Input Soliton Research Articles

Effective soliton order approach for scaling of pulse self-compression in hollow-core fibers

Optical solitons can undergo extreme temporal and spectral reshaping at high pulse intensities. These dynamics can be utilized to extract few-cycle pulses in the negative dispersion region in the case of higher-order spatial modes in hollow fibers. One can achieve self-compression up to few-cycle duration in hollow capillary fibers without any external optical post-compression schemes using this technique. These intense few-cycle pulses are an essential tool for revealing the ultrafast dynamics in the femtosecond to attosecond timescale, where the tunability and scalability of few-cycle pulses are a necessity. Utilizing the soliton dynamics, we can scale the pulses up to multi-millijoule energies as well as terawatts of peak power. Scaling relations are relations that can be used to produce propagation dynamics that are invariant and essentially identical for multiple sets of input conditions. But, for the same input soliton order, the scaling relations derived under different dispersion conditions, such as different gas pressure, result in somewhat different scaling laws. This leads to an ambiguity in the compression factor and compression length for any particular soliton order N. It is thus necessary to find an accurate soliton order which can scale the self-compression dynamics over different dispersion conditions. We numerically simulate soliton self-compression in an argon gas-filled HCF across a wide range of dispersion conditions and present a set of efficient scaling laws for soliton dynamics. We introduce an effective soliton order Neff for explaining the behavior of the dynamics in systems with high third-order dispersion (TOD) such as the HCF. The proficiency of the new scaling laws over the earlier scaling laws in literature is elucidated in this work. Thus, an inclusive set of scaling laws for generating high-energy few-cycle pulses are defined which are critical for generating single and trains of attosecond pulses, as well as electron and ion acceleration strategies in intense laser pulses.

Generation of High Power Ultrashort Pulses in Tapered Yb-Doped PCF Through Self-Similar Compression

We present a numerical approach for analysing simultaneous amplification and compression of a chirped hyperbolic secant soliton using a tapered Yb-doped photonic crystal fiber (PCF) based self-similar compressor. Theoretical studies reveal the conservation of input soliton during the amplification process due to self-similar property, which in turn helps for high quality compression of amplified soliton. In order to satisfy the self-similar condition, we note that the Yb-doped fiber should exhibit a decreasing group velocity dispersion (GVD). Such a constraint is met using a tapered PCF in our work, which is modeled using a fully vectorial effective index method (FVEIM). Influence of spatial and spectral dependent gain, saturation energy, amplified spontaneous emission (ASE), dispersion and nonlinearity on pulse propagation are analyzed using the combined solution of dynamic rate equations (DRE) and the generalized nonlinear Schrödinger equation (GNLSE). Numerical outcomes upon solving the aforementioned equations show that a 1 ps pulse is compressed down to a pulsewidth of 55.4 fs with a peak power of 1.03 kW in a total fiber length of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L=2.5$ </tex-math></inline-formula> m and taper ratio of 2.34. Overall quality of the compression scheme is evidenced by a relatively high compression factor (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>c</i></sub> ) = 18.12, and low percentage of pedestal energy ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$PE$ </tex-math></inline-formula> ) = 10.95 %

Bistable soliton switching dynamics in a PT -symmetric coupler with saturable nonlinearity

We investigate the switching dynamics in a $\mathcal{PT}$-symmetric fiber coupler composed of a saturable nonlinear material as the core. In such a saturable nonlinear medium, bistable solitons may evolve due to the balance between dispersion and saturable nonlinearity, which we extend in the context of the $\mathcal{PT}$-symmetric coupler. Our investigations of power-controlled and phase-sensitive switching show richer soliton switching dynamics than the currently existing conventional counterparts, which may lead to ultrafast and efficient all-optical switching dynamics at very low power owing to the combined effects of $\mathcal{PT}$ symmetry and saturable nonlinearity. In addition to the input power, the relative phase of the input solitons and saturable coefficient are additional controlling parameters that efficiently tailor the switching dynamics. Also, we provide a suitable range of system and pulse parameters that would be helpful for the practical realization of the coupler to use in all-optical switching devices and photonic circuits. Finally, we develop a variational approach to analytically investigate the switching dynamics in such $\mathcal{PT}$-symmetric couplers that excellently predicts the numerical findings.

Generation of broadband parabolic pulses based on a pre-chirper free, core-pumped nonlinear fiber amplifier for coherent anti-Stokes Raman imaging

We report the generation of parabolic pulses with broadband spectrum from a core-pumped Yb-doped fiber amplifier seeded by a dispersion managed fiber oscillator. The net cavity dispersion of Yb-doped oscillator was continuously changed from 0.074 to -0.170ps2, which enabled us to achieve dissipative soliton, stretched pulse and soliton mode-locking operations. Spectral evolution processes in the core-pumped nonlinear fiber amplifier seeded by various input solitons were investigated experimentally and theoretically. Our finding indicates that cavity dispersion of oscillator can be used to engineer the input pulse parameter for amplifier, thus forming a pre-chirper free fiber amplification structure. In the experiment, we obtained 410-mW parabolic pulses with spectral bandwidth up to 56 nm. In combination with a passively synchronized frequency-doubled Er-doped fiber laser, we have demonstrated coherent anti-Stokes Raman imaging. The compact dual-color fiber laser source may facilitate practical applications of nonlinear biomedical imaging beyond the laboratory environment.

Simulating an all-optical quantum controlled-NOT gate using soliton scattering by a reflectionless potential well

We present a protocol for the quantum controlled-NOT gate which is based on two qubits operation by investigating the soliton scattering through a reflectionless potential well in an optical system. We consider the set up of two input solitons with different intensities scattered by a reflectionless potential well with a control soliton placed at the center of the potential. The two input solitons correspond to the target qubit while either the presence or absence of control soliton in the potential well or the presence or absence of control potential well corresponds to the control qubit. We achieve the desired performance of the quantum logic gate by exploiting the intensity difference between the two input solitons and we find this to be possible within a finite width of a velocity of incidence for the two solitons. The calculation of transport coefficients ensures the feasibility of building a quantum controlled-NOT gate. This protocol demonstrates the prospect of soliton scattering by a potential well for quantum information processing. Especially, the setup with control potential as a control qubit allows realization of the CNOT operation with the negligible amount of radiation.

All-optical computing circuits half-subtractor and comparator based on soliton interactions

The speed limitations of electronic processors have created a demand for a high bandwidth and ultra-fast computing circuits. By replacing the electric logic gates with photonic ones, a high bandwidth and fast photonic microprocessor will be achieved which will overcome the speed limitations of electronic circuits. Digital photonic logic circuits are key elements in the next generation optical computers. In this paper, all-optical logical half-subtractor and digital comparator are designed based on spatial optical solitons. These computational gates are designed simply with repulsive and attractive interactions of three inphase and out of phase spatial optical solitons in a bulky nonlinear Kerr medium. With tuning the phase input solitons and exploiting inphase and out of phase soliton interactions a high functional circuit with broad operational bandwidth, high switching speed and high contrast ratio between ON/OFF states is achieved by a simple structure.

Dynamic diffractive resonant radiation in a linearly chirped nonlinear waveguide array

We theoretically and numerically investigate the evolution of discrete soliton in a 1D linearly chirped nonlinear waveguide array (WA). The discrete soliton is self-accelerated inside the transversely chirped WA and emits a \textit{dynamic diffractive resonant radiation} (DifRR). The radiation appears when soliton wave-number matched with linear radiation wave. Unlike uniform WA, the DifRR can be excited even for zero wave-number of input soliton when the waveguide channels are chirped. The transverse modulation due to chirp conceptually imposes a linear potential which acts as a perturbation to soliton dynamics and leads to a monotonous wave-number shift of the propagating wave. Exploiting perturbative variational analysis we determine the equation of motion of soliton wave-number and use it to establish a modified phase-matching condition which takes into account the soliton wave-number shift and efficiently predicts the dynamic DifRR. A startling effect like generation of dual DifRR occurs as a result of the interplay between self-accelerated soliton and its initial wave-number. We exploit the modified phase matching relation to understand this unique phenomenon of dual radiation and find a satisfactory agreement with numerical result in radiation wave-number calculation.

Solitons in liquid crystals with competing nonlinearities

We employ a model which is proposed by P. S. Jung et al. [see P. S. Jung et al. Opt. Express 25 (2017) 23893–23897] to analytically demonstrate properties of individual bright solitons in liquid crystals with competing nonlinearities. These results are confirmed by the numerical simulations. In addition, we numerically find that the competition between thermal and reorientational nonlinearities can lead to the formation of bright or dark-like solitons whose formation depends on the intensity profiles of the input beams. We show that the competing nonlinearities drastically affect the interaction of out-of-phase bright solitons, such as the change of attraction of out-of-phase bright solitons into repulsion force at certain initial separations of the input solitons.

Fate of a Soliton in a High Order Spatial Mode of a Multimode Fiber.

We show numerically that under certain conditions noise-induced soliton self-mode conversion dominates over soliton self-frequency shift for a soliton in a high order spatial mode of a multimode optical fiber. The input soliton has to be group index matched to a lower order mode for a frequency separation for which the Raman gain is non-negligible, and this condition determines the wavelength of the pulse growing from noise. The phenomenon has no known analogs in single-mode or graded-index fibers. The results demonstrate that it is possible for a noise-induced physical process to dominate over a seeded one even for noise levels at the fundamental limit.

Phase-controlled stable solitons in nonlinear fibers

Bright and grey coupled solitons with complex envelopes are obtained as exact solutions of the system describing doped optical nonlinear fibers. The solitons formed are found to be free of amplitude and phase instabilities during their evolution, leading to the realization of stable soliton propagation. The phase of the input solitons plays a crucial role in the formation of tanh–sech paired pulses. This soliton is not supported in a two-level atomic medium and is exclusive to the Λ system.

Ultra-fast electro-optic switching control using a soliton pulse within a modified add-drop multiplexer

We have proposed the use of a soliton pulse that propagates within a modified add-drop filter, which is made of a GaAsInP/P material. It is in the form of a Panda-ring resonator, from which a bright/dark soliton pulse is input into a system via an input port. The conversion between bright and dark soliton pulses is introduced at the 3 dB coupler, i.e. the change in phase of π/2. But it is not superimposed each other. The output solitons obtained at the through and drop ports are bight and dark solitons respectively. Both signals can be used to form “ON’ and “OFF” or “1” and “0”, which are useful for the digital bit generation. The switching speed of the system can be improved by employing the two nonlinear side rings. In application, secure output bits can be arranged by using the alternative input solitons or the control ports, where the input bright and dark solitons can be converted into output bits. This means that the output bits can be randomly switched between “1” and “0”, which can be identified by the sender. Moreover, the additional information can be multiplexed via the add port and transmitted in either free space or optical fiber via the whispering gallery mode and through port outputs. Finally, the electro-optic switching can be transferred and the electronic switching by the embedded stacked layers, where the ultrafast switching of light input can lead the ultrafast electrical switching speed. The switching speed of ~ 5 fs and the offset time of ~ 220 fs of the “on” and OFF” are achieved by using the selected ring parameters.

Micro-optical probe model using integrated triple microring resonators for vertical depth identification

The nonlinear microring resonator system is designed and the triple vertically Panda rings arranged for 3D imaging probe generation. The required whispering gallery modes (WGM) probe can be generated by controlling the input soliton and the reflected power within the microring system. It can be configured to be a microring conjugate mirror (MCR) and theoretically confirmed by the obtained nonlinear four-wave mixing output. The different depths of the MCCs are arranged by the differences of the vertical heights, which can offer the triple vertical probe requirement. The analytical solution of the WGM probe output is derived and the selected simulation results investigated. The results obtained have shown that the triple WGM probes can be generated and used for the 3D imaging detection, from which the two surface depths are ~ 2 and 4 µm are plotted, the calculated and the different colored shades seen. In application, such a proposed system may be used for the 3D imaging of the soft tissues (cells) investigations.

PHz-Wide Spectral Interference Through Coherent Plasma-Induced Fission of Higher-Order Solitons.

We identify a novel regime of soliton-plasma interactions in which high-intensity ultrashort pulses of intermediate soliton order undergo coherent plasma-induced fission. Experimental results obtained in gas-filled hollow-core photonic crystal fiber are supported by rigorous numerical simulations. In the anomalous dispersion regime, the cumulative blueshift of higher-order input solitons with ionizing intensities results in pulse splitting before the ultimate self-compression point, leading to the generation of robust pulse pairs with PHz bandwidths. The novel dynamics closes the gap between plasma-induced adiabatic soliton compression and modulational instability.

Effect of initial chirp on supercontinuum generation in dispersion decreasing fibers

Numerical simulations based on generalized nonlinear Schrödinger equation are used to study the effect of initial chirp on supercontinuum generation in dispersion decreasing fibers. The simulation results show that the effect of initial chirp on SC generation is highly related to the choices of pumping conditions and fiber parameters. When the pumping condition and the fiber parameters are different, the effect of initial chirp on SC generation may follow different patterns. To better discuss the effects of pulse parameters and fiber parameters on SC generation, the three normalized parameters: input soliton order, normalized dispersion slope and normalized effective fiber length are introduced. For a given input soliton order and a given normalized dispersion slope, there exists an optimal normalized effective fiber length for generating a flattest SC spectrum. On the condition of normalized effective fiber length in the vicinity of its optimal value, when DDF has small normalized dispersion slope, proper positive chirps can significantly enhance the SC bandwidth, while negative chirps or too large positive chirps suppresses the SC bandwidth. There is a wide range of positive chirps that can enhance the SC bandwidth, but the range of proper positive chirps become narrower as input soliton order decreases; When DDF has a large normalized dispersion slope and the pump pulse is a lower-order soliton, the enhancement of SC bandwidth by initial chirp is insignificant, and the widest SC spectrum is generated when the initial chirp is close to zero.

Design of optimum supercontinuum spectrum generation in a dispersion decreasing fiber

In this paper, the optimum supercontinuum (SC) spectrum generation in a dispersion decreasing fiber is presented. Three normalized parameters for the pump pulse and SC fiber are introduced. It is found that the shape of an SC spectrum is uniquely specified by the input soliton order, the normalized dispersion slope and the normalized effective fiber length. For a pumping condition with a given input soliton order and a given normalized dispersion slope, by optimizing the normalized effective fiber length, the residual spectral peak in the SC spectrum can be suppressed effectively, and a broad SC spectrum with optimum spectral flatness can be obtained.

Modelling evanescent field components in metal-oxide core waveguides for nonlinear applications

In a thin film planar geometry, the guiding effect due to the linear index results in light confinement in the thin film layer, at the same time causing evanescent waves to decay into the outer substrate or cladding layers. The magnitude of the field in the cladding is dependent on the characteristics of the waveguide and the wavelength of the wave. In this paper, we have modelled four metal-oxide core waveguides with prime focus on the evanescent field as light propagates through these optical structures. ZnO waveguide structure is taken as the benchmark. The evanescent path resembles a soliton consistent with the input soliton solution. A comparison is also carried out with a lower metal oxide core, MgO and a higher index TiO2. The variation in refractive index with input wavelength induces second order nonlinearity in these waveguide structures. For the simulated structures, mode field distributions are plotted against the refractive index. The magnitude of evanescent field also reduces with an increase in the input wavelength for the structures. The nature of the soliton path is insightful for the development of evanescent field based sensors. Optical waveguides with metal-oxide cores can act as a cheaper substitution to nanophotonic devices and integrated optics applications. With the study of evanescent phenomena in such structures, a minimally invasive manufacturing method without disturbance to the core may be made beneficial.

Soliton switching study using new normalized nonlinear Schrödinger equations

Soliton switching in a nonlinear directional coupler (NLDC) is studied by using new normalized nonlinear Schrödinger equations (NLSE). The resulted equations have one parameter κLD only, this feature greatly simplifies the numerical study of soliton coupling in a NLDC, and it enables us to derive the soliton switching conditions based on numerical analysis. Numerical results show that most of the input soliton energy remains in the launched waveguide when input soliton normalized peak power is bigger than 2.5. It is contrary to the existing theoretical expectations which were derived using variational approach. The fundamental soliton switching conditions is also expressed in terms of input soliton pulse width. In addition, it is found that frequency chirp degrades soliton switching performance in a NLDC.

Two-dimensional solitons and clusters in dissipative lattices

We study the dynamics of two-dimensional spatial solitons in the structured optical medium modeled by the complex Ginzburg–Landau equation with cubic–quintic nonlinearity and a spatially periodic modulation of the local gain–loss coefficient [a dissipative lattice (DL)]. The analysis, following the variation of the DL’s amplitude and period, reveals several dynamical scenarios: stable or unstable propagation of a single dissipative soliton (the unstable propagation entails generation of an irregular multisoliton cluster), transformation of the input soliton into stable or unstable regular clusters patterned as the underlying DL, and decay of the input. Most results are obtained by means of systematic simulations, but the boundary of the single-soliton stability domain is explained analytically.

Phase-induced switching in fiber nonlinear directional coupler

A numerical study of soliton switching characteristics and the maximum output coupling by the relative phase change of a control pulse is carried out for input powers, coupled coefficient and input soliton width. It is shown that input powers ratio, coupled coefficient and input soliton width play important roles in this mode of soliton switching and that these effects may lead to useful soliton switching if the relative phase of the control pulse is monitored judiciously.

Optical quantum transmitter with finesse of 30 at 800-nm central wavelength using microring resonators

A microring resonator (MRR) system incorporating an add/drop system is presented. The finesse of the proposed system can be determined using the full width at half maximum (FWHM) and free spectrum range (FSR) of the generated multiple soliton pulses. The central wavelength of the bright input soliton pulse has been selected as 800 nm, at which a ring system with better sensitivity shows high finesse that is suitable for applications to many optical communication systems such as optical transmitters and sensors. Simulation results show that FSR of 0.3 nm and 1.1 ns and FWHM of 10 pm and 36.6 ps could be obtained. Therefore, a system with finesse of 30 can be obtained; in such a system, the MRR system shows high performance. This system can be used in optical communication networks as a transmitter system for optical soliton pulses with finesse of 30, and theses pulses can be detected via an optical receiver.