Discrete optics in femtosecond-laser-written photonic structures

Over the last few years arrays of evanescently coupled waveguides have been brought into focus as a particular representation of functionalized optical materials, in which the dispersion and diffraction of propagating light can be specifically tuned. Moreover, it turns out that the light evolution in these systems shares fundamental similarities to the quantum evolution of particle wavefunctions, so that waveguide arrays can act as a model system for emulating quantum mechanics. Recently, a novel technique was developed with which waveguides can be directly 'written' into various optical bulk materials using femtosecond laser pulses, which allows for the realization of a variety of innovative concepts which are not feasible using other fabrication methods. The aim of this tutorial is to give an introduction to this topic.

[1]  R. Morandotti,et al.  Observation of discrete surface solitons. , 2006, Physical review letters.

[2]  J. S. Aitchison,et al.  Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations , 1999 .

[3]  S. Kawata Near-Field Optics and Surface Plasmon Polaritons , 2001 .

[4]  Andreas Tünnermann,et al.  Discrete nonlinear localization in femtosecond laser written waveguides in fused silica. , 2005, Optics express.

[5]  Yaron Silberberg,et al.  Discrete Solitons in Optics , 2008 .

[6]  Tsuneo Mitsuyu,et al.  Photowritten optical waveguides in various glasses with ultrashort pulse laser , 1997 .

[7]  J. Kutz,et al.  Nonlinear femtosecond pulse reshaping in waveguide arrays , 2008, 0805.2580.

[8]  A. Tünnermann,et al.  Observation of diffraction-managed discrete solitons in curved waveguide arrays , 2008 .

[9]  Y. Kivshar,et al.  Nonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays. , 2007, Optics express.

[10]  A. Tünnermann,et al.  Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate , 2008 .

[11]  Andreas Tünnermann,et al.  Light evolution in arbitrary two-dimensional waveguide arrays , 2007 .

[12]  Y. Kivshar,et al.  Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays. , 2006, Optics letters.

[13]  Wolfgang Sohler,et al.  Discrete Talbot effect in waveguide arrays. , 2005, Physical review letters.

[14]  S. Debbarma,et al.  Femtosecond laser written channel waveguides in tellurite glass. , 2006, Optics express.

[15]  M. Holthaus,et al.  Collapse of minibands in far-infrared irradiated superlattices. , 1992, Physical review letters.

[16]  V. Krylov,et al.  Surface acoustic waves in inhomogeneous media , 1995 .

[17]  S. M. Jensen The Nonlinear Coherent Coupler , 1982 .

[18]  L. Esaki,et al.  Tunneling in a finite superlattice , 1973 .

[19]  Anna Bezryadina,et al.  Observation of two-dimensional surface solitons. , 2007, Physical review letters.

[20]  Daniel W. Hewak,et al.  Fabrication and characterization of femtosecond laser written waveguides in chalcogenide glass , 2007, 2110.10471.

[21]  C. Zener A theory of the electrical breakdown of solid dielectrics , 1934 .

[22]  Andreas Tünnermann,et al.  Efficient frequency doubling in femtosecond laser-written waveguides in lithium niobate , 2006 .

[23]  S. Longhi Self-imaging and modulational instability in an array of periodically curved waveguides. , 2005, Optics letters.

[24]  Yaron Silberberg,et al.  Discretizing light behaviour in linear and nonlinear waveguide lattices , 2003, Nature.

[25]  J. Aitchison,et al.  Exact dynamic localization in curved AlGaAs optical waveguide arrays. , 2007 .

[26]  P. Laporta,et al.  Observation of dynamic localization in periodically curved waveguide arrays. , 2005, Physical review letters.

[27]  A. Davydov,et al.  Solitons and energy transfer along protein molecules. , 1977, Journal of theoretical biology.

[28]  Andreas Tünnermann,et al.  Nonlinear refractive index of fs-laser-written waveguides in fused silica. , 2006, Optics express.

[29]  F. Lederer,et al.  Spectral resolved dynamic localization in curved fs laser written waveguide arrays. , 2008, Optics express.

[30]  U. Peschel,et al.  Optical Bloch oscillations in waveguide arrays. , 1998, Optics letters.

[31]  Andreas Tünnermann,et al.  Discrete diffraction in two-dimensional arrays of coupled waveguides in silica. , 2004, Optics letters.

[32]  D. Christodoulides,et al.  Discrete self-focusing in nonlinear arrays of coupled waveguides. , 1988, Optics letters.

[33]  Suzuki,et al.  Site-selective laser-spectroscopy studies of the intrinsic 1.9-eV luminescence center in glassy SiO2. , 1995, Physical review. B, Condensed matter.

[34]  Andreas Tünnermann,et al.  Quasi-incoherent propagation in waveguide arrays , 2007 .

[35]  Mario Bertolotti,et al.  IV Nonlinear Wave Propagation in Planar Structures , 1989 .

[36]  Andreas Tünnermann,et al.  Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica. , 2006, Optics express.

[37]  Nicholas F. Borrelli,et al.  Study of femtosecond-laser-written waveguides in glasses , 2002 .

[38]  Martin Richardson,et al.  Optical properties of infrared femtosecond laser-modified fused silica and application to waveguide fabrication , 2005 .

[39]  G. Nenciu Dynamics of band electrons in electric and magnetic fields: rigorous justification of the effective Hamiltonians , 1991 .

[40]  Demetrios N. Christodoulides,et al.  Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices , 2003, Nature.

[41]  Mordechai Segev,et al.  Two-dimensional optical lattice solitons. , 2003, Physical review letters.

[42]  Andreas Tünnermann,et al.  Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate , 2007 .

[43]  F. Dreisow,et al.  Observation of two-dimensional lattice interface solitons , 2008, 2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science.

[44]  Krzysztof Patorski,et al.  I The Self-Imaging Phenomenon and its Applications , 1989 .

[45]  P. L. Kelley,et al.  Self-focusing of optical beams , 1965, International Quantum Electronics Conference, 2005..

[46]  S. Risbud,et al.  Structural changes in fused silica after exposure to focused femtosecond laser pulses. , 2001, Optics letters.

[47]  Tow Chong Chong,et al.  Microstructure in lithium niobate by use of focused femtosecond laser pulses , 2004 .

[48]  U. Peschel,et al.  Visual observation of Zener tunneling. , 2006, Physical review letters.

[49]  A. Tünnermann,et al.  Image reconstruction in segmented femtosecond laser-written waveguide arrays , 2008 .

[50]  K. Itoh,et al.  Ultrafast Processes for Bulk Modification of Transparent Materials , 2006 .

[51]  Andre Stesmans,et al.  Defects induced in fused silica by high fluence ultraviolet laser pulses at 355 nm , 2002 .

[52]  A. Tünnermann,et al.  Angular surface solitons in sectorial hexagonal arrays. , 2008, Optics letters.

[53]  Observation of Two-Dimensional Surface Solitons in Asymmetric Waveguide Arrays , 2007, 0704.3837.

[54]  S. Longhi Polychromatic optical Bloch oscillations. , 2009, Optics letters.

[55]  Charles H. Townes,et al.  Self-trapping of optical beams , 1964 .

[56]  A Bräuer,et al.  Anomalous refraction and diffraction in discrete optical systems. , 2002, Physical review letters.

[57]  F. Bloch Über die Quantenmechanik der Elektronen in Kristallgittern , 1929 .

[58]  R. Morandotti,et al.  Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons. , 2003, Physical review letters.

[59]  E. Mazur,et al.  Femtosecond laser micromachining in transparent materials , 2008 .

[60]  S. Nolte,et al.  Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics , 2003 .

[61]  Mordechai Segev,et al.  Spatial photonics in nonlinear waveguide arrays. , 2005, Optics express.

[62]  Tal Carmon,et al.  Observation of discrete solitons in optically induced real time waveguide arrays. , 2003, Physical review letters.

[63]  A. Szameit,et al.  Diffraction control in periodically curved two-dimensional waveguide arrays. , 2007, Optics express.

[64]  O. Bryngdahl Image formation using self-imaging techniques* , 1973 .

[65]  P. Laporta,et al.  Imaging of Bloch oscillations in erbium-doped curved waveguide arrays. , 2006, Optics letters.

[66]  P. St. J. Russell,et al.  Optics of Floquet-Bloch waves in dielectric gratings , 1986 .

[67]  Andreas Tünnermann,et al.  Second-order coupling in femtosecond-laser-written waveguide arrays. , 2008, Optics letters.

[68]  I. Mansour,et al.  An improved procedure to calculate the refractive index profile from the measured near-field intensity , 1996 .

[69]  R. Gordon,et al.  Harmonic oscillation in a spatially finite array waveguide. , 2004, Optics letters.

[70]  Mordechai Segev,et al.  Surface lattice solitons. , 2006, Optics letters.

[71]  David A. B. Miller,et al.  Optical investigation of Bloch oscillations in a semiconductor superlattice. , 1992 .

[72]  A. Tünnermann,et al.  Bloch-Zener oscillations in binary superlattices. , 2009, Physical review letters.

[73]  R. Morandotti,et al.  Optical modes at the interface between two dissimilar discrete meta-materials. , 2007, Optics express.

[74]  Andreas Tünnermann,et al.  Inscription of optical waveguides in crystalline silicon by mid-infrared femtosecond laser pulses. , 2005, Optics letters.

[75]  James A. Piper,et al.  Ultrafast laser written active devices , 2009 .

[76]  J. S. Aitchison,et al.  Discrete Spatial Optical Solitons in Waveguide Arrays , 1998 .

[77]  Martin Richardson,et al.  Femtosecond laser fabrication of tubular waveguides in poly(methyl methacrylate). , 2004, Optics letters.

[78]  Alain Hache,et al.  Discrete surface solitons. , 2005, Optics letters.

[79]  E.C.M. Pennings,et al.  Optical multi-mode interference devices based on self-imaging: principles and applications , 1995 .

[80]  Dunlap,et al.  Dynamic localization of a charged particle moving under the influence of an electric field. , 1986, Physical review. B, Condensed matter.

[81]  Alain Barthélémy,et al.  Propagation soliton et auto-confinement de faisceaux laser par non linéarité optique de Kerr , 1985 .

[82]  Mario Bertolotti,et al.  Nonlinear waves in solid state physics , 1990 .

[83]  Ts Paunska,et al.  Guided-wave-produced plasmas , 2000 .

[84]  Roberto Osellame,et al.  Micromachining of photonic devices by femtosecond laser pulses , 2008 .

[85]  C. Martijn de Sterke,et al.  Bloch Oscillations in an Array of Curved Optical Waveguides , 1999 .

[86]  A. Tünnermann,et al.  Polychromatic dynamic localization in curved photonic lattices , 2009 .

[87]  S. Longhi Quantum‐optical analogies using photonic structures , 2009 .

[88]  Andreas Bräuer,et al.  Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays , 1999 .

[89]  S. Longhi Image reconstruction in segmented waveguide arrays. , 2008, Optics letters.

[90]  D. Milam Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica. , 1998, Applied optics.