Nonlinear Optical Applications Research Articles

Investigating the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation: an iterative framework for nonlinear wave dynamics

Abstract This paper addresses the solution of the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation using the Conformable Laplace Decomposition Method (CLDM). The CDGSK equation, a fundamental model in wave dynamics and fluid mechanics, is explored for its applications in quantum mechanics and nonlinear optics. By employing fractional calculus, we demonstrate how fractional derivatives influence the physical characteristics of wave propagation in both optical and quantum systems. The exact solutions obtained provide insight into soliton behavior, essential for understanding wave-particle interactions in quantum fields and light–matter interactions in optics. The fractional nature of the equation allows for more accurate modeling of non-integer order dynamics commonly found in optical fibers and quantum waveguides. The CLDM method proves to be highly effective, providing approximate solutions with minimal computational effort. These findings offer significant contributions to the fields of quantum mechanics and nonlinear optics, where the fractional CDGSK equation can be applied to solve complex wave equations with great accuracy.

Regulating Second‐Harmonic Generation in 2D Chiral Perovskites Through Achiral Organic Spacer Cation Alloying Strategy

AbstractThe inherent structural flexibility and chiroptical activity of 2D chiral perovskites make them promising for the nonlinear optical (NLO) application. A comprehensive understanding of the second‐harmonic generation (SHG) mechanism in 2D chiral perovskites is essential for developing NLO devices. However, the rational design of 2D chiral perovskite structures to regulate SHG properties remains challenging. Herein, to regulate SHG response, an achiral organic spacer cation alloying strategy is employed to construct a series of 2D chiral perovskites. Through the measurement of temperature‐dependent photoluminescence (PL) spectra, it is revealed that the material design strategy can effectively modulating self‐trapped exciton (STE) emission. More importantly, it is confirmed that there is a competitive relationship between STE emission and SHG in 2D chiral perovskites. Meanwhile, the microscopic imaging of circularly polarized‐SHG is demonstrated in chiral perovskites. This work will not only advance the understanding of the SHG mechanism in 2D chiral perovskites but also provide inspiration for the rational design and synthesis of perovskites for NLO devices.

Electrically switchable chiral nonlinear optics in an achiral ferroelectric 2D van der Waals halide perovskite.

Two-dimensional (2D) van der Waals (vdW) semiconductors play a key role in developing nanoscale nonlinear optical devices. 2D Ruddlesden-Popper lead halide perovskites (RPPs) expand the potential of using 2D vdW semiconductors in nonlinear optical applications because they exhibit electrically switchable and chiral second-order optical nonlinearity originating from the emergence of ferroelectricity and chirality. However, electrically switchable chiral nonlinear optics has not yet been realized because of the difficulty in electrically manipulating chiral structures. Here, we demonstrate that chiral second-harmonic generation (SHG) can be electrically induced and switched in an achiral biaxial ferroelectric 2D RPP. We observe reversible and continuous electrical switching of SHG circular dichroism and large nonlinear chiroptical activity. Polarization-resolved SHG imaging reveals that electrical poling induces the ferroelectric multidomain structure arising from the biaxial nature of the material, and the planar chirality appears. Our findings show a simple electrical control of the nonlinear chiroptical responses and establish chiral nonlinear optics based on ferroelectric 2D RPPs.

Analytical solutions and instability analysis of truncated M-fractional coupled dispersionless equations

Abstract This paper comprehensively investigates the truncated M-fractional coupled dispersionless equations, a nonlinear system of partial differential equations characterized by its M-fractional derivative. The Jacobi elliptic function expansion method is employed to derive analytical solutions for the coupled system. In addition, the modulation instability of the solutions is thoroughly explored, providing a detailed exposition of the mathematical framework governing the system. The analytical solutions are graphically illustrated and analyzed to highlight their physical significance. These findings have significant applications in nonlinear optics, offering new insights into wave propagation and stability within such systems.

A Porphyrin-Based MOF Thin Film with Oriented Nanosheet Arrays for Optimizing a Nonlinear Optical Response.

Developing two-dimensional (2D) hybrid nanosheet arrays integrating inorganic and organic components is highly significant for third-order nonlinear optical (NLO) applications. Herein, an oriented 2D porphyrin-based MOF (ZnTPyP(Co)) thin film composed of vertically stacked ultrathin nanosheets was fabricated via the liquid-phase epitaxial (LPE) layer-by-layer (LBL) method. The prepared ZnTPyP(Co) thin film exhibits an outstanding third-order NLO response with a high third-order nonlinear susceptibility of ∼2.63 × 10-7 esu, which is ascribed to the hybrid nanosheet array structure. Additionally, experimental Z-scan measurement and theoretical calculations also demonstrate that the substitution of Co metal ions in the porphyrinic core can increase the level of delocalization of the porphyrinic group and contribute to the material's enhanced NLO properties. These findings not only provide new film candidates for NLO application but also highlight the potential of 2D MOF nanosheets in advanced optical devices.

Physical and Optical Properties of Tellurium Dioxide-Based Quaternary Glasses: Potential for Nonlinear Optical Applications

Physical and Optical Properties of Tellurium Dioxide-Based Quaternary Glasses: Potential for Nonlinear Optical Applications

A methodical investigation on stilbazolium derivative substituted with 2,4-Dichlorobenzaldehyde as a donor: An effective crystal for optical device fabrication

For a couple of decades, nonlinear optics (NLO) has garnered significant attention due to its widespread application in optical systems. In this viewpoint, a new 2-[2(2,4-Dichloro-phenyl)vinyl]methyl-1-pyridinium iodide (DCPI) crystal was grown through slow evaporation process for NLO application. Single Crystal X-ray diffraction (SCXRD) study reveals that the DCPI crystallized centrosymmetric (P-1) space group. The CHN elemental analysis and NMR spectroscopy assess the purity of the material. The vinyl (CC) group formation in DCPI was asserted by the Fourier-transform infrared (FT-IR) spectrum. The Hirshfeld surface analysis confirms the presence of hydrogen bonds in the crystal structure through its contribution percentage (27 %) to the overall intermolecular interaction. DCPI crystal exhibits 80 % transparency in the visible region. Luminescence studies assess the green light-emitting characteristics of the DCPI crystal. The etching and Atomic Force Microscopy (AFM) studies confirm that the DCPI crystal has a flat surface with minimum dislocations. Z-scan studies found the third-order nonlinear characteristics of the crystal. Overall, the article illustrates the appropriateness of DCPI crystal in fabricating optical devices through its significant optical characteristics.

Revealing the Role of Electronic Effect to Modulate the Photophysics and Z-Scan Responses of o-Locked GFP Chromophores.

Three novel core green fluorescent protein (GFP) chromophore analogues, based on a doubly locked conformation and variable electronic effects by replacing one hydrogen with bromine, iodine, and methyl, respectively, have been synthesized to modulate the push-pull effect. These chromophores exhibited intramolecular H-bonding, as evidenced by single-crystal X-ray and 1H NMR studies. The fluorescence quantum yields (ϕf) of all of the chromophores were found to be more than an order of magnitude higher (∼0.2) than the unlocked chromophores (∼0.01). It was found that the electronic effect did affect the nonradiative rates, as the quantum yields were found to vary with respect to different analogues in the same solvents. The effect of the push-pull effect was also evident by a higher Stokes-shifted emission in the case of the methyl derivative with respect to the bromo- and iodo-analogues. Furthermore, the emission spectra of these GFP chromophores were found to show positive solvatochromism, which was supported by a quantum chemical calculation. A detailed study, correlating the observed spectral changes with various solvent functions and supported by computational results, established a facile proton transfer, followed by twisted intramolecular charge transfer (TICT) to be the major nonradiative channels of these chromophores. Besides, a completely novel usage of these chromophores was explored for the first time by studying their third-order nonlinear optical characteristics in DMSO using a single-beam Z-scan technique. All of the chromophores exhibited tunable nonlinear refraction (NLR) and nonlinear absorption (NLA) properties that depend upon different substituent groups present in the chromophores. Here, the NLR was due to the effect of self-defocusing, whereas the NLA was triggered by reverse saturable absorption, which is attributed to the two-photon absorption (TPA) process. Surprisingly, the efficiency of the TPA ability of the chromophores was found to be a function of the induced electronic effect. Hence, this work opens a new route for the utility of the ortho-locked GFP chromophores in the field of nonlinear optical applications.

The substituent effect on pulsed laser beam self-action manifestation in azo-azomethine PMMA composites thin films in visible and near IR ranges

Efficiency of nonlinear optical response was studied for a set of azo-azomethines dyes with substituted electron-withdrawing/donating groups, being embedded in poly(methyl methacrylate) (PMMA) matrix, via self-action effects manifestation of mode-locked Nd:YAG laser single pulses in visible at 532 nm, and in near IR at 1064 nm ranges. Photoinduced variations of refractive index and optical absorption/bleaching are crucially dependent on electron-donating/accepting substituents' properties with |Re(χ(3))| ∼ 10−7 esu and |Im(χ(3))| ∼ 10−9 esu efficiencies correspondingly at moderate laser excitation up to 10 MW/cm2. Incorporation of the azomethine group has provided tendency for fractional self-focusing effect manifestation in visible range against reference Azo dye, while at 1064 nm – self-defocusing one. For some dyes magnitudes of |Re(χ(3))| in near IR range are comparable and even higher than for the corresponding ones at 532 nm due to resonant cascaded three photon excitation into the peak vicinity of π→π∗ transitions of the dyes. It was established linear relationship between second-order hyperpolarizabilities under pulsed and CW laser excitation in visible range, being preliminary irradiated within full spectra of UV lamp for CW laser diagnostics mode. It proofs a suggestion that picosecond range single pulses transfer dyes into the same excited state as full spectrum of a mercury lamp irradiation – conventional tool for the smart molecules’ isomerization. Analysis of the experimental data has shown a high potential for the azo-azomethines dyes doped polymer composites in nonlinear optical applications.

Global Selection Rules and Giant Enhanced Harmonic Generations in LiNbO3 Nonlinear Meta‐Optics

AbstractNonlinear optical metasurfaces provide nanoscale‐level control of harmonic waves, making them highly promising platforms for both fundamental research and applications in nonlinear optics. However, the traditional selection rules theory, which has long served as a guiding principle for nonlinear meta‐optics, is local and neglects the significance of meta‐atomic lattice symmetry. In addition, achieving high‐efficiency harmonic generation along with nonlinear optical Pancharatnam‐Berry (PB) phase control remains challenging. To this end, a novel global selection rule jointly determined by the symmetries of both meta‐atom and lattice is proposed. Nonlinear metasurfaces designed based on this theory enable frequency conversions forbidden by previous local selection rules. A more comprehensive relationship between the nonlinear PB phase and the meta‐atomic rotation angle is revealed. Moreover, an efficient nonlinear PB metasurface platform for second harmonic generations is first demonstrated using LiNbO3 thin films with aligned crystal orientations in a hybrid design. The normalized conversion efficiency reaches approximately two orders of magnitude higher than that of existing nonlinear PB metasurfaces working in the near‐infrared band. These findings not only shed light on the underlying mechanisms of nonlinear light‐matter interactions, but also open up exciting possibilities in terahertz, entangled photon pairs, and high harmonic generations.

Sympathetic Mechanism for Vibrational Condensation Enabled by Polariton Optomechanical Interaction.

We demonstrate a macrocoherent regime in exciton-polariton systems, where nonequilibrium polariton Bose-Einstein condensation coexists with macroscopically occupied vibrational states. Strong exciton-vibration coupling induces an effective optomechanical interaction between cavity polaritons and vibrational degrees of freedom of molecules, leading to vibrational amplification in a resonant blue-detuned configuration. This interaction provides a sympathetic mechanism to achieve vibrational condensation with potential applications in cavity-controlled chemistry, nonlinear, and quantum optics.

Growth of L-asparagine monohydrate organic single crystals: An experimental and DFT computational approach for nonlinear optical applications

Good optical quality of L-asparagine monohydrate (C4H8N2O3.H2O) organic single crystal has been grown by adopting natural slow evaporation process at room temperature from aqueous solutions. The lattice parameters obtained by powder X-ray diffraction data revealed orthorhombic crystal system of the harvested crystal. The morphology and planes of the crystal have been identified. The molecular vibrations and functional groups have been specified by Fourier transform infrared (FTIR) spectroscopy studies. Energy dispersive X-ray (EDX) study has been availed to find out the elements constituting the crystal. Scanning electron microscopy, (SEM), provided the surface morphology of the crystal. The dependence of dielectric properties on frequency and temperature have been investigated and the electronic polarizability (α) has been determined. UV–vis spectral analysis shows that the crystal possesses good optical transmittance in the visible part of the energy spectrum. The optical band gap and the Urbach energy have been determined from lower absorption edge. Third order nonlinear susceptibility χ(3), nonlinear refractive index (n2), and linear susceptibility χ(1) have been calculated by Miller's generalized rule. The first-principle computation of band structure of electrons and the electron density of states have been discussed, which suggest that the crystals possess direct band gap. Density Functional Theory (DFT) with B3LYP function by Gaussian09W software was utilized to calculate HOMO-LUMO energy gap as well as non-linear optical parameters namely, linear polarizability (α), hyperpolarizability (β and γ) and dipole moment (μ) of L-asparagine monohydrate crystal. All the findings prove that L-asparagine monohydrate is a promising NLO crystal.

Structural characterisation of a cyanomesogen by X-ray diffraction and computational methods

The work reports the structural analysis of a cyanomesogen namely, p-cyanobenzylidene p-nonyloxyaniline belonging to the Schiff base class of compounds. It exhibits a partial bilayer/inter-digitated smectic Ad phase and a nematic phase. Polarising Optical Microscopy (POM) and Differential Scanning Calorimetry (DSC) studies have been carried out to study phase sequence and transition temperatures. Micro-structural parameters, like molecular length, spacing, crystallite size, activation energy and micro-strain, have been estimated and pair correlation function (PCF) studies have been done for exhibited mesophases using the X-ray diffraction technique. The study investigated the surface, electronic and optical properties of a compound by computational studies like Density Functional Theory (DFT) and Hirshfeld surface analysis (HSA) methods using the DFT B3LYP/6-311++G(d,p) level basis set. The results reveal that the polarity associated with the polar groups and alkoxy chain lengths, contributes majorly to the mesomorphic characteristics and stability. The Highest Occupied Molecular Orbitals (HOMO) and Lowest Unoccupied Molecular Orbitals (LUMO) analyses of the DFT optimised molecule give electronic and geometrical parameters, atomic charge distribution, polarisability factors which are used to interpret the characteristics of the mesophases and their suitability for electro-optical and non-linear optical applications of the compound in terms of the predicted data.

Multi-Noncentrosymmetric Polar Order in 2D Hybrid Lead Chloride with Broadband Emission and High-Temperature Second-Harmonic Generation Switching.

Two-dimensional lead halide perovskites represent a fascinating class of hybrid semiconductors for solar cell, light-emitting, nonlinear optical (NLO), and ferroelectric applications. A notable subset within this category is luminescent ferroelectrics, which have garnered considerable attention for their potential in integrated photoelectronic devices. In this study, we employed an organic amine halogenation strategy (also referred to as halogen engineering), which is renowned for its efficacy in inducing polar order through crystal engineering. Consequently, we synthesized a layered Ruddlesden-Popper (RP) lead chloride comprising 3-chloropropylammonium cations (CPA+), with the chemical formula CPA2PbCl4. This compound features as many as four temperature-dependent crystal phases, with phase transitions observed at T1 = 353.1 K (343.9 K), T2 = 211.7 K (208.6 K), and T3 = 182.0 K (178.2 K) in the heating (cooling) cycles. Employing a multitechnique approach─including thermal analysis, X-ray diffraction, dielectric and pyroelectric current measurements, Raman spectroscopy, and second-harmonic generation (SHG) studies─we determined the mechanisms of the structural phase transitions. Our findings demonstrate polar order of phase II (space group Cmc21), phase III (space group Pna21), and phase IV (space group Pca21), while also confirming the centrosymmetric nature of phase I (space group Cmce). X-ray diffraction data revealed that the I to II PT is of a ferroelectric nature, devoid of ferroelastic strain, a conclusion further supported by pyroelectric measurements. CPA2PbCl4 features negative linear thermal expansion and broadband emission, which transitions to white light above 180 K. Remarkably, CPA2PbCl4 also demonstrates high-temperature SHG on-off switching with a high contrast ratio of 300:1 along with good switching stability, as evidenced by SHG cycling studies at heating/cooling rates ranging from 5 to 50 K/min. This SHG study also sets new standards for the field of SHG switching by providing a method to quantify the thermal responsiveness of SHG-switchable materials using the treq (time requirement) parameter. Overall, our findings show that the halogenation strategy has led to the discovery of a rare example of an RP perovskite exhibiting coexistence of white-light emission, SHG on-off thermal bistability, ferroelectricity, and negative linear thermal expansion.

Crystal growth, linear optical, thermal, mechanical and third-order nonlinear optical properties of 1,3-diphenyl prop‑2-en-1-one single crystals

This work brings out the viability of the chalcone derivative (E)-1,3-diphenyl-2-propen-1-one (DPP) for industrial applications in nonlinear optical technology and device fabrication, through investigations on its crystal structure and nonlinear optical properties. The unit cell features of the DPP single crystals grown by slow evaporation solution growth method have been determined and hkl values indexed. The optical transparency of DPP in the near infrared and visible range is found to be admirable and an optical bandgap of 3.42 eV is revealed in the UV–Vis-NIR analysis. The work hardening coefficient (n) of DPP, determined as 2 from Vickers microhardness measurement, shows the moderate mechanical strength of the crystal. The Laser Damage Threshold value of 3.9 GW/cm2 sheds light on the high tolerance of DPP to optical damage and suggests its suitability in device fabrication. The potential of DPP crystal in nonlinear optical applications is suggested from its superior value of 1.16×10−7 esu for third order susceptibility and appealing values of other nonlinear optical parameters.

Intensity-dependent SA-RSA switching in nickel-chromium transition metal oxide nanoparticles

Semiconductor systems are suitable materials for nonlinear-optical applications because of their large optical nonlinearities and rapid response. In this work, NiCrxFe2-xO4 nanoparticles for x = 0.5, 1, 1.5, 2 are synthesized by the co-precipitation method, and its structural, vibrational, and nonlinear optical properties are characterized. All the prepared samples belong to a cubic spinel structure except the sample x = 2, with a rhombohedral structure, with crystallite sizes ranging from 30 to 40 nm and a bandgap ranging from 3.3 eV to 4eV. The aqueous samples show a saturable absorption on irradiating a 532 nm pulsed laser at low intensities and reverse saturable absorption with saturation effects at higher intensities.

DFT study of electronic and nonlinear optical properties of alkaline earth metals and superalkalis doped all-cis-1, 2, 3, 4, 5, 6-hexafluorocyclohexane as an efficient excess electron system

Continual advancements are being pursued to discover innovative strategies for developing materials with remarkable nonlinear optical (NLO) response. Herein, electronic, geometric, thermodynamic and NLO properties of excess electron systems based on stacked Janus dimer, all-cis-1,2,3,4,5,6-hexafluorocyclohexane (C6H6F6)2 are thoroughly investigated. The excess electron systems are designed by doping alkaline earth metals (AEMs) on fluorine face and superalkalis on hydrogen face of Janus dimer. The higher values of vertical ionization energies (VIE) and interaction energies (Eint), confirm the electronic and thermodynamic stabilities of the designed complexes, respectively. Natural bond orbital (NBO) analysis is performed, and the excess electron character of the complexes is confirmed through frontier molecular orbital (FMO) analysis by highest occupied molecular orbital (HOMO) iso-densities. FMO shows a significant decrease in energy gaps (Egap) of the complexes (i.e., Eg = 1.80–3.12 eV), compared to the stacked Janus dimer (i.e., Eg = 9.41 eV). The transparency of the complexes to UV region is confirmed through UV–vis analyses, revealing their maximum absorption in visible and near-IR regions. The higher NLO response of the designed excess electron systems is further proved by the greater values of first hyperpolarizability (β o ) i.e., up to 1.70 × 106 au. Moreover, the time dependent-density functional theory (TD-DFT) computations and two-level model are employed to investigate the controlling factors of hyperpolarizability, illustrating the contribution of transition energy (∆E3), change in dipole moment (∆μ) and oscillator strength (f o ) in controlling the β o . Ab-initio molecular dynamics (AIMD) simulation further confirm that the designed superalkalide complexes are kinetically and thermally stable. The thorough investigation of these excess electron systems proves them an appropriate candidate for NLO applications.

Integrated chirped photonic-crystal cavities in gallium phosphide for broadband soliton generation

Chirped mirrors have underpinned advances in ultra-fast lasers based on bulk optics but have yet to be fully exploited in integrated photonics, where they could provide a means to engineer otherwise unattainable dispersion profiles for a range of nonlinear optical applications, including soliton frequency comb generation. The vast majority of integrated resonators for frequency combs make use of microring geometries, in which only waveguide width and height are varied to engineer dispersion. Here, we present an integrated photonic-crystal Fabry–Pérot resonator made of gallium phosphide (GaP), a material exhibiting a Kerr nonlinearity 200 times larger than that of silicon nitride and a high refractive index that permits the creation of strongly chirped photonic-crystal mirrors. Leveraging the additional degrees of freedom provided by integrated chirped mirrors, we disentangle optical losses from dispersion. We obtain an overall dispersion that is more anomalous than that achievable in both silicon nitride and gallium phosphide ring resonators with the same free-spectral range (FSR), while simultaneously obtaining higher quality factors than those of GaP ring resonators. With subharmonic pulsed pumping at an average power of 23.6 mW, we are able to access stable dissipative Kerr frequency combs in a device with a FSR of 55.9 GHz. We demonstrate soliton formation with a 3-dB bandwidth of 3.0 THz, corresponding to a pulse duration of 60 fs. This approach to cavity design based on photonic-crystal reflectors offers nearly arbitrary dispersion engineering over the optical transparency window of the nonlinear material.

Study of Solvent Dependent on Third-Order Nonlinear Optical and Thermo-Optic Coefficient of Malachite Green Dye.

This study reveals the solvent dependent third-order nonlinear optical (NLO) features of malachite green (MG) dye using Z-scan technique. MG dye is dissolved in polar solvents, including DMF, DMSO, ethanol, acetone, methanol, and 1-propanol. The study employs the Z-scan instrument, using a continuous wave (CW) laser as the excitation source, operating at a wavelength of 650nm. The closed aperture (CA) and open aperture (OA) Z-scan techniques are used to assess the nonlinear indices of refraction (n2) and nonlinear coefficient of absorption (β) of MG dye. MG dye demonstrates both saturable absorption (SA) and reverse saturable absorption (RSA) in the OA Z-scan results, due to negative and positive NLO absorption coefficients. MG dye proves a self-defocusing NLO refractive index while operating under low-power conditions. The third-order NLO susceptibility (χ3) of MG dye in various liquids are calculated to be the order of 10-6 esu. Multilinear regression fit is applied here to investigate the various intermolecular interactions between the solute and solvent. MG dye exhibited large thermo-optic coefficient of the order of 10- 3 K- 1 is observed. The results give important new information about the characteristics of MG dye and indicate potential sources of material for NLO applications in future.

Impact of gamma irradiation on optical and nonlinear properties of Indium chloride phthalocyanine thin films

This study investigates the impact of gamma radiation on indium chloride phthalocyanine (lnPcCl) thin films, which were prepared via vacuum thermal evaporation. x-ray diffraction revealed the amorphous structure of the films, with increasing gamma doses causing more noticeable structural disorders. Optical analysis showed a slight decrease in the optical band gap energy and a significant reduction in the fundamental band gap energy. Additionally, higher gamma doses led to decreased transmittance and increased reflectance. The study also observed substantial enhancements in nonlinear optical parameters, such as third-order nonlinear susceptibility (χ(3)) and nonlinear refractive index (n 2). These findings suggest the potential of gamma-irradiated lnPcCl films for advanced optoelectronic and nonlinear optical applications.