Kerr-type Nonlinear Media Research Articles

Nonlinear TE-polarized SPPs on a graphene cladded parallel plate waveguide

We consider the transverse electric (TE) surface plasmon polaritons (SPPs) supported by a graphene parallel plate waveguide bounded by Kerr-type nonlinear media in the mid-infrared and terahertz frequencies. Through theoretical analysis of the exact dispersion relations, we reveal the existence conditions of the even mode and odd mode of nonlinear TE SPPs in this system. To be specific, if the linear permittivity of the nonlinear cladding is larger than the permittivity of the core, it only supports the even mode and two branches of the dispersion curve exist. However, when the linear permittivity of the nonlinear cladding is smaller than the permittivity of the core, both even and odd modes can be supported. Moreover, it is found that the propagation constant of even and odd modes decreases with the increasing Fermi energy of graphene.

Coupled soliton−breather, breather−breather and breather−soliton pair formation in Kerr type nonlinear media

Abstract In this paper, we have investigated coupled propagation of two coaxially co-propagating and mutually incoherent bright beams in Kerr type nonlinear media, including formation of rhythmic breather pairs. We have proposed existence lines for these rhythmic breather pairs. Moreover, we have also provided a detailed explanation of coupled soliton−breather, breather−breather and breather−soliton pair formation in the parameter space of beam power and beam width ratio. Finally, a law of formation of coupled rhythmic breather pairs has been proposed.

3D wave-packet propagation in inhomogeneous and nonlinear media of Kerr type

Complex geometrical optics (CGO) is applied to spatiotemporal evolution of 3D Gaussian wave packets in nonlinear media of Kerr type. We propose ordinary differential equations (ODEs) for wave packet parameters, which can be derived immediately from the complex eikonal equation and the complex transport equation. The eikonal equation can be used to derive ordinary differential equations for spatial and temporal widths, omitting the complicated variational process used in nonlinear optics. For the combined effect of diffraction, anomalous dispersion and nonlinear refraction we observe two solutions for temporal and spatial widths of the packet propagating in a nonlinear medium of Kerr type: diffraction/dispersion widening and spatiotemporal collapse. Moreover, we discuss the evolution of a 3D Gaussian wave packet in nonlinear inhomogeneous fiber and we present conditions for stable propagation without the collapse effect. We also discuss the influence of initial spatial and temporal chirps on 3D Gaussian wave packet evolution in nonlinear media of Kerr type and in nonlinear inhomogeneous fibers. We demonstrate the ability of CGO method to describe the evolution of a 3D wave packet in a nonlinear dispersive and strongly nonlocal medium, including the existence of a new type of spatiotemporal Gaussian soliton: an accessible spatiotemporal soliton. Moreover, the CGO method is applied to solve a novel problem of the interaction of a pair of 3D Gaussian wave packets in a nonlinear medium of Kerr type.

Mixed solitons in a (2+1)-dimensional multicomponent long-wave-short-wave system.

We derive a (2+1)-dimensional multicomponent long-wave-short-wave resonance interaction (LSRI) system as the evolution equation for propagation of N-dispersive waves in weak Kerr-type nonlinear medium in the small-amplitude limit. The mixed- (bright-dark) type soliton solutions of a particular (2+1)-dimensional multicomponent LSRI system, deduced from the general multicomponent higher-dimensional LSRI system, are obtained by applying the Hirota's bilinearization method. Particularly, we show that the solitons in the LSRI system with two short-wave components behave like scalar solitons. We point out that for an N-component LSRI system with N>3, if the bright solitons appear in at least two components, interesting collision behavior takes place, resulting in energy exchange among the bright solitons. However, the dark solitons undergo standard elastic collision accompanied by a position shift and a phase shift. Our analysis on the mixed bound solitons shows that the additional degree of freedom which arises due to the higher-dimensional nature of the system results in a wide range of parameters for which the soliton collision can take place.

Nonlinear all-optical WDM based on spatial solitons in optical communication spectral regions

A new design of nonlinear all-optical wavelength division multiplexer (WDM) based on spatial solitons in optical communication spectral regions was proposed. By using the swing effect of spatial solitons in a Kerr-type nonlinear medium, the proposed nonlinear waveguide structure could function as an all-optical WDM. The numerical results show that the transmission efficiency is higher than 94%. The device separates spatial solitons interaction in a Kerr-type nonlinear medium and can be used in WDM networks with fixed-tuned receiver and tunable transmitter. It would be a potential key component in the applications of ultra-high-speed and ultra-high-capacity optical communications and optical data processing systems.

Surface plasmons of a graphene parallel plate waveguide bounded by Kerr-type nonlinear media

The exact dispersion relations of the transverse magnetic surface plasmons (SPs) supported by a graphene parallel plate waveguide (PPWG), surrounded on one or both sides by Kerr-type nonlinear media, are obtained analytically. It is shown that if self-focusing nonlinear materials are chosen as the surrounding media, the SPs localization length (LL) is decreased, while their propagation length (PL) remains unchanged, as compared to those of a typical graphene PPWG. Moreover, PL and LL of the SPs are considerably affected by adjusting nonlinear parts of the dielectric permittivities of the nonlinear media. It is found that using an appropriate defocusing nonlinear material as a substrate of the graphene PPWG, which is surrounded on one side by the nonlinear medium, leads to noticeable enhancement of the propagation and localization characteristics of the surface plasmons. The results presented here can be useful for enhancing capabilities of plasmonic devices based on the graphene PPWG for sensing and waveguide applications.

Elliptical Gaussian beam propagation in inhomogeneous and nonlinear fibres of Kerr type

In this paper complex geometrical optics (CGO) is applied for the evolution of elliptical Gaussian beam (GB) propagating in nonlinear media of Kerr type. Instead of solving commonly accepted Nonlinear Schrodinger Equation, we propose equations of geometrical optics: complex eikonal equation and complex transport equation. Eikonal equation let us derive immediately the ordinary differential equations for principle widths omitting this way complicated variational process used in nonlinear optics. From the transport equation we obtain first order ordinary differential equation for complex amplitude evolution and conservation principle for energy flux in the GB cross-section. We prove in this paper that principle curvatures of the wave front can introduce into the description the additional ellipticity of the beam, which can effectively limit collapse effect. Moreover, we discus the evolution of elliptical Gaussian beam in nonlinear inhomogeneous fibre and we present conditions for stable propagation in the region without collapse effect. Under these conditions GB approaches asymptotically to stationary solutions when parameters of the fibre changes along propagation distance. We discus in this paper also the influence of initial wave front curvatures on Gaussian beam evolution in nonlinear medium of Kerr type and in nonlinear inhomogeneous fibre. We demonstrate high ability and effectively of CGO method as compared with commonly accepted methods of nonlinear optics such as variational method approach and method of moments. Moreover, we compare obtained results with solutions of Nonlinear Schrodinger Equation for ordinary and rotating elliptical beam propagating in nonlinear medium of Kerr type.

Spatiotemporal complex geometrical optics for wavepacket evolution in inhomogeneous and nonlinear media of Kerr type

In this paper complex geometrical optics (CGO) is applied to spatiotemporal evolution of 2D Gaussian wavepackets in nonlinear media of Kerr type. Instead of solving the commonly accepted nonlinear Schrödinger equation (NLS), we propose equations of geometrical optics: a complex eikonal equation and a complex transport equation. The eikonal equation lets us derive immediately the ordinary differential equations for spatial and temporal widths, omitting in this way the complicated variational process used in nonlinear optics. Moreover, the obtained CGO equations for actual spatial and temporal widths happen to be identical to those obtained by the variational method approach. From the transport equation we obtain the first order ordinary differential equation for complex amplitude evolution and the conservation principle for energy flux in the packet cross-section. For the combined effect of diffraction, anomalous dispersion and nonlinear refraction, we observe three types of solution for temporal and spatial widths of the packet propagating in a nonlinear medium of Kerr type: the diffraction/dispersion widening, the stationary solution and the solution under the effect of the spatiotemporal collapse. Moreover, we discuss the evolution of the 2D Gaussian wavepacket in a nonlinear inhomogeneous waveguide and we present conditions for stable propagation without the collapse effect. Under these conditions the wavepacket asymptotically approaches stationary solutions when the parameters of the waveguide change over the propagation distance. The paper also discusses the influence of initial spatial and temporal chirps on Gaussian wavepacket evolution in nonlinear media of Kerr type and in nonlinear inhomogeneous waveguides. Moreover, we notice that the equations for temporal and spatial widths of the 2D wavepacket have the same structure as the equations for the evolution of the elliptical Gaussian beam. Thus, the description of the 2D spatiotemporal wavepacket can be inspired by the properties of the elliptical GB, which is the essential conclusion of the paper.

Gaussian beam evolution in nonlinear media of Kerr type

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. PCGO deals with ordinary differential equations for the beam amplitude and for complex curvature of the wave front which describe evolution of axially symmetric GB in Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in medium of Kerr type. Full Text: PDF References Yu. A. Kravtsov, "Complex rays and complex caustics", Radiophys. Quantum Electronics 10, 719−730 (1967). CrossRef J. B. Keller and W. Streifer, "Complex rays with application to Gaussian beams", J. Opt. Soc. Am. 61, 40−43 (1971) CrossRef G. A. Deschamps, "Gaussian beam as a bundle of complex rays", Electron. Lett. 7(23), 684−685 (1971). CrossRef Yu. A. Kravtsov, G.W. Forbes, and A.A. Asatryan, "Theory and applications of complex rays", in Progress in Optics, edited by E.Wolf, 39, 1−62 (Elsevier, Amsterdam, 1999). CrossRef S. J. Chapman, J.M. Lawry, J.R. Ockendon, and R.H. Tew, "On the theory of complex rays", SIAM Review 41, 417−509 (1999). CrossRef Yu. A. Kravtsov, P. Berczynski, "Gaussian beams in inhomogeneous media: a review", Stud. Geophys. Geod. 51(1), 1-36 (2007). CrossRef Yu. A. Kravtsov, "Geometrical Optics in Engineering Physics", Alpha Science International, UK (2005) S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, "Self-focusing and light diffraction in nonlinear medium", Soviet Phys. Uspekhi 10, 609-636 (1968). CrossRef S. A. Akhmanov, R.V. Khokhlov, and A. P. Sukhorukov, "Self-focusing, Self-defocusing and Self-modulation of Laser Beams", in Laser Handbook, F.T.Arecchi and E.O. Shulz-Dubois, Eds. (Elsevier, New York, 1972), Vol. 2, 1151-1228.6 S303 (2004). P. Berczyński, Yu. Kravtsov, "Gaussian beam evolution in nonlinear inhomogeneous fibres", Photonics Letters of Poland, Vol 4, No 1, 26-28 (2012). CrossRef

Beam steering using optical parametric amplification in Kerr medium: a space-time analogy of parametric slow-light

In a way analogous to a light pulse that can be optically delayed via slow light propagation in Kerr-type nonlinear media, we theoretically demonstrate that beam steering and spatial walk-off compensation can be achieved in noncollinear optical parametric amplification. We identify this effect as a result of the quadratic phase shift induced by parametric amplification that leads to the cancellation of the spatial walk-off and collinear propagation of all beams though they have different wavevectors. Experimental evidence is reported of a soliton array steering in a Kerr slab waveguide.

The existence of solutions for the problem in the optical lattice with nonlocal nonlinearity

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discuss the solitons solution for a class of nonlinear Schrodinger equations in the optical lattice with nonlocal nonlinearity. We also show via a uniform priori estimate that existence and uniqueness of the global solution for the initial problem.

Surface plasmons at the interface between graphene and Kerr-type nonlinear media

The properties of surface plasmons localized at the interface between graphene and Kerr-type nonlinear substrates are investigated analytically. Although the relative propagation distance remains the same, the dispersion of graphene plasmons may be affected much by the inevitable nonlinear effect of substrates. Specifically, the wavelength of graphene plasmons can be tuned by adjusting the nonlinear permittivity of substrates.

Optical surface TM-waves at the boundary of a nonlinear Kerr-type medium

Solutions for a nonlinear system of Maxwell’s equations and for a corresponding boundary problem describing the propagation of a surface TM-wave (p-polarization) along an interface with an optically nonlinear Kerr-type medium are presented. An analytical expression for the intensity of an integrated flux J0 carried by such a wave along the interface between two media has been derived as a function of both the wave propagation constant ξ and the optical characteristics of the adjacent media. It is shown that flux intensities corresponding to the same values of the propagation constant ξ are much smaller for p-polarization than for s-polarization.

Simulation and Analysis of Multisoliton Generation Using a PANDA Ring Resonator System

A novel system of multisoliton generation using nonlinear equations of the propagating signals is presented. This system uses a PANDA ring resonator incorporated with an add/drop filter system. Using resonant conditions, the intense optical fields known as multisolitons can be generated and propagated within a Kerr-type nonlinear medium. The present simulation results show that multisolitons can be controlled by using additional Gaussian pulses input into the add port of the PANDA system. For the soliton pulse in the microring device, a balance should be achieved between dispersion and nonlinear lengths. Chaotic output signals from the PANDA ring resonator are input into the add/drop filter system. Chaotic signals can be filtered by using the add/drop filter system, in which multi dark and bright solitons can be generated. In this work multi dark and bright solitons with an FWHM and an FSR of 425pm and 1.145 nm are generated, respectively, where the Gaussian pulse with a central wavelength of 1.55 μm and power of 600 mW is input into the system.

Multi Soliton Generation for Enhance Optical Communication

We propose a new optical system that can be used to form the multi-soliton pulses within the micro-ring resonators. The system consists of two micro-ring resonators and an add/drop multiplexer that can be integrated into a single system. The large bandwidth signal is generated by using a soliton pulse propagating in a Kerr-type nonlinear medium. The tuned soliton pulses in either spatial or temporal modes are obtained by using the add/drop multiplexer. Results show the generation of multi-soliton pulses within the micro-ring resonator can be achieved for long distance communication. This results in an increase in the number of channels and spaces with a large free spectrum range (FSR) of 650 pm for dense wavelength division multiplexing (DWDM).

Multicomponent coherently coupled and incoherently coupled solitons and their collisions

We consider the integrable multicomponent coherently coupled nonlinear Schrödinger (CCNLS) equations describing simultaneous propagation of multiple fields in Kerr-type nonlinear media. The correct bilinear equations of m-CCNLS equations are obtained using a non-standard type of Hirota's bilinearization method, and the more general bright one solitons with single-hump and double-hump profiles including special flat-top profiles are obtained. The solitons are classified as coherently coupled solitons and incoherently coupled solitons depending upon the presence and absence of coherent nonlinearity arising due to the existence of the co-propagating modes/components. Further, the more general two-soliton solutions are obtained using this non-standard bilinearization approach, and various fascinating collision dynamics are pointed out. Particularly, we demonstrate that the collision between coherently coupled solitons and incoherently coupled solitons displays a non-trivial behaviour in which the former always undergoes energy switching accompanied by an amplitude-dependent phase-shift and change in the relative separation distance, leaving the latter unaltered. But the collision between coherently coupled solitons alone is found to be a standard elastic collision. Our study also reveals the important fact that the collision between incoherently coupled solitons arising in the m-CCNLS system with m = 2 is always elastic, whereas for m > 2 the collision becomes intricate, and for this case the m-CCNLS system exhibits interesting energy-sharing collision of solitons characterized by intensity redistribution, amplitude-dependent phase-shift and change in relative separation distance, which is similar to that of the multicomponent Manakov soliton collisions. This suggests that the m-CCNLS system can also be a suitable candidate for soliton collision-based optical computing in addition to the Manakov system.

Switching behavior of a nonlinear Mach–Zehnder interferometer: Saturating nonlinearity

This paper uses the Beam Propagation Method to investigate numerically the switching behavior of a Nonlinear Mach–Zehnder Interferometer (NMZI). A saturating-type nonlinearity has been considered for the present investigations. It is shown that the input versus output characteristics change drastically when a Kerr type nonlinear medium is replaced by a saturating type nonlinear medium. In contrast to an NMZI with Kerr nonlinearity, where only quantitative behavior changes with NMZI length, quantitative as well as qualitative behaviors change in the case of a saturating nonlinearity. We propose an all-optical stabilizer and MZI with stable “ON” and “OFF” states on the basis of our investigation.

Analytical Treatment of Parametric Effects in a Ring Resonator

We propose two systems of a nano-waveguide to study the effects of ring resonator radii and coupling coefficient. The first proposed system is introduced as a single ring resonator. The change of the center wavelength from the output signal is monitored and analyzed. It shifts towards higher wavelength of the spectrum. The multistage ring resonator system consists of two micro and a nano ring resonators that can be integrated into a single system. The soliton pulse propagating within a Kerr type nonlinear medium is used to generate the large bandwidth signals. By using the suitable parameters, for instance, the input power of soliton, coupling coefficients, and ring radii, the short-wave and millimetre-wave output signals can simultaneously be generated in a multi-stage ring resonator (MMRR). We found that by using the MMRR, a desired response can be achieved over a broader portion of the spectrum compared to the single-stage ring resonator (SMRR) in which it is more preferable in applications.

Radio Wave Generation Using Dark and Bright Soliton

In this study we propose a new system for radio wave using a soliton pulse within a micro waveguide and nano-waveguide. The system consists of two micro ring resonators and a nano ring resonator that can be integrated into a single system. The input soliton power, coupling coefficients, and ring radii, are used to control the short-wave and millimeter-wave output signals being generated and filtered in a single system. The large bandwidth signal is generated using a soliton pulse within a Kerr-type nonlinear medium. The signals with broad bandwidth or wavelength can then be generated. Results obtained have shown the potential of using this system for a broad light spectra generation.

White light generation and amplification using a soliton pulse within a nano-waveguide for the potential of solar energy conversion use

We propose a novel system of a nano-waveguide that can be used to generate the continuous optical spectra, i.e. white light. A system consists of two micro and a nanoring resonators that can be integrated into a single system. The large bandwidth signal is generated by using a soliton pulse propagating within a Kerr type nonlinear medium, whereas the continuous bandwidth or wavelength of light signal can be performed. Results obtained have shown the potential of using such system for white light source generation and amplification, which is discussed in detail. The amplified pulse can be stored within a nano-waveguide, which is allowed to form the continuous spectrum after amplification. Alternatively, the low level solar radiation can be amplified, and the bandwidth signals can also be enlarged.