Weak Birefringence Research Articles

Wave patterns of the coupled nonlinear Schrödinger equations in photonic crystal fibers with four-wave mixing

Abstract In this paper, we examine the behavior of modulation instability within photonic crystals. The model employed is the coherent coupled nonlinear Schrödinger equation, incorporating weak birefringence and four-wave mixing, which arises at the edge of the optical mode. The linear analysis is used to derive the modulation instability spectrum. Throughout the modulation instability spectrum, we identify both stable and unstable modes, thereby confirming the breakdown of the plane wave. For certain four-wave mixing parameters, the amplitude of the modulation instability spectrum and its bandwidths expand, creating an opening for localized structures to emerge. Another aspect of this study has been demonstrated in normal and anomalous dispersion regimes where an increasing initial amplitude of the plane wave is fulfilled. Specifically, numerical simulations highlight the occurrence of Benjamin-Feir instability, where wave patterns emerge under the influence of four-wave mixing. Additionally, solitonic waves are generated, demonstrating the presence of Akhmediev breathers and other modulated structures, confirming that photonic crystals with four-wave mixing are conducive to these formations. The findings from this study could inform future research in the development of nonlinear photonic waveguides.

Annealing temperature-dependent induced supramolecular chiroptical response of copolymer thin films studied by pump-modulated transient circular dichroism spectroscopy

Copolymer thin films showing induced supramolecular chirality are of considerable interest for optoelectronic applications such as organic light-emitting diodes. Here, we introduce a new helicene-like chiral additive with two octyloxy substituents which displays excellent chiral induction properties in an achiral polyfluorene copolymer, leading to a circular dichroism (CD) response of up to 10,000 mdeg. This chiral inducer also displays very good thermal stability, which enables us to perform an extended study on the induced chiroptical properties of the cholesteric copolymer thin films annealed at different temperatures in the range 140–260 °C. Starting from about 180 °C, a distinct change in the morphology of the CD-active film is observed by CD microscopy, from micrometre-size granular to extended CD-active regions, where the latter ones display skewed distributions of the dissymmetry parameter gabs. Broadband Müller matrix spectroscopy finds a pronounced CD and circular birefringence (CB) response and only weak linear dichroism (LD, LD’) and linear birefringence (LB, LB’). Ultrafast transient CD spectroscopy with randomly polarised excitation reveals a clean mirror-image-type transient response, which shows a second-order decay of the S1 population due to singlet–singlet annihilation processes.

Repetition rate difference, stability and polarization extinction ratio of single-cavity polarization-multiplexed fiber laser with weak birefringence

We investigated a stable single-cavity polarization-multiplexed ring fiber laser with weak birefringence. The feasibility of the weak intrinsic residual birefringence to induce polarization-multiplexed pulses with low repetition rate difference under dual/triple-comb modes is experimentally verified. The significant evolution of the relative stability and polarization extinction ratio, and its physical mechanism are revealed when adjusting the linear intracavity loss. These results provide further understanding of the influence of birefringence amount, loss, dispersion, and multiple pulse interaction on the polarization-multiplexed pulses. Meanwhile, the intriguing pulse characteristics such as low repetition rate difference, qualified relative stability and unique wavelength/polarization multiplexing are experimentally obtained, showing the high potential to promote the wide applicability and performance improvement of multiple-comb metrology such as dual/triple-comb frequency measurement.

Resonantly Enhanced Optical Birefringence in Ultrathin High‐Index WS2 Metasurfaces

AbstractOptical birefringence plays an important role in the manipulation of polarization states of light. However, the weak birefringence in common birefringent materials restricts the device thickness to tens of microns for desired phase retardation. Although recent advances in dielectric metasurfaces have enabled remarkable birefringence using structurally anisotropic nanostructures, the refractive index contrast between the dielectric and the air cladding fundamentally limits the thickness of metasurfaces to a fraction of a micron to obtain the required phase retardation. Here, birefringent resonances in high‐index tungsten disulfide (WS2) metasurfaces are utilized to push the thickness limit down to the deep subwavelength scale. The inherent high‐index property of WS2 enables birefringent resonances in WS2 metasurfaces which consist of anisotropic nanostructures with a thickness of only 50 nm. Such birefringent resonances enhance the light‐matter interaction and produce an unprecedented birefringence (Δneff) about 4. As a result, it is experimentally realized that circular‐to‐linear polarization conversion with a normalized efficiency of ≈90% within an incident angle range up to ±10°. The results break the fundamental limit of birefringent devices and provide strategies for creating ultimate thin polarization optical devices.

Suppression of polarization instability in ultrashort Fabry–Pérot fiber laser

Due to the weak birefringence from the intracavity fiber, vector solitons are easily generated in GHz-fundamental-repetition-rate mode-locked fiber lasers, which can exhibit diverse time-varying polarization dynamics. These soliton dynamics can lead to polarization instability of the pulse train, which prevents industrial and scientific applications that require stable and uniform pulse trains. However, it is hard to suppress the polarization instability due to insufficient space for inserting traditional polarizers and difficulties in enhancing the fiber birefringence in the ultrashort fiber laser cavity. To this end, here we propose an alternative method that can effectively transform the vector solitons into scalar solitons by exploring gold nanorod (GNR) film as a polarizer in the laser cavity. First, the theoretical studies of polarization dynamics in ultrashort Fabry–Pérot (FP) fiber lasers with and without intracavity GNR film are conducted. The results indicate that the use of GNR film can significantly suppress the polarization instability and generate scalar solitons. Then, the large-scale preparation of GNRs with longitudinal surface plasmon resonance absorption peak of >1380 nm is realized by a two-step seed-mediated method, and the GNR film with an operation wavelength range covering the C + L band is fabricated by electrospinning. Finally, we apply the GNR film to a 2-cm-long FP fiber laser, and convert polarization rotation vector solitons to linearly polarized solitons (LPSs) at 1.5 μm. The polarization extinction ratio of the improved LPS pulse train is up to 33 dB.

Hydrazone organics modulation for h-shaped nanosecond pulse generation in 1.3-km ultra-long mode-locked erbium-doped fiber laser

We report an ultra-long erbium-doped fiber laser based on hydrazone organisms that generates a tunable h-shaped pulse at the trailing edge and can readily convert nanosecond pulses into h-shaped pulse. By changing the polarization state in the cavity of the ultra-long laser, the nanosecond pulse can be converted to an h-shaped pulse at a certain power level. At this time, the pump power is increased, ranging from 208.2 mW to 393.2 mW, and the pulse trailing edge can be tuned regularly, with a tuning range from 8.2 ns to 17.9 ns. The experimental results show that the variation of the h-shaped pulse along the width is related to the clamping effect of the peak power and the weak birefringence effect. In conclusion, the investigation of ultra-long laser resonators based on real saturable absorbers is helpful to further explore the anomalous dispersion range of ultra-long round-trip pulses and their potential applications.

Influence of Defects-Induced Stresses on Birefringence in SrTiO3 Single Crystals

Significant applications of SrTiO3 single crystals in electronics require knowledge about the influence of structural imperfections on their optical properties. Birefringence temperature changes were investigated in a few SrTiO3 single crystals in a broad temperature range, from 85 K to 250 K. The birefringence was found to be a non-linear function below the transition Ts at 105 K, and non-linear changes in the optical indicatrix orientation accompanied it. A weak residual birefringence was permanently present a dozen degrees above the phase transition temperature Ts. This is mainly connected with dislocations, which induce local stresses and shift transition points even up to about 200 K. The essential role of imperfections on optical properties was studied in a SrTiO3 24° bi-crystal reduced at 1000 K and under low oxygen pressure. In such an intentionally defected crystal, an increase of non-linearities in Δn(T) dependence was observed below and above the transition point Ts.

The Effect of Mesogenic Coronas on the Type and Anisotropy of Gold Nanoparticle Superlattices: When Can the Tail Wag the Dog?

The correlation between the size of nanoparticles, the structure and shape of mesogenic ligands and the ensuing assembly behaviour is not really understood. Closer inspection shows very surprising features. Here, 2- and 4-nm gold nanoparticles (NPs) were synthesized, and grafted with a forked ligand containing two rod-like mesogens in its branches: one cholesterol, the other with azobenzene. The 4-nm NPs also contained n-hexylthiol as co-ligand. They were found to form a FCC cubic superlattice, whereas the 2-nm NPs form hexagonal HCP with weak birefringence, hence with partially oriented ligands. The structures were compared with those of related systems containing a range of different azobenzene-to-cholesterol ratios, all giving body-centred tetragonal superlattices with various degrees of anisotropy. Geometric analysis is presented in terms of the asphericity of the NPs' surroundings, requirement for space-filling and structural anisotropy. Some general rules are derived to help design the soft corona around the NPs in order to obtain superlattices with the desired structure and anisotropy.

Periphyton (microbiome) of filamentous algae studied by polarization microscopy, aided also by some contrasting optical methods.

Polarization microscopy, possibly together with some contrast techniques (dark field and color phase contrast), was used to study the periphyton (microbiome) growing on filamentous green algae. The material containing filamentous algae with periphyton on the surface was collected in the villages of Sýkořice and Zbečno (Křivoklátsko Protected Landscape Area). The objects were studied in a LOMO MIN-8 St. Petersburg polarizing microscope and a Carl Zeiss Jena NfpK laboratory microscope equipped with an In Ph 160 basic body with variable dark field or color phase contrast and a Nikon D70 DSLR digital camera. Cells of filamentous algae of the genera Cladophora, Vaucheria, and Oedogonium were studied and the periphyton attached to them formed by cyanobacteria of the genera Chamaesiphon and Pleurocapsa and algae of the genera Characium, including diatoms of the genera Eunotia and Synedra. In all cases, the cell walls of the host algae showed a very strong birefringence. In contrast, the walls of cyanobacteria of the genera Chamaesiphon and Pleurocapsa were characterized by a much weaker birefringence (Pleurocapsa somewhat thicker), and the diatom frustules of the genera Eunotia and Synedra were almost without a birefringence. Strongly birefringent granules were found in the cytoplasm of the green alga of the genus Characium, which forms periphyton on the filamentous green algae of the genus Vaucheria. The periphyton on the filamentous alga of the genus Oedogonium, formed by cyanobacteria of the genus Pleurocapsa and diatoms of the genera Eunotia and Synedra, deposited in a massive layer of mucus containing birefringent crystals, showed a particularly strong birefringence. At the end of the vegetation of filamentous algae, their parts and remnants of periphyton (diatom frustules and crystals) became part of the detritus at the bottom of the culture vessel. The use of polarization microscopy in the study of filamentous algae with periphyton on the surface allows us not only to determine the birefringence of the observed structures, but also to partially deduce their chemical composition, or regular arrangement ofparticles, so-called shape birefringence.

Generation of h–Shaped pulse in a mode–Locked erbium-doped fiber laser

In this paper, the generation of h-shaped pulse is demonstrated in a nonlinear polarization rotation mode-locked erbium-doped fiber laser (MLEDFL). The length of the entire cavity is about 2506 m to enhance the nonlinear effect in the cavity. The multi-pulse state is obtained firstly under the certain pump power and polarization state. By further adjusting the polarization controller the h-shaped pulse with sharp top and flat bottom is generated under the pump power of ∼100 mW. And the duration of pulse is tuned with a range of 54.63–470 ns. The width and intensity of pulse trailing part vary differently during the process of increasing pulse width. The results indicate that the peak power clamping effect and weak birefringence effect dominate in different h-shaped pulse forming process.

All-SBS fiber-based setup for optical frequency comb generation utilizing a pump recycling technique and comb line isolation by implementing Brillouin amplification.

We describe an all-stimulated Brillouin scattering (SBS) fiber-based setup for the generation, amplification, and isolation of frequency components from an optical frequency comb (OFC). The cascaded SBS-OFC is obtained by utilizing pump and Stokes power recycling techniques. A total of >15 comb lines within a 45 dB bandwidth, having an average power of 16 dBm, is observed in the 1550 nm wavelength region of operation. By implementing a polarizer-analyzer setup exploiting the weak birefringence in silica fibers, we amplified and isolated the first Stokes component of the generated comb. The isolated component at 1550.03 nm was amplified by ≈55dB. In order to verify the isolation of a single comb line, the SBS-OFC is intensity modulated using sinusoidal signals of different frequencies, and the modulation is detected after the comb line isolation. We also observe that with the increase in Brillouin pump power during comb line isolation, the spontaneous Brillouin noise acts as a limitation to the selective amplification process.

On the selection of materials for high-power laser optics based on analysis of focus shift and aberration induced by thermal gradient

Non-uniform (gradient) heating due to absorption of laser radiation in optical elements causes thermal lensing and paraxial focus shift and aberration leading to change in size and intensity profile of focused spot in optics operating with high-power lasers. Analysis of primary physical effects of geometrical deformation of optical surfaces in the form of aspheric bulges and transformation of the material into a gradient refractive medium makes it possible to estimate quantitatively the focus shift and aberrations for single-mode and multimode lasers, to formulate optimal relationships between the physical properties of optical materials for reduction of thermo-optical effects through compensating the effects from material thermal expansion by the effects due to change in the refractive index—condition of self-compensation or athermalization. Comparison of characteristics Temperature Coefficient of the Optical Pathlength and Thermo-Optical Ratio allows determining the optimal materials for the optics for high-power lasers: athermal crystalline quartz and specialty glasses, sapphire with extremely high thermal conductivity ensuring minimal temperature gradients. Optics made of these materials exhibit minimized thermal focus shift and aberration even when absorption of laser energy in bulk material and coatings, by contamination, scratches, and other surface defects. Weak birefringence of crystalline quartz and sapphire does not prevent their successive use in laser optics.

Comparison of the thermal focus shift and aberration between the single-mode and multimode lasers

Thermal lensing is a well-known but typically undesired effect during the use of laser optics. Nonuniform (gradient) heating due to absorption of high-power laser radiation in optical elements causes thermal lensing, paraxial focus shift, and aberration leading to changes in size and intensity profile of the focused spot in optics. Therefore, an analysis of primary physical effects of geometrical deformation of optical surfaces in the form of aspheric bulges and transformation of the material into a gradient refractive medium was conducted to quantitatively estimate the focus shift and aberrations. Since focus shift effects are different in the case of single-mode and multimode lasers, for both laser modes, the optimal relationships between the physical properties of optical materials for reduction in thermo-optical effects through compensating the material thermal expansion by the change in the refractive index—condition of self-compensation or athermalization were formulated. A comparison of the characteristics, namely, temperature coefficient of the optical pathlength and thermo-optical ratio allowed determination of the optimal materials for the optics for both single-mode and multimode high-power lasers: athermal crystalline quartz and specialty glasses, sapphire with extremely high thermal conductivity ensure minimal temperature gradients. Optics made of these materials exhibit a minimized thermal focus shift and aberration even during the absorption of laser energy in the bulk material and coatings by contamination, scratches, and other surface defects. Weak birefringence of crystalline quartz and sapphire does not prevent their successive use in laser optics.

Four-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi-Pasta-Ulam-Tsingou recurrence.

Modulation instability, breather formation, and the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomena are studied in this article. Physically, such nonlinear systems arise when the medium is slightly anisotropic, e.g., optical fibers with weak birefringence where the slowly varying pulse envelopes are governed by these coherently coupled Schrödinger equations. The Darboux transformation is used to calculate a class of breathers where the carrier envelope depends on the transverse coordinate of the Schrödinger equations. A "cascading mechanism" is utilized to elucidate the initial stages of FPUT. More precisely, higher order nonlinear terms that are exponentially small initially can grow rapidly. A breather is formed when the linear mode and higher order ones attain roughly the same magnitude. The conditions for generating various breathers and connections with modulation instability are elucidated. The growth phase then subsides and the cycle is repeated, leading to FPUT. Unequal initial conditions for the two waveguides produce symmetry breaking, with "eye-shaped" breathers in one waveguide and "four-petal" modes in the other. An analytical formula for the time or distance of breather formation for a two-waveguide system is proposed, based on the disturbance amplitude and instability growth rate. Excellent agreement with numerical simulations is achieved. Furthermore, the roles of modulation instability for FPUT are elucidated with illustrative case studies. In particular, depending on whether the second harmonic falls within the unstable band, FPUT patterns with one single or two distinct wavelength(s) are observed. For applications to temporal optical waveguides, the present formulation can predict the distance along a weakly birefringent fiber needed to observe FPUT.

Effect of Single and Dual Hydrothermal Treatments on the Resistant Starch Content and Physicochemical Properties of Lotus Rhizome Starches.

Heat-moisture treatment (HMT) changed the morphology and the degree of molecular ordering in lotus rhizome (Nelumbo nucifera Gaertn.) starch granules slightly, leading to some detectable cavities or holes near hilum, weaker birefringence and granule agglomeration, accompanied with modified XRD pattern from C- to A-type starch and lower relative crystallinity, particularly for high moisture HMT modification. In contrast, annealing (ANN) showed less impact on granule morphology, XRD pattern and relative crystallinity. All hydrothermal treatment decreased the resistant starch (from about 27.7–35.4% to 2.7–20%), increased the damage starch (from about 0.5–1.6% to 2.4–23.6%) and modified the functional and pasting properties of lotus rhizome starch pronouncedly. An increase in gelatinization temperature but a decrease in transition enthalpy occurred after hydrothermal modification, particularly for hydrothermal modification involved with HMT. HMT-modified starch also showed higher pasting temperature, less pronounced peak viscosity, leading to less significant thixotropic behavior and retrogradation during pasting-gelation process. However, single ANN treatment imparts a higher tendency of retrogradation as compared to native starch. For dual hydrothermally modified samples, the functional properties generally resembled to the behavior of single HMT-modified samples, indicating the pre- or post-ANN modification had less impact on the properties HMT modified lotus rhizome starch.

The novel form of amyloidosis derived from EGF-containing fibulin-like extracellular matrix protein 1 (EFEMP1) preferentially affects the lower gastrointestinal tract of elderly femalesa.

To characterise the clinicopathological features of amyloidosis due to EGF-containing fibulin-like extracellular matrix protein 1 (EFEMP1), a newly described amyloid type. We identified cases by searching the Mayo Clinic amyloid liquid chromatography and tandem mass spectrometry typing database for specimens with the universal amyloid signature proteins, abundant EFEMP1 spectra and absence of other specific amyloid precursor proteins. We also developed an immunohistochemical stain for EFEMP1 applicable to formalin-fixed tissue sections and performed electron microscopy in one case. We identified 33 specimens from 32 patients with EFEMP1 amyloid. Most patients were female (91%) with a mean age of 75years, and most specimens (94%) were from the bowel. EFEMP1 amyloid was incidentally identified in specimens biopsied/resected for a variety of clinical indications. In bowel specimens, EFEMP1 amyloid involved blood vessels and interstitium of the lamina propria, submucosa and/or muscularis propria. Although the EFEMP1 deposits were weakly to moderately Congo red-positive with absent to weak birefringence, they were strongly positive for EFEMP1 by immunohistochemistry, had the characteristic fibrillar ultrastructure of amyloid and were readily identified by mass spectrometry. EFEMP1 amyloid is a recently described novel amyloid type that predominantly affects the bowel of elderly females. Because EFEMP1 amyloid is only weakly Congo red-positive, it may be overlooked without a high index of suspicion. However, its characteristic microanatomical distribution is highlighted by immunohistochemistry and its identity is readily confirmed by mass spectrometry. Based on its distinctive features, we propose that EFEMP1 amyloidosis be considered a new amyloid type.

Simultaneous use of Interphako interference contrast and polarization microscopy in the study of microorganisms.

Simultaneous application of polarization microscopy and Interphako interference contrast has been used to study the internal structure of algal cells. The interference contrast technique showed fine cell structures (important is the selection of interference colors according to the Mach-Zehnder interferometer setting). In a polarization microscope, the crossed polarization filters together with the first-order quartz compensator mounted turntable showed the maximum birefringence of the individual structures. Material containing green algae was collected in the villages Sýkořice and Zbečno, Protected Landscape Area (PLA) Křivoklátsko. The objects were studied in a Carl Zeiss Jena NfpK laboratory microscope equipped with an In 160 base body with an Interphako In contrast interference module including a Mach-Zehnder interferometer with variable phase contrast, a special condenser with interchangeable aperture plates, a turntable, a Meopta Praha polarizer, a LOMO Sankt Petersburg analyzer, and a quartz compensator with first-order red and the digital camera DSLR Nikon D 70. Green algae of three orders were studied: Siphonocladales, Zygnematales, and Desmidiales. Anisotropic structures were found in all studied representatives of the green algae of the phylum Chlorophyta. Especially their cell walls showed strong birefringence (in all representatives of these orders). On the other hand, a representative of the order Siphonocladales (the genus Cladophora, Cladophoraceae, Ulvophyceae) was rarely found to display weak birefringent granules of storage substances due to the setting of the Mach-Zehnder interferometer and the use of the first-order compensator (interference colors are intensified). In addition, a very weak birefringence of periphyton cells (microbial biofilm) was found. In the study of the second algae of the genus Spirogyra (Zygnemataceae, Zygnematales, Conjugatophyceae), a strongly birefringent connecting wall between algal cells was found in contrast to the weaker birefringence of the peripheral wall. It was the use of Interphako interference contrast together with polarization filters and a first-order quartz compensator that particularly emphasized the central part of the connecting wall. In the study of the twinned Pleurotaenium algae (Desmidiaceae, Desmidiales, Conjugatophyceae), a strongly birefringent wall was found along the periphery of the cell with a nucleus in the middle part (isthmus). In this narrowing in the center of the cell, a sharply delimited birefringent edge of the cell wall is visible, especially when using Interphako interference contrast along with crossed polarization filters and a first-order quartz compensator. In conclusion, Interphako interference contrast provides a high degree of image contrast in a microscope and, if suitably simultaneously complemented by polarization microscopy (including a first-order quartz compensator), it will allow us to infer some of the composition of the investigated structures. However, working with Interphako interference contrast is considerably more difficult (setting Mach-Zehnder interferometer) than using other contrast techniques (positive and negative phase contrast, color contrast, relief contrast, and dark field).

Effect of Ultrasonic and Microwave Dual-Treatment on the Physicochemical Properties of Chestnut Starch.

This work examined the effect of ultrasound and microwave treatments, separate and in combination, on the physicochemical and functional properties of chestnut starch. The results revealed that the ultrasonic-microwave (UM) and microwave-ultrasonic (MU) dually modified samples exhibited more severe surface damage, weaker birefringence, and lower relative crystallinity and gelatinization enthalpy than the native and single-treated starches. The UM samples showed the highest oil absorption capacity, and the MU samples showed the highest water absorption capacity and the best freeze-thaw stability (five cycles) among all samples. The swelling power, peak, trough, final, and breakdown viscosities, and pasting temperature all decreased regardless of single or dual modification. This study provides a reference for potential industrial applications of ultrasound and microwave treatments for the modification of chestnut starch.

Shear-Induced Isotropic-Nematic Transition in Poly(ether ether ketone) Melts.

In a previous work on a poly(ether ether ketone) (PEEK) melt, above its nominal melting temperature (Tm ≅ 335 °C), a severe Cox-Merz rule failure was observed. The abrupt decrease in the apparent shear viscosity was ascribed to the formation of flow-induced crystallization precursors. Here shear rheology and reflection polariscope experiments are utilized to unravel the structural changes occurring under shear on a similar PEEK melt above Tm. Three regimes of the flow curve were identified from low (0.01 s-1) to high shear rates (1000 s-1): (I) an isotropic structure with weak birefringence due to polymer chain orientation and mild shear thinning for γ̇ < 1 s-1, (II) an isotropic-nematic transition accompanied by strong birefringence, two steady-state viscosities, and large nematic polydomain director fluctuations, and (III) shear-thinning behavior with an η ∼ γ̇-0.5 dependence for γ̇ > 20 s-1, typically found in nematic fluids. The findings reported in this experimental work suggest that the nematic phase may represent the early stage of the formation of shear-induced crystallization precursors.

Period doubling eigenstates in a fiber laser mode-locked by nonlinear polarization rotation.

Due to the weak birefringence of single mode fibers, solitons generated in fiber lasers are indeed vector pulses and exhibit periodic parameter change including polarization evolution even when there is a polarizer inside the cavity. Period doubling eigenstates of solitons generated in a fiber laser mode-locked by the nonlinear polarization rotation, i.e., period doubling of polarization components of the soliton, are numerically explored in detail. We found that, apart from the synchronous evolution between the two polarization components, there exists asynchronous development depending on the detailed operation conditions. In addition, period doubling of one polarization component together with period-one of another polarization component can be achieved. When the period tripling window is obtained, much complexed dynamics on the two polarization components could be observed.