Abstract

We present a theoretical and experimental analysis of the instantaneous lineshape of Fourier domain mode-locked (FDML) lasers, yielding good agreement. The simulations are performed employing a recently introduced model for FDML operation. Linewidths around 10 GHz are found, which is significantly below the sweep filter bandwidth. The effect of detuning between the sweep filter drive frequency and cavity roundtrip time is studied revealing features that cannot be resolved in the experiment, and shifting of the instantaneous power spectrum against the sweep filter center frequency is analyzed. We show that, in contrast to most other semiconductor based lasers, the instantaneous linewidth is governed neither by external noise sources nor by amplified spontaneous emission, but it is directly determined by the complex FDML dynamics.

© 2011 OSA

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References

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  1. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express 11(22), 2953–2963 (2003).
    [CrossRef] [PubMed]
  2. 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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
    [CrossRef] [PubMed]
  3. R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13(9), 3513–3528 (2005).
    [CrossRef] [PubMed]
  4. 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]
  5. 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. Express 18(14), 14685–14704 (2010).
    [CrossRef] [PubMed]
  6. T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. 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]
  13. 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]

2011 (1)

2010 (2)

2009 (2)

2008 (1)

2006 (2)

2005 (1)

2003 (1)

2000 (1)

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 (1)

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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor-lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[CrossRef]

Biedermann, B.

Biedermann, B. R.

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]

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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

de Boer, J. F.

Eigenwillig, C. M.

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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

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 , “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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of semiconductor-lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[CrossRef]

Hsu, K.

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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Huber, R.

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[CrossRef] [PubMed]

B. R. Biedermann, W. Wieser, C. M. Eigenwillig, T. Klein, and R. Huber, “Direct measurement of the instantaneous linewidth of rapidly wavelength-swept lasers,” Opt. Lett. 35(22), 3733–3735 (2010).
[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. Express 18(14), 14685–14704 (2010).
[CrossRef] [PubMed]

C. Jirauschek, B. Biedermann, and R. Huber, “A theoretical description of Fourier domain mode locked lasers,” Opt. Express 17(26), 24013–24019 (2009).
[CrossRef]

B. R. Biedermann, W. Wieser, C. M. Eigenwillig, T. Klein, and R. Huber, “Dispersion, coherence and noise of Fourier domain mode locked lasers,” Opt. Express 17(12), 9947–9961 (2009).
[CrossRef] [PubMed]

T. Klein, W. Wieser, B. R. Biedermann, C. M. Eigenwillig, G. Palte, and R. Huber, “Raman-pumped Fourier-domain mode-locked laser: analysis of operation and application for optical coherence tomography,” Opt. Lett. 33(23), 2815–2817 (2008).
[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. Express 14(8), 3225–3237 (2006).
[CrossRef] [PubMed]

R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13(9), 3513–3528 (2005).
[CrossRef] [PubMed]

Iftimia, N.

Jirauschek, C.

Klein, T.

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 , “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]

Palte, G.

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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Schuman, J. S.

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 , “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]

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 , “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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Taira, K.

Tearney, G. J.

Wieser, W.

Wojtkowski, M.

Yun, S. H.

IEEE J. Quantum Electron. (2)

C. H. Henry, “Theory of the linewidth of semiconductor-lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[CrossRef]

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]

Opt. Express (7)

R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13(9), 3513–3528 (2005).
[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. Express 14(8), 3225–3237 (2006).
[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. Express 18(14), 14685–14704 (2010).
[CrossRef] [PubMed]

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[CrossRef] [PubMed]

C. Jirauschek, B. Biedermann, and R. Huber, “A theoretical description of Fourier domain mode locked lasers,” Opt. Express 17(26), 24013–24019 (2009).
[CrossRef]

S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express 11(22), 2953–2963 (2003).
[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. Express 17(12), 9947–9961 (2009).
[CrossRef] [PubMed]

Opt. Lett. (3)

Science (1)

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 , “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Setup of the polarization maintaining FDML laser with outcouplers numbered 1 to 3. (b) Measurement setup for the instantaneous linewidth using a pulse generator, an electro-optical modulator and an optical spectrum analyzer. (c) Sweep filter center wavelength over time. (d) Simulated output power over time.

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

Experimental (red) and simulated (blue) instantaneous power spectra after the SOA at (a) 1.3 µs and (b) 3.3 µs for no detuning.

Fig. 4
Fig. 4

Theoretical (blue) and experimental (red) power spectra at 7.3 µs for (a) no detuning, for (b) a detuning of −2 Hz and for (c) a detuning of + 2 Hz.

Fig. 5
Fig. 5

(a) Simulated instantaneous power spectrum for α = 5 (red) and α = 0 (blue), the sweep filter transmission function is drawn in black. (b) The instantaneous power spectrum for α = 5 (red) and α = 0 (blue) but without ASE.

Equations (1)

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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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