Abstract

Dispersion-flattened dispersion-decreased all-normal dispersion (DFDD-ANDi) photonic crystal fibers have been identified as promising candidates for high-spectral-power coherent supercontinuum (SC) generation. However, the effects of the unintentional birefringence of the fibers on the SC generation have been ignored. This birefringence is widely present in nonlinear non-polarization maintaining fibers with a typical core size of 2 µm, presumably due to the structural symmetry breaks introduced in the fiber drawing process. We find that an intrinsic form-birefringence on the order of 10−5 profoundly affects the SC generation in a DFDD-ANDi photonic crystal fiber. Conventional simulations based on the scalar generalized nonlinear Schrödinger equation (GNLSE) fail to reproduce the prominent observed features of the SC generation in a short piece (9-cm) of this fiber. However, these features can be qualitatively or semi-quantitatively understood by the coupled GNLSE that takes into account the form-birefringence. The nonlinear polarization effects induced by the birefringence significantly distort the otherwise simple spectrotemporal field of the SC pulses. We therefore propose the fabrication of polarization-maintaining DFDD-ANDi fibers to avoid these adverse effects in pursuing a practical coherent fiber SC laser.

© 2012 OSA

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2011 (6)

L. E. Hooper, P. J. Mosley, A. C. Muir, W. J. Wadsworth, and J. C. Knight, “Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion,” Opt. Express 19(6), 4902–4907 (2011).
[CrossRef] [PubMed]

H. Tu, Y. Liu, J. Lægsgaard, D. Turchinovich, M. Siegel, D. Kopf, H. Li, T. Gunaratne, and S. A. Boppart, “Cross-validation of theoretically quantified fiber continuum generation and absolute pulse measurement by MIIPS for a broadband coherently controlled optical source,” Appl. Phys. B (2011), doi:.
[CrossRef]

A. Hartung, A. M. Heidt, and H. Bartelt, “Design of all-normal dispersion microstructured optical fibers for pulse-preserving supercontinuum generation,” Opt. Express 19(8), 7742–7749 (2011).
[CrossRef] [PubMed]

A. M. Heidt, A. Hartung, G. W. Bosman, P. Krok, E. G. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express 19(4), 3775–3787 (2011).
[CrossRef] [PubMed]

A. Hartung, A. M. Heidt, and H. Bartelt, “Pulse-preserving broadband visible supercontinuum generation in all-normal dispersion tapered suspended-core optical fibers,” Opt. Express 19(13), 12275–12283 (2011).
[CrossRef] [PubMed]

A. M. Heidt, J. Rothhardt, A. Hartung, H. Bartelt, E. G. Rohwer, J. Limpert, and A. Tünnermann, “High quality sub-two cycle pulses from compression of supercontinuum generated in all-normal dispersion photonic crystal fiber,” Opt. Express 19(15), 13873–13879 (2011).
[CrossRef] [PubMed]

2010 (3)

2009 (4)

2008 (3)

2007 (7)

2006 (4)

2005 (4)

B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22(3), 687–693 (2005).
[CrossRef]

P. Falk, M. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13(19), 7535–7540 (2005).
[CrossRef] [PubMed]

M. Adachi, K. Yamane, R. Morita, and M. Yamashita, “Sub-5-fs pulse compression of laser output using photonic crystal fiber with short zero-dispersion wavelength,” Jpn. J. Appl. Phys. 44(47), L1423–L1425 (2005).
[CrossRef]

M. Tianprateep, J. Tada, and F. Kannari, “Influence of polarization and pulse shape of femtosecond initial laser pulses on spectral broadening in microstructure fibers,” Opt. Rev. 12(3), 179–189 (2005).
[CrossRef]

2004 (10)

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241(4-6), 339–348 (2004).
[CrossRef]

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. Folkenberg, and M. Nielsen, “Experimental study of polarization properties of highly birefringent photonic crystal fibers,” Opt. Express 12(24), 5931–5939 (2004).
[CrossRef] [PubMed]

Z. Zhu and T. Brown, “Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,” Opt. Express 12(5), 791–796 (2004).
[CrossRef] [PubMed]

Z. Zhu and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21(2), 249–257 (2004).
[CrossRef]

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93(18), 183901 (2004).
[CrossRef] [PubMed]

A. Efimov, A. Taylor, F. Omenetto, A. Yulin, N. Joly, F. Biancalana, D. Skryabin, J. Knight, and P. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express 12(26), 6498–6507 (2004).
[CrossRef] [PubMed]

D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. 92(12), 123905 (2004).
[CrossRef] [PubMed]

F. Druon and P. Georges, “Pulse-compression down to 20 fs using a photonic crystal fiber seeded by a diode-pumped Yb:SYS laser at 1070 nm,” Opt. Express 12(15), 3383–3396 (2004).
[CrossRef] [PubMed]

J. Thornes, P. Poon, and M. E. Anderson, “Single-iteration compression of femtosecond laser pulses,” J. Opt. Soc. Am. B 21(7), 1387–1390 (2004).
[CrossRef]

G. McConnell and E. Riis, “Ultra-short pulse compression using photonic crystal fibre,” Appl. Phys. B 78(5), 557–563 (2004).
[CrossRef]

2003 (11)

T. Südmeyer, F. Brunner, E. Innerhofer, R. Paschotta, K. Furusawa, J. C. Baggett, T. M. Monro, D. J. Richardson, and U. Keller, “Nonlinear femtosecond pulse compression at high average power levels by use of a large-mode-area holey fiber,” Opt. Lett. 28(20), 1951–1953 (2003).
[CrossRef] [PubMed]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90(11), 113904 (2003).
[CrossRef] [PubMed]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301(5640), 1705–1708 (2003).
[CrossRef] [PubMed]

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82(14), 2197–2199 (2003).
[CrossRef]

A. Proulx, J.-M. Ménard, N. Hô, J. Laniel, R. Vallée, and C. Paré, “Intensity and polarization dependences of the supercontinuum generation in birefringent and highly nonlinear microstructured fibers,” Opt. Express 11(25), 3338–3345 (2003).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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H. Tu, Y. Liu, J. Lægsgaard, D. Turchinovich, M. Siegel, D. Kopf, H. Li, T. Gunaratne, and S. A. Boppart, “Cross-validation of theoretically quantified fiber continuum generation and absolute pulse measurement by MIIPS for a broadband coherently controlled optical source,” Appl. Phys. B (2011), doi:.
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H. Tu, Y. Liu, J. Lægsgaard, U. Sharma, M. Siegel, D. Kopf, and S. A. Boppart, “Scalar generalized nonlinear Schrödinger equation-quantified continuum generation in an all-normal dispersion photonic crystal fiber for broadband coherent optical sources,” Opt. Express 18(26), 27872–27884 (2010).
[CrossRef] [PubMed]

H. Tu and S. A. Boppart, “Optical frequency up-conversion by supercontinuum-free widely-tunable fiber-optic Cherenkov radiation,” Opt. Express 17(12), 9858–9872 (2009).
[CrossRef] [PubMed]

H. Tu and S. A. Boppart, “Versatile photonic crystal fiber-enabled source for multi-modality biophotonic imaging beyond conventional multiphoton microscopy,” Proc. SPIE7569, 75692CD (2010).

Tünnermann, A.

Turchinovich, D.

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
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Unterhuber, A.

Urbanczyk, W.

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241(4-6), 339–348 (2004).
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Vallée, R.

Várallyay, Z.

Z. Várallyay, J. Fekete, Á. Bányász, and R. Szipőcs, “Optimizing input and output chirps up to the third-order for sub-nanojoule, ultra-short pulse compression in small core area PCF,” Appl. Phys. B 86(4), 567–572 (2007).
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Vozzi, C.

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K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90(11), 113904 (2003).
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K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90(11), 113904 (2003).
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V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77(2-3), 319–324 (2003).
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S. Lakó, J. Seres, P. Apai, J. Balázs, R. S. Windeler, and R. Szipőcs, “Pulse compression of nanojoule pulses in the visible using microstructure optical fiber and dispersion compensation,” Appl. Phys. B 76(3), 267–275 (2003).
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J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
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Wong, G. K.

Wullert, J. R.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28(4), 908–920 (1992).
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Appl. Phys. B (5)

H. Tu, Y. Liu, J. Lægsgaard, D. Turchinovich, M. Siegel, D. Kopf, H. Li, T. Gunaratne, and S. A. Boppart, “Cross-validation of theoretically quantified fiber continuum generation and absolute pulse measurement by MIIPS for a broadband coherently controlled optical source,” Appl. Phys. B (2011), doi:.
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Z. Várallyay, J. Fekete, Á. Bányász, and R. Szipőcs, “Optimizing input and output chirps up to the third-order for sub-nanojoule, ultra-short pulse compression in small core area PCF,” Appl. Phys. B 86(4), 567–572 (2007).
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V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77(2-3), 319–324 (2003).
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IEEE J. Quantum Electron. (1)

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28(4), 908–920 (1992).
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Nature (2)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
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Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
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Opt. Commun. (1)

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241(4-6), 339–348 (2004).
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Opt. Express (24)

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. Folkenberg, and M. Nielsen, “Experimental study of polarization properties of highly birefringent photonic crystal fibers,” Opt. Express 12(24), 5931–5939 (2004).
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Z. Zhu and T. Brown, “Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,” Opt. Express 12(5), 791–796 (2004).
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J. Dudley, X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, R. Trebino, St. Coen, and R. Windeler, “Cross-correlation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: simulations and experiments,” Opt. Express 10(21), 1215–1221 (2002).
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A. Efimov, A. Taylor, F. Omenetto, A. Yulin, N. Joly, F. Biancalana, D. Skryabin, J. Knight, and P. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express 12(26), 6498–6507 (2004).
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B. Washburn, S. Ralph, and R. Windeler, “Ultrashort pulse propagation in air-silica microstructure fiber,” Opt. Express 10(13), 575–580 (2002).
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A. Michie, J. Canning, I. Bassett, J. Haywood, K. Digweed, M. Åslund, B. Ashton, M. Stevenson, J. Digweed, A. Lau, and D. Scandurra, “Spun elliptically birefringent photonic crystal fibre,” Opt. Express 15(4), 1811–1816 (2007).
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A. Argyros, J. Pla, F. Ladouceur, and L. Poladian, “Circular and elliptical birefringence in spun microstructured optical fibres,” Opt. Express 17(18), 15983–15990 (2009).
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A. Proulx, J.-M. Ménard, N. Hô, J. Laniel, R. Vallée, and C. Paré, “Intensity and polarization dependences of the supercontinuum generation in birefringent and highly nonlinear microstructured fibers,” Opt. Express 11(25), 3338–3345 (2003).
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B. J. Chick, J. W. Chon, and M. Gu, “Polarization effects in a highly birefringent nonlinear photonic crystal fiber with two-zero dispersion wavelengths,” Opt. Express 16(24), 20099–20105 (2008).
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H. Tu and S. A. Boppart, “Optical frequency up-conversion by supercontinuum-free widely-tunable fiber-optic Cherenkov radiation,” Opt. Express 17(12), 9858–9872 (2009).
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P. Falk, M. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13(19), 7535–7540 (2005).
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F. Druon and P. Georges, “Pulse-compression down to 20 fs using a photonic crystal fiber seeded by a diode-pumped Yb:SYS laser at 1070 nm,” Opt. Express 12(15), 3383–3396 (2004).
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A. M. Heidt, A. Hartung, G. W. Bosman, P. Krok, E. G. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express 19(4), 3775–3787 (2011).
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A. Hartung, A. M. Heidt, and H. Bartelt, “Pulse-preserving broadband visible supercontinuum generation in all-normal dispersion tapered suspended-core optical fibers,” Opt. Express 19(13), 12275–12283 (2011).
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G. Humbert, W. Wadsworth, S. Leon-Saval, J. Knight, T. Birks, P. St. J. Russell, M. Lederer, D. Kopf, K. Wiesauer, E. Breuer, and D. Stifter, “Supercontinuum generation system for optical coherence tomography based on tapered photonic crystal fibre,” Opt. Express 14(4), 1596–1603 (2006).
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M.-L. V. Tse, P. Horak, F. Poletti, N. G. Broderick, J. H. Price, J. R. Hayes, and D. J. Richardson, “Supercontinuum generation at 1.06 mum in holey fibers with dispersion flattened profiles,” Opt. Express 14(10), 4445–4451 (2006).
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H. Tu, Y. Liu, J. Lægsgaard, U. Sharma, M. Siegel, D. Kopf, and S. A. Boppart, “Scalar generalized nonlinear Schrödinger equation-quantified continuum generation in an all-normal dispersion photonic crystal fiber for broadband coherent optical sources,” Opt. Express 18(26), 27872–27884 (2010).
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L. E. Hooper, P. J. Mosley, A. C. Muir, W. J. Wadsworth, and J. C. Knight, “Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion,” Opt. Express 19(6), 4902–4907 (2011).
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A. Hartung, A. M. Heidt, and H. Bartelt, “Design of all-normal dispersion microstructured optical fibers for pulse-preserving supercontinuum generation,” Opt. Express 19(8), 7742–7749 (2011).
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H. Wang, C. P. Fleming, and A. M. Rollins, “Ultrahigh-resolution optical coherence tomography at 1.15 mum using photonic crystal fiber with no zero-dispersion wavelengths,” Opt. Express 15(6), 3085–3092 (2007).
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A. M. Heidt, J. Rothhardt, A. Hartung, H. Bartelt, E. G. Rohwer, J. Limpert, and A. Tünnermann, “High quality sub-two cycle pulses from compression of supercontinuum generated in all-normal dispersion photonic crystal fiber,” Opt. Express 19(15), 13873–13879 (2011).
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W. Q. Zhang, S. Afshar V, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17(21), 19311–19327 (2009).
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D. Turchinovich, X. Liu, and J. Laegsgaard, “Monolithic all-PM femtosecond Yb-fiber laser stabilized with a narrow-band fiber Bragg grating and pulse-compressed in a hollow-core photonic crystal fiber,” Opt. Express 16(18), 14004–14014 (2008).
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X. Liu, J. Laegsgaard, and D. Turchinovich, “Highly-stable monolithic femtosecond Yb-fiber laser system based on photonic crystal fibers,” Opt. Express 18(15), 15475–15483 (2010).
[CrossRef] [PubMed]

Opt. Lett. (13)

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
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T. Südmeyer, F. Brunner, E. Innerhofer, R. Paschotta, K. Furusawa, J. C. Baggett, T. M. Monro, D. J. Richardson, and U. Keller, “Nonlinear femtosecond pulse compression at high average power levels by use of a large-mode-area holey fiber,” Opt. Lett. 28(20), 1951–1953 (2003).
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R. L. Fork, C. H. Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12(7), 483–485 (1987).
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M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22(8), 522–524 (1997).
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Z. Zhu and T. G. Brown, “Stress-induced birefringence in microstructured optical fibers,” Opt. Lett. 28(23), 2306–2308 (2003).
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R. J. Kruhlak, G. K. Wong, J. S. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, and J. C. Knight, “Polarization modulation instability in photonic crystal fibers,” Opt. Lett. 31(10), 1379–1381 (2006).
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M. J. Steel, T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26(8), 488–490 (2001).
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K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28(22), 2258–2260 (2003).
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Opt. Rev. (1)

M. Tianprateep, J. Tada, and F. Kannari, “Influence of polarization and pulse shape of femtosecond initial laser pulses on spectral broadening in microstructure fibers,” Opt. Rev. 12(3), 179–189 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90(11), 113904 (2003).
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F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93(18), 183901 (2004).
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D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. 92(12), 123905 (2004).
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Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
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Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
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Science (1)

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301(5640), 1705–1708 (2003).
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Other (5)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).

H. Tu and S. A. Boppart, “Versatile photonic crystal fiber-enabled source for multi-modality biophotonic imaging beyond conventional multiphoton microscopy,” Proc. SPIE7569, 75692CD (2010).

Nonlinear Photonic Crystal Fiber NL-1050-NEG-1, http://www.nktphotonics.com

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, Dordrecht, 2002).

SuperK series supercontinuum lasers, http://www.nktphotonics.com SC series supercontinuum lasers, http://www.fianium.com

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Figures (8)

Fig. 1
Fig. 1

(a) Dispersion engineering of DFDD-ANDi PCFs; (b) Dispersion engineering of ZDW PCFs; (c) Comparison of supercontinuum generation in a DFDD-ANDi PCF and a ZDW PCF.

Fig. 2
Fig. 2

Three representative paths for pulse compression of fiber supercontinuum.

Fig. 3
Fig. 3

(a) Comparison of measured spectrum and spectral phase of SC pulses with calculated spectrum and spectral phase from S-GNLSE. The spectrum of pump laser is also shown. (b) Temporal intensity profiles of uncompressed and compressed SC pulses. Inset: cross-section image of the DFDD-ANDi PCF.

Fig. 4
Fig. 4

(a)-(l): Calculated spectrum and polarization partition ratio (px) of SC from C-GNLSE at a number of linear birefringence values B, nonlinear length LNL, and incident angles θ. Red labels or curves indicate the significant departures from the S-GNLSE-based simulations on an isotropic fiber. (m)-(o): Observed spectrum of SC at a number of nonlinear length LNL.

Fig. 5
Fig. 5

Schematic of PCF SC generation and corresponding measurements of total spectrum and polarization properties. Two pinch plates may be used to stress the PCF through lateral force.

Fig. 6
Fig. 6

(a) Intensity of 1041-nm CW light as a function of half wave-plate rotation when the polarizer is set along one of the two principal axes of the fiber (red or blue curve); (b) Left: intensity of 1041-nm CW light as a function of polarizer rotation at several cutback lengths when the incident polarization is set at 45° to the x-axis; Right: diagram shows the corresponding evolution of the polarization state in the fiber; (c) Intensity of 0.36 W SC as a function of half wave-plate rotation when the polarizer is set along one of the two principal axes of the fiber (red or blue curve).

Fig. 7
Fig. 7

(a) Dependence of slow-axis depolarization on fiber length, average fiber transmission power, and lateral stress; (b) Dependence of fast-axis depolarization on fiber length and average fiber transmission power; (c) Dependence of polarization partition ratio px in two principal axes on fiber length and average fiber transmission power. At 0.36 W, the px values in two axes reach a constant in long (>80 cm) fibers.

Fig. 8
Fig. 8

(a) Two representative designs of PM PCFs; (b) Calculated temporal profile of the SC from a 27-cm PM DFDD-ANDi PCF with a slow-axis pump; (c) Calculated spectrum and spectral phase of the SC from a 27-cm PM DFDD-ANDi PCF with a slow-axis pump; (d) Observed spectrum of a unstressed 27-cm DFDD-ANDi PCF with a fast-axis pump; (e) Observed spectrum of a unstressed 27-cm DFDD-ANDi PCF with a slow-axis pump; (f) Observed spectrum of a stressed 27-cm DFDD-ANDi PCF with a slow-axis pump.

Equations (5)

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U 1 z iΔ β 0 U 2 2 + Δ β 1 2 U 2 τ k2 i k+1 β k k! k U 1 τ k = 1 L NL ( i 1 ω 0 τ )( f R U 1 h R (ττ')[ | U 1 (τ') | 2 + | U 2 (τ') | 2 ]dτ'+( 1 f R ) U 1 [ 2 3 | U 1 | 2 + 4 3 | U 2 | 2 ] )
U 2 z iΔ β 0 U 1 2 + Δ β 1 2 U 1 τ k2 i k+1 β k k! k U 2 τ k = 1 L NL ( i 1 ω 0 τ )( f R U 2 h R (ττ')[ | U 2 (τ') | 2 + | U 1 (τ') | 2 ]dτ'+( 1 f R ) U 2 [ 2 3 | U 2 | 2 + 4 3 | U 1 | 2 ] )
U x = U 1 + U 2 2 exp( iΔ β 0 2 z ) U y = U 1 U 2 2 exp( iΔ β 0 2 z )
U 1 = U z=0 2 exp( iθ ) U 2 = U z=0 2 exp( iθ )
h R (t)= τ 1 2 + τ 2 2 τ 1 τ 2 2 exp( t τ 2 )sin( t τ 1 )

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