χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons

Cascading is the process by which the exchange of energy between optical beams interacting via second order nonlinearities (χ(2)) leads to various effects such as nonlinear phase shifts, the generation of new beams, all-optical transistor action, the formation of soliton-like (solitary) waves, etc. Here we review the fundamentals of the processes and discuss experimental verification of the effects and various related applications.

[1]  A. Piskarskas,et al.  Linear transformation of pulse chirp through a cascaded optical second-order process. , 1995, Optics letters.

[2]  Keith J. Blow,et al.  Ultrafast Fiber Switching Devices and Systems , 1993 .

[3]  R. Schiek,et al.  All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity , 1994 .

[4]  D. Mihalache,et al.  Multiple‐humped bright solitary waves in second‐order nonlinear media , 1996 .

[5]  Q. X. Li,et al.  Mode locking with linear and nonlinear phase shifts , 1993 .

[6]  Gaetano Assanto,et al.  Cascading effects in type II second-harmonic generation: applications to all-optical processing , 1995 .

[7]  G I Stegeman,et al.  Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides. , 1994, Optics letters.

[8]  A. Stabinis,et al.  Effective sum frequency pulse compression in nonlinear crystals , 1991 .

[9]  S. Silvestri,et al.  Fivefold femtosecond pulse compression by sum frequency generation , 1996 .

[10]  Jamal T. Manassah,et al.  Amplitude and phase of a pulsed second-harmonic signal , 1987 .

[11]  X. Zhao,et al.  Parametric mode locking , 1992 .

[12]  L. A. Ostrovskiĭ.  Self-action of Light in Crystals , 1967 .

[13]  G. Assanto,et al.  Polarization spatial chaos in second-harmonic generation. , 1994, Optics letters.

[14]  GianPiero Banfi,et al.  Optical frequency mixing through cascaded second‐order processes in β‐barium borate , 1993 .

[15]  Andrey Kobyakov,et al.  Vectorial type-II interaction in cascaded quadratic nonlinearities — an analytical approach , 1996 .

[16]  G. Stegeman,et al.  Phase-controlled transistor action by cascading of second-order nonlinearities in KTP. , 1994, Optics letters.

[17]  Stegeman,et al.  Observation of two-dimensional spatial solitary waves in a quadratic medium. , 1995, Physical review letters.

[18]  A. Kaplan.  Eigenmodes of X((2)) wave mixings: cross-induced second-order nonlinear refraction. , 1993, Optics letters.

[19]  Ivan Prochazka,et al.  Mode-locking of the 1.66 μm transition of an Er: YAlO3 laser , 1993 .

[20]  Y. Kivshar,et al.  Spatial optical solitons governed by quadratic nonlinearity. , 1994, Optics letters.

[21]  Curtis R. Menyuk,et al.  Solitary waves due to ?^(2): ?^(2) cascading , 1994 .

[22]  H. Wilhelmsson,et al.  Solution of the equations for nonlinear interaction of three damped waves , 1976 .

[23]  G I Stegeman,et al.  Large nonlinear phase shifts in second-order nonlinear-optical processes. , 1993, Optics letters.

[24]  Lederer,et al.  Collision of solitary waves in media with a second-order nonlinearity. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[25]  Curtis R. Menyuk,et al.  Soliton robustness in optical fibers , 1993 .

[26]  E. Popov,et al.  Phase-matched guided-wave optical bistability in chi ((2)) optical resonators. , 1995, Optics letters.

[27]  Y. Chen.  Stability of black solitons in media with arbitrary nonlinearity. , 1996, Optics letters.

[28]  W E Moerner,et al.  Second-order cascading as the origin of large third-order effects in organic single-crystal-core fibers. , 1994, Optics letters.

[29]  K. Stankov,et al.  Frequency-doubling mode locker: the influence of group-velocity mismatch. , 1991, Optics letters.

[30]  K. Stankov.  Mode locking by a frequency-doubling crystal: generation of transform-limited ultrashort light pulses. , 1989, Optics Letters.

[31]  C. Bosshard.  Cascading of Second‐Order Nonlinearities in Polar Materials , 1996 .

[32]  G I Stegeman,et al.  Large nonlinear phase modulation in quasi-phase-matched KTP waveguides as a result of cascaded second-order processes. , 1993, Optics letters.

[33]  G. Cerullo,et al.  Group-velocity mismatch compensation in continuous-wave lasers mode locked by second-order nonlinearities. , 1995, Optics letters.

[34]  D. W. Hughes,et al.  Coupled Cavity Mode-locking Using Nonlinear Amplitude Modulators , 1990 .

[35]  P. Laporta,et al.  A diode‐pumped nonlinear mirror mode‐locked Nd:YAG laser , 1994 .

[36]  Nonlinear Schrodinger solitons in media with non-zero second-order nonlinear susceptibility , 1993 .

[37]  A. Takada,et al.  Laser beam cleanup with photorefractive two-beam coupling. , 1995, Optics letters.

[38]  R. T. Lynch,et al.  An organic crystal with an exceptionally large optical second‐harmonic coefficient: 2‐methyl‐4‐nitroaniline , 1979 .

[39]  A. Barthélémy,et al.  Cross-phase modulation from second-harmonic to fundamental in cascaded second order processes; application to switching , 1995 .

[40]  Yaochun Shen.  Principles of nonlinear optics , 1984 .

[41]  H. Gibbs.  Optical Bistability Controlling Light With Light , 1985 .

[42]  G Valiulis,et al.  Femtosecond high-contrast pulses from a parametric generator pumped by the self-compressed second harmonic of a Nd:glass laser. , 1995, Optics letters.

[43]  Yuri S. Kivshar,et al.  Modulational instabilities and optical solitons due to competition of χ(2) and χ(3) nonlinearities , 1996 .

[44]  S Trillo,et al.  Optical solitons supported by competing nonlinearities. , 1995, Optics letters.

[45]  S. Saltiel,et al.  Extremely long train of ultra short pulses from an actively mode-locked pulsed Nd: YAG laser , 1991 .

[46]  B. Luther-Davies,et al.  Frequency-doubling pulse compressor for picosecond high-power neodymium laser pulses. , 1992, Optics letters.

[47]  Gijsbertus J.M. Krijnen,et al.  Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime , 1996 .

[48]  F. Calogero.  Universality and integrability of the nonlinear evolution PDE’s describing N‐wave interactions , 1989 .

[49]  K. Stankov.  25 ps pulses from a Nd:YAG laser mode locked by a frequency doubling β‐BaB2O4 crystal , 1991 .

[50]  Charles N. Ironside,et al.  An all-optical switch employing the cascaded second-order nonlinear effect , 1993 .

[51]  Alejandro B. Aceves,et al.  Self-induced transparency solitons in nonlinear refractive periodic media , 1989, Annual Meeting Optical Society of America.

[52]  A. Laubereau,et al.  Evidence for chirp reversal and self-compression in a femtosecond optical parametric oscillator , 1991 .

[53]  Buryak.  Stationary soliton bound states existing in resonance with linear waves. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[54]  J. Perry,et al.  Synthesis of organic salts with large second-order optical nonlinearities. , 1994, Science.

[55]  Andrew G. White,et al.  Cascaded second-order nonlinearity in an optical cavity , 1996 .

[56]  M. Fejer,et al.  Quasi-phase-matched second harmonic generation: tuning and tolerances , 1992 .

[57]  Koshiba,et al.  Multidimensional solitons in quadratic nonlinear media. , 1993, Physical review letters.

[58]  J. Zyss,et al.  Linear and nonlinear optical properties of N-4-nitrophenyl L-prolinol single crystals , 1990 .

[59]  D. N. Klyshko,et al.  Phase modulation and self-modulation of light in three-photon processes , 1974 .

[60]  S. Wabnitz,et al.  Two-wave mixing in a quadratic nonlinear medium: bifurcations, spatial instabilities, and chaos. , 1992, Optics letters.

[61]  J. Fujimoto,et al.  2.3-ps pulses from a Kerr-lens mode-locked lamp-pumped Nd:YLF laser with a microdot mirror. , 1993, Optics letters.

[62]  Sharp,et al.  Observation of self-trapping of an optical beam due to the photorefractive effect. , 1993, Physical review letters.

[63]  N. Kothari,et al.  Transient second-harmonic generation: influence of effective group-velocity dispersion , 1988 .

[64]  François Hache,et al.  Ti:sapphire second-harmonic-pumped visible range femtosecond optical parametric oscillator , 1994 .

[65]  K. Stankov,et al.  Nonlinear mirror based on raman interactions , 1991 .

[66]  M. Sypek,et al.  Coupled solitons in waveguides with cascaded second order nonlinearity , 1994 .

[67]  Buryak,et al.  Self-trapping of light beams and parametric solitons in diffractive quadratic media. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[68]  J. Aitchison,et al.  All-optical switching based on nondegenerate phase shifts from a cascaded second-order nonlinearity. , 1993, Optics letters.

[69]  Pascual,et al.  Ab initio model-potential embedded-cluster study of Jahn-Teller parameters and electronic transition energies of Cr2+ in oxide and fluoride octahedral coordination. , 1996, Physical review. B, Condensed matter.

[70]  G. Cerullo,et al.  Nonlinear mirror mode locking of a cw Nd:YLF laser. , 1994, Optics letters.

[71]  Rasmussen,et al.  Formation of stable solitons in quadratic nonlinear media. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[72]  Vittorio Degiorgio,et al.  Induced ‘third-order’ nonlinearity via cascaded second-order effects in organic crystals of MBA-NP , 1994 .

[73]  Pascal Baldi,et al.  Intensity dependent mode competition in second harmonic generation in multimode waveguides , 1995 .

[74]  G. Stegeman,et al.  Self-focusing and self-defocusing by cascaded second-order effects in KTP. , 1992, Optics letters.

[75]  J. Jethwa,et al.  A new mode-locking technique using a nonlinear mirror , 1988 .

[76]  C. Flytzanis,et al.  Infrared dispersion of third-order susceptibilities in dielectrics: Retardation effects , 1976 .

[77]  K. Stankov,et al.  A mirror with an intensity-dependent reflection coefficient , 1988 .

[78]  Peter Unsbo.  Phase conjugation by cascaded second-order nonlinear-optical processes , 1995 .

[79]  K. Stankov,et al.  Compensation of group-velocity mismatch in the frequency-doubling modelocker , 1992 .

[80]  Marko Zgonik,et al.  second- and third-order optical nonlinearities in ABO3 compounds measured in fast four-wave mixing experiments , 1992 .

[81]  Stegeman,et al.  One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[82]  Kivshar.  Gap solitons due to cascading. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[83]  Kang,et al.  Observation of Manakov spatial solitons in AlGaAs planar waveguides. , 1996, Physical review letters.

[84]  G I Stegeman,et al.  Interaction of one-dimensional bright solitary waves in quadratic media. , 1995, Optics letters.

[85]  A Kobyakov,et al.  Analytical approach to all-optical modulation by cascading. , 1995, Optics letters.

[86]  Z. Y. Ou.  Observation of nonlinear phase shift in CW harmonic generation , 1996 .

[87]  G. Cerullo,et al.  Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities. , 1995, Optics letters.

[88]  David J. Hagan,et al.  Phase-insensitive, Single wavelength, All-Optical transistor Based on second-Order nonlinearities , 1996 .

[89]  L. Torner,et al.  Two-dimensional solitons with second-order nonlinearities. , 1995, Optics letters.

[90]  Gijsbertus J.M. Krijnen,et al.  All‐optical integrated Mach–Zehnder switching due to cascaded nonlinearities , 1996 .

[91]  A. Piskarskas,et al.  Generation of femtosecond pulses through second-harmonic compression of the output of a Nd:YAG laser. , 1995, Optics letters.

[92]  J. Barr.  Numerical simulation of a modelocked laser with an intracavity nonlinear mirror based on second harmonic generation , 1991 .

[93]  H. Eichler,et al.  Spectroscopic and laser properties of Er3+-doped monoclinic BaY2F8 single crystals , 1990 .

[94]  A. Barthélémy,et al.  All-optical transistor action by polarisation rotation during type-II phase-matched second harmonic generation , 1995 .

[95]  Wang,et al.  Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[96]  Koshiba,et al.  Dark solitons generated by second-order parametric interactions. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[97]  Luigi A. Lugiato,et al.  Observation of bistability and delayed bifurcation in a triply resonant optical parametric oscillator , 1995 .

[98]  Mihalache,et al.  Walking Solitons in Quadratic Nonlinear Media. , 1996, Physical review letters.

[99]  Günter,et al.  Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect. , 1995, Physical review letters.

[100]  N. Bloembergen,et al.  Interactions between light waves in a nonlinear dielectric , 1962 .

[101]  G I Stegeman,et al.  All-optical switching in a hybrid Mach-Zehnder interferometer as a result of cascaded second-order nonlinearity. , 1995, Optics letters.

[102]  Gerald R. Meredith,et al.  Cascading in optical third-harmonic generation by crystalline quartz , 1981 .

[103]  C. Menyuk,et al.  Stability of solitons in birefringent optical fibers. I: equal propagation amplitudes. , 1987, Optics letters.

[104]  Pelinovsky,et al.  Instability of solitons governed by quadratic nonlinearities. , 1995, Physical review letters.

[105]  Trillo,et al.  Periodical waves, domain walls, and modulational instability in dispersive quadratic nonlinear media. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[106]  S. Trillo,et al.  Modulational instability in second-harmonic generation. , 1995, Optics letters.

[107]  Jean-Claude Diels,et al.  Generation of extended pulse trains of minimum duration by passive negative feedback applied to solid-state Q-switched lasers , 1992 .

[108]  Eli Yablonovitch,et al.  Anisotropic Interference of Three-Wave and Double Two-Wave Frequency Mixing in GaAs , 1972 .

[109]  K. Stankov.  Methods of passive and active mode locking using intracavity optical frequency mixing. , 1989, Optics letters.

[110]  Erich P. Ippen,et al.  Principles of passive mode locking , 1994 .

[111]  M. Karpierz.  Coupled solitons in waveguides with second- and third-order nonlinearities. , 1995, Optics letters.

[112]  Marko Zgonik,et al.  Cascading nonlinearities in optical four-wave mixing , 1996 .

[113]  H A Haus,et al.  Nonlinear Schrödinger equation for optical media with quadratic nonlinearity. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[114]  P. W. Smith,et al.  Observation of spatial optical solitons in a nonlinear glass waveguide. , 1990, Optics letters.

[115]  Partha P Banerjee,et al.  Principles of Nonlinear Optics , 1989 .

[116]  P. St. J. Russell,et al.  All-optical high gain transistor action using second-order nonlinearities , 1993 .

[117]  Xie,et al.  Stability of scalar spatial solitons in cascadable nonlinear media. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[118]  J. Taran,et al.  Pulse distortions in mismatched second harmonic generation , 1972 .

[119]  Zhen-he Zhu,et al.  The fluctuation model of a mode-locked laser using a mirror with intensity-dependent reflection coefficient , 1990 .

[120]  M. Yamashita,et al.  Compression of nonamplified femtosecond pulses using nonlinear organic fibers , 1991 .

[121]  C R Menyuk,et al.  Excitation of solitons with cascaded chi((2)) nonlinearities. , 1994, Optics letters.

[122]  George I. Stegeman,et al.  All-optical waveguide switching , 1990 .

[123]  K. Stankov.  Negative feedback using a nonlinear mirror for the generation of a long train of short light pulses , 1991 .

[124]  R. Schiek,et al.  Nonlinear refraction caused by cascaded second-order nonlinearity in optical waveguide structures , 1993 .

[125]  D. Kaup.  The solution of the general initial value problem for the full three dimensional three-wave resonant interaction , 1981 .

[126]  G. Gallot,et al.  Cascaded second-order effects in the femtosecond regime in beta-barium borate: self-compression in a visible femtosecond optical parametric oscillator. , 1995, Optics letters.

[127]  Peter D. Drummond,et al.  Simulton solutions for the parametric amplifier , 1993 .

[128]  V. Petrov,et al.  Theory of active-passive mode-locking of solid-state lasers using a nonlinear mirror , 1990 .

[129]  Partha P. Banerjee,et al.  Self-phase Modulation in Quadratically Nonlinear Media , 1993 .

[130]  J. Barr.  Modelocking using mirrors with intensity dependent reflection coefficients , 1989 .

[131]  L. Kador.  Kramers-Kronig Relations in Nonlinear Optics , 1995 .

[132]  V. Kubeček,et al.  Mode locking of a Nd:YAlO/sub 3/ laser at 1.08 and 1.34 mu m wavelengths using a single LiIO/sub 3/ crystal , 1991 .

[133]  M. Yamashita,et al.  Femtosecond-response, highly third-order nonlinear 4-(N, N-dimethylamino)-3-acetamidonitrobenzene crystal cored fiber , 1990 .

[134]  Alexander M. Rubenchik,et al.  Soliton stability in plasmas and hydrodynamics , 1986 .

[135]  K. Stankov,et al.  Frequency-domain analysis of the mode-locking process in a laser with a second-harmonic nonlinear mirror. , 1991, Optics letters.

[136]  Drummond,et al.  Simultaneous solitary-wave solutions in a nonlinear parametric waveguide. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[137]  Mansoor Sheik-Bahae,et al.  Coherent interactions for all-optical signal processing via quadratic nonlinearities , 1995 .

[138]  Giuseppe Leo,et al.  VERSATILE BISTABLE GATE BASED ON QUADRATIC CASCADING IN A BRAGG PERIODIC STRUCTURE , 1996 .

[139]  T. Carruthers,et al.  Passive laser mode locking with an antiresonant nonlinear mirror. , 1990, Optics letters.

[140]  A. L. Belostotsky,et al.  Nonlinear phase change in type II second-harmonic generation under exact phase-matched conditions. , 1994, Optics letters.

[141]  L. Torner,et al.  Beam steering by chi((2)) trapping. , 1995, Optics letters.

[142]  A. Buryak,et al.  Elliptically polarised solitons in birefringent optical fibers , 1994 .

[143]  L. Torner,et al.  Stationary trapping of light beams in bulk second-order nonlinear media , 1995 .

[144]  David J. Williams,et al.  Introduction to Nonlinear Optical Effects in Molecules and Polymers , 1991 .

[145]  Raymond Y. Chiao,et al.  Self - modulation of picosecond pulses in electro - optic crystals , 1970 .

[146]  V. Kubeček,et al.  Mode locking of a Nd:YAlO(3) laser at the 1.34-microm transition by a second-harmonic nonlinear mirror. , 1991, Optics letters.

[147]  Buryak,et al.  Twin-hole dark solitons. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[148]  Robert C. Eckardt,et al.  Phase matching limitations of high efficiency second harmonic generation , 1984 .

[149]  A. Reiman,et al.  Space-time evolution of nonlinear three-wave interactions. II. Interaction in an inhomogeneous medium , 1979 .

[150]  L. Torner,et al.  Stability of spatial solitary waves in quadratic media. , 1995, Optics letters.

[151]  G. Assanto.  Transistor action through nonlinear cascading in Type II interactions. , 1995, Optics letters.

[152]  S Trillo,et al.  All-optical processing by means of vectorial interactions in second-order cascading: novel approaches. , 1994, Optics letters.

[153]  Modulational stability in dispersive optical systems with cascaded nonlinearity , 1996 .

[154]  Peter Günter,et al.  Electro-optic effects in molecular crystals , 1993 .

[155]  Stationary solitary waves with second-order nonlinearities☆ , 1995 .

[156]  P Di Trapani,et al.  Self-diffraction through cascaded second-order frequency-mixing effects in Beta-barium borate. , 1993, Optics letters.

[157]  David J. Hagan,et al.  All‐optical modulation via nonlinear cascading in type II second‐harmonic generation , 1995 .

[158]  E Popov,et al.  Second-harmonic-generation-induced optical bistability in prism or grating couplers. , 1995, Optics letters.

[159]  Myoungsik Cha,et al.  Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm , 1994 .

[160]  L. Torner,et al.  Soliton excitation and mutual locking of light beams in bulk quadratic nonlinear crystals , 1996 .

[161]  G I Stegeman,et al.  Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium. , 1995, Optics letters.

[162]  Mario Bertolotti,et al.  All-optical switching via second harmonic generation in a nonlinearly asymmetric directional coupler , 1994 .

[163]  J. Boyd,et al.  Wideband CO2 Laser Second Harmonic Generation Phase Matched in GaAs Thin‐Film Waveguides , 1971 .

[164]  Kuipers,et al.  Phase modulation in second-order nonlinear-optical processes. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[165]  Y. Kivshar,et al.  Dark solitons in dispersive quadratic media. , 1995, Optics letters.

[166]  Mansoor Sheik-Bahae,et al.  all optical switching devices based on large nonlinear phase shifts from second harmonic generation , 1993 .

[167]  J. Stewart Aitchison,et al.  Mixed-mode spatial solitons in semiconductor waveguides , 1997 .

[168]  D. W. Hughes,et al.  Coupled cavity modelocking of a Nd:YAG laser using second-harmonic generation , 1989 .

[169]  Akhmediev,et al.  Stationary solitonlike pulses in birefringent optical fibers. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[170]  George I. Stegeman,et al.  All‐optical switching by spatial walkoff compensation and solitary‐wave locking , 1996 .

[171]  G I Stegeman,et al.  All-optical switching in lithium niobate directional couplers with cascaded nonlinearity. , 1996, Optics letters.