Abstract

In the diffraction of a supercontinuum source, a redistribution of amplitude and phase at the focal region is incurred by the coupling between the supercontinuum and the spatial phase caused by the lens diffraction, making it extremely difficult to predict the focal behaviour. We show that the coupling between the temporal phase of a SC source and the spatial phase from the diffraction by a low numerical aperture (NA) lens causes dramatic alterations in the spectra and the temporal coherence near the focal region, and that this effect is maximized in points of singularity. Furthermore, we show that such an enhancement in temporal coherence can be controlled by the pulse evolution through the photonic crystal fiber, in which nonlinear and disperive effects such as the soliton fission process provides the key phase evolution necessary for dramatically changing the coherence time of the focused electromagnetic wave.

© 2009 Optical Society of America

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    [CrossRef]
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2008 (2)

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

B. J. Chick, J. W. M. Chon and M. Gu, "Polarization effects in a highly birefringent nonlinear photonic crystal fiber with two-zero dispersion wavelengths," Opt. Express 16, 20099-20080 (2008).
[CrossRef] [PubMed]

2006 (1)

J. M. Dudley, G. Genty and S. Coen, "Supercontinuum generation in photonic crystal fiber," Mod. Phys. Rev. 78, 113-1184 (2006).

2005 (2)

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto and M. Takeda, "Phase singularities in analytic signal of whitelight speckle pattern with application to micro-displacement measurement," Opt. Comm. 248, 59-68 (2005).
[CrossRef]

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

2004 (1)

2003 (3)

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 28, 1123-1125 (2003).
[CrossRef] [PubMed]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

2002 (3)

J. M. Dudley and S. Coen, "Coherence properties of supecontinuum sprectra generated in photonic crystal and tapered optical fibers," Opt. Exp. 27, 1180-1182 (2002).

Th. Udem, R. Holzwarth, and T. W. Hansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (1)

1998 (2)

J. C. Knight, J. Broeng, T. A. Birks and P. St. J. Russell, "Photonic band cap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

L. Sereda and M. Bertolotti, "Coherence properties of nonstationary light wave fields," J. Opt. Soc. Am. A 15, 695-705 (1998).
[CrossRef]

1995 (1)

1967 (1)

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, "Self-Steepening of light pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Bertolotti, M.

Biancalana, F.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks and P. St. J. Russell, "Photonic band cap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks and P. St. J. Russell, "Photonic band cap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Carruthers, A. E.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

Chick, B. J.

Chon, J. W. M.

Chudoba, C.

Cizmar, T.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty and S. Coen, "Supercontinuum generation in photonic crystal fiber," Mod. Phys. Rev. 78, 113-1184 (2006).

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

J. M. Dudley and S. Coen, "Coherence properties of supecontinuum sprectra generated in photonic crystal and tapered optical fibers," Opt. Exp. 27, 1180-1182 (2002).

Corwin, K. L.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

De Martini, F.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, "Self-Steepening of light pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Dholakia, K.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

Diddams, S. A.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty and S. Coen, "Supercontinuum generation in photonic crystal fiber," Mod. Phys. Rev. 78, 113-1184 (2006).

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

J. M. Dudley and S. Coen, "Coherence properties of supecontinuum sprectra generated in photonic crystal and tapered optical fibers," Opt. Exp. 27, 1180-1182 (2002).

Efimov, A.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

Ferrari, A.

Fischer, P.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

Fujimoto, J. G.

Fukui, K.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

Gbur, G.

G. Gbur, T. D. Visser and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Genty, G.

J. M. Dudley, G. Genty and S. Coen, "Supercontinuum generation in photonic crystal fiber," Mod. Phys. Rev. 78, 113-1184 (2006).

Ghanta, R. K.

Gu, M.

Gustafson, T. K.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, "Self-Steepening of light pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Hansch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Hanson, S. G.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto and M. Takeda, "Phase singularities in analytic signal of whitelight speckle pattern with application to micro-displacement measurement," Opt. Comm. 248, 59-68 (2005).
[CrossRef]

Hartl, I.

Herrmann, J.

A. V. Husakou and J. Herrmann, "Supercontinuum generation higher-order solutions by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Higashi, T.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

Hilligsøe, K. M.

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Husakou, A. V.

A. V. Husakou and J. Herrmann, "Supercontinuum generation higher-order solutions by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Ishii, N.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto and M. Takeda, "Phase singularities in analytic signal of whitelight speckle pattern with application to micro-displacement measurement," Opt. Comm. 248, 59-68 (2005).
[CrossRef]

Isobe, K.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

Itoh, K.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

Keiding, S. R.

Kelley, P. L.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, "Self-Steepening of light pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Knight, J. C.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks and P. St. J. Russell, "Photonic band cap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Ko, T. H.

Larsen, J. J.

Li, P.

Li, X. D.

Liu, Z. W.

Matsunaga, S.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

Mazilu, M.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

Miyamoto, Y.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto and M. Takeda, "Phase singularities in analytic signal of whitelight speckle pattern with application to micro-displacement measurement," Opt. Comm. 248, 59-68 (2005).
[CrossRef]

Morris, J. E.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

Newbury, N. R.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

Omenetto, F. G.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

Paulsen, H. N.

Ranka, J. K.

Reece, P. J.

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Cizmar, P. Fischer and K. Dholakia, "Optical micromanipulation using supercontinuum Laguerre Gaussian and Gaussian beams," Opt. Express 16, 1011-10129 (2008).
[CrossRef]

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

Russell, P. St. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks and P. St. J. Russell, "Photonic band cap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Sereda, L.

Shi, K. B.

Skryabin, D. V.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

Stentz, A. J.

Takeda, M.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto and M. Takeda, "Phase singularities in analytic signal of whitelight speckle pattern with application to micro-displacement measurement," Opt. Comm. 248, 59-68 (2005).
[CrossRef]

Taylor, A.J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A.J. Taylor, "Transformation and control of ultrashort pulses in dispersion-engineered photonic crystal fibers," Nature 474, 511-515 (2003).
[CrossRef]

Thøgersen, J.

Townes, C. H.

F. De Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, "Self-Steepening of light pulses," Phys. Rev. 164, 312-323 (1967).
[CrossRef]

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Visser, T. D.

G. Gbur, T. D. Visser and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Wang, W.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto and M. Takeda, "Phase singularities in analytic signal of whitelight speckle pattern with application to micro-displacement measurement," Opt. Comm. 248, 59-68 (2005).
[CrossRef]

Watanabe, W.

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

Weber, K.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

Windeler, R. S.

Windler, R. S.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber and R. S. Windler, "Fundamental noise limitations to supercontinuum generation in microstructured fiber," Phys. Rev. Lett. 90, 112904 (2003).
[CrossRef]

Wolf, E.

G. Gbur, T. D. Visser and E. Wolf, "Anomalous behavior of spectra near phase singularities of focused waves," Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Yin, S. Z.

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

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

Jpn. J. Appl. Phys. (1)

K. Isobe, W. Watanabe, S. Matsunaga, T. Higashi, K. Fukui and K. Itoh, "Multi-spectral two-photon excited fluorescence microscopy using supercontinuum light source," Jpn. J. Appl. Phys. 44, L167-L169 (2005).
[CrossRef]

Mod. Phys. Rev. (1)

J. M. Dudley, G. Genty and S. Coen, "Supercontinuum generation in photonic crystal fiber," Mod. Phys. Rev. 78, 113-1184 (2006).

Nature (2)

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Supplementary Material (2)

» Media 1: MOV (1635 KB)     
» Media 2: MOV (2948 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

An illustration of pulse diffraction by a low NA lens. (a) shows how the path length and the NA affect the pulse distribution as the temporal envelope passes through the focus. (b) shows the observation frames of the intensity profile in the focus.

Fig. 2.
Fig. 2.

The temporal effects of a SC propagating through the focus of a low NA (0.1) objective. (a) On axis diffraction centered at the focal point (the full temporal evolution of the SC on the axis can be viewed from the supplementary Media 1). (b) On axis diffraction centered at u 0=5π. (c) Radial and axial diffraction pattern centered at the focal point (the full temporal evolution of the SC in the radial and axial direction can be viewed from the supplementary Media 2). (d) Complete axial and temporal diffraction field. The SC field was calculated with a peak power of 2500W and a pulse width of 0.1ps with the dispersion and nonlinear parameters as described by Chick et. al. [19].

Fig. 3.
Fig. 3.

The coherence time within a focused SC for the stationary and the non-stationary cases. (a) Axial and radial distribution of the coherence time for the 0.1 NA lens for the stationary case; (b) Axial and radial distribution of the coherence time for the 0.1 NA lens for the non-stationary case; (c) Effect of NA on the coherence time on the axis for the stationary case; and (d) Effect of NA on the coherence time on the axis for the non-stationary case.

Fig. 4.
Fig. 4.

Propagation of an ultrashort hyperbolic secant pulse through a nonlinear photonic crystal fiber. (a) field propagation as a function of fiber length (b) coherence time in the focal region for different length fiber. The peak input power to the photonic crystal fiber is 2500W with a pulse duration of 100fs. (1) represents the cross section used for Fig. 3d (blue).

Fig. 5.
Fig. 5.

Mean frequency distribution of the focused SC in the axial and radial plane of a 0.1 NA lens for stationary (a) and non-stationary (b) cases.

Equations (6)

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U1(u,v,ω)=iωNA2ceiuNA2baU(ω)J0(vρ)e12iuρ2ρdρ
U1(u,v,ω)=ωNA2ucU(ω)eiuNA2(e12ib2ue12ia2u)
g1(z1,t1:z2,t2)=U*(z1,t1)U(z2,t2)[U(z1,t1)2U(z2,t2)2]12
g1(u0,v0,τ)=U1*(u0,v0,t),U1(u0,v0,t+τ)U1(u0,v0,t),U1(u0,v0,t)
g1(u0,v0,τ)=U1*(u,v0,t)U1(u+u0,v0,t+τ)[U1(u,v0,t)2U1(u+u0,v0,t+τ)2]12
τc(u0,v0)=g1(u0,v0,τ)2dτ

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