Abstract

Nonlinear frequency mixing as a means to coherently convert light to new frequencies is widely used in many branches of optics. This process requires momentum conservation through phase matching (PM). In free-space optics, PM is achieved through angle tuning the medium with respect to the incoming light—here we explore an in-fiber analogue: PM using spatial modes of the fiber. We demonstrate over two octaves (400–1700 nm) of coherent spectral translation generated by intermodal four-wave mixing between subsets of 11 different Bessel-like fiber modes. These interactions are facilitated by the unique mode-coupling resistance of this subset of azimuthally symmetric, zero orbital angular momentum fiber modes. Their stability allows overcoming previous limitations of multimode nonlinear-optical systems imposed by mode coupling, hence enabling long interaction lengths, large effective mode areas, and a highly multimode basis set with which a new degree of freedom for versatile PM can be obtained.

© 2015 Optical Society of America

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References

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2014 (1)

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S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, Laser Photonics Rev. 2, 429 (2008).
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2007 (1)

2006 (1)

2004 (3)

2003 (3)

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D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
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J. Hansryd, P. A. Andreksen, M. Westlund, J. Lim, P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
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2000 (2)

J. K. Ranka, R. S. Windeler, A. J. Stentz, Opt. Lett. 25, 25 (2000).
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1982 (1)

R. H. Stolen, J. E. Bjorkholm, IEEE J. Quantum Electron. 18, 1062 (1982).
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R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
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Feder, K.

Fini, J. M.

Foster, M. A.

Gaeta, A. L.

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, A. L. Gaeta, Opt. Express 15, 12949 (2007).
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D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
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D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
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R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
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Hansryd, J.

J. Hansryd, P. A. Andreksen, M. Westlund, J. Lim, P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[Crossref]

Headley, C.

Hedekvist, P. O.

J. Hansryd, P. A. Andreksen, M. Westlund, J. Lim, P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
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Holdsworth, J.

Hollberg, L. W.

J. Ye, H. Schnatz, L. W. Hollberg, IEEE J. Quantum Electron. 9, 1041 (2003).
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Hölzer, P.

Horak, P.

Jakobsen, D.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, D. Jakobsen, Appl. Phys. Lett. 101, 161106 (2012).
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Jiang, X.

R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
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Joly, N.

Joly, N. Y.

King, B.

Kippenberg, T. J.

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
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Knight, J. C.

Koch, K. W.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
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Konorov, S. O.

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[Crossref]

Legge, S.

Lim, J.

J. Hansryd, P. A. Andreksen, M. Westlund, J. Lim, P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[Crossref]

Lingle, R.

R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
[Crossref]

Lipson, M.

Liu, X.

Luther-Davies, B.

B. J. Eggleton, B. Luther-Davies, K. Richardson, Nat. Photonics 5, 141 (2011).

Mak, K. F.

Marquez, M. P.

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[Crossref]

Mestre, M. A.

R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
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J. A. Giordmaine, R. C. Miller, Phys. Rev. Lett. 14, 973 (1965).
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Monberg, E.

Müller, D.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
[Crossref]

Nguyen, D.

Nicholson, J. W.

Omenetto, F. G.

Ortigosa-Blanch, A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[Crossref]

Ortiz, R.

Ouzounov, D. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
[Crossref]

Pedersen, M. E. V.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, D. Jakobsen, Appl. Phys. Lett. 101, 161106 (2012).
[Crossref]

Piracha, M. U.

Poletti, F.

Ramachandran, S.

P. Steinvurzel, J. Demas, B. Tai, Y. Chen, L. Yan, S. Ramachandran, Opt. Lett. 39, 743 (2014).
[Crossref]

P. Steinvurzel, K. Tantiwanichapan, M. Goto, S. Ramachandran, Opt. Lett. 36, 4671 (2011).
[Crossref]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, Laser Photonics Rev. 2, 429 (2008).
[Crossref]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, F. V. DiMarcello, Opt. Lett. 31, 1797 (2006).
[Crossref]

J. Demas, P. Steinvurzel, B. Tai, Y. Chen, S. Ramachandran, in CLEO, OSA Technical Digest (online) (OSA, 2013), paper CTu2E.5.

L. Rishøj, Y. Chen, P. Steinvurzel, K. Rottwitt, S. Ramachandran, in CLEO, OSA Technical Digest (online) (OSA, 2012), paper CTu3M.6.

Ranka, J. K.

Richardson, K.

B. J. Eggleton, B. Luther-Davies, K. Richardson, Nat. Photonics 5, 141 (2011).

Rishøj, L.

L. Rishøj, Y. Chen, P. Steinvurzel, K. Rottwitt, S. Ramachandran, in CLEO, OSA Technical Digest (online) (OSA, 2012), paper CTu3M.6.

Rottwitt, K.

L. Rishøj, Y. Chen, P. Steinvurzel, K. Rottwitt, S. Ramachandran, in CLEO, OSA Technical Digest (online) (OSA, 2012), paper CTu3M.6.

Russell, P. St. J.

Ryf, R.

R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
[Crossref]

Salem, R.

Schnatz, H.

J. Ye, H. Schnatz, L. W. Hollberg, IEEE J. Quantum Electron. 9, 1041 (2003).
[Crossref]

Serebrannikov, E. E.

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[Crossref]

Shabahang, S.

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[Crossref]

Silcox, J.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
[Crossref]

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[Crossref]

Steinvurzel, P.

P. Steinvurzel, J. Demas, B. Tai, Y. Chen, L. Yan, S. Ramachandran, Opt. Lett. 39, 743 (2014).
[Crossref]

P. Steinvurzel, K. Tantiwanichapan, M. Goto, S. Ramachandran, Opt. Lett. 36, 4671 (2011).
[Crossref]

J. Demas, P. Steinvurzel, B. Tai, Y. Chen, S. Ramachandran, in CLEO, OSA Technical Digest (online) (OSA, 2013), paper CTu2E.5.

L. Rishøj, Y. Chen, P. Steinvurzel, K. Rottwitt, S. Ramachandran, in CLEO, OSA Technical Digest (online) (OSA, 2012), paper CTu3M.6.

Stentz, A. J.

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, IEEE J. Quantum Electron. 18, 1062 (1982).
[Crossref]

R. H. Stolen, J. E. Bjorkholm, A. Ashkin, Appl. Phys. Lett. 24, 308 (1974).
[Crossref]

Sun, Y.

R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
[Crossref]

Supradeepa, V. R.

Tai, B.

P. Steinvurzel, J. Demas, B. Tai, Y. Chen, L. Yan, S. Ramachandran, Opt. Lett. 39, 743 (2014).
[Crossref]

J. Demas, P. Steinvurzel, B. Tai, Y. Chen, S. Ramachandran, in CLEO, OSA Technical Digest (online) (OSA, 2013), paper CTu2E.5.

Tantiwanichapan, K.

Tao, G.

Tarasevitch, A.

Taylor, A. J.

Thomas, M. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
[Crossref]

Tkach, R. W.

R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle, IEEE Photon. Technol. Lett. 25, 539 (2013).
[Crossref]

Travers, J. C.

Turner, A. C.

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[Crossref]

Venkataraman, N.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, A. L. Gaeta, Science 301, 1702 (2003).
[Crossref]

von der Linde, D.

Wadsworth, W. J.

Wang, K.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, D. Jakobsen, Appl. Phys. Lett. 101, 161106 (2012).
[Crossref]

Weiner, A. M.

C. T. Cundiff, A. M. Weiner, Nat. Photonics 4, 760 (2010).
[Crossref]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[Crossref]

Westbrook, P. S.

Westlund, M.

J. Hansryd, P. A. Andreksen, M. Westlund, J. Lim, P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[Crossref]

Windeler, R. S.

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Supplementary Material (1)

» Supplement 1: PDF (1028 KB)     

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Figures (4)

Fig. 1.
Fig. 1. (a) Tuning PM in bulk materials by changing the angle of the incident light with respect to the crystal’s optical axis. (b) Tuning PM in multimode waveguides by changing mode orders, analogous to (a). (c) Wavevector diagrams: propagation constant versus transverse wavenumber for singlemode (left) and multimode (right) fibers. Green lines are pump waves, whereas red and blue lines are Stokes and anti-Stokes waves, respectively.
Fig. 2.
Fig. 2. (a) Effective index versus wavelength for LP0,6LP0,18 modes. Black line is a linear fit of LP0,6 mode over 700–1400 nm. (b) Experimental setup: microchip Nd:YAG laser (λ=1064nm, 19.56 kHz repetition rate, 0.5 ns pulse) and Yb-doped fiber amplifier (34.7 kW peak power) coupled through the LPG and 16.3 m of sample fiber (Supplement 1, S.1). Insets (left to right): LP0,6 mode generated by the LPG, cross section of the custom double-clad HOM guiding fiber, and diagnostic equipment. The far-field output of the sample fiber is pictured in a real-color image—concentric rings of different colors are the far-field patterns of Bessel beams and indicate that different colors are produced in different mode orders.
Fig. 3.
Fig. 3. Output spectra and mode images from intermodal FWM. Red, topmost spectrum was obtained with a fiber of length 16.3 m; lower spectra correspond to 10.3, 8.3, 6.3, 4.3, 2.3, and 1.3 m fiber lengths, respectively (offset for clarity), for 34.7 kW of input peak power. Detector is saturated at the pump wavelength; actual power at 1064 nm is 20 dB above that shown in the spectra. Left inset spectrum is a zoomed-in view of the 16.3 m spectrum, highlighting intermodal peaks in the visible region. Mode images (using 10 nm bandpass filters) are shown for representative portions of the continuum spectrum [(a) and (b)], and each of the discrete peaks [(c)–(l)]. Between 700 and 1400 nm, the mode remains LP0,6; each of the discrete peaks in the visible corresponds to LP0,m modes of increasing radial order.
Fig. 4.
Fig. 4. (a) Simulated intersections between the straight line fit and effective indices of Fig. 2(a), compared to measured wavelengths of spectral peaks for each mode order. (b) Calculated effective area for FWM (AFWM) for all valid processes of a given anti-Stokes mode order. Lowest AFWM processes are expected to dominate for spontaneous mode and color generation, and correspond to the process described in Eq. (2). (c) Schematic representation of the cascade process described in Eq. (2). Each anti-Stokes LP0,m peak is generated by one photon from the pump laser (LP0,6 at 1064 nm), and one photon in the LP0,m1 mode. In each case, the Stokes photon is generated in the long-wavelength portion of the LP0,6 continuum.

Equations (2)

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AFWM=[Fj*(x,y)Fk*(x,y)Fl(x,y)Fm(x,y)dA]1,
β0,6P1|λ=1064nm+β0,m1P2=β0,mAS+β0,6S.

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