Laser shaping and optical power limiting of pulsed Laguerre–Gaussian laser beams of high-order radial modes in fullerene C60

We study the strong nonlinear optical dynamics of nanosecond pulsed Laguerre–Gaussian laser beams of high-order radial modes with zero orbital angular momentum propagating in the fullerene C60molecular medium. It is found that the spatiotemporal profile of the incident pulsed Laguerre–Gaussian laser beam is strongly reshaped during its propagation in the C60molecular medium. The centrosymmetric temporal profile of the incident pulse gradually evolves into a noncentrosymmetric meniscus shape, and the on-axis pulse duration is clearly depressed. Furthermore, the field intensity is distinctly attenuated due to the field-intensity-dependent reverse saturable absorption, and clear optical power limiting behavior is observed for different orders of the input pulsed Laguerre–Gaussian laser beams before the takeover of the saturation effect;the lower the order of the Laguerre–Gaussian beam, the lower the energy transmittance.

Study on the optical limiting properties of the mixed liquid of carbon black suspensions and green tea solution by multi-pulse laser

The optical limiting properties of the mixed liquid of carbon black suspensions （CBS） and green tea solution were studied by using an 8 ns laser pulse at 532 nm. The optical limiting effects of the CBS and mixed liquid have been compared between 5 and 10 Hz repetition frequencies with nanosecond laser pulse. The experimental results indicate that the optical limiting threshold of the sample with the incidence laser at 10 Hz repetition frequency is lower than at 5 Hz repetition frequency. The possible reasons for the influence of the repetition frequency on the samples are discussed. And by observing the optical radiant distributions when the laser pulse passing through different samples, a possible mechanism for the observed effects is suggested. At the same time, the result shows that the optical limiting of CBS is the dominant factor to optical limiting of the mixed liquid.

Analyzing the Effect of the Intra-Pixel Position of Small PSFs for Optimizing the PL of Optical Subpixel Localization

Subpixel localization techniques for estimating the positions of point-like images captured by pixelated image sensors have been widely used in diverse optical measurement fields.With unavoidable imaging noise,there is a precision limit(PL)when estimating the target positions on image sensors,which depends on the detected photon count,noise,point spread function(PSF)radius,and PSF’s intra-pixel position.Previous studies have clearly reported the effects of the first three parameters on the PL but have neglected the intra-pixel position information.Here,we develop a localization PL analysis framework for revealing the effect of the intra-pixel position of small PSFs.To accurately estimate the PL in practical applications,we provide effective PSF(e PSF)modeling approaches and apply the Cramér–Rao lower bound.Based on the characteristics of small PSFs,we first derive simplified equations for finding the best PL and the best intra-pixel region for an arbitrary small PSF;we then verify these equations on real PSFs.Next,we use the typical Gaussian PSF to perform a further analysis and find that the final optimum of the PL is achieved at the pixel boundaries when the Gaussian radius is as small as possible,indicating that the optimum is ultimately limited by light diffraction.Finally,we apply the maximum likelihood method.Its combination with e PSF modeling allows us to successfully reach the PL in experiments,making the above theoretical analysis effective.This work provides a new perspective on combining image sensor position control with PSF engineering to make full use of information theory,thereby paving the way for thoroughly understanding and achieving the final optimum of the PL in optical localization.

Tailoring optical properties of TiO_2 in silica glass for limiting applications

We present the linear and nonlinear optical studies on TiO2-SiO2 nanocomposites with varying compositions. Opti- cal band gap of the material is found to vary with the amount of SiO2 in the composite. The phenomenon of two-photon absorption （TPA） in TiO2/SiO2 nanocomposites has been studied using open aperture Z-scan technique. The nanocom- posites show better nonlinear optical properties than pure TiO2, which can be attributed to the surface states and weak dielectric confinement of TiO2 nanoparticles by SiO2 matrix. The nanocomposites are thermally treated and similar studies are performed. The anatase form of TiO2 in the nanocomposites shows superior properties relative to the amorphous and rutile counterpart. The involved mechanism is explained by rendering the dominant role played by the excitons in the TiO2 nanoparticles.

Measurement of stimulated Brillouin scattering(SBS) threshold based on waveform variation of SBS optical limiting

This paper proposes a method for measuring the stimulated Brillouin scattering （SBS） threshold based on waveform variation of SBS optical limiting. The output waveforms for different pump power densities are numerically simulated, and validated in the Nd：YAG seed-injected laser system. The results indicate that SBS does not take place in the case of a low pump power density and thus the output power scales up linearly with pump power. Once the pump power density exceeds the SBS threshold, SBS takes place and thereby the energies are transferred from pump to Stokes. As a result, a small shoulder appears in the trailing edge of the output waveform, which provides another method to determine the SBS threshold.

Optical power limiting of ultrashort hyper-Gaussian pulses in cascade three-level system

Propagation of strong femtosecond hyper-Gaussian pulses in a cascade three-level molecular system is studied by solving numerically the Maxwell–Bloch equations by the iterative predictor-corrector finite-difference time-domain method.Optical power limiting behavior induced by strong nonlinear two-photon absorption is observed for different orders of the femtosecond hyper-Gaussian pulses. Pulses of a higher order temporal profile are found to have a wider power range of optical limiting but a larger output saturation intensity. Both the output saturation value and the damage threshold of optical power limiting decrease with pulse duration increasing. The decrease of the pulse area along the pulse propagation is much slower than that obtained from the two-photon area theorem due to invalidity of the slowly varying amplitude approximation and the monochromatic field hypothesis.

Two-photon Absorption and Optical Power Limiting Properties of Two Novel Dibenzothiophene-based Chromophores

Two novel V-shaped symmetric chromophores： E-2,8-bis（4-vinyl-4-carbazol-9-yl）diben- zothiophene （abbreviated as SK-G1） and E-2,8-bis（4-vinyl-4-triphenylamino） dibenzothiophene （abbreviated as ST-G1） have been synthesized and characterized. Their two photon absorption properties were measured by the open-aperture femtosecond Z-scan technique and the nanosecond nonlinear optical transmission （NLT）, respectively, when pumped by Ti： sapphire laser at 750 nm and 800 nm.

Performance analysis of optical burst switching node with limited wavelength conversion capabilities

The systematical and scalable frameworks were provided for estimating the blocking probabilities under asynchronous traffic in optical burst switching(OBS) nodes with limited wavelength conversion capability(LWCC) . The relevant system architectures of limited range and limited number of wavelength converters(WCs) deployed by a share-per-fiber(SPF) mode were developed,and the novel theoretical analysis of node blocking probability was derived by combining the calculation of discouraged arrival rate in a birth-death process and two-dimensional Markov chain model of SPF. The simulation results on single node performance verify the accuracy and effectiveness of the analysis models. Under most scenarios,it is difficult to distinguish the plots generated by the analysis and simulation. As the conversion degree increases,the accuracy of the analysis model worsens slightly. However,the utmost error on burst loss probability is far less than one order of magnitude and hence,still allows for an accurate estimate. Some results are of actual significance to the construction of next-generation commercial OBS backbones.

Capacity Scaling Limits and New Advancements in Optical Transmission Systems

Optical transmission technologies have gone through several generations of development.Spectral efficiency has significant ly improved,and industry has begun to search for an answer to a basic question：What are the fundamental linear and nonlin ear signal channel limitations of the Shannon theory when there is no compensation in an optical fiber transmission system？Next-generation technologies should exceed the 100G transmis sion capability of coherent systems in order to approach the Shannon limit.Spectral efficiency first needs to be improved be fore overall transmission capability can be improved.The means to improve spectral efficiency include more complex modulation formats and channel encoding/decoding algorithms,prefiltering with multisymbol detection,optical OFDM and Ny quist WDM multicarrier technologies,and nonlinearity compen sation.With further optimization,these technologies will most likely be incorporated into beyond-100G optical transport sys tems to meet bandwidth demand.

PREPARATION OF SOLUBLE SUBSTITUTED POLYACETYLENE OPTICAL LIMITING MATERIAL

Two novel polyacetylenes bearing nonlinear optical chromophoric group poly（3-（4-[4-（n-butyloxy） phenylazophenyl]carbonyl）oxy-1-propyne） （poly（1a）） and poly（3-（4-[4-（n-heptyloxy）phenylazophenyl]carbonyl）-oxy-l- propyne） （poly（lb）） were synthesized with [Rh（nbd）Cl]2-EtaN as catalysts. These polyacetylenes are soluble by using an alkyl spacer and an alkyloxyl group as a substituent. They were characterized by FTIR, NMR, GPC and UV-Vis and their optical limiting and nonlinear optical properties were investigated using 8 ns pulse at 532 nm wavenumber. The results show that these soluble functional polyacetylenes possess optical limiting properties and large nonlinear optical properties and poly（1b） possesses better optical limiting and nonlinear optical properties than poly（ 1 a）.

Thiophene-fluorene derivatives with high three-photon absorption activities and their application to optical power limiting

The three-photon absorption （3PA） properties of two thiophene-fluorene derivatives （abbreviated as MOTFTBr and ATFTBr） have been determined by using a Q-switched Nd：YAG laser pumped with 38ps pulses at 1064nm in DMF. The measured 3PA cross-sections are 152×10^-78cm^6s^2 and 139× 10^-78cm^6s^2, respectively. The optimized structures were obtained by AM1 calculations and the results indicate that these two molecules show nonplanar structures, and attaching different donors has different effects on the molecular structure. The charge density distributions during the excitation were also systematically studied by using AM1 method. In addition, an obvious optical power limiting effect induced by 3PA has been demonstrated for both derivatives.

Numerical analyses on optical limiting performances of chloroindium phthalocyanines with different substituent positions

Optical limiting properties of two soluble chloroindium phthalocyanines with a- and β-alkoxyl substituents in nanosecond laser field have been studied by solving numerically the coupled singlet-triplet rate equation together with the paraxial wave field equation under the Crank-Nicholson scheme. Both transverse and longitudinal effects of the laser field on photophysical properties of the compounds are considered. Effective transfer time between the ground state and the lowest triplet state is defined in reformulated rate equations to characterize dynamics of singlet-triplet state population transfer. It is found that both phthalocyanines exhibit good nonlinear optical absorption abilities, while the compound with a-substituent shows enhanced optical limiting performance. Our ab-initio calculations reveal that the phthalocyanine with a-substituent has more obvious electron delocalization and lower frontier orbital transfer energies, which are responsible for its preferable photophysical properties.

Investigation on the effect of beam divergence angle upon output waveform based on stimulated Brillouin scattering optical limiting

This paper investigates the effect of beam divergence angle on output waveform based on stimulated Brillouin scattering optical limiting.Output waveforms in the case of different pump divergence angles are numerically simulated,and validated in a Nd：YAG seed-injected laser system.The results indicate that a small pump divergence angle can lead to good interaction between pump and Stokes,and a platform can be easily realized in the transmitted waveform.In contrast,a peak followed by the platform appears when the divergence angle becomes large.

Optical Limiting Response in Er^(3+)-Doped TeO_2-Nb_2O_5-ZnO Glass

The nonlinear absorption properties of Er^3＋ doped telluride glass were investigated with picosecond laser pulses. The optical limiting response was measured with a transmission technique and reverse saturable absorption （RSA） with a Z-scan technique, which proved that the glass was a promising material for practical optical limiters. The experimental resulted showed that the excited absorption was responsible for the measured RSA, resulting in the optical limiting response. The measured data could be well simulated with a rate equation model to obtain the absorption cross sections of the excited state.

Synthesis, Structure, and Optical Limiting Properties of an Axial Substituted Bis(8-oxide quinoline)zirconium Phthalocyanine

A novel bis(8-oxide quinoline)zironium phthalocyanine [(OQ)2 Zr Pc] with two 8-oxide quinolone anions at the same axial positions has been successfully synthesized and its chemical structure has been assigned by the 1 H NMR, MS and two-dimensional correlation infrared(2D-IR) spectroscopy as well as by single-crystal X-ray structural analysis. It possessed a moderately effective nonlinear absorption coefficient βeff of 6.69×10-14cm/GW at 532 nm in DMF solution, implying it is a promising candidate for nonlinear optical materials.

Spectroscopic Properties and Three-photon Absorption Induced Optical Limiting of Series of Novel Nonlinear Chromophores

Three novel nonlinear chromophores with symmetric D-π-D molecular structure and extended conjugated length were synthesized. Solvatochromism analysis shows great symmetric intramolecular charge transfer occurring in chromophores by the enhancement in the dipole moment between the ground and excited states. The properties of optical power limiting induced by three-photon absorption （3PA） are demonstrated. Large 3PA coefficients and the corresponding molecular cross sections as high as 10^-74 cm^6s^2 were obtained for nanosecond laser pulses at 1.06μm from nonlinear transmission measurements.

Theoretical Analysis on Optical Limiting Properties of Newly Synthesized Graphene Oxide-Porphyrin Composites

Optical limiting （OL） properties and two-photon absorption （TPA） of a series of covalently linked graphene oxide-porphyrin composite materials have been investigated by numerically solving the rate equations and field intensity equation with an iterative predictor-corrector finite-difference time-domain technique in nanosecond time domain. Our results show that graphene oxide-porphyrin composites exhibit enhanced OL behavior and possess larger TPA cross section compared with individual porphyrins. Interestingly~ unlike the previous result that porphyrin with heavier central metal shows better nonlinear abilities than that with- out metal substitute, graphene oxide-metal free porphyrin composite has stronger nonlinear absorption properties compared with graphene oxide-metal porphyrin composite. The com- putational results are in reasonable agreement with the experimental ones. Special attention has been paid to the influence of thickness of the medium and pulse width on TPA cross sections, which presents that larger TPA cross sections are obtained as the medium is thicker or the pulse duration is wider.

Characterization and Optimization of Photonic Crystal Optical Power Limiters

In the work, there have been investigated the optical power limiting effects which occur in the nonlinear photonic crys-tals possessing saturable Kerr nonlinearity. The method is proposed which allows exact determination of the parame-ters of the structure as well as the radiation parameters which provide the limiting effect.

Variation of Two-photon Absorption Cross Sections and Optical Limiting of Compounds Induced by Static Electric Field

By numerically solving the Maxwell-Bloch equations using an iterative predictor-corrector finite-difference time-domain technique, we investigate propagating properties of a few-cycle laser pulse in a 4,4＇-bis（di-n-butylamino） stilbene （BDBAS） molecular medium when a static electric field exists. Dynamical two-photon absorption （TPA） cross sections are obtained and optical limiting （OL） behavior is displayed. The results show that when the static electric field intensity increases, the dynamical TPA cross section is enhanced and the OL behavior is improved. Moreover, both even- and odd-order harmonic spectral components are generated with existence of the static electric field because it breaks the inversion symmetry of the BDBAS molecule. This work provides a method to modulate the nonlinear optical properties of the BDBAS compounds.

A Polypyrrole Hybrid Material Self-Assembled with Porphyrin: Facial Synthesis and Enhanced Optical Limiting Properties

Polypyrrole/porphyrin nanohybrid (PPy/Tpp(OH)4 nanohybrid) have been synthesized through a self-assembled approach, and the assynthesized PPy/Tpp(OH)4 nanohybrid are characterized by Fourier-transform infrared, X-ray photoelectron spectroscopy, Raman spectroscopy, thermogravimetric analysis, Ultraviolet-visible absorption, scanning electron microscopy, and steady state fluorescence spectroscopic techniques. Formation of the PPy/Tpp(OH)4 nanohybrid dramatically improved the solubility and processability of the PPy-based nanomaterial. The nonlinear optical (NLO) properties of PPy/Tpp(OH)4 nanohybrid were measured by Z-scan at 532 nm with nanosecond laser pulse, the results indicating that PPy/Tpp(OH)4 nanohybrid exhibits a enhanced NLO property in comparison with the benchmark PPy and Tpp(OH)4 due to a combination of mechanisms.