Abstract

The first theoretical model of Fourier domain mode locking operation is presented. A specially tailored dynamic equation in a moving spectral reference frame is derived, enabling efficient numerical treatment, despite the broad laser spectrum and the extremely long cavity. The excellent agreement of the presented theory with experiment over a wide range of operation parameters enables a quantitative assessment of the relevant physical effects, such as the spectral loss modulation and gain saturation dynamics, amplified spontaneous emission, linewidth enhancement, and self-phase modulation.

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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. Express 14(8), 3225–3237 (2006).
    [CrossRef] [PubMed]
  2. D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007).
    [CrossRef]
  3. R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: Unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. 31(20), 2975–2977 (2006).
    [CrossRef] [PubMed]
  4. 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. Express 15(23), 15115–15128 (2007).
    [CrossRef] [PubMed]
  5. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
    [CrossRef] [PubMed]
  6. V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
    [CrossRef] [PubMed]
  7. J. M. Schmitt, R. Huber, and J. G. Fujimoto, “Limiting ischemia by fast Fourier-domain imaging,” in Optical Coherence Tomography in Cardiovascular Research, E. Regar, P. W. Serruys, and T. G. van Leeuwen, eds. (Informa HealthCare, London, 2007), p. 257.
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).
  9. A. Bilenca, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Numerical study of wavelength-swept semiconductor ring lasers: the role of refractive-index nonlinearities in semiconductor optical amplifiers and implications for biomedical imaging applications,” Opt. Lett. 31(6), 760–762 (2006).
    [CrossRef] [PubMed]
  10. D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000).
    [CrossRef]

2008

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

2007

2006

2000

D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000).
[CrossRef]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Adler, D. C.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007).
[CrossRef]

R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: Unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. 31(20), 2975–2977 (2006).
[CrossRef] [PubMed]

An, X.

Bilenca, A.

Bouma, B. E.

Cassioli, D.

D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000).
[CrossRef]

Caswell, A. W.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, Y.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007).
[CrossRef]

Chen, Y. L.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Connolly, J.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007).
[CrossRef]

Duker, J. S.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[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. Express 15(23), 15115–15128 (2007).
[CrossRef] [PubMed]

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007).
[CrossRef]

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. Express 14(8), 3225–3237 (2006).
[CrossRef] [PubMed]

R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: Unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. 31(20), 2975–2977 (2006).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Gorczynska, I.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Herold, R. E.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Huber, R.

Kranendonk, L. A.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Mecozzi, A.

D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000).
[CrossRef]

Okura, Y.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Sanders, S. T.

Schmitt, J.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007).
[CrossRef]

Schuman, J. S.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Scotti, S.

D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000).
[CrossRef]

Srinivasan, V. J.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

Urata, Y.

Wojtkowski, M.

Yun, S. H.

IEEE J. Quantum Electron.

D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000).
[CrossRef]

Invest. Ophthalmol. Vis. Sci.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Nat. Photonics

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Other

J. M. Schmitt, R. Huber, and J. G. Fujimoto, “Limiting ischemia by fast Fourier-domain imaging,” in Optical Coherence Tomography in Cardiovascular Research, E. Regar, P. W. Serruys, and T. G. van Leeuwen, eds. (Informa HealthCare, London, 2007), p. 257.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).

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Figures (5)

Fig. 1
Fig. 1

Setup of the FDML laser.

Fig. 2
Fig. 2

(a) Experimentally measured SOA power gain (linear scale) as a function of optical frequency for various values of the incident optical power. (b) Experimentally measured overall cavity power loss (linear scale) as a function of optical frequency. The sweep filter has been tuned to maximum transmission at each measured frequency.

Fig. 3
Fig. 3

(a) Frequency offset ω 0 and corresponding center wavelength λ 0 of the sweep filter versus time. (b) Instantaneous output power versus time, as obtained from experiment (solid line) and from a simulation with ASE (dashed line) and without ASE (dotted line).

Fig. 4
Fig. 4

Simulated instantaneous output power versus time, as obtained by neglecting various effects. (a) No detuning. (b) Detuning by δ = 10   Hz .

Fig. 5
Fig. 5

Theoretical (solid curves) and experimental (crosses) instantaneous output power versus time for various degrees of detuning: (a) δ = ± 10   Hz ; (b) δ = ± 20   Hz .

Equations (4)

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z A = [ g ( z , i t ) ( 1 i α ) a ( z , i t ) i D 2 ( z ) t 2 + D 3 ( z ) t 3 + i γ ( z ) | A | 2 ] A .
u = A exp ( i t ω 0 ( t ' )   d t ' ) .
z u = exp ( i t ω 0   d t ' ) [ g ( i t ) ( 1 i α ) a ( i t ) i D 2 t 2 + D 3 t 3 ]       × [ exp ( -i t ω 0   d t ' ) u ] + [ i γ | u | 2 a s ( i t ) ] u .
z u = [ g ( ω 0 ) ( 1 i α ) a ( ω 0 ) + i ω 0 2 D 2 + i ω 0 3 D 3 -i D 2 t 2 + i γ | u | 2 a s ( i t ) ] u ,

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