Optical-axis perturbation in nonplanar ring resonators

Several findings on the optical-axis perturbation of nonplanar ring resonators have been obtained identical by utilizing the augmented 5 × 5 matrix formulation and augmented 6 × 6 matrix formulation, respectively. It has been found out that in the whole region of 0 < L/R < 2, the longer the mirror radius, the higher the sensitivity of optical-axis decentration, while the total cavity length is L and the radius of the curvature mirrors is R. The sensitivity of optical-axis tilt in the region of 0 < L/R < 2 has been carried out too. The optical-axis decentration and optical-axis tilt inside the region of L/R > 2 have been discussed. The differences of the optical-axis perturbation between planar and nonplanar ring resonators have also been analyzed. These interesting findings are important to the cavity design of nonplanar ring resonators.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Matrix methods in treating decentred optical systems

A set of matrix methods treating decentred optical systems in the paraxial approximation is reviewed. Misalignment phenomena of optical systems can generally be described by an augmented 4×4 matrix; propagation of optical rays in an asymmetric, inhomogeneous medium by a 3×3 matrix. In order to simplify the operations with these matrices, ray transfer flow graphs are introduced.A lot of optical problems can be solved in a clear and simple manner, including optical arrays. Some examples are given.     

Nonlinear optical properties of Cu nanoclusters by ion implantation in silicate glass

Metal nanocluster composite glass prepared by 180 keV Cu ions into silica with dose of 1 × 10¹⁷ ions/cm² has been studied. The microstructural properties of the nanoclusters were analysed by optical absorption spectra and transmission electron microscopy (TEM). Third-order nonlinear optical properties of the nanoclusters were measured at 1064 nm and 532 nm excitations using Z-scan technique. The nonlinear refraction index, nonlinear absorption coefficient, and the real and imaginary parts of the third-order nonlinear susceptibility were deduced. The mechanisms responsible for the nonlinear response were discussed. Absolute third-order nonlinear susceptibility χ⁽³⁾ of this kind of sample was determined to be 2.1 × 10⁻⁷ esu at 532 nm and 1.2 × 10⁻⁷ esu at 1064 nm, respectively.     

Measurement of nonlinear refractive index of ethyl red by interference of capillary

Using the intensity distribution of interference fringes formed by a capillary filled with transparent liquid, the variations in refractive index (RI) of nonlinear optical materials, corresponding to change of the intensity at the centre of fringes for a period, were deduced. With this conclusion, we measured variations in RI of ethyl red (ER) solution excited by a 535-nm-15 mW-laser, and found that the change of RI is 0.00504 and the corresponding effective index of refraction is −1.06 × 10⁻⁹, for which the order of magnitude is same as that measured by Z-scan. The influences on the accuracy of the method, such as temperature, beam and fringe contrast, were analyzed. This is a novel and simple method for measuring the RI of nonlinear optical materials.     

Algebraic treatments of the problems of the spin-1/2 particles in the one- and two-dimensional geometry: A systematic study

We consider solutions of the 2 × 2 matrix Hamiltonians of the physical systems within the context of the su (2) and su (1, 1) Lie algebras. Our technique is relatively simple when compared with those of others and treats those Hamiltonians which can be treated in a unified framework of the Sp (4, R) algebra. The systematic study presented here reproduces a number of earlier results in a natural way as well as leads to a novel finding. Possible generalizations of the method are also suggested.     

Beam concentration and homogenization for high power laser diode bar

A novel optical element is presented and applied for beam concentration and homogenization of laser diode (LD) bar. It consists of a tapered SiO₂-rod with twisted surfaces which is designed and optimized by the optical system design software and fabricated by a curved surface grinder and an optical polishing lathe. Results show that a rectangular output beam spot with uniform intensity distributions both at slow and fast axis is obtained at the output facet of the rod and the beam size is only 1.3 mm ∗ 0.8 mm.     

Determinations of the transient thermal lensing effect in metal cluster Polymer {WS4Cu4I2(bpe)3}n solution by the use of the Z-scan

The nonlinear optical (NLO) properties of a novel cluster Polymer {WS₄Cu₄I₂(bpe)₃}_n solution are studied by using Z-scan technique with laser pulses of 4.5 ns pulse-width at a wavelength of 532 nm. The results show that the cluster solution possesses strong nonlinear absorption and refraction. Nonlinear refraction of the cluster is composed of third-order nonlinear refraction and transient thermal effect. The thermal effect is mainly due to the strong nonlinear absorption. Numerical simulations obtained by solving simultaneously photo-acoustic and electromagnetic wave equations, agrees basically with experimental results.     

Changes in generalized Stokes parameters of stochastic electromagnetic beams on propagation through ABCD optical systems and in the turbulent atmosphere

Using the derived formulas for the transformation of 2 × 2 cross-spectral density matrix of the stochastic electromagnetic beams propagating through ABCD optical systems and in the turbulent atmosphere, the changes in the generalized Stokes parameters of the beams propagating under these conditions can be investigated directly. Some typical numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams passing through free space, focal system, dual-focus system, and the turbulent atmosphere with different structure parameters. Further extensions are also pointed out.     

Nonlinear optical properties in SrTiO3 thin films by pulsed laser deposition

Well-crystallized 250 nm-thick SrTiO₃ thin films on fused-quartz substrate were prepared by pulsed laser deposition. The band-gap of SrTiO₃ thin film by transmittance spectra is equal to 3.50 eV, larger than 3.22 eV for the bulk crystal. The nonlinear optical properties of the films were examined with picosecond pulses at 1.064 μm excitation. A large two-photon absorption (TPA) with absorption coefficient of 87.7 cm/GW was obtained, larger than 51.7 cm/GW for BaTiO₃ thin films. The nonlinear refractive index n₂ is equal to 5.7×10⁻¹⁰ esu with a negative sign, larger than 0.267×10⁻¹¹ esu for bulk SrTiO₃. The large TPA is attributed to intermediate energy levels introduced by the grain boundaries, and the optical limiting behaviors stemming from both TPA and negative nonlinear refraction were also discussed.     

The nonlinear refraction and absorption dependence on the thermal effect for 4 ns pulse duration in binuclear Zn(II) phthalocyanine solution

The influence of thermal effect on the third-order nonlinear optical properties of binuclear Zn(II) phthalocyanine in chloroform solution was studied. The nonlinear refraction and absorption of the sample was measured by using Z-scan technique with 4 ns laser pulses at 532 nm wavelength. The opposite signs of the effective nonlinear refraction index were observed by changing the focal length of focusing lens from 10 cm to 20 cm in the experimental setup. Changing the focusing lens increased the beam waist radius from 7 μm to 20 μm. The nonlinear absorption coefficient was reduced about 200 times based on changing the fluence or beam waist radius. The drastic changes in the third-order nonlinear optical parameters were attributed to thermal effect. To investigate the role of thermal effects even further the effective nonlinear refraction and absorption coefficients were studied by using different repetition rates, input powers and concentrations.     

Influence of initial surface reconstruction on the interface structure of HfO2/GaAs

We show that the bonding structures and electrical properties of the HfO₂/GaAs interface can be controlled by a choice of the reconstruction on the initial GaAs surface. Electron-beam evaporation of HfO₂ onto the c(4 × 4) surface yielded As-O bonds at the interface, while Ga-O bonds were dominant at the interfaces formed on the (2 × 4) and (4 × 6) surfaces. Influences of the initial surface reconstruction on the interface structure persisted even after annealing at 673 K. Electrical characterization of Ir/HfO₂/GaAs capacitors indicated that the interfacial As-O bonds cause weak Fermi level pinning. It was also suggested that the interfaces dominated by the Ga-O bonds have trapping states in the upper half of the GaAs bandgap.     

Photorefractive spatial solitons as waveguiding elements for optical telecommunication

Spatial solitons permit optical waveguiding. This holds true for the soliton write beam (i.e. the driving laser beam), as well as for additional probe beams, which may carry optically encoded information. This feature of spatial solitons is of significant interest for applications in optical telecommunication. We present systematic experimental investigations on single and multiple spatial solitons in the infrared spectral regime (i.e. around optical telecommunication wavelengths), applied as controllable all-optical devices. In particular, we present the implementations of a Y-coupler as an optical signal divider, a switchable Y-coupler as an optical add multiplexer, and a novel design for a 1 × 3 optical beam switch, i.e. applied as a router for infrared signal beams. We report large waveguiding efficiencies up to 40% and transmission rates of 90 Tbit/s in our setups. The presented experimental data are confirmed by numerical simulations.     

Fabrication of the slanted electrode matrix on tilting 4.5° (1 1 1) silicon

The slanted low electrode matrix is designed and fabricated on one tilting 4.5° (1 1 1) silicon wafer to reduce the actuating voltage of 8×8 micro-electromechanical systems (MEMS) optical switch matrix. Due to compact size of the upper electrode chip and (1 1 1) silicon anisotropic etching in KOH solution, photomask is designed which is to fabricate the slanted low electrode matrix that can be matched with the upper electrode chip and every slanted low electrode has enough space for actuating cantilever. The experimental results show that all of the applied voltages for the full range of actuating micromirrors of 8×8 MEMS optical switch matrix are in the range of 67.2±0.5 V. It is demonstrated that the fabricated slanted low electrode matrix has good consistency and every slanted low electrode can be precisely aligned with one-to-one corresponding upper electrodes.     

Electron microscopic study on interfacial characterization of electroless Ni-W-P plating on aluminium alloy

The interface between electroless plating Ni-W-P deposit and aluminium alloy (Al) matrix at different temperature heated for 1 h was studied using transmission electron microscope. The results show that the interface between as-deposited Ni-W-P deposit and Al matrix is clear. There are no crack and cavity. The bonding of Ni-W-P deposit and Al matrix is in good condition. The Ni-W-P plating is nanocrystalline phase (5-6 nm) in diameter. After being heated at 200 °C for 1 h, the interface of Ni-W-P deposit and Al matrix is clear, without the appearance of the diffusion layer. There exist a diffusion layer and educts of intermetallic compounds of nickle and aluminium such as Al₃Ni, Al₃Ni₂, NiAl, Ni₅Al₃ and so on between Ni-W-P deposit and Al matrix after being heated at 400 °C for 1 h.     

First-principles study of CoO films on MnO (1 1 1): Stability and interfacial structure

Based on the generalized gradient approximation, full potential linearized augmented plane-wave (FP-LAPW) calculations have been performed to study the stability and the interfacial structure of CoO/MnO (1 1 1). The surface energy, the strain energy and the binding energy are calculated and discussed. The calculations revealed that the CoO/MnO (1 1 1) is a stable interface structure. Also examined were the electronic properties and the atomic spin magnetic moments of the interface. It was found that the interface exhibited half-metallic property and the atomic magnetic moments were obviously weakened at the interface for metal atoms compared with the corresponding magnetic moments in bulk material.     

Mutual alignment errors due to localized distortion in free-space laser communication links

Instead of Zernike polynomials, truncated Gaussian function is proposed to express localized wave-front deformation in studying mutual alignment errors in free-space laser communication links, which simplifies the calculation. Mutual alignment errors include pointing and tracking errors which depend on transmitting and receiving optical system, respectively. It is shown that both pointing and tracking errors depend on three parameters (the center value A, the radius a and the distance d) of Gaussian localized distortion and change regularly as they increase. The maximum pointing and tracking errors always appear around A = 0.4λ (rms = π). Moreover, pointing error is more sensitive to localized wave-front deformation than tracking error. Beam truncation ratio has great influence on pointing error, and obscuration ratio has less influence on pointing and tracking errors except that antenna secondary mirror shelters parts of the localized deformation. To reduce the influence of localized aberrations, the principles how to choose the optical devices with large aperture are given, and a method that aligns the pointing direction to compensate pointing and tracking errors is suggested. The work will contribute to the design of free-space laser communication systems.     

A pulsed dye laser with grazing incidence and folded cavity

A novel design of a transversally pumped pulsed dye laser resonator using grazing incidence in a folded astigmatic cavity is described. The stability conditions, beam waist and output divergence of the oscillating mode are derived from the ray transfer matrix for this cavity. A diffraction limited gaussian beam is obtained. The linewidth can be adjusted down to 610 MHz without using any intracavity etalon.     

Optical alignment tolerances in double-side irradiated self-written waveguide-induced fiber arrays packages

In this paper, we present our experimental study on the optical alignment tolerance between the couplings of single-mode fibers (SMFs) connected with a double-side irradiation-induced self-written waveguide (SWW). The study firstly focuses on the coupling of two SMFs and then on the two fiber arrays (FAs) for parallel optical communication. The SWW was formed in dye-dispersed epoxy materials by the photopolymerization technique. Rhodamine 6G dye was dispersed in epoxy, which is commonly used in the photonic packaging industry as a bonding adhesive. Using double-side irradiated SWW, we found the alignment tolerance for such optical interconnect to relax significantly. All the formed SWWs were evaluated in terms of optical loss. In our study, up to 4 µm misalignment tolerance was allowed for only 1 dB loss penalty. In addition, the optical interconnect formed by this technique was also able to tolerate up to ± 10 µm lateral shift with only 1 dB extra loss. The wavelength-dependent loss (from 1520 to 1610 nm) and polarization-dependent loss were less than 0.4 dB. The double-side irradiated SWW-induced couplings between two FAs also provided low optical loss. They were found to be less sensitive to temperature changes, and no significant distortion in the digital signal transmission test was observed. We believe that the findings are useful and applicable to other dye-dispersed epoxy material systems for relaxing the alignment tolerance of the optical interconnects in various photonic packaging situations.     

Coating formation by plasma electrolytic oxidation on ZC71/SiC/12p-T6 magnesium metal matrix composite

Plasma electrolytic oxidation (PEO) of a ZC71/SiC/12p-T6 magnesium metal matrix composite (MMC) is investigated in relation to coating growth and corrosion behaviour. PEO treatment was undertaken at 350 mA cm⁻² (rms) and 50 Hz with a square waveform in stirred 0.05 M Na₂SiO₃.5H₂O/0.1 M KOH electrolyte. The findings revealed thick, dense oxide coatings, with an average hardness of 3.4 GPa, formed at an average rate of ∼1 μm min⁻¹ for treatment times up to 100 min and ∼0.2 μm min⁻¹ for later times. The coatings are composed mainly of MgO and Mg₂SiO₄, with an increased silicon content in the outer regions, constituting <10% of the coating thickness. SiC particles are incorporated into the coating, with formation of a silicon-rich layer at the particle/coating interface due to exposure to high temperatures during coating formation. The distribution of the particles in the coating indicated growth of new oxide at the metal/coating interface. The corrosion rate of the MMC in 3.5% NaCl is reduced by approximately two orders of magnitude by the PEO treatment.