Nonlinear Channel Waveguides Research Articles

Squeezed states generation in an array of Linear and Nonlinear Waveguides

We demonstrate the generation of squeezed states of light due to the second harmonic generation and Kerr effect in an array of nonlinear waveguides mediated through a linear one. We characterized the electromagnetic field by a quantum mechanical Hamiltonian and the density operator time evolution is obtained from the Von-Neumann equation of motion. Using the quasiprobability positive P of phase space representation, the classical Fokker-Planck equation is obtained from the master equation and translated to its classical matching set of nonlinear differential equations. We showed that because of the new possibilities of correlation between the linear and nonlinear channel waveguides, highly nonclassical light may be produced.

Thermo-optically tunable spectral broadening in a nonlinear ultra-silicon-rich nitride Bragg grating

Spectral tunability methods used in optical communications and signal processing leveraging optical, electrical, and acousto-optic effects typically involve spectral truncation that results in energy loss. Here we demonstrate temperature tunable spectral broadening using a nonlinear ultra-silicon-rich nitride device consisting of a 3-mm-long cladding-modulated Bragg grating and a 7-mm-long nonlinear channel waveguide. By operating at frequencies close to the grating band edge, in an apodized Bragg grating, we access strong grating-induced dispersion while maintaining low losses and high transmissivity. We further exploit the redshift in the Bragg grating stopband due to the thermo-optic effect to achieve tunable dispersion, leading to varying degrees of soliton-effect compression and self-phase-modulation-induced spectral broadening. We observe an increase in the bandwidth of the output pulse spectrum from 69 to 106 nm as temperature decreases from 70°C to 25°C, in good agreement with simulated results using the generalized nonlinear Schrödinger equation. The demonstrated approach provides a new avenue to achieve on-chip laser spectral tuning without loss in pulse energy.

Design of dispersion-engineered As2Se3 channel waveguide for mid-infrared region supercontinuum generation

In recent years, low cost and scalable integrated optics compatible planar waveguides have emerged for an ultrabroadband supercontinuum generation between ultraviolet and mid-infrared region applications. A 20-mm-long integrated photonics compatible highly nonlinear As2Se3 channel waveguide, which exhibited wider as well as lower magnitude and nearly flat anomalous dispersion region, designed and modeled by employing GeAsSe glass for its upper and lower claddings. Using pump source at 6 μm with a pulse duration of 170-fs, an ultrabroadband long wavelength region supercontinuum broadening covering the wavelength from 3.5 μm to 15 μm could be predicted with the largest input peak power of 10 kW. Increasing the power further to 20 kW does not enhance the supercontinuum expansion noticeably beyond 15 μm. This numerical demonstration could be the longest supercontinuum generation by an on-chip integrated photonics compatible planar waveguide which can be used for a variety of mid-infrared region applications.

Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide

We theoretically investigate the dispersion relation of small-amplitude optical waves superimposing upon a beam of polarized monochromatic light propagating along a single-mode channel waveguide characterized by an instantaneous and spatially local Kerr nonlinearity. These small luminous fluctuations propagate along the waveguide as Bogoliubov elementary excitations on top of a one-dimensional dilute Bose quantum fluid evolve in time. They consequently display a strongly renormalized dispersion law, of Bogoliubov type. Analytical and numerical results are found in both the absence and the presence of one- and two-photon losses. Silicon and silicon-nitride waveguides are used as examples. We finally propose an experiment to measure this Bogoliubov dispersion relation, based on a stimulated four-wave mixing and interference spectroscopy techniques.

Scheme for on-chip verification of transverse mode entanglement using the electro-optic effect.

A key ingredient in emerging quantum-enhanced technologies is the ability to coherently manipulate and detect superpositions of basis states. In integrated optics implementations, transverse spatial modes supported by multimode structures offer an attractive carrier of quantum superpositions. Here we propose an integrated dynamic mode converter based on the electro-optic effect in nonlinear channel waveguides for deterministic transformations between mutually non-orthogonal bases of spatial modes. We theoretically show its capability to demonstrate a violation of a Bell-type Clauser-Horne-Shimony-Holt inequality by measuring spatially mode-entangled photon pairs generated by an integrated photon pair source. The proposed configuration, numerically studied for the potassium titanyl phosphate (KTP) material, can be easily implemented using standard integrated optical fabrication technology.

All-optical intensity modulation of near infrared light in a liquid crystal channel waveguide

We demonstrate a nonlinear optical channel waveguide made of E7 nematic liquid crystal infiltrated in a silica on silicon groove. Near infrared light at the wavelength of 1560 nm fiber coupled to the core of the liquid crystal waveguide was optically modulated by an optical beam with power below 25 mW by exploiting the optical Freedericks transition. By modeling the optical molecular reorientation in the nematic liquid crystal confined in a waveguiding geometry we are able to reproduce the experimental results.

Self-phase modulation at visible wavelengths in nonlinear ZnO channel waveguides

We report the observation of nonlinear optical effects in the visible spectrum using ZnO channel waveguides. We demonstrate sixfold spectral broadening and a 2π phase shift due to self-phase modulation in ZnO channel waveguides using femtosecond optical pulses with a center wavelength of 840 nm. We measured a value for the nonlinear parameter γ of 13.9±3.0 W−1 m−1, which is more than 1300 times that of a highly nonlinear fiber. The calculated intensity-dependent refractive index is found to be consistent with previously reported values of bulk single-crystal ZnO.

All-optical logic gates based on nonlinear slot-waveguide couplers

A novel design of all-optical logic gates based on nonlinear slot-waveguide couplers is proposed. NOT, OR, and AND logic gates can be realized by a simple single optical-directional coupler configuration. Strong polarization dependencies of slot waveguides are effectively utilized for realizing polarization-independent optical-directional couplers in the linear regime and polarization-dependent all-optical switches in the nonlinear regime. All the simulations performed in this paper were performed for three-dimensional nonlinear channel waveguide structures by using rigorous numerical schemes based on the full-vector finite-element method specially formulated for nonlinear optical waveguides.

Optical bistability in nonlinear waveguides with photonic crystals

AbstractA new way to reduce the critical power of the bistable behavior in nonlinear optical waveguides is presented. This is achieved by embedding circular photonic crystals (PCs), satisfying the Bragg condition, along a channel waveguide. Three different schemes are analyzed: PCs in the core region only, PCs in the cladding region only, and a partial fulfillment of the core with PCs. All cases presented a decreasing of the critical or threshold power. Our numerical simulations, using the finite‐element method, show the possibility to reduce up to three times the critical power, as compared to a conventional nonlinear channel waveguide. Threshold powers as low as 30 μW can be achieved. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 41: 40–43, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20040

Red, green, and blue simultaneous generation in aperiodically poled Zn-diffused LiNbO3:Er3+/Yb3+ nonlinear channel waveguides

In this work, continuous-wave broadly tunable simultaneous generation of red (650–690 nm), green (520–575 nm), and blue (425–495 nm) light in aperiodically poled Zn-diffused LiNbO3:Er3+/Yb3+ channel waveguides is reported after Ti:sapphire excitation in the 850–990 nm range. The red and green emissions arise from energy transfer and upconversion mechanisms between Yb3+ and Er3+ ions, while the blue light with a maximum efficiency of 0.04% W−1 cm−1 is produced by quasi-phase matching processes.

Blue Light by SHG in Diode Pumped LiNbO3 Waveguides

In this work, second harmonic generation (SHG) in nonlinear channel waveguides by quasi phase matching is reported. The photorefractive damage resistant waveguides were fabricated by Zn-diffusion technique using periodic poled lithium niobate wafers (PPLN). The SH wave, at 397.8 nm, was generated by using a CW diode laser with emission wavelength at 795.6 nm and 1 W peak power was used as fundamental wave. The nonlinear waveguides exhibit a stable conversion even at room temperature with no sign of deterioration induced by the optical damage.

All-optical diode based on second-harmonic generation in an asymmetric waveguide

We numerically investigate the response of a quadratically nonlinear channel waveguide for second-harmonic generation, in which the insertion of a localized phase discontinuity allows the simple implementation of directional nonreciprocity in the fundamental-frequency transmission.

A novel quasi-phase-matching frequency doubling technique

A new quasi-phase-matching technique for efficient second-harmonic generation is reported. It is based on the spatial periodic modulation of the light intensity along the propagation direction, rather than the conventional spatial periodic modulation of the nonlinear optical coefficients. It can be realized by using a novel dual-channel waveguide frequency doubler structure for the desired light intensity distribution. This dual-channel waveguide device has major advantages including very small beam size, high light intensity within long nonlinear-waveguide interaction length, highly efficient second-harmonic generation, ease in fabrication of the nonlinear channel waveguides without any spatially periodic poling, and low waveguide propagation losses. The new quasi-phase-matching technique can also be applied to third-harmonic generation and other nonlinear optics processes.

Combined Ion-Beam and Laser-Beam Synthesis of Silver Oxide Nanoclusters in Soda-Lime Glass

AbstractIon beam deposition offers a number of interesting possibilities for creating nonlinear materials for photonic devices such as waveguides. Ion beams have been used by a number of groups to create metal and semiconductor nanocrystallites in silica and other glassy substrates in a geometry suitable for shallow channel waveguides. In this paper, we describe the use of He ion beams to initiate nucleation of Ag nanocrystallites in ion-exchanged soda-lime glass. The nanocrystallites are remarkably uniform in size, and exhibit substantial third-order optical nonlinearity. The combination of ion exchange and ion implantation has an advantage over conventional implantation techniques because it produces guiding layers deep enough (several microns) to form practical channel waveguides. In addition, we have shown that it is possible, by means of subsequent laser irradiation, to further alter the properties of the nonlinear composite material. In this particular case, irradiation by visible or infrared laser beams following ion implantation induces oxidation of the silver nanocrystallites, as documented by Auger analysis of the composite material. Furthermore, the third-order nonlinearity of the composite material changes sign, changing a self-focusing nonlinearity into one which is self-defocusing. These experiments suggest a number of possibilities for combining ion- and laser-beam irradiation to create laterally structured waveguide materials as well as nonlinear channel waveguides.

A scalar finite element analysis of nonlinear optical channel waveguides using isoparametric elements

AbstractWith a view to increasing the efficiency of the scalar finite element for nonlinear optical channel waveguides, triangular isoparametric elements are introduced. In addition, the numerical integration formula by Hammer et al. is used for the integration needed for deriving the element matrix. The numerical analysis is carried out for the nonlinear optical fibers. It is confirmed that accurate solutions can be obtained by the present method with a small‐size calculation. Also, the analysis of a nonlinear graded channel optical waveguide is carried out for the first time. The effect of the refractive index profile of the substrate on the optical power dependence of the effective index of the guided mode is investigated.

Variational analysis of nonlinear channel waveguides

The dynamics of a two-dimensional optical beam propagating in a nonlinear channel waveguide is investigated by means of a variational technique. Through this analysis, one can determine the eigenmodes (self-trapped modes) of the structure. Their stability has also been checked numerically.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An efficient scalar finite element formulation for nonlinear optical channel waveguides

A self-consistent numerical approach based on the scalar finite element method is described for the analysis of both TE-like and TM-like nonlinear guided waves in optical channel waveguides. In order to improve the convergence and accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. Numerical results are presented for nonlinear elliptical core optical fibers, and it is confirmed that in this approach, highly accurate solutions can be obtained with small scale computation. Furthermore, graded-index nonlinear optical channel waveguides are also analyzed, and the influence of refractive-index profiles on propagation characteristics of the nonlinear guided waves is investigated. >

A new method for the calculation of propagation constants and field profiles of guided modes of nonlinear channel waveguides based on the effective index method

In this paper, an extension of the effective index method (EIM) to waveguiding structures containing ideal or saturable third-order nonlinear materials is presented. By applying separation of variables to the dominant field component, the complete problem is subdivided into two scalar problems in the lateral and transverse direction, as in the case of the normal EIM. Making use of the strong transverse confinement, as observed in most real waveguide structures, the nonlinear index changes of the various transverse sections can be lumped into nonlinear effective indexes of the equivalent layered planar structures. By using these nonlinear effective indexes in self-consistent field calculations in the transverse direction, a complete approximate solution is obtained. In this way, the amount of computational effort required for the calculation of the effective indexes and field profiles of the waveguides can be reduced significantly.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simulation of strong nonlinear effects in optical waveguides

Nonlinear optical channel waveguides are modeled. It is demonstrated that a saturable nonlinear permittivity model is essential mathematically when strong nonlinear effects are simulated, so that the nonlinear wave equation possesses realistic solutions. Several precautionary factors in the numerical simulation of self-focusing behavior are addressed. For example, care must be exercised when the threshold power is calculated for some nonlinear structure exhibiting an abrupt all-optical switching phenomenon.

Time-resolved characteristics of nonlinear whispering-gallery modes along optical channel waveguides: competition between spontaneous and induced symmetry-breaking transitions and their frustration

Numerical results for the time-resolved characteristics of stationary pulsed beams that propagate in Kerr-like nonlinear channel waveguides bent with a uniform radius of curvature are reported for what is to our knowledge the first time. Some interesting phenomena, relevant to the intrapulse switching between an ordinary guided mode and a solitonlike mode (a nonlinear whispering-gallery mode) and to competition between the spontaneous and the induced symmetry-breaking transitions, are observed and discussed.