Abstract

Understanding the dynamics of Fourier domain mode-locked (FDML) lasers is crucial for determining physical coherence limits, and for finding new superior methods for experimental realization. In addition, the rich interplay of linear and nonlinear effects in a laser ring system is of great theoretical interest. Here we investigate the dynamics of a highly dispersion-compensated setup, where over a bandwidth of more than 100 nm, a highly coherent output with nearly shot-noise-limited intensity fluctuations was experimentally demonstrated. This output is called the sweet-spot. We show by numerical simulation that a finite amount of residual dispersion in the fiber delay cavity of FDML lasers can be compensated by the group delay dispersion in the swept bandpass filter, such that the intensity trace exhibits no dips or high-frequency distortions, which are the main source of noise in the laser. In the same way, a small detuning from the ideal sweep filter frequency can be tolerated. Furthermore, we find that the filter’s group delay dispersion improves the coherence properties of the laser, and acts as a self-stabilizing element in the cavity. Our theoretical model is validated against experimental data, showing that all relevant physical effects for the sweet-spot operating regime are included.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

N. Lippok, M. Siddiqui, B. J. Vakoc, and B. E. Bouma, “Extended coherence length and depth ranging using a Fourier-domain mode-locked frequency comb and circular interferometric ranging,” Phys. Rev. Appl. 11(1), 014018 (2019).
[Crossref]

S. Slepneva, B. O’Shaughnessy, A. G. Vladimirov, S. Rica, E. A. Viktorov, and G. Huyet, “Convective Nozaki-Bekki holes in a long cavity OCT laser,” Opt. Express 27(11), 16395–16404 (2019).
[Crossref]

2018 (1)

2017 (4)

2015 (2)

C. Jirauschek and R. Huber, “Wavelength shifting of intra-cavity photons: Adiabatic wavelength tuning in rapidly wavelength-swept lasers,” Biomed. Opt. Express 6(7), 2448–2465 (2015).
[Crossref]

S. Karpf, M. Eibl, W. Wieser, T. Klein, and R. Huber, “A time-encoded technique for fibre-based hyperspectral broadband stimulated Raman microscopy,” Nat. Commun. 6(1), 6784 (2015).
[Crossref]

2014 (2)

L. Reznicek, T. Klein, W. Wieser, M. Kernt, A. Wolf, C. Haritoglou, A. Kampik, R. Huber, and A. S. Neubauer, “Megahertz ultra-wide-field swept-source retina optical coherence tomography compared to current existing imaging devices,” Graefe’s Arch. Clin. Exp. Ophthalmol. 252(6), 1009–1016 (2014).
[Crossref]

M. Bonesi, M. Minneman, J. Ensher, B. Zabihian, H. Sattmann, P. Boschert, E. Hoover, R. Leitgeb, M. Crawford, and W. Drexler, “Akinetic all-semiconductor programmable swept-source at 1550 nm and 1310 nm with centimeters coherence length,” Opt. Express 22(3), 2632–2655 (2014).
[Crossref]

2013 (3)

2012 (2)

2011 (5)

S. Todor, B. Biedermann, W. Wieser, R. Huber, and C. Jirauschek, “Instantaneous lineshape analysis of Fourier domain mode-locked lasers,” Opt. Express 19(9), 8802–8807 (2011).
[Crossref]

X. Huang, Z. Zhang, C. Qin, Y. Yu, and X. Zhang, “Optimized quantum–well semiconductor optical amplifier for RZ-DPSK signal regeneration,” IEEE J. Quantum Electron. 47(6), 819–826 (2011).
[Crossref]

S. L. Girard, M. Piché, H. Chen, G. W. Schinn, W.-Y. Oh, and B. E. Bouma, “SOA fiber ring lasers: Single-versus multiple-mode oscillation,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1513–1520 (2011).
[Crossref]

D. C. Adler, W. Wieser, F. Trepanier, J. M. Schmitt, and R. A. Huber, “Extended coherence length Fourier domain mode locked lasers at 1310 nm,” Opt. Express 19(21), 20930–20939 (2011).
[Crossref]

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 (2)

B. C. Lee, E.-J. Jung, C.-S. Kim, and M. Y. Jeon, “Dynamic and static strain fiber Bragg grating sensor interrogation with a 1.3 µm Fourier domain mode-locked wavelength-swept laser,” Meas. Sci. Technol. 21(9), 094008 (2010).
[Crossref]

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]

2009 (4)

B. R. Biedermann, W. Wieser, C. M. Eigenwillig, and R. Huber, “Recent developments in Fourier Domain Mode Locked lasers for optical coherence tomography: Imaging at 1310 nm vs. 1550 nm wavelength,” J. Biophotonics 2(6-7), 357–363 (2009).
[Crossref]

Y. Mao, C. Flueraru, S. Sherif, and S. Chang, “High performance wavelength-swept laser with mode-locking technique for optical coherence tomography,” Opt. Commun. 282(1), 88–92 (2009).
[Crossref]

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

T.-H. Tsai, C. Zhou, D. C. Adler, and J. G. Fujimoto, “Frequency comb swept lasers,” Opt. Express 17(23), 21257–21270 (2009).
[Crossref]

2008 (3)

2007 (3)

2006 (3)

2005 (2)

R. Clavero, F. Ramos, J. M. Martinez, and J. Marti, “All-optical flip-flop based on a single SOA-MZI,” IEEE Photonics Technol. Lett. 17(4), 843–845 (2005).
[Crossref]

L. A. Kranendonk, R. J. Bartula, and S. T. Sanders, “Modeless operation of a wavelength-agile laser by high-speed cavity length changes,” Opt. Express 13(5), 1498–1507 (2005).
[Crossref]

2004 (2)

N. Nishizawa, Y. Chen, P. Hsiung, E. P. Ippen, and J. G. Fujimoto, “Real-time, ultrahigh-resolution, optical coherence tomography with an all-fiber, femtosecond fiber laser continuum at 1.5 µm,” Opt. Lett. 29(24), 2846–2848 (2004).
[Crossref]

H. J. S. Dorren, X. Yang, A. K. Mishra, Z. Li, H. Ju, H. de Waardt, G.-D. Khoe, T. Simoyama, H. Ishikawa, H. Kawashima, and T. Hasama, “All-optical logic based on ultrafast gain and index dynamics in a semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1079–1092 (2004).
[Crossref]

2001 (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]

1997 (3)

J. Mørk and A. Mecozzi, “Theory of nondegenerate four-wave mixing between pulses in a semiconductor waveguide,” IEEE J. Quantum Electron. 33(4), 545–555 (1997).
[Crossref]

A. Mecozzi and J. Mørk, “Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3(5), 1190–1207 (1997).
[Crossref]

A. Mecozzi and J. Mørk, “Saturation induced by picosecond pulses in semiconductor optical amplifiers,” J. Opt. Soc. Am. B 14(4), 761–770 (1997).
[Crossref]

1996 (1)

L. F. Tiemeijer, P. J. A. Thijs, T. van Dongen, J. J. M. Binsma, and E. J. Jansen, “Self-phase modulation coefficient of multiple-quantum-well optical amplifiers,” IEEE Photonics Technol. Lett. 8(7), 876–878 (1996).
[Crossref]

1994 (3)

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
[Crossref]

P. J. A. Thiis, L. F. Tiemeijer, J. J. M. Binsma, and T. van Dongen, “Progress in long-wavelength strained-layer InGaAs(P) quantum-well semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 30(2), 477–499 (1994).
[Crossref]

H. Chaté, “Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation,” Nonlinearity 7(1), 185–204 (1994).
[Crossref]

1993 (1)

F. Kano, T. Yamanaka, N. Yamamoto, Y. Yoshikuni, H. Mawatari, Y. Tohmori, M. Yamamoto, and K. Yokoyama, “Reduction of linewidth enhancement factor in InGaAsP-InP modulation-doped strained multiple-quantum-well lasers,” IEEE J. Quantum Electron. 29(6), 1553–1559 (1993).
[Crossref]

1992 (1)

H. Chaté and P. Manneville, “Stability of the Bekki-Nozaki hole solutions to the one-dimensional complex Ginzburg-Landau equation,” Phys. Lett. A 171(3-4), 183–188 (1992).
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1991 (3)

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1989 (1)

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1985 (1)

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Agrawal, G. P.

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Biedermann, B. R.

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Cao, Y.

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Chang, S.

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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).
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Chen, H.

S. L. Girard, M. Piché, H. Chen, G. W. Schinn, W.-Y. Oh, and B. E. Bouma, “SOA fiber ring lasers: Single-versus multiple-mode oscillation,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1513–1520 (2011).
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Chen, Z.

Chudoba, C.

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L. F. Tiemeijer, P. J. A. Thijs, P. J. de Waard, J. J. M. Binsma, and T. v. Dongen, “Dependence of polarization, gain, linewidth enhancement factor, and K factor on the sign of the strain of InGaAs/InP strained-layer multiquantum well lasers,” Appl. Phys. Lett. 58(24), 2738–2740 (1991).
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de Waardt, H.

H. J. S. Dorren, X. Yang, A. K. Mishra, Z. Li, H. Ju, H. de Waardt, G.-D. Khoe, T. Simoyama, H. Ishikawa, H. Kawashima, and T. Hasama, “All-optical logic based on ultrafast gain and index dynamics in a semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1079–1092 (2004).
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Devgan, P.

Dorren, H. J. S.

H. J. S. Dorren, X. Yang, A. K. Mishra, Z. Li, H. Ju, H. de Waardt, G.-D. Khoe, T. Simoyama, H. Ishikawa, H. Kawashima, and T. Hasama, “All-optical logic based on ultrafast gain and index dynamics in a semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1079–1092 (2004).
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Draxinger, W.

T. Pfeiffer, M. Petermann, W. Draxinger, C. Jirauschek, and R. Huber, “Ultra low noise Fourier domain mode locked laser for high quality megahertz optical coherence tomography,” Biomed. Opt. Express 9(9), 4130–4148 (2018).
[Crossref]

T. Pfeiffer, W. Draxinger, W. Wieser, T. Klein, M. Petermann, and R. Huber, “Analysis of FDML lasers with meter range coherence,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XXI, vol. 10053 (International Society for Optics and Photonics, 2017), p. 100531T.

Drexler, W.

Eibl, M.

S. Karpf, M. Eibl, W. Wieser, T. Klein, and R. Huber, “A time-encoded technique for fibre-based hyperspectral broadband stimulated Raman microscopy,” Nat. Commun. 6(1), 6784 (2015).
[Crossref]

T. Pfeiffer, W. Wieser, T. Klein, M. Petermann, J.-P. Kolb, M. Eibl, and R. Huber, “Flexible A-scan rate MHz OCT: Computational downscaling by coherent averaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 96970S.

J. P. Kolb, T. Klein, M. Eibl, T. Pfeiffer, W. Wieser, and R. Huber, “Megahertz FDML laser with up to 143nm sweep range for ultrahigh resolution OCT at 1050nm,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 969703.

Eigenwillig, C. M.

Ensher, J.

Favire, F.

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
[Crossref]

Feng, X.

Flanders, D.

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
[Crossref]

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]

Flueraru, C.

Y. Mao, C. Flueraru, S. Sherif, and S. Chang, “High performance wavelength-swept laser with mode-locking technique for optical coherence tomography,” Opt. Commun. 282(1), 88–92 (2009).
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Freude, W.

Fujimoto, J. G.

T.-H. Tsai, C. Zhou, D. C. Adler, and J. G. Fujimoto, “Frequency comb swept lasers,” Opt. Express 17(23), 21257–21270 (2009).
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B. R. Biedermann, W. Wieser, C. M. Eigenwillig, G. Palte, D. C. Adler, V. J. Srinivasan, J. G. Fujimoto, and R. Huber, “Real time en face Fourier-domain optical coherence tomography with direct hardware frequency demodulation,” Opt. Lett. 33(21), 2556–2558 (2008).
[Crossref]

L. A. Kranendonk, R. Huber, J. G. Fujimoto, and S. T. Sanders, “Wavelength-agile H2O absorption spectrometer for thermometry of general combustion gases,” Proc. Combust. Inst. 31(1), 783–790 (2007).
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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]

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).
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N. Nishizawa, Y. Chen, P. Hsiung, E. P. Ippen, and J. G. Fujimoto, “Real-time, ultrahigh-resolution, optical coherence tomography with an all-fiber, femtosecond fiber laser continuum at 1.5 µm,” Opt. Lett. 29(24), 2846–2848 (2004).
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I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air–silica microstructure optical fiber,” Opt. Lett. 26(9), 608–610 (2001).
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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]

B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XVI, vol. 8213 (International Society for Optics and Photonics, 2012), p. 82130M.

Ghanta, R. K.

Girard, S. L.

S. L. Girard, M. Piché, H. Chen, G. W. Schinn, W.-Y. Oh, and B. E. Bouma, “SOA fiber ring lasers: Single-versus multiple-mode oscillation,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1513–1520 (2011).
[Crossref]

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]

Grigoryan, V. S.

Guan, B.-O.

Haritoglou, C.

L. Reznicek, T. Klein, W. Wieser, M. Kernt, A. Wolf, C. Haritoglou, A. Kampik, R. Huber, and A. S. Neubauer, “Megahertz ultra-wide-field swept-source retina optical coherence tomography compared to current existing imaging devices,” Graefe’s Arch. Clin. Exp. Ophthalmol. 252(6), 1009–1016 (2014).
[Crossref]

Hartl, I.

Hasama, T.

H. J. S. Dorren, X. Yang, A. K. Mishra, Z. Li, H. Ju, H. de Waardt, G.-D. Khoe, T. Simoyama, H. Ishikawa, H. Kawashima, and T. Hasama, “All-optical logic based on ultrafast gain and index dynamics in a semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1079–1092 (2004).
[Crossref]

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]

Hegarty, S. P.

Heim, P. J.

B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XVI, vol. 8213 (International Society for Optics and Photonics, 2012), p. 82130M.

Helmy, A. S.

Herold, R. E.

Hoover, E.

Hsieh, J. J.

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
[Crossref]

Hsiung, P.

Huang, D.

M. Wan, F. Li, X. Feng, X. Wang, Y. Cao, B.-O. Guan, D. Huang, J. Yuan, and P. K. A. Wai, “Time and Fourier domain jointly mode locked frequency comb swept fiber laser,” Opt. Express 25(26), 32705–32712 (2017).
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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).
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Huang, X.

X. Huang, Z. Zhang, C. Qin, Y. Yu, and X. Zhang, “Optimized quantum–well semiconductor optical amplifier for RZ-DPSK signal regeneration,” IEEE J. Quantum Electron. 47(6), 819–826 (2011).
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Huber, R.

T. Pfeiffer, M. Petermann, W. Draxinger, C. Jirauschek, and R. Huber, “Ultra low noise Fourier domain mode locked laser for high quality megahertz optical coherence tomography,” Biomed. Opt. Express 9(9), 4130–4148 (2018).
[Crossref]

C. Jirauschek and R. Huber, “Efficient simulation of the swept-waveform polarization dynamics in fiber spools and Fourier domain mode-locked (FDML) lasers,” J. Opt. Soc. Am. B 34(6), 1135–1146 (2017).
[Crossref]

S. Karpf, M. Eibl, W. Wieser, T. Klein, and R. Huber, “A time-encoded technique for fibre-based hyperspectral broadband stimulated Raman microscopy,” Nat. Commun. 6(1), 6784 (2015).
[Crossref]

C. Jirauschek and R. Huber, “Wavelength shifting of intra-cavity photons: Adiabatic wavelength tuning in rapidly wavelength-swept lasers,” Biomed. Opt. Express 6(7), 2448–2465 (2015).
[Crossref]

L. Reznicek, T. Klein, W. Wieser, M. Kernt, A. Wolf, C. Haritoglou, A. Kampik, R. Huber, and A. S. Neubauer, “Megahertz ultra-wide-field swept-source retina optical coherence tomography compared to current existing imaging devices,” Graefe’s Arch. Clin. Exp. Ophthalmol. 252(6), 1009–1016 (2014).
[Crossref]

T. Klein, R. André, W. Wieser, T. Pfeiffer, and R. Huber, “Joint aperture detection for speckle reduction and increased collection efficiency in ophthalmic MHz OCT,” Biomed. Opt. Express 4(4), 619–634 (2013).
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C. M. Eigenwillig, W. Wieser, S. Todor, B. R. Biedermann, T. Klein, C. Jirauschek, and R. Huber, “Picosecond pulses from wavelength-swept continuous-wave Fourier domain mode-locked lasers,” Nat. Commun. 4(1), 1848 (2013).
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W. Wieser, G. Palte, C. M. Eigenwillig, B. R. Biedermann, T. Pfeiffer, and R. Huber, “Chromatic polarization effects of swept waveforms in FDML lasers and fiber spools,” Opt. Express 20(9), 9819–9832 (2012).
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S. Todor, B. Biedermann, R. Huber, and C. Jirauschek, “Balance of physical effects causing stationary operation of Fourier domain mode-locked lasers,” J. Opt. Soc. Am. B 29(4), 656–664 (2012).
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S. Todor, B. Biedermann, W. Wieser, R. Huber, and C. Jirauschek, “Instantaneous lineshape analysis of Fourier domain mode-locked lasers,” Opt. Express 19(9), 8802–8807 (2011).
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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).
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B. R. Biedermann, W. Wieser, C. M. Eigenwillig, and R. Huber, “Recent developments in Fourier Domain Mode Locked lasers for optical coherence tomography: Imaging at 1310 nm vs. 1550 nm wavelength,” J. Biophotonics 2(6-7), 357–363 (2009).
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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, G. Palte, D. C. Adler, V. J. Srinivasan, J. G. Fujimoto, and R. Huber, “Real time en face Fourier-domain optical coherence tomography with direct hardware frequency demodulation,” Opt. Lett. 33(21), 2556–2558 (2008).
[Crossref]

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]

L. A. Kranendonk, R. Huber, J. G. Fujimoto, and S. T. Sanders, “Wavelength-agile H2O absorption spectrometer for thermometry of general combustion gases,” Proc. Combust. Inst. 31(1), 783–790 (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]

T. Pfeiffer, W. Wieser, T. Klein, M. Petermann, J.-P. Kolb, M. Eibl, and R. Huber, “Flexible A-scan rate MHz OCT: Computational downscaling by coherent averaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 96970S.

J. P. Kolb, T. Klein, M. Eibl, T. Pfeiffer, W. Wieser, and R. Huber, “Megahertz FDML laser with up to 143nm sweep range for ultrahigh resolution OCT at 1050nm,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 969703.

T. Pfeiffer, W. Draxinger, W. Wieser, T. Klein, M. Petermann, and R. Huber, “Analysis of FDML lasers with meter range coherence,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XXI, vol. 10053 (International Society for Optics and Photonics, 2017), p. 100531T.

Huber, R. A.

Huyet, G.

Hwang, D. M.

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
[Crossref]

Ippen, E. P.

Ishikawa, H.

H. J. S. Dorren, X. Yang, A. K. Mishra, Z. Li, H. Ju, H. de Waardt, G.-D. Khoe, T. Simoyama, H. Ishikawa, H. Kawashima, and T. Hasama, “All-optical logic based on ultrafast gain and index dynamics in a semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1079–1092 (2004).
[Crossref]

Jansen, E. J.

L. F. Tiemeijer, P. J. A. Thijs, T. van Dongen, J. J. M. Binsma, and E. J. Jansen, “Self-phase modulation coefficient of multiple-quantum-well optical amplifiers,” IEEE Photonics Technol. Lett. 8(7), 876–878 (1996).
[Crossref]

Jayaraman, V.

B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XVI, vol. 8213 (International Society for Optics and Photonics, 2012), p. 82130M.

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).
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B. C. Lee, E.-J. Jung, C.-S. Kim, and M. Y. Jeon, “Dynamic and static strain fiber Bragg grating sensor interrogation with a 1.3 µm Fourier domain mode-locked wavelength-swept laser,” Meas. Sci. Technol. 21(9), 094008 (2010).
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N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi, and K. E. Stubkjaer, “Measurement of carrier lifetime and linewidth enhancement factor for 1.5-µm ridge-waveguide laser amplifier,” IEEE Photonics Technol. Lett. 3(7), 632–634 (1991).
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Stubkjaer, K. E.

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi, and K. E. Stubkjaer, “Measurement of carrier lifetime and linewidth enhancement factor for 1.5-µm ridge-waveguide laser amplifier,” IEEE Photonics Technol. Lett. 3(7), 632–634 (1991).
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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).
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[Crossref]

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L. F. Tiemeijer, P. J. A. Thijs, T. van Dongen, J. J. M. Binsma, and E. J. Jansen, “Self-phase modulation coefficient of multiple-quantum-well optical amplifiers,” IEEE Photonics Technol. Lett. 8(7), 876–878 (1996).
[Crossref]

L. F. Tiemeijer, P. J. A. Thijs, P. J. de Waard, J. J. M. Binsma, and T. v. Dongen, “Dependence of polarization, gain, linewidth enhancement factor, and K factor on the sign of the strain of InGaAs/InP strained-layer multiquantum well lasers,” Appl. Phys. Lett. 58(24), 2738–2740 (1991).
[Crossref]

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L. F. Tiemeijer, P. J. A. Thijs, T. van Dongen, J. J. M. Binsma, and E. J. Jansen, “Self-phase modulation coefficient of multiple-quantum-well optical amplifiers,” IEEE Photonics Technol. Lett. 8(7), 876–878 (1996).
[Crossref]

P. J. A. Thiis, L. F. Tiemeijer, J. J. M. Binsma, and T. van Dongen, “Progress in long-wavelength strained-layer InGaAs(P) quantum-well semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 30(2), 477–499 (1994).
[Crossref]

L. F. Tiemeijer, P. J. A. Thijs, P. J. de Waard, J. J. M. Binsma, and T. v. Dongen, “Dependence of polarization, gain, linewidth enhancement factor, and K factor on the sign of the strain of InGaAs/InP strained-layer multiquantum well lasers,” Appl. Phys. Lett. 58(24), 2738–2740 (1991).
[Crossref]

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Tohmori, Y.

F. Kano, T. Yamanaka, N. Yamamoto, Y. Yoshikuni, H. Mawatari, Y. Tohmori, M. Yamamoto, and K. Yokoyama, “Reduction of linewidth enhancement factor in InGaAsP-InP modulation-doped strained multiple-quantum-well lasers,” IEEE J. Quantum Electron. 29(6), 1553–1559 (1993).
[Crossref]

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Tsai, T.-H.

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L. F. Tiemeijer, P. J. A. Thijs, P. J. de Waard, J. J. M. Binsma, and T. v. Dongen, “Dependence of polarization, gain, linewidth enhancement factor, and K factor on the sign of the strain of InGaAs/InP strained-layer multiquantum well lasers,” Appl. Phys. Lett. 58(24), 2738–2740 (1991).
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N. Lippok, M. Siddiqui, B. J. Vakoc, and B. E. Bouma, “Extended coherence length and depth ranging using a Fourier-domain mode-locked frequency comb and circular interferometric ranging,” Phys. Rev. Appl. 11(1), 014018 (2019).
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L. F. Tiemeijer, P. J. A. Thijs, T. van Dongen, J. J. M. Binsma, and E. J. Jansen, “Self-phase modulation coefficient of multiple-quantum-well optical amplifiers,” IEEE Photonics Technol. Lett. 8(7), 876–878 (1996).
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P. J. A. Thiis, L. F. Tiemeijer, J. J. M. Binsma, and T. van Dongen, “Progress in long-wavelength strained-layer InGaAs(P) quantum-well semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 30(2), 477–499 (1994).
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Wan, M.

Wang, J.

Wang, M. C.

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
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S. Karpf, M. Eibl, W. Wieser, T. Klein, and R. Huber, “A time-encoded technique for fibre-based hyperspectral broadband stimulated Raman microscopy,” Nat. Commun. 6(1), 6784 (2015).
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L. Reznicek, T. Klein, W. Wieser, M. Kernt, A. Wolf, C. Haritoglou, A. Kampik, R. Huber, and A. S. Neubauer, “Megahertz ultra-wide-field swept-source retina optical coherence tomography compared to current existing imaging devices,” Graefe’s Arch. Clin. Exp. Ophthalmol. 252(6), 1009–1016 (2014).
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T. Klein, R. André, W. Wieser, T. Pfeiffer, and R. Huber, “Joint aperture detection for speckle reduction and increased collection efficiency in ophthalmic MHz OCT,” Biomed. Opt. Express 4(4), 619–634 (2013).
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C. M. Eigenwillig, W. Wieser, S. Todor, B. R. Biedermann, T. Klein, C. Jirauschek, and R. Huber, “Picosecond pulses from wavelength-swept continuous-wave Fourier domain mode-locked lasers,” Nat. Commun. 4(1), 1848 (2013).
[Crossref]

W. Wieser, G. Palte, C. M. Eigenwillig, B. R. Biedermann, T. Pfeiffer, and R. Huber, “Chromatic polarization effects of swept waveforms in FDML lasers and fiber spools,” Opt. Express 20(9), 9819–9832 (2012).
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S. Todor, B. Biedermann, W. Wieser, R. Huber, and C. Jirauschek, “Instantaneous lineshape analysis of Fourier domain mode-locked lasers,” Opt. Express 19(9), 8802–8807 (2011).
[Crossref]

D. C. Adler, W. Wieser, F. Trepanier, J. M. Schmitt, and R. A. Huber, “Extended coherence length Fourier domain mode locked lasers at 1310 nm,” Opt. Express 19(21), 20930–20939 (2011).
[Crossref]

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]

B. R. Biedermann, W. Wieser, C. M. Eigenwillig, and R. Huber, “Recent developments in Fourier Domain Mode Locked lasers for optical coherence tomography: Imaging at 1310 nm vs. 1550 nm wavelength,” J. Biophotonics 2(6-7), 357–363 (2009).
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B. R. Biedermann, W. Wieser, C. M. Eigenwillig, G. Palte, D. C. Adler, V. J. Srinivasan, J. G. Fujimoto, and R. Huber, “Real time en face Fourier-domain optical coherence tomography with direct hardware frequency demodulation,” Opt. Lett. 33(21), 2556–2558 (2008).
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T. Pfeiffer, W. Draxinger, W. Wieser, T. Klein, M. Petermann, and R. Huber, “Analysis of FDML lasers with meter range coherence,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XXI, vol. 10053 (International Society for Optics and Photonics, 2017), p. 100531T.

J. P. Kolb, T. Klein, M. Eibl, T. Pfeiffer, W. Wieser, and R. Huber, “Megahertz FDML laser with up to 143nm sweep range for ultrahigh resolution OCT at 1050nm,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 969703.

T. Pfeiffer, W. Wieser, T. Klein, M. Petermann, J.-P. Kolb, M. Eibl, and R. Huber, “Flexible A-scan rate MHz OCT: Computational downscaling by coherent averaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 96970S.

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Wolf, A.

L. Reznicek, T. Klein, W. Wieser, M. Kernt, A. Wolf, C. Haritoglou, A. Kampik, R. Huber, and A. S. Neubauer, “Megahertz ultra-wide-field swept-source retina optical coherence tomography compared to current existing imaging devices,” Graefe’s Arch. Clin. Exp. Ophthalmol. 252(6), 1009–1016 (2014).
[Crossref]

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N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi, and K. E. Stubkjaer, “Measurement of carrier lifetime and linewidth enhancement factor for 1.5-µm ridge-waveguide laser amplifier,” IEEE Photonics Technol. Lett. 3(7), 632–634 (1991).
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F. Kano, T. Yamanaka, N. Yamamoto, Y. Yoshikuni, H. Mawatari, Y. Tohmori, M. Yamamoto, and K. Yokoyama, “Reduction of linewidth enhancement factor in InGaAsP-InP modulation-doped strained multiple-quantum-well lasers,” IEEE J. Quantum Electron. 29(6), 1553–1559 (1993).
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F. Kano, T. Yamanaka, N. Yamamoto, Y. Yoshikuni, H. Mawatari, Y. Tohmori, M. Yamamoto, and K. Yokoyama, “Reduction of linewidth enhancement factor in InGaAsP-InP modulation-doped strained multiple-quantum-well lasers,” IEEE J. Quantum Electron. 29(6), 1553–1559 (1993).
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Yang, X.

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F. Kano, T. Yamanaka, N. Yamamoto, Y. Yoshikuni, H. Mawatari, Y. Tohmori, M. Yamamoto, and K. Yokoyama, “Reduction of linewidth enhancement factor in InGaAsP-InP modulation-doped strained multiple-quantum-well lasers,” IEEE J. Quantum Electron. 29(6), 1553–1559 (1993).
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Yoshikuni, Y.

F. Kano, T. Yamanaka, N. Yamamoto, Y. Yoshikuni, H. Mawatari, Y. Tohmori, M. Yamamoto, and K. Yokoyama, “Reduction of linewidth enhancement factor in InGaAsP-InP modulation-doped strained multiple-quantum-well lasers,” IEEE J. Quantum Electron. 29(6), 1553–1559 (1993).
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Yu, Y.

X. Huang, Z. Zhang, C. Qin, Y. Yu, and X. Zhang, “Optimized quantum–well semiconductor optical amplifier for RZ-DPSK signal regeneration,” IEEE J. Quantum Electron. 47(6), 819–826 (2011).
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Yuan, J.

M. Wan, F. Li, X. Feng, X. Wang, Y. Cao, B.-O. Guan, D. Huang, J. Yuan, and P. K. A. Wai, “Time and Fourier domain jointly mode locked frequency comb swept fiber laser,” Opt. Express 25(26), 32705–32712 (2017).
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F. Li, K. Nakkeeran, J. N. Kutz, J. Yuan, Z. Kang, X. Zhang, and P. K. A. Wai, “Eckhaus instability in the Fourier-domain mode locked fiber laser cavity,” arXiv preprint arXiv:1707.08304 (2017).

Yun, S. H.

Zabihian, B.

Zah, C.-E.

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
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F. Li, K. Nakkeeran, J. N. Kutz, J. Yuan, Z. Kang, X. Zhang, and P. K. A. Wai, “Eckhaus instability in the Fourier-domain mode locked fiber laser cavity,” arXiv preprint arXiv:1707.08304 (2017).

Zhang, Z.

X. Huang, Z. Zhang, C. Qin, Y. Yu, and X. Zhang, “Optimized quantum–well semiconductor optical amplifier for RZ-DPSK signal regeneration,” IEEE J. Quantum Electron. 47(6), 819–826 (2011).
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Biomed. Opt. Express (3)

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[Crossref]

X. Huang, Z. Zhang, C. Qin, Y. Yu, and X. Zhang, “Optimized quantum–well semiconductor optical amplifier for RZ-DPSK signal regeneration,” IEEE J. Quantum Electron. 47(6), 819–826 (2011).
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[Crossref]

C.-E. Zah, R. Bhat, B. N. Pathak, F. Favire, W. Lin, M. C. Wang, N. C. Andreadakis, D. M. Hwang, M. A. Koza, T.-P. Lee, Z. Wang, D. Darby, D. Flanders, and J. J. Hsieh, “High-performance uncooled 1.3-µm AlxGayIn1−x−yAs/InP strained-layer quantum-well lasers for subscriber loop applications,” IEEE J. Quantum Electron. 30(2), 511–523 (1994).
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H. J. S. Dorren, X. Yang, A. K. Mishra, Z. Li, H. Ju, H. de Waardt, G.-D. Khoe, T. Simoyama, H. Ishikawa, H. Kawashima, and T. Hasama, “All-optical logic based on ultrafast gain and index dynamics in a semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1079–1092 (2004).
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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).
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C. Jirauschek, B. Biedermann, and R. Huber, “A theoretical description of Fourier domain mode locked lasers,” Opt. Express 17(26), 24013–24019 (2009).
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[Crossref]

W. Wieser, G. Palte, C. M. Eigenwillig, B. R. Biedermann, T. Pfeiffer, and R. Huber, “Chromatic polarization effects of swept waveforms in FDML lasers and fiber spools,” Opt. Express 20(9), 9819–9832 (2012).
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F. Li, K. Nakkeeran, J. N. Kutz, J. Yuan, Z. Kang, X. Zhang, and P. K. A. Wai, “Eckhaus instability in the Fourier-domain mode locked fiber laser cavity,” arXiv preprint arXiv:1707.08304 (2017).

T. Pfeiffer, W. Draxinger, W. Wieser, T. Klein, M. Petermann, and R. Huber, “Analysis of FDML lasers with meter range coherence,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XXI, vol. 10053 (International Society for Optics and Photonics, 2017), p. 100531T.

T. Kraetschmer and S. T. Sanders, “Ultrastable Fourier domain mode locking observed in a laser sweeping 1363.8 – 1367.3 nm,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2009), p. CFB4.

B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XVI, vol. 8213 (International Society for Optics and Photonics, 2012), p. 82130M.

J. P. Kolb, T. Klein, M. Eibl, T. Pfeiffer, W. Wieser, and R. Huber, “Megahertz FDML laser with up to 143nm sweep range for ultrahigh resolution OCT at 1050nm,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 969703.

T. Pfeiffer, W. Wieser, T. Klein, M. Petermann, J.-P. Kolb, M. Eibl, and R. Huber, “Flexible A-scan rate MHz OCT: Computational downscaling by coherent averaging,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XX, vol. 9697 (International Society for Optics and Photonics, 2016), p. 96970S.

Corning, “Corning HI 1060 & RC HI 1060 specialty optical fibers,” https://www.corning.com/media/worldwide/csm/documents/HI%201060%20Specialty%20Fiber%20PDF.pdf .

Corning, “Corning SMF-28 optical fiber product information,” http://www.princetel.com/datasheets/smf28e.pdf .

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Figures (9)

Fig. 1.
Fig. 1. Schematic illustration of the FDML laser setup for ultra-stable operation.
Fig. 2.
Fig. 2. (a) Simulated intensity trace of a forward and backward sweep in the sweet-spot operation mode with no hole formation, although dispersion is present in the fiber cavity, which is measured as the maximum GD difference due to $\tau _{\mathrm {g}}\left (\omega \right )$ . Here $\lambda _s$ is the relative center frequency of the swept FP filter $\omega _s$ in respect to wavelength. Note that $\omega _s = 0$ refers to the center frequency $\omega _c$ of the sweep. (b) Hole formation beyond a threshold of a finite amount of residual dispersion.
Fig. 3.
Fig. 3. (a) Number of holes in the intensity trace and (b) the averaged instantaneous linewidth within a roundtrip dependent on the residual dispersion in the fiber delay cavity, compared for the case with and without a GD in the FP bandpass filter.
Fig. 4.
Fig. 4. (a) Evolution of the IF within a single roundtrip for different roundtrip numbers in the sweet-spot regime with a residual dispersion of 56 fs. (b) Instantaneous lineshapes at particular positions in the sweep of roundtrip (RT) 150 000.
Fig. 5.
Fig. 5. (a) Long-term evolution of the averaged linewidth within one roundtrip for different amounts of residual dispersion. (b) Short-term evolution of the linewidth showing stationary operation, starting at roundtrip 40000 sampled at every 10th roundtrip.
Fig. 6.
Fig. 6. (a) IF evolution for different amounts of residual dispersion at the output of the SOA. (b) The same as in (a) but with no GD in FP bandpass filter.
Fig. 7.
Fig. 7. (a) Long-term drift of the IF at specific points in time or equivalently of single wavelengths over 40 000 roundtrips when switching on a fiber dispersion of 100 fs after 10 000 roundtrips until the quasi-steady-state is reached. (b) Zoom into the first 1000 roundtrips compared to the dispersion accumulation in the fiber (solid line).
Fig. 8.
Fig. 8. (a) Measured intensity trace of a laser with a non-dispersion-compensated SMF-28 fiber cavity. The backward sweep of 104 nm is centered around 1307 nm at a filter sweep frequency of 363 kHz. (b) Zoom into a noisy region in the intensity trace, showing the hole dynamics. (c) Identical zoom into the experimentally obtained sweet-spot. (d) A simulated intensity trace of the case in (a) and (e) zoom into noisy region for comparison. (f) Zoom into the sweet-spot with a residual dispersion of 84 fs.
Fig. 9.
Fig. 9. (a) Measured hole in a laser setup which was detuned by −100 mHz from the ultra-stable regime. (b) A hole extracted from simulation with the SOA parameters used in this work, see Table 1. (c) Hole for the SOA parameters from [58], yet with a longer duration than in the experiment. (d) Fringe-distorted hole for the SOA parameters in (c) which could not be observed in experimentally measured intensity traces.

Tables (1)

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Table 1. Simulation Parameters

Equations (18)

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u out , fiber ( τ ) = κ f u in , fiber ( τ ) exp { i L f [ 1 2 β 2 ω s 2 ( τ ) + 1 6 β 3 ω s 3 ( τ ) + 1 24 β 4 ω s 4 ( τ ) ] + i φ cFBG ( τ ) + i γ κ f | u in , fiber ( τ ) | 2 1 2 L f ( 1 + R ) }
u o u t , S O A ( τ ) = u i n , S O A ( τ ) exp { 0.5 h ( τ ) [ 1 i α ] }
h ( τ ) τ = h 0 [ w s ( τ ) + ω c ] h ( τ ) τ c | u i n , S O A ( τ ) + u A S E ( τ ) | 2 P s a t [ w s ( τ ) + ω c ] τ c [ e h ( τ ) 1 ]
U o u t , F P ( ω ) = U i n , F P ( ω ) H ( ω )
H ( ω ) = T m a x 1 i 2 ω / Δ ω
u o u t ( τ ) = u i n ( τ ) exp [ i τ d ω s ( τ ) ] ,
Δ f I F = 1 / ( 2 π ) L f ω s ( τ ) ω s ( τ ) τ [ β 2 + 1 2 β 3 ω s ( τ ) + 1 6 β 4 ω s 2 ( τ ) ]
G D ( ω ) = 2 Δ ω 1 1 + ( 2 ω / Δ ω ) 2 .
u ( τ ) = A ( τ ) exp [ i φ ( τ ) ] .
φ ( τ ) = [ Ω ( τ ) ω c ] d τ
u d ( τ ) = A ( τ τ d ) exp [ i φ ( τ ) ] .
A ( τ τ d ) = k = 0 ( τ d τ ) k k ! A ( τ ) ,
( τ ) j A ( τ ) [ i ω s ( τ ) ] j u ( τ ) exp [ i φ ( τ ) ]
u d ( τ ) = [ k = 0 ( τ d τ ) k k ! A ( τ ) ] exp [ i φ ( τ ) ]
= [ A ( τ ) + ( τ d ) τ A ( τ ) + ( τ d ) 2 2 ! 2 τ 2 A ( τ ) + ] exp [ i φ ( τ ) ]
= u ( τ ) + ( τ d ) [ i ω s ( τ ) ] u ( τ ) + ( τ d ) 2 2 ! [ i ω s ( τ ) ] 2 u ( τ ) +
= u ( τ ) [ 1 i ( τ d ) ω s ( τ ) + [ i ( τ d ) ω s ( τ ) ] 2 2 ! + ]
= u ( τ ) exp [ i ( τ d ) ω s ( τ ) ] .

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