Reanalysis of optical-axis perturbation in nonplanar ring resonators in ray matrix approach with appropriate coordinate systems

Ray matrix approach with appropriate coordinate systems has been proposed in this paper. It is employed to analyze the optical-axis perturbation in nonplanar ring resonators. The sensitivities of optical-axis decentration (SD) and optical-axis tilt (ST) in nonplanar resonators with 90° and 270° image rotation are discussed in detail in the region of 0 < K < 8, where K is the ratio of the total cavity length to the radius of the curvature mirrors. There are both four singular points in the whole region of 0 < K < 8. On the left of the first singularity, it is found that the longer the mirror radius, the less the optical-axis decentration sensitivity. This is opposite the behavior of planar ring resonators, but the behaviors of optical-axis tilt sensitivity in planar and nonplanar ring resonators are similar. It is worth to note that SD and ST in the nonplanar resonator with certain parameters have the similar singularities. The analysis in this paper is important for the cavity design and alignment of nonplanar ring resonators.     

Ring resonator with multimode waveguide turning-mirror couplers in InGaAsP-InP

Compact In_0.67Ga_0.33As_0.6P_0.4/In_0.71Ga_0.29As_0.74P_0.26 on InP single ring resonators incorporating 2 × 2 multimode interference (MMI) turning-mirror couplers with cross coupling factor of 0.15 have been demonstrated. The form of race tracks is a 15-degree arc of 260 μm radius joined with a 60-degree arc of 110 μm radius, and finished with another 15-degree arc of 260 μm radius. The MMI turning-mirror coupler of 128 μm in length is used in the single ring resonators, which correspond to free spectral ranges of 82 GHz. A contrast of 4 dB, a finesse of nearly 3 and full-width at half-maximum (FWHM) of 0.24 nm for the drop port have been achieved in this single ring resonator. From the experimental value T_max/T_min of 21 dB, the experiment coupling factor coincides with the simulation.     

The effect of geometry and post-annealing on surface acoustic wave characteristics of AlN thin films prepared by magnetron sputtering

This paper describes experimental relationship between surface acoustic wave (SAW) properties of two-port SAW resonators based on polycrystalline aluminum nitride (AlN) thin films grown on Si substrates by using a pulsed reactive magnetron sputtering system and their geometry's parameters. Moreover, the influence of post-deposition heat treatment on SAW properties of AlN thin films was investigated at different annealing temperature (600 °C and 900 °C). The measurement results show the number of the inter-digital transducers (IDT) finger pairs (N), the number of reflectors grating pairs (R) and the IDT center-to-center distance (L) related to insertion loss of SAW resonators. The best result of insertion loss was 15.6 dB for SAW resonators with R = 160 pair, N = 5 pair and L = 750 μm. At the same geometry parameters, the SAW velocity and insertion loss were improved slightly after annealing at 600 °C and were worse for the films annealed at 900 °C by changes in the surface morphology and stress on the film.     

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L × U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1/2πR. For quark separations obeying L > L_c ? 0.97 ∗ R the chiral symmetry is restored at this temperature, but for L < L_c ? 0.97 ∗ R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T_χSB ? 0.154/L. All of these phase transitions are of first order.     

A new design of tunable four-port wavelength demultiplexer by photonic crystal ring resonators

A four-channel wavelength demultiplexer based on photonic crystal ring resonators (PCRR), which can be used for photonic integrated circuits, is designed. Dropping efficiency and Q factor of single improved ring are 100% and 842, respectively. In order to achieve the structure of demultiplexer, three improved rings have been used, that every ring has an individual inner rod radius; it means that each ring has a varying resonant wavelength. The results of simulation using finite-difference time-domain (FDTD) method in our proposed structure reveals an average transmitted power higher than 90% for each output port, Channel spacing is about 8 nm and bandwidth for each individual channel is about 2.8 nm. The mean value of the crosstalk between output channels and the area of the proposed structure are about −29 dB and 317 μm², respectively. By changing the radius of inner rods, various wavelengths can be chosen, therefore this device is tunable.     

Domain walls confined in magnetic nanotubes with uniaxial anisotropy

We present calculations of the different domain wall structures confined in magnetic nanotubes, such as transverse wall, asymmetric vortex wall, branch fashion wall, and horse-saddle wall. The wall structures were calculated by micromagnetic simulations. The tube radii R=50 nm and 100 nm, and aspect ratios length/radius L/R≤15 were considered. The magnetic phase diagrams of the stability of different kinds of the domain walls were plotted as function of the tube aspect ratio L/R and the tube thickness (difference of the outer and inner tube radii).     

Optical characterization of mechanically tunable microwire based resonators by changing ring radius and wire diameter

Three tunable microring resonators were assembled using 3.5, 2.5, and 2 μm diameter of poly(trimethylene terephthalate) (PTT) wires, respectively. Their free spectral ranges (FSRs) and quality (Q) factors were measured by reducing ring radius of the microrings. For specific wire diameter and operating wavelength, the FSR increases continuously while the Q increases to a maximum value firstly and then decreases with a reduction of the ring radius. For specific ring radius and operating wavelength, the FSR increases a little and the Q decreases with a decrease of the wire diameter.     

Characterization of spherical particles using high-order neural networks and scanning flow cytometry

We retrieve the radius R, real n and imaginary k parts of the refractive index of homogeneous spherical particles using angular distribution of the light-scattering intensity. To solve the inverse light-scattering problem we use a high-order neural-network technique. The effect of network parameters on optimization is examined. The technique is evaluated for noise-corrupted input data at 0.6 μm<R<10.6 μm, 1.02<n<1.38, and 0<k<0.03. The errors of retrieval for nonabsorbing particles do not exceed 0.05 μm for radius and 0.015 for refractive index. The experimental verification is fulfilled by experimental data retrieved by means of a scanning flow cytometer. The light-scattering profiles of polystyrene beads and spherized red blood cells are processed with the high-order neural networks and a non-linear regression at Mie theory. The parameters retrieved by the high-order neural networks correlate well with the parameters retrieved by the least-square method.     

Ultra high Q crystalline microcavities

We report on the fabrication technique of ultra high Q optical crystalline whispering gallery mode microresonators and discuss their properties. The technique is suitable for the majority of available optical crystals and for production of resonators with small size. To validate the method, we made CaF₂ resonators with Q factors exceeding 4 × 10⁸ and a diameter smaller than 100 μm. A single mode resonator has also been fabricated. Possible utilization of these new resonators in quantum optics is discussed.     

Self-reproducing ray-cluster and misalignment of gas laser resonator having a coaxial discharge chamber

A laser resonator with two annular spherical mirrors is studied. The self-reproducing mode of this resonator is established by means of a self-reproducing ray-cluster. Its existence condition and area are analyzed and provided for the first time. The resonator's adjusting accuracy is analyzed in detail and the relevant calculation for typical cases is illuminated. The tolerance of mirror center displacement from the axis of the coaxial discharge chamber is proved to be about 0-0.15 mm, and the tilt tolerance 0-6″, when resonator length L≈1 m, the radius of curvature of the two mirrors ρ≈5-10 L, and the loss of applicable radial width of the coaxial discharge chamber for light propagation is smaller than 1 mm. The object-image relation of the resonator and its application in adjustment of the resonator are also discussed.     

Development and investigation of an optical tilt sensor

An optical tilt sensor was developed and its performance was investigated. The tilt sensor set-up consisted of a laser light source, lenses and an image sensor. A precision reference tilt sensor was also installed on the same stage, and the measurement results of tilt angles using the optical and reference tilt sensors were correlated. The correlation coefficient (R-value) obtained under ideal conditions was 0.99454, indicating that the optical tilt sensor could produce as accurate measurements as the precision reference tilt sensor. The R-value decreased to 0.97714 and 0.93209 when the image sensor was shifted backwards and forwards from the focal plane by 1 mm, respectively. The R-value decreased to 0.96840 when the tilt sensor was performed with the room light turned on. There were not significant differences in the measurement results obtained with air conditioners turned on and off, indicating that the optical tilt sensor was robust and was not sensitive to the surrounding air turbulence. These findings are useful for the final design of the optical tilt sensor.     

Heat capacity of CeIrSi3 under pressure

We measured the heat capacity of CeIrSi₃ (100 mK<T<6 K) under high pressure up to P=1.38 GPa. The measurements have been used a quasiadiabatic method utilizing a CuBe piston-cylinder pressure cell in a dilution refrigerator. At 0 GPa, a sharp anomaly which indicates the antiferromagnetically transition is observed at T_N=5 K. T_N decreases monotonically with increasing pressure up to P=1.38 GPa. The magnetic entropy is released below T_N only 19% of R ln 2 at 0 GPa. And the magnetic entropy decreases with increasing pressure up to 1.38 GPa, 64% compared to that at 0 GPa.     

Unified path integral treatment for generalized Hulthén and Woods-Saxon potentials

A rigorous path integral discussion of the s states for a diatomic molecule potential with varying shape, which generalizes the Hulthén and the Woods-Saxon potentials, is presented. A closed form of the Green’s function is obtained for different shapes of this potential. For λ ? 1 and (1/η)lnλ<r<∞, the energy spectrum and the normalized wave functions of the bound states are derived. When the deformation parameter λ is 0 < λ < 1 or λ < 0, it is found that the quantization conditions are transcendental equations that require numerical solutions. The special cases corresponding to a screened potential (λ = 1), the deformed Woods-Saxon potential (λ = q e^ηR), and the Morse potential (λ = 0) are likewise treated.     

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

Background and objective

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0° to 40°, revealed the existence of an anomalous “pseudo-Rayleigh” mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n = 1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40° for various elastic and viscoelastic cylinder materials.

Method

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0° ? α < 90°. The “pure” resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

Results and conclusion

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka? 0.1 at a critical angle α_c bounded by the longitudinal and shear waves coupling angles θ_L=sin^-1(c/c_L) and θ_S=sin^-1(c/c_S) such that θ_L<α_c<θ_S (where c_L and c_S are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle θ_L<α_c<θ_S result from the excitation of the monopole (n = 0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 ?ka? 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle θ_R=sin^-1(c/c_R) (where c_R is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n = 1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder’s surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.     

Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows

An equilibrium of a planar, piecewise-C¹, continuous system of differential equations that crosses a curve of discontinuity of the Jacobian of its vector field can undergo a number of discontinuous or border-crossing bifurcations. Here we prove that if the eigenvalues of the Jacobian limit to λL±iωL on one side of the discontinuity and −λR±iωR on the other, with λL,λR>0, and the quantity Λ=λL/ωL−λR/ωR is nonzero, then a periodic orbit is created or destroyed as the equilibrium crosses the discontinuity. This bifurcation is analogous to the classical Andronov-Hopf bifurcation, and is supercritical if Λ<0 and subcritical if Λ>0.     

The effects of elements doping on transport and thermoelectric properties of Sr3Ti2O7

The Ruddlesden–Popper (RP) phase compounds (Sr_0.95R_0.05)₃Ti₂O₇ (R=Er, Y, Dy, Gd, Eu, Sm, Nd and La) were prepared, and their transport and thermoelectric properties were investigated. The results indicate that high-T electrical resistivity ρ (300 K<T<1000 K) increases monotonically with temperature and basically has a relation ρ∝T^M, with M varying from 0.91 to 1.92 at temperatures T>~650 K, suggesting acoustic phonon scattering is dominant. At low temperatures (5 K<T<300 K), ρ for (Sr_0.95R_0.05)₃Ti₂O₇ (R=Nd and La) decreases monotonously with decreasing temperature, whereas ρ for (Sr_0.95R_0.05)₃Ti₂O₇ (R=Er, Y, Dy, Gd, Eu and Sm) decreases first, and then increases instead as T decreases to a critical temperature T_c. Moreover, electrical conductivity σ∝T^1/2 holds at lower temperatures, indicating that the electron–electron interaction caused by the presence of disorder dominates the transport process at the low temperatures. Besides, experiments show that at T<~400 K the lattice thermal conductivity of the doped compounds basically decreases with increase of the atomic mass of dopants. Generally, the figure of merit (ZT) at 1000 K increases first, and then decreases with the increase of the dopants' ionic radius, and the largest ZT is achieved in (Sr_0.95Gd_0.05)₃Ti₂O₇ mainly owing to its lower lattice thermal conductivity.     

Neutral and charged excitons in a quantum tube

The optical transition energies of neutral and charged excitons in a quantum tube are calculated as a function of the Aharonov-Bohm magnetic flux Φ. The oscillation amplitude of the ground state energy of the electron-hole relative motion is shown to be larger in a quantum tube than a quantum ring with strong confinement in the axis direction. We find a double maxima structure in the optical transition energy for a quantum tube with radius R = 0.5 in units of the effective Bohr radius because of the difference in the Φ dependencies between the single electron energy and the relative-motion energy of a charged exciton state.     

Combinatorial study of phase transformation characteristics of a Ti-Ni-Pd shape memory thin film composition spread in view of microactuator applications

Phase transformation characteristics of a Ti-Ni-Pd shape memory thin film composition spread have been investigated. The thin film composition spread was fabricated from elemental targets using an ultra-high vacuum combinatorial magnetron sputter-deposition system and subsequent annealing at 500 °C for 1 h in situ. Automated temperature-dependent resistance measurements (R(T)), energy dispersive X-ray analysis (EDX) and X-ray diffraction measurements (XRD) have been applied for the high-throughput characterization of the composition spread. Reversible phase transformations within the measurement range of −40 to 250 °C within the Ti-Ni-Pd system were observed for compositions with Ti content between 50 and ∼59 at.%. For Ti-richer films, Ti₂Ni and Ti₂Pd precipitates are inhibiting reversible phase transformations. The transformation temperatures and the thermal hysteresis were determined from R(T) measurements. Rising transformation temperatures with increasing Pd content and significantly lower thermal hysteresis for the B2-B19, compared to the B2-R-B19′ transformations were found in good agreement with published data. For low Pd contents (<7-12 at.%, depending on the Ti content) two-stage B2-R-B19′ transformations were observed. Compositions with higher Pd contents showed a single-stage B2-B19 transformation. Increasing Ti content within the B2-B19 transformation region results in a linear increase of the thermal hysteresis and decreasing transformation temperatures.     

Experimental investigation on submicron rib waveguide microring/racetrack resonators in silicon-on-insulator

In experiment, characteristics of silicon microring/racetrack resonators in submicron rib waveguides have been systematically investigated. It is demonstrated that only a transverse-electric mode is guided for a ratio of slab height to rib height h/H = 0.5. Thus, these microring/racetrack resonators can only function for quasi-transverse-electric mode, while they get rid of transverse-magnetic polarization. Electron beam lithography and inductively coupled plasma etching were employed and improved to reduce sidewall roughness for low propagation loss and high performance resonators. Then, the effects of waveguide dimensions, coupling region design, waveguide roughness, and oxide cladding for the resonators have been considered and analyzed.     

Observation of triangle pits in PbSe grown by molecular beam epitaxy

PbSe thin films on BaF₂ (1 1 1) were grown by molecular beam epitaxy with different selenium beam flux. Evolution of PbSe surface morphologies with Se/PbSe beam flux ratio (R_f) has been studied by atomic force microscopy and high-resolution X-ray diffraction. Growth spirals with monolayer steps on PbSe surface are obtained using high beam flux ratio, R_f ≥ 0.6. As R_f decreases to 0.3, nano-scale triangle pits are formed on the surface and the surface of PbSe film changes to 3D islands when R_f = 0. Glide of threading dislocations in 〈1 1 0〉{1 0 0}-glide system and Pb-rich atom agglomerations are the formation mechanism of spiral steps and triangle pits. The nano-scale triangle pits formed on PbSe surface may render potential applications in nano technology.