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N. - C. Panoiu, R. M. Osgood, Jr., B. A. Malomed
“Semi-discrete composite solitons in arrays of quadratically nonlinear waveguides” Opt. Lett. 31, (2006). We demonstrate that an array of discrete waveguides on a slab substrate, both featuring the χ(2) nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite solitons are identified: ones consisting of a discrete fundamental-frequency (FF) component in the waveguide array, coupled to a continuous second-harmonic (SH) component in the slab waveguide, and solitons with an inverted FF/SH structure. Twisted bound states of the fundamental solitons are found too. In contrast with usual systems, the intersite-centered fundamental solitons and bound states with the twisted continuous components are stable, in an almost entire domain of their existence.
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J. F. McMillan, X. Yang, N. - C. Panoiu, R. M. Osgood, Jr., C. W. Wong
“Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides” Opt. Lett. 31, (2006). We investigate for the first time the enhancement of the stimulated Raman scattering in slow-light Silicon-on-Insulator (SOI) photonic crystal line defect waveguides. By applying the Bloch-Floquet formalism to the guided modes in a planar photonic crystal, we develop a formalism that relates the intensity of the down-shifted Stokes signal to the pump intensity and the modal group velocities. The formalism is then applied to two prospective schemes for enhanced stimulated Raman generation in slow-light photonic crystal waveguides. The results demonstrate a maximum factor of 104 (66,000) enhancement with respect to SOI channel waveguides. Effects of two photon absorption, intrinsic scattering, and disorder with respect to slow-light Raman generation towards optically-pumped silicon amplifiers and lasers are also discussed.
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X. Chen, N. - C. Panoiu, and R. M. Osgood, Jr.
“Theory of Raman-mediated pulsed amplification in silicon-wire waveguides” IEEE J. Quantum Electron. 42, 160 (2006). We present a comprehensive theoretical study of pulsed stimulated Raman scattering in silicon wires. The pulse dynamics is described by a system of coupled equations, which describes intrinsic waveguide optical losses, phase shift and losses due to free-carriers (FCs) generated through two-photon absorption (TPA), first- and second-order frequency dispersion, self-phase and cross-phase modulation, TPA losses, and the interpulse Raman interaction. Furthermore, the influence of the FCs on the pulse dynamics is incorporated through a rate equation. The corresponding system of equations has then been numerically integrated, and phenomena such as noise-seeded Raman amplification, pulsed Raman amplification, and Raman-mediated pulse interaction have been described.
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S. Zhang, W. Fan, N. - C. Panoiu, K. J. Malloy, R. M. Osgood, Jr., and S. R. J. Brueck
“Demonstration of near-infrared negative-index-metamaterials” Phys. Rev. Lett. 95, 137404 (2005). Metal-based negative refractive-index materials have been extensively studied in the microwave region. However, negative-index metamaterials have not been realized at near-IR or visible frequencies due to difficulties of fabrication and to the generally poor optical properties of metals at these wavelengths. In this Letter, we report the first fabrication and experimental verification of a transversely structured metal-dielectric-metal multilayer exhibiting a negative refractive index around 2 μm. Both the amplitude and the phase of the transmission and reflection were measured experimentally, and are in good agreement with a rigorous coupled wave analysis.
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N. - C. Panoiu, R. M. Osgood, Jr., B. A. Malomed, F. Lederer, D. Mazilu, and D. Mihalache
“Parametric light bullets supported by quasi-phase-matched quadratically nonlinear crystals” Phys. Rev. E 71, 036615 (2005). We present a comprehensive analysis of the dynamics of three-dimensional spatiotemporal nonspinning and spinning solitons in quasi-phased-matched (QPM) gratings. By employing an averaging approach based on perturbation theory, we show that the soliton's stability is strongly affected by the QPM-induced third-order nonlinearity (which is always of a mixed type, with opposite signs in front of the corresponding self-phase and cross-phase modulation terms). We study the dependence of the stability of the spatiotemporal soliton (STS) on its energy, spin, the wave-vector mismatch between the fundamental and second harmonics, and the relative strength of the intrinsic quadratic and QPM-induced cubic nonlinearities. In particular, all the spinning solitons are unstable against fragmentation, while zero-spin STS's have their stability regions on the system's parameter space.
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S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. - C. Panoiu, and R. M. Osgood, Jr.
“Near-infrared double negative metamaterials” Opt. Express 13, 4922 (2005). We numerically demonstrate a metamaterial with both negative ε and negative μ over an overlapping near-infrared wavelength range resulting in a low loss negative-index material. Parametric studies optimizing this negative index are presented. This structure can be easily fabricated with standard semiconductor processing techniques.
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M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr.
“Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method” IEEE J. Quantum Electron. 41, 1244 (2005). An approach based on the finite-difference time-domain (FDTD) method is developed for simulating the dynamics of vertical-cavity surface-emitting lasers (VCSELs). The material response is incorporated in our FDTD algorithm by the effective semiconductor Bloch equations, and its effects are accounted for through a resonant polarization term in the Maxwell's equations. Moreover, nonlinear gain saturation is incorporated through a gain suppression factor in the equation governing the dynamics of the resonant polarization. This approach is verified by modeling a λ-cavity VCSEL, with a multiple quantum-well (MQW) gain region; the corresponding continuous-wave operation is obtained at the expected wavelength. The dynamics of ultrashort pulses generated by a monolithic passively mode-locked one-dimensional VCSEL with a MQW gain region and a single QW saturable absorber are studied and it is demonstrated that a stable mode-locked pulse train can be generated. It is also demonstrated that with our FDTD approach subcycle temporal precision can be achieved. The need for this fine temporal resolution is established by investigating pulse propagation through the semiconductor saturable absorber. Fine features of the spatial profile of the mode-locked pulses are also examined within this approach. This knowledge of the fine spatial features is then used for lowering the current threshold through gain structure optimization. Various approaches for the reduction of the total simulation time are also discussed.
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N.-C. Panoiu and R. M. Osgood, Jr.
“Subwavelength nonlinear plasmonic nanowire” Nano Lett. 4, 2427 (2004). We investigate numerically, by means of the finite-difference time-domain method, the propagation characteristics of surface plasmon-polariton (SPP) modes excited in an optical nanowire consisting of a chain of Ag spheres embedded in dielectric shells made of materials with optical Kerr nonlinearity. It is demonstrated that, in the linear limit, the nanowire supports two SPP modes, a transverse and a longitudinal one, separated by Δλ = 20 nm. Furthermore, the dependence of the transmission characteristics of these SPP modes, on both the pulse peak power and Kerr coefficient of the dielectric shell, is investigated. Nonlinear optical phenomena, such as power dependence of mode frequency, switching, or optical limiting, are observed and discussed.
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M. Bahl, H. Rao, N.-C. Panoiu, and R. M. Osgood, Jr.
“Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm” Opt. Lett. 29, 1689 (2004). An approach based on the finite-difference time-domain method is developed for simulating the dynamics of passive mode locking in vertical-cavity surface-emitting lasers (VCSELs). The material response is modeled by the effective semiconductor Bloch equations through a resonant polarization term in the Maxwell's equations. Nonlinear gain saturation is incorporated through a gain compression factor in the equation governing the dynamics of the resonant polarization. An extended-cavity VCSEL with a quantum-well saturable absorber is simulated, and stable mode-locking pulses are obtained. Fine features of the spatial profile of the mode-locked pulses are also studied within this approach.
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N.-C. Panoiu, M. Bahl, and R. M. Osgood, Jr.
“ All-optical tunability of a nonlinear photonic crystal channel drop filter” Opt. Express 12, 1605 (2004). We report a numerical analysis of an optically tunable channel drop filter that consists of a resonant cavity side-coupled to a waveguide embedded in a two-dimensional nonlinear photonic crystal. We first introduce a numerical method that allows us to calculate the photonic band structure of a nonlinear photonic crystal, as well as the frequency and field profile of cavity and waveguide modes. Then, we use this numerical method to study the dependence of the resonant frequency of a cavity side-coupled to a waveguide, on the optical power in the waveguide.
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N. - C. Panoiu, M. Bahl, and R. M. Osgood, Jr.,
“Ultrafast optical tuning of superprism effect in nonlinear photonic crystals” J. Opt. Soc. Am. B 21, 1500 (2004). A comprehensive analysis of optically tunable superprism effect in a two-dimensional nonlinear photonic crystal is presented. We demonstrate that,
under certain circumstances, if one modifies the band structure of the crystal
through the Kerr effect induced by a pump beam, the refraction angle of the
transmitted signal beam can be tuned over tens of degrees. Two complementary geometries are considered,
namely air-holes in a dielectric background and dielectric rods surrounded by air, and in both cases both
the TE and TM polarizations are studied. It is demonstrated that due to the field enhancement
at the position of the rods, the superprism effect is larger if the latter configuration is used.
We also show that, due to the slow light effect, in both cases
the optical power required to tune the refracted angle is dramatically reduced
if the frequency of the pump beam is close to a photonic band-gap edge.
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N. - C. Panoiu, D. Mihalache, D. Mazilu, I. V. Mel’nikov, J. S. Aitchison, F. Lederer, and R. M. Osgood, Jr.,
“Dynamics of dual-frequency solitons under the influence of frequency-sliding filters, third-order dispersion, and intrapulse Raman scattering” IEEE J. Sel. Top. Quantum Electron. 10, 885 (2004). We analyze the structure of the optical field emerging
from a superposition of two solitonlike pulses with different
frequencies and arbitrary phase-shift between them, and show
that the optical output contains either symmetric or antisymmetric
two-soliton states. Furthermore, we study numerically
the dynamics of these emerging two-soliton states under the
influence of perturbative effects that are important for optical
communications systems: frequency-sliding filters, third-order
dispersion, and intrapulse Raman scattering.
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N.-C. Panoiu, D. Mihalache, D. Mazilu, F. Lederer, and R. M. Osgood, Jr.
“Vectorial spatial solitons in bulk periodic quadratically nonlinear media” J. Opt. B: Quantum and Semiclassical Optics 6, S351 (2004). We present a comprehensive analysis of the generation, propagation, and characteristic properties
of two-dimensional spatial solitons formed in quasi-phase matched gratings through Type-II vectorial
interaction. By employing an averaging approach based on asymptotic expansion theory, we show
that the dynamics of soliton propagation in the grating and their stability properties are strongly
in°uenced by induced Kerr-like nonlinearities. Finally, through extensive numerical simulations, we
verify the validity of our theoretical predictions.
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N. - C. Panoiu, M. Bahl, and R. M. Osgood, Jr., “Optically tunable superprism effect in nonlinear photonic crystals” Opt. Lett. 28, 2503 (2003). An analysis of the tunable superprism effect in a two-dimensional nonlinear photonic crystal is presented.
We show that, by shifting the photonic bands of the crystal through the Kerr effect induced by a pump beam, one can tune the refraction angle of a
transmitted signal beam over tens of degrees. We also demonstrate that the optical power required to tune the refracted angle is dramatically reduced.
if the frequency of the pump beam is close to a bandgap edge.
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N. - C. Panoiu, D. Mihalache, H. Rao, and R. M. Osgood, Jr., “Spatial solitons in type II quasi-phase-matched slab waveguides” Phys. Rev. E Rapid Communications 68, 065603(R) (2003). The existence and dynamics of one-dimensional spatial solitons formed upon propagation in quasiphasematched
gratings, through three-wave parametric interaction, is analyzed. We study the general case in which
the grating exhibits a periodic modulation of both the refractive index and the second-order susceptibility. It is
demonstrated that for negative effective wave vector mismatch the induced third-order nonlinearities increase
the domain of soliton instability. Finally, the dependence of the efficiency of the second harmonic generation
process in the soliton regime, on the parameters of the grating, is discussed.
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N. - C. Panoiu and R. M. Osgood, Jr., “Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials” Phys. Rev. E 68, 016611 (2003). We study numerically the influence of the frequency dispersion of the dielectric function of metals on the physical
properties of negative-refractive-index metamaterials. A numerical analysis is performed using the transfer matrix formalism in conjunction with the
finite-difference time-domain method. We analyze the dependence of the transmission and absorption properties of a slab of split-ring-type resonators
on the parameters characterizing the frequency dispersion of the metallic dielectric function: plasma frequency and damping frequency. Then, using these
transmission and reflection coefficients, we show that the refractive index remains negative near the resonant frequency of the rings, despite the presence
of frequency dispersion. We also determine the dependence of the position and width of the band gaps of a slab of such a metamaterial on the material
dispersion. Finally, we also discuss the influence of the shape of the split-ring resonators on the transmission and reflection coefficients. The calculations
are performed for both two- and three-dimensional structures.
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N. - C. Panoiu, D. Mihalache, D. Mazilu, F. Lederer, and R. M. Osgood, Jr., “Two-dimensional solitons in quasi-phase-matched quadratic crystals” Phys. Rev. E 68, 016608 (2003). We study the existence and dynamics of two-dimensional spatial solitons in crystals that exhibit a periodic modulation
of both the refractive index and the second-order susceptibility for achieving quasi-phase-matching. Far from resonances between the domain length of the periodic crystal and the diffraction length of the beams, it is demonstrated that the properties of the solitons in this quasi-phase-matched geometry are strongly influenced by the induced third-order nonlinearities. The stability properties of the two-dimensional solitons are analyzed as a function of the total power, the effective wave-vector mismatch between the first and second harmonics, and the relative strength between the induced third-order nonlinearity and the effective second-order nonlinearity. Finally, the formation of two-dimensional solitons from a Gaussian beam excitation is investigated numerically.
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N. - C. Panoiu and R. M. Osgood, Jr., “Numerical investigation of negative refractive index metamaterials at infrared and
optical frequencies” Opt. Commun. 223, 331 (2003). An analysis of the transmission properties of a slab of metallic split-ring resonators at near infrared and optical frequencies
is presented. We focus on the influence of the parameters characterizing the intrinsic frequency dispersion of the metallic rings on the physical properties of recently
introduced materials that exhibit a negative refractive index. It is demonstrated that, when a mesh of thin metallic wires is added, at the resonant frequency
ω0 ~150 THz the refractive index of the resulting metamaterial is negative within a frequency hand Δω ~50 THz. The numerical
analysis is performed using the transfer matrix formalism.
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M. Bahl, N. - C. Panoiu, and R. M. Osgood, Jr., “Nonlinear optical effects in a two-dimensional photonic crystal
containing one-dimensional Kerr defects” Phys. Rev. E 67, 056604 (2003). The nonlinear optical effects induced by a one-dimensional (1D) line defect, made of Kerr material, in a 2D
photonic crystal are studied. Comprehensive ab initio numerical simulations based on the finite-difference time-domain method show efficient third-harmonic
generation in a photonic crystal waveguide consisting of the 1D defect line. The relationship between the third harmonic generation process and the nonlinear
modal properties of the waveguide is discussed. We investigate optical limiting in such a device, that is, control of the transmitted power as a function of the
Kerr-induced variation of the refractive index. Power dependent spectral changes in such a device and its use as a frequency selector are also examined.
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N. - C. Panoiu, I. V. Melnikov, D. Mihalache, C.
Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical
signal” (review article) J. Opt. B: Quantum and Semiclassical Optics 4,
R53 (2002). We present a comprehensive analysis of the
generation of optical solitons in a monomode optical fibre from a
superposition of soliton-like optical pulses at different frequencies. It
is demonstrated that the structure of the emerging optical field is highly
dependent on the number of input channels, the inter-channel frequency
separation, the time shift between the pulses belonging to adjacent
channels, and the polarization of the pulses. Also, it is found that there
exists a critical frequency separation above which wavelength-division
multiplexing with solitons is feasible and that this critical frequency
increases with the number of transmission channels. Moreover, for the case
in which only two channels are considered, we analyse the propagation of
the emerging two-soliton solutions in the presence of several
perturbations important for optical networks: bandwidth-limited
amplification, nonlinear amplification, and amplitude and phase
modulation. Finally, the influence of the birefringence of the fibre on
the structure of the emerging optical field is discussed.
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N. - C. Panoiu, I. V. Melnikov, D. Mihalache, C. Etrich, and F.
Lederer, “Multiwavelength pulse transmission in an optical fibre - amplifier system” Quantum Electronics 32,
1009 (2002). The structure and dynamics of solitary waves created in the interaction of multiwavelength pulses in a single-mode optical
fibre with amplification, filtering, and amplitude modulation is analysed. It is shown that there is a critical wavelength separation between channels above which
wavelength-division multiplexing with solitons is feasible and that this separation increases with the number of channels. | |
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C. Etrich, N. - C. Panoiu, D. Mihalache, and F.
Lederer, “Limits for interchannel frequency separation in a soliton
wavelength-division multiplexing system” Phys. Rev. E 63,
016609 (2001). We identify the required interchannel frequency
separation of the input field for a soliton wavelength-division
multiplexing (WDM) system. It is found that the critical frequency
separation above which WDM with solitons is feasible increases with the
number of transmission channels. Moreover, it is shown that a combination
of time- and wavelength-division multiplexing yields the largest
transmission capacity. Finally, the structure of the soliton spectra which
correspond to the frequency separation smaller than the critical frequency
is discussed. | |
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V. Melnikov, D. Mihalache, N. - C. Panoiu, F. Ginovart,
and A. Zamudio Lara, “Coherent amplification of dual-frequency optical
solitons in a doped fiber” Opt. Commun. 191, 133
(2001). It is found that the temporal behavior of
sub-picosecond optical soliton-like pulses propagating through a fiber
amplifier exhibits large deviations from the predictions based on standard
soliton interaction theories. Both cases of adiabatic and pure coherent
amplification of these dual-frequency solitons are studied. We show that
it is possible to generate either a dual-frequency bound soliton state or
a soliton train, The structure of the emerging optical state depends on
the balance between the retarded coherent response introduced by an
inverted two-level medium, nonresonant cubic nonlinearity, group-velocity
dispersion, and Raman self-scattering. | |
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A. V. Kiryanov, I. V. Melnikov, N. - C. Panoiu, F. Ginovart, and A. Zamudio Lara, “Coherent effects in a dual-frequency soliton interaction” Laser Physics 11, 522 (2001). The temporal structure of subpicosecond
dual-frequency optical solitons propagating through a fiber amplifier is
found to evolve either to a dual-frequency bound soliton state or a
soliton train. The structure of the emerging optical state mainly depends
on the balance between a retarded coherent response which is due to an
inverted two-level medium and nonresonant cubic
nonlinearity. | |
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N. - C. Panoiu, D. Mihalache, D. Mazilu, L. - C. Crasovan, I. V. Melnikov, F. Lederer, “Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrodinger equation” Chaos 10, 625 (2000). A comprehensive
analysis is presented of the propagation of symmetry-endowed two-soliton
solutions under the influence of various perturbations important in
nonlinear optics. Thus, we begin by introducing the analytical expressions
of these two-soliton solutions. Then, by considering perturbations which
preserve the initial symmetry of the two-soliton solutions, the dependence
of the soliton parameters on the propagation distance is determined by
using an adiabatic perturbation method. As perturbations of this kind,
important for soliton-based communication systems, we consider the
bandwidth-limited amplification, nonlinear amplification, and amplitude
and phase modulation. Moreover, the results obtained by the adiabatic
perturbation method are compared with those obtained by direct numerical
simulations of the corresponding governing differential
equations. | |
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I. V.
Melnikov, D. Mihalache, and N. - C. Panoiu, “Localized multidimensional
femtosecond optical pulses in an off-resonance two-level medium” Opt. Commun. 181, 345 (2000). The propagation of a
femtosecond optical pulse in a multidimensional off-resonance two-level
medium is studied. Within the quasiadiabatic following approach, the
evolution of the pulse is governed by a generalized
Kadomtsev-Petviashvili equation with coupling between the
spatial and temporal profile. The presence of this coupling can have a
dramatic influence on the dynamics of the optical pulse. Thus, one can
observe effects which cannot be described within the framework of the
slowly-varying envelope approximation. In particular, we show that due to
the interaction between the transient diffraction and the electrodynamic
absorption, stable, localized multidimensional pulses can be formed.
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[27] |
N. - C. Panoiu, “Anomalous diffusion in two-dimensional potentials with hexagonal symmetry” Chaos 10, 166 (2000). The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. |
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[28] |
N. - C. Panoiu, I. V. Melnikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation in optical fibers for a dual-frequency input” Phys. Rev. E 60, 4868 (1999). We analyze scenarios
of soliton generation in an ideal fiber for an input that consists of
either two in-phase or out-of-phase solitonlike optical pulses at
different frequencies. In both cases the relationship between the
structure of the emerging solitons and;the frequency separation of the
initial solitons is studied both analytically and numerically. Depending
on the value of the frequency detuning, if the two initial solitons are in
phase (symmetric input), two bound solitons with equal amplitudes
(breather), a single soliton, or a pair of solitons, which have equal
amplitudes and exhibit opposite velocities, can be generated. When the two
initial solitons are out-of-phase (antisymmetric input), only the last
scenario takes place. Also, we calculated the threshold values of the
frequency separation at which the structure of the emerging solitons
changes. Moreover, we demonstrated that two of these critical frequencies
correspond to cusplike maxima of the energy density of the radiative
modes. Finally, we show that these analytical results are entirely
verified by numerical simulations. |
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D. Mihalache, I. V. Melnikov, and N. - C. Panoiu, “Novel femtosecond optical solitons in weakly excited semiconductors” Proc. SPIE, vol. 3405, 353 (1998). We apply the
quasiadiabatic approximation for the femtosecond pulse propagation in a
collection of excitons in the case of weak interaction between the optical
pulse and the semiconductor medium. Using the semiconductor Maxwell-Bloch
equations beyond the slowly varying envelope approximation we show that
the dynamics of femtosecond pulse propagation is described by the modified
Korteweg-de Vries equation. Bright solitons superimposed on a continuous
wave background are found and their stability against low amplitude
perturbations is investigated. Possible experiments in semiconductor
systems such as GaAs/AlGaAs are discussed. | |
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[30] |
D. Mihalache, L. - C. Crasovan, and N. - C. Panoiu, “On a coupled system of equations describing pulse propagation in quadratic media” J. Phys. A 30, 5855 (1997). In the slowly varying
envelope approximation we derive the basic equations that describe the
propagation of ultrashort purses in quadratically nonlinear media in which
a wave at a fundamental frequency interacts with its second harmonic. In
the governing equations we keep linear terms that account for both
second-and third-order dispersion and nonlinear terms describing both
nonlinear dispersion and self-steepening of the purse edge. We then
perform the Painleve singularity structure analysis of the most general
system of coupled partial differential equations we derived. In a specific
case, when third-order dispersion is negligible, by using a Hirota-like
method, we found zero-and one-parameter families of bright (fundamental
frequency) and dark (second harmonic) solitary waves which travel at a
locked group velocity. |
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[31] |
I. V. Melnikov, D. Mihalache, F. Moldoveanu, and N. - C. Panoiu, “Quasiadiabatic following of femtosecond optical pulses in a weakly excited semiconductor” Phys. Rev. A 56, 1569 (1997). Using semiconductor
Maxwell-Bloch equations, we analyze the response of an ensemble of
1s excitons driven by a femtosecond optical pulse beyond the
traditional approach of slowly varying amplitudes and phases. For optical
pulses of a given duration, we show that the off-resonance optical field
can evolve into a stable soliton. Besides hyperbolic-secant solitons, we
find a single soliton with nonzero asymptotics that is stable against
low-amplitude perturbations and whose form is not affected by
collisions. |
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[32] |
I. V. Melnikov, D. Mihalache, F. Moldoveanu, and N. - C. Panoiu, “Non-envelope formulation for femtosecond optical pulses in semiconductors” JETP Lett. 65, 393 (1997). We analyze the response of an ensemble of 1s-excitons driven by a femtosecond optical pulse, beyond traditional "slowly varying amplitudes" approach. For optical pulses of a given duration it is shown that the off-resonance optical field can evolve into a stable soliton with nonzero asymptotic behavior. |
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[33] |
D. Mihalache, L. - C. Crasovan, N. - C. Panoiu, F. Moldoveanu, and D. - M. Baboiu, “Timing jitter of femtosecond solitons in monomode optical fibers” Opt. Eng. 35, 1611 (1996). We study the propagation over long distances under the influence of the Raman effect of certain subpicosecond solitons, which are solutions of a perturbed nonlinear Schrödinger equation describing the propagation of light pulses in monomode optical fibers. We calculate the corresponding propagation distance limit due to the intrapulse Raman scattering soliton timing jitter. A formula that describes the soliton timing jitter effect due to the influence of amplified spontaneous emission noise on soliton group velocity induced by the coupling between amplitude and velocity is given and the propagation distance limit of soliton communication systems caused by this effect is evaluated. |
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[34] |
N. - C.
Panoiu, D. Mihalache, and D. - M. Baboiu, “Dark-soliton timing jitter
caused by fluctuations in initial pulse shape” Phys. Rev. A 52, 4182 (1995). The dark-soliton
timing jitters caused by fluctuations in either the soliton initial phase
angle or the background amplitude when such a soliton propagates in a
monomode optical fiber under the influence of the stimulated Raman
scattering are investigated and compared with those that exist when the
stimulated Raman scattering is not present. In addition, it is
demonstrated that in the presence of the stimulated Raman scattering,
there exists a distance at which, for the negative soliton initial phase
angle, the dark-soliton timing jitter caused by fluctuations in the
background amplitude becomes zero. |
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[35] |
D. - M. Baboiu, D. Mihalache, and N. - C. Panoiu, “Combined influence of amplifier noise and intrapulse Raman scattering on the bit-rate limit of optical fiber communication systems” Opt. Lett. 20, 1865 (1995). Amplified spontaneous emission noise generates fluctuations in soliton energy and therefore fluctuations in the Raman self-frequency shift and in the group velocity. The corresponding timing jitter is found to be the main limitation for communication distances less than 1500 km. |
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[36] |
D. Mihalache, N. - C. Panoiu, F. Moldoveanu, D. Mazilu, and D. - M. Baboiu, “Evolution of bright femtosecond solitons under the Raman perturbation” Proc. SPIE, vol. 2461, 226 (1995). We used the Riemann Problem Method with a 3 X 3 matrix system to find the single soliton solution for a perturbed nonlinear Schrodinger equation in the most compact form. The considered equation describes bright ultrashort pulse propagation in properly tailored monomode optical fibers. The propagation of different single soliton solutions under the influence of the self-induced Raman effect was illustrated. Unlike the single soliton solution of the standard nonlinear Schrodinger equation we found that one of the our soliton solution can exhibit instability which leads to soliton fission. |
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[37] |
D. Mihalache, N. - C. Panoiu, F. Moldoveanu, D. Mazilu, and D. - M. Baboiu, “The Riemann problem method for solving a perturbed nonlinear Schrodinger equation describing pulse propagation in optical fibres” J. Phys. A 27, 6177 (1994). We used the Riemann problem method with a 3*3 matrix system to find the femtosecond single soliton solution for a perturbed nonlinear Schrodinger equation which describes bright ultrashort pulse propagation in properly tailored monomode optical fibres. Compared with the Gel'fand-Levitan-Marchenko approach, the major advantage of the Riemann problem method is that it provides the general single soliton solution in a simple and compact form. Unlike the standard nonlinear Schrodinger equation, here the single soliton solution exhibits periodic evolution patterns. |
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[38] |
D. Mihalache, D. Mazilu, N. - C. Panoiu, F. Moldoveanu, and D. - M. Baboiu, “Propagation of subpicosecond soliton-like pulses in optical fibers” Optica Applicata XXIV, 197 (1994). We investigated the possibility of propagation under the influence of the Raman effect of certain subpicosecond soliton-like pulses which are solutions of a perturbed nonlinear Schrodinger equation describing the propagation of light waves in monomode optical fibres. We calculated the propagation distance limits of long-haul transmission systems caused by the intrapulse Raman scattering soliton timing jitter and the amplified spontaneous emission noise induced timing jitter. |
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[39] |
D. Mihalache, N. Truta, N. - C. Panoiu, and D. - M. Baboiu “Analytic method for solving the modified nonlinear Schrodinger equation describing soliton propagation along optical fibers” Phys. Rev. A 47, 3190 (1993). We give a direct method for obtaining exact solutions of the modified nonlinear Schrödinger equation iut+ epsilon uxx+2p||u||2u+2iq(||u||2u)x =0 describing the propagation of light pulses in optical fibers. By using a suggestive particlelike description, we classify all the obtained analytical solutions into one of the following categories: the ``algebraic'' soliton, the one-soliton solution, the bright solitary waves, and the regular periodic solutions which are very important from the physical point of view. |
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[[40] |
D. Mihalache, L. Torner, F. Moldoveanu, N. - C. Panoiu, and N. Truta, “Inverse scattering approach to femtosecond solitons in monomode optical fibers” Phys. Rev. E 48, 4699 (1993). Using the
inverse-scattering transform with 3 |
|
[41] |
D. Mihalache and N. - C. Panoiu, “Analytic method for solving the nonlinear Schrodinger equation describing pulse propagation in dispersive optical fibers” J. Phys. A 26, 2679 (1993). The authors give a method for obtaining new exact solutions of the nonlinear Schrodinger equation describing pulse propagation in optical fibres for both the anomalous and the normal dispersion regime. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system whose solution determines the exact solutions of the nonlinear Schrodinger equation. By using the phase diagrams associated with the corresponding nonlinear differential equations they classify all the obtained solutions into one of the following categories: bright or dark solitary waves, bright or dark soliton solutions, rational (algebraic) bright or dark solitons, regular or singular periodic waves and stationary solutions. They give a set of particular solutions which describe the periodic wave patterns that are generated by the temporal self-phase modulation instability, the periodic evolution of bright solitons on a continuous wave background and the collision of two dark waves with equal amplitudes. |
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[42] |
D. Mihalache, L. Torner, F. Moldoveanu, N. - C. Panoiu and N. Truta, “Soliton solutions for a perturbed nonlinear Schrodinger equation” J. Phys. A 26, L757 (1993). Using the inverse scattering transform the authors found one-parameter and the breather-like four-parameter soliton solutions of a perturbed nonlinear Schrodinger equation which describes the pulse propagation in optical fibres in the femtosecond regime. |
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[43] |
D. Mihalache and N. - C. Panoiu, “Exact solutions for nonlinear Schrodinger equation for normal dispersion regime in optical fibers” Phys. Rev. A 45, 6730 (1992). We describe a method for obtaining exact solutions of the nonlinear Schrödinger equation for describing pulse propagation in optical fibers in the normal-group-velocity-dispersion regime. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system whose solutions determine the exact solutions of the nonlinear Schrödinger equation. |
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[44] |
D.
Mihalache and N. - C. Panoiu, “Exact solutions of nonlinear Schrodinger
equation for positive group velocity dispersion” J. Math. Phys. 33, 2323 (1992). A method is
given for obtaining new exact solutions of nonlinear
Schrödinger equation describing the propagation of pulses in optical
fibers for positive group-velocity dispersion. The method is
based on the construction of a certain complete integrable
finite-dimensional dynamical system, whose solutions determine
the exact solutions of nonlinear Schrödinger equation. The set
of exact analytic solutions contains dark solitary waves, dark
soliton, periodic, and stationary solutions which are very important
from a physical point of
view. |