Abstract

In a harmonically mode locked laser, the supermode noise peaks in the RF spectrum can be observed directly because they are separated from the driving frequency and its harmonics of the active mode locker. Using a simple theoretical model, we showed that the intensities of the supermode noise peaks will decrease if the coherence of the laser output decreases. We harmonically mode locked a Fourier domain mode locked (FDML) fiber laser to the third order. We observed that the supermode noise peak intensities decrease significantly when the detune between the sweeping frequency of the tunable filter and the cavity resonant frequency increases. It is therefore possible to use the supermode noise peaks to monitor the frequency detune of the tunable filter for auto-calibration of FDML fiber lasers.

© 2013 Optical Society of America

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References

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  1. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express14(8), 3225–3237 (2006).
    [CrossRef] [PubMed]
  2. S. W. Huang, A. D. Aguirre, R. A. Huber, D. C. Adler, and J. G. Fujimoto, “Swept source optical coherence microscopy using a Fourier domain mode-locked laser,” Opt. Express15(10), 6210–6217 (2007).
    [CrossRef] [PubMed]
  3. R. Huber, D. C. Adler, V. J. Srinivasan, and J. G. Fujimoto, “Fourier domain mode locking at 1050 nm for ultra-high-speed optical coherence tomography of the human retina at 236,000 axial scans per second,” Opt. Lett.32(14), 2049–2051 (2007).
    [CrossRef] [PubMed]
  4. L. Huo, J. Xi, K. Hsu, and X. Li, “OCT Imaging with discrete-frequency Fourier domain mode-locked laser,” in Biomedical Optics and 3-D Imaging (2010), paper BSuC6.
  5. K. Murari, J. Mavadia, J. Xi, and X. Li, “Self-starting, self-regulating Fourier domain mode locked fiber laser for OCT imaging,” Biomed. Opt. Express2(7), 2005–2011 (2011).
    [CrossRef] [PubMed]
  6. D. Chen, C. Shu, and S. He, “Multiple fiber Bragg grating interrogation based on a spectrum-limited Fourier domain mode-locking fiber laser,” Opt. Lett.33(13), 1395–1397 (2008).
    [CrossRef] [PubMed]
  7. H. D. Lee, E. J. Jung, M. Y. Jeong, and C. S. Kim, “Linearized interrogation of FDML FBG sensor system using PMF Sagnac interferometer,” Proc. SPIE7503, 750355 (2009).
    [CrossRef]
  8. B. C. Lee and M. Y. Jeon, “Remote fiber sensor based on cascaded Fourier domain mode-locked laser,” Opt. Commun.284(19), 4607–4610 (2011).
    [CrossRef]
  9. L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express15(23), 15115–15128 (2007).
    [CrossRef] [PubMed]
  10. W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Ultra-rapid dispersion measurement in optical fibers,” Opt. Express17(25), 22871–22878 (2009).
    [CrossRef] [PubMed]
  11. W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express18(14), 14685–14704 (2010).
    [CrossRef] [PubMed]
  12. B. R. Biedermann, W. Wieser, C. M. Eigenwillig, T. Klein, and R. Huber, “Dispersion, coherence and noise of Fourier domain mode locked lasers,” Opt. Express17(12), 9947–9961 (2009).
    [CrossRef] [PubMed]
  13. C. Jirauschek, B. Biedermann, and R. Huber, “A theoretical description of Fourier domain mode locked lasers,” Opt. Express17(26), 24013–24019 (2009).
    [CrossRef] [PubMed]
  14. B. Howley, Z. Shi, Y. Jiang, and R. T. Chen, “Thermally tuned optical fiber for true time delay generation,” Opt. Laser Technol.37, 29–32 (2005).
    [CrossRef]
  15. M. Becker, D. J. Kuizenga, and A. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron.8(8), 687–693 (1972).
    [CrossRef]
  16. N. Onodera, “Supermode beat suppression in harmonically mode-locked erbium-doped fibre ring lasers with composite cavity structure,” Electron. Lett.33(11), 962–963 (1997).
    [CrossRef]
  17. F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B19(11), 2609–2621 (2002).
    [CrossRef]
  18. O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
    [CrossRef]
  19. K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
    [CrossRef]
  20. S. Slepneva, B. Kelleher, B. O’Shaughnessy, S. P. Hegarty, A. G. Vladimirov, and G. Huyet, “Dynamics of Fourier domain mode-locked lasers,” Opt. Express21(16), 19240–19251 (2013).
    [CrossRef] [PubMed]

2013 (2)

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

S. Slepneva, B. Kelleher, B. O’Shaughnessy, S. P. Hegarty, A. G. Vladimirov, and G. Huyet, “Dynamics of Fourier domain mode-locked lasers,” Opt. Express21(16), 19240–19251 (2013).
[CrossRef] [PubMed]

2011 (2)

K. Murari, J. Mavadia, J. Xi, and X. Li, “Self-starting, self-regulating Fourier domain mode locked fiber laser for OCT imaging,” Biomed. Opt. Express2(7), 2005–2011 (2011).
[CrossRef] [PubMed]

B. C. Lee and M. Y. Jeon, “Remote fiber sensor based on cascaded Fourier domain mode-locked laser,” Opt. Commun.284(19), 4607–4610 (2011).
[CrossRef]

2010 (1)

2009 (4)

2008 (1)

2007 (3)

2006 (1)

2005 (1)

B. Howley, Z. Shi, Y. Jiang, and R. T. Chen, “Thermally tuned optical fiber for true time delay generation,” Opt. Laser Technol.37, 29–32 (2005).
[CrossRef]

2002 (2)

F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B19(11), 2609–2621 (2002).
[CrossRef]

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

1997 (1)

N. Onodera, “Supermode beat suppression in harmonically mode-locked erbium-doped fibre ring lasers with composite cavity structure,” Electron. Lett.33(11), 962–963 (1997).
[CrossRef]

1972 (1)

M. Becker, D. J. Kuizenga, and A. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron.8(8), 687–693 (1972).
[CrossRef]

Adler, D. C.

Aguirre, A. D.

An, X.

Becker, M.

M. Becker, D. J. Kuizenga, and A. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron.8(8), 687–693 (1972).
[CrossRef]

Biedermann, B.

Biedermann, B. R.

Blondel, M.

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

Caswell, A. W.

Chen, D.

Chen, R. T.

B. Howley, Z. Shi, Y. Jiang, and R. T. Chen, “Thermally tuned optical fiber for true time delay generation,” Opt. Laser Technol.37, 29–32 (2005).
[CrossRef]

Dai, Y.

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Deparis, O.

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

Eigenwillig, C. M.

Emplit, P.

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

Fujimoto, J. G.

Grein, M. E.

Haelterman, M.

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

Haus, H. A.

He, S.

Hegarty, S. P.

Herold, R. E.

Howley, B.

B. Howley, Z. Shi, Y. Jiang, and R. T. Chen, “Thermally tuned optical fiber for true time delay generation,” Opt. Laser Technol.37, 29–32 (2005).
[CrossRef]

Huang, S. W.

Huber, R.

W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express18(14), 14685–14704 (2010).
[CrossRef] [PubMed]

W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Ultra-rapid dispersion measurement in optical fibers,” Opt. Express17(25), 22871–22878 (2009).
[CrossRef] [PubMed]

C. Jirauschek, B. Biedermann, and R. Huber, “A theoretical description of Fourier domain mode locked lasers,” Opt. Express17(26), 24013–24019 (2009).
[CrossRef] [PubMed]

B. R. Biedermann, W. Wieser, C. M. Eigenwillig, T. Klein, and R. Huber, “Dispersion, coherence and noise of Fourier domain mode locked lasers,” Opt. Express17(12), 9947–9961 (2009).
[CrossRef] [PubMed]

L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express15(23), 15115–15128 (2007).
[CrossRef] [PubMed]

R. Huber, D. C. Adler, V. J. Srinivasan, and J. G. Fujimoto, “Fourier domain mode locking at 1050 nm for ultra-high-speed optical coherence tomography of the human retina at 236,000 axial scans per second,” Opt. Lett.32(14), 2049–2051 (2007).
[CrossRef] [PubMed]

R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express14(8), 3225–3237 (2006).
[CrossRef] [PubMed]

Huber, R. A.

Huyet, G.

Ippen, E. P.

Jeon, M. Y.

B. C. Lee and M. Y. Jeon, “Remote fiber sensor based on cascaded Fourier domain mode-locked laser,” Opt. Commun.284(19), 4607–4610 (2011).
[CrossRef]

Jeong, M. Y.

H. D. Lee, E. J. Jung, M. Y. Jeong, and C. S. Kim, “Linearized interrogation of FDML FBG sensor system using PMF Sagnac interferometer,” Proc. SPIE7503, 750355 (2009).
[CrossRef]

Ji, Y.

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Jiang, L. A.

Jiang, Y.

B. Howley, Z. Shi, Y. Jiang, and R. T. Chen, “Thermally tuned optical fiber for true time delay generation,” Opt. Laser Technol.37, 29–32 (2005).
[CrossRef]

Jirauschek, C.

Jung, E. J.

H. D. Lee, E. J. Jung, M. Y. Jeong, and C. S. Kim, “Linearized interrogation of FDML FBG sensor system using PMF Sagnac interferometer,” Proc. SPIE7503, 750355 (2009).
[CrossRef]

Kelleher, B.

Kim, C. S.

H. D. Lee, E. J. Jung, M. Y. Jeong, and C. S. Kim, “Linearized interrogation of FDML FBG sensor system using PMF Sagnac interferometer,” Proc. SPIE7503, 750355 (2009).
[CrossRef]

Klein, T.

Kranendonk, L. A.

Kuizenga, D. J.

M. Becker, D. J. Kuizenga, and A. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron.8(8), 687–693 (1972).
[CrossRef]

Lee, B. C.

B. C. Lee and M. Y. Jeon, “Remote fiber sensor based on cascaded Fourier domain mode-locked laser,” Opt. Commun.284(19), 4607–4610 (2011).
[CrossRef]

Lee, H. D.

H. D. Lee, E. J. Jung, M. Y. Jeong, and C. S. Kim, “Linearized interrogation of FDML FBG sensor system using PMF Sagnac interferometer,” Proc. SPIE7503, 750355 (2009).
[CrossRef]

Lee, H. L. T.

Li, J.

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Li, X.

Lin, J.

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Mavadia, J.

Mégret, P.

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

Murari, K.

O’Shaughnessy, B.

Okura, Y.

Onodera, N.

N. Onodera, “Supermode beat suppression in harmonically mode-locked erbium-doped fibre ring lasers with composite cavity structure,” Electron. Lett.33(11), 962–963 (1997).
[CrossRef]

Pottiez, O.

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

Ram, R. J.

Rana, F.

Roman, K.

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

Sanders, S. T.

Shi, Z.

B. Howley, Z. Shi, Y. Jiang, and R. T. Chen, “Thermally tuned optical fiber for true time delay generation,” Opt. Laser Technol.37, 29–32 (2005).
[CrossRef]

Shu, C.

Siegman, A.

M. Becker, D. J. Kuizenga, and A. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron.8(8), 687–693 (1972).
[CrossRef]

Slepneva, S.

Srinivasan, V. J.

Urata, Y.

Vladimirov, A. G.

Wang, R.

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Wieser, W.

Wojtkowski, M.

Xi, J.

Xu, K.

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Yin, F.

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Biomed. Opt. Express (1)

Electron. Lett. (1)

N. Onodera, “Supermode beat suppression in harmonically mode-locked erbium-doped fibre ring lasers with composite cavity structure,” Electron. Lett.33(11), 962–963 (1997).
[CrossRef]

IEEE J. Quantum Electron. (2)

O. Pottiez, O. Deparis, K. Roman, M. Haelterman, P. Emplit, P. Mégret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron.38(3), 252–259 (2002).
[CrossRef]

M. Becker, D. J. Kuizenga, and A. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron.8(8), 687–693 (1972).
[CrossRef]

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

Laser Phys. Lett. (1)

K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013).
[CrossRef]

Opt. Commun. (1)

B. C. Lee and M. Y. Jeon, “Remote fiber sensor based on cascaded Fourier domain mode-locked laser,” Opt. Commun.284(19), 4607–4610 (2011).
[CrossRef]

Opt. Express (8)

L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express15(23), 15115–15128 (2007).
[CrossRef] [PubMed]

W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Ultra-rapid dispersion measurement in optical fibers,” Opt. Express17(25), 22871–22878 (2009).
[CrossRef] [PubMed]

W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express18(14), 14685–14704 (2010).
[CrossRef] [PubMed]

B. R. Biedermann, W. Wieser, C. M. Eigenwillig, T. Klein, and R. Huber, “Dispersion, coherence and noise of Fourier domain mode locked lasers,” Opt. Express17(12), 9947–9961 (2009).
[CrossRef] [PubMed]

C. Jirauschek, B. Biedermann, and R. Huber, “A theoretical description of Fourier domain mode locked lasers,” Opt. Express17(26), 24013–24019 (2009).
[CrossRef] [PubMed]

R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express14(8), 3225–3237 (2006).
[CrossRef] [PubMed]

S. W. Huang, A. D. Aguirre, R. A. Huber, D. C. Adler, and J. G. Fujimoto, “Swept source optical coherence microscopy using a Fourier domain mode-locked laser,” Opt. Express15(10), 6210–6217 (2007).
[CrossRef] [PubMed]

S. Slepneva, B. Kelleher, B. O’Shaughnessy, S. P. Hegarty, A. G. Vladimirov, and G. Huyet, “Dynamics of Fourier domain mode-locked lasers,” Opt. Express21(16), 19240–19251 (2013).
[CrossRef] [PubMed]

Opt. Laser Technol. (1)

B. Howley, Z. Shi, Y. Jiang, and R. T. Chen, “Thermally tuned optical fiber for true time delay generation,” Opt. Laser Technol.37, 29–32 (2005).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

H. D. Lee, E. J. Jung, M. Y. Jeong, and C. S. Kim, “Linearized interrogation of FDML FBG sensor system using PMF Sagnac interferometer,” Proc. SPIE7503, 750355 (2009).
[CrossRef]

Other (1)

L. Huo, J. Xi, K. Hsu, and X. Li, “OCT Imaging with discrete-frequency Fourier domain mode-locked laser,” in Biomedical Optics and 3-D Imaging (2010), paper BSuC6.

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Figures (9)

Fig. 1
Fig. 1

The average RF spectra of signals defined in (1) with cavity mode phase variation Δϕ = 0 and supermode phase variation Δψ = 0, 0.05π, 0.25π, 0.5π and π. The RF spectra shown are the average of 100 random samples.

Fig. 2
Fig. 2

The average RF spectra of signals defined in (1) with supermode phase variation Δψ = 0 and cavity mode phase variation Δϕ = 0, 0.25π, 0.5π, 0.75π and π. The RF spectra shown are the average of 100 random samples.

Fig. 3
Fig. 3

The average RF spectra of signals defined in (1) with Δψ = 0, Δϕ = 0 and δψ = 0, 10−5π, 0.001π, 0.1π, and π. Each of the RF spectra shown is the average of 100 random samples.

Fig. 4
Fig. 4

Schematic of an FDML fiber laser. The cavity is comprised of a semiconductor optical amplifier (SOA), an isolator (ISO), a section of dispersion shifted fiber (DSF), a fiber Fabry-Pérot tunable filter (FFP-TF) driven by a swept driver, and a coupler to output the signal.

Fig. 5
Fig. 5

(a) Integrated spectra and (b) waveforms from the fundamentally mode locked FDML fiber laser with different detunes for Vamp = 100 mV. The sweeping frequency of the FFP-TF is 43.041 kHz and relative detunes are ± 10 Hz, and ± 20 Hz.

Fig. 6
Fig. 6

The RF spectra of the fundamentally mode locked FDML fiber laser output signals with sweeping frequency detunes of 0 (black), 10 (red), 20 (blue), 30 (magenta), and 40 Hz (green).

Fig. 7
Fig. 7

(a) The integrated spectra and (b) waveforms of the FDML fiber laser harmonically mode locked at the third order for Vamp = 500 mV. The scan frequency of the FFP-TF is 129.125 kHz and relative detunes are ± 5Hz, and ± 15 Hz.

Fig. 8
Fig. 8

The RF spectra of the FDML fiber laser with sweeping frequency at 129.125 kHz and relative detunes of ± 5Hz and ± 15 Hz.

Fig. 9
Fig. 9

The peak intensities of the RF spectra at the third harmonic frequency (solid squares) and the cavity resonant frequency (open circles) versus frequency detune.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

E(t)= k=1 N A k e i ψ k ( m=0 M1 B Nm+k e i ϕ Nm+k e i2π f Nm+k t ) ,
ψ k j = ψ k j1 +rand[1,1]Δ ψ k , ψ k 0 =rand[1,1]π,
ϕ Nm+k j = ϕ Nm+k 0 + rand[1,1]Δ ϕ Nm+k ,
ψ k 0 = ψ ¯ k 0 + rand [ 1 , 1 ] δ ψ k
V(t) = V amp ×sin(2π f drive t)+ V bias ,
f cav = c n× l cav ,

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