted feedback laser,” Appl. Phys. Lett.53(9), 734–736 (1988). [CrossRef]
- H. Sabert and E. Brinkmeyer, “Pulse generation in fiber lasers with frequency shifted feedback,” J. Lightwave. Technol.12, 1360–1368 (1994). [CrossRef]
- G. Bonnet, S. Balle, T. Kraft, and K. Bergmann, “Dynamics and self-modelocking of a titanium-sapphire laser with intracavity frequency shifted feedback,” Opt. Commun.123, 790–800 (1996). [CrossRef]
- J. M. Sousa and O. G. Okhotnikov, “Short pulse generation and control in Er-doped frequency-shifted-feedback fiber lasers,” Opt. Commun.183, 227–241 (2000). [CrossRef]
- M. P. Nikodem, H. Sergeant, P. Kaczmarek, and K. M. Abramski, “Actively mode-locked fiber laser using acousto-optic modulator,” Proc. SPIE7141, 71410B (2008). [CrossRef]
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