Three-dimensional Beam Propagation Research Articles

Modeling liquid-crystal devices with the three-dimensional full-vector beam propagation method

Simulation of light propagation within nematic liquid-crystal (LC) devices is considered, of which the director is aligned normal to the z axis. A three-dimensional full-vector finite-difference beam propagation method for an anisotropic medium is presented and an alternating direction implicit scheme is adopted. Simulations of light propagation in a bulk polarization converter, a waveguide with a LC covering layer, and an integrated polarization splitter and optical switch are presented. Comparison with an existing simulation method is carried out for beam behavior within the bulk polarization converter. The effect of strong surface anchoring of a LC cell on the beam behaviors within the integrated switch is also demonstrated.

Preparation of a planar multimode interference coupler with a graded-index profile using polysilane with photobleaching properties

To investigate the viability of a planar graded-index multimode waveguide fabricated using a new method (to our knowledge) employing polysilane with photobleaching properties, we designed a planar two-way multimode power splitter based on multimode interference, with a core possessing a vertically parabolic and horizontally uniform index profile. We carried out mode propagation analysis using the Marcatili model and optimization using a three-dimensional beam-propagation method. The prototype was fabricated by means of multiple dicing after UV exposure and heat treatment in air. Index profile measurements using a special end-face reflection method showed it to have a vertically graded-index profile with relative index difference of 0.0456. Output beam profile observation using a CCD camera showed that it successfully divided the beam planewise.

Bilevel mode converter between a silicon nanowire waveguide and a larger waveguide

A bilevel mode converter is analyzed for providing low-loss coupling between the small fundamental mode of a silicon nanowire waveguide and the larger mode of a conventional silicon-on-insulator (SOI) rib waveguide. The bilevel converter can also be used to improve the coupling efficiency between a lensed fiber and a silicon nanowire waveguide. The mode converter consists of two tapers formed at different levels. The top taper comprises a parabolic and sine taper, which is optimized to improve the mode conversion efficiency. Numerical analyses are given by using a three-dimensional semivectorial beam propagation method. The design has good tolerance against misalignment of the two masks needed for the double etch.

Submersion Sensor Using Bending-Sensitive Fiber

A sensor using bending sensitive fiber (BSF) was studied for real-time long-distance sensing of submersion. The structure of the submersion sensor effectively used the relationship between buoyant force and bending loss of the BSF. A three-dimensional finite-difference beam propagation method (3D FD-BPM) was used to select the bending dimension of the proposed submersion sensor. The operation of the submersion sensor utilizing the BSF was also investigated using 3D FD-BPM. As results of experiments, the submersion sensor fabricated showed a change of optical power from -17 to -1 dB at 1550 nm when the selected sensing region was submerged. In addition, the BSF was easily connected to a single mode fiber (SMF) by fusionsplicing. The BSF exhibited a -1 dB loss when connected to a SMF at both ends.

Three-dimensional beam propagation model for the optical path of light through a nematic liquid crystal

A three-dimensional beam propagation model is presented which, given a director profile, calculates the electric and magnetic fields for a light wave as it travels through a liquid crystal structure using a predictive-corrector Crank–Nicholson numerical method and adjusts for impedance effects in the direction of propagation. The results from the model are compared to both analytical solutions for simpler director profiles and other optical models for more complicated director profiles.

Antiresonant reflecting optical waveguide-type vertical-cavity surface emitting lasers: comparison of full-vector finite-difference time-domain and 3-D bidirectional beam propagation methods

The cold-cavity modal characteristics of an antiresonant optical waveguide-type cylindrical vertical-cavity surface-emitting laser (VCSEL) are investigated through numerical simulations using a three-dimensional (3-D) bidirectional beam propagation method (BD-BPM) and a full-vector axisymmetric finite-difference time-domain (FDTD) method. Good agreement between the BPM- and FDTD-computed radial mode profiles as well as the mode-dependent radiation losses is obtained. The results of this paper establish the accuracy of the BD-BPM technique for simulating this class of devices and confirm effective-index method predictions that antiresonance conditions for cylindrical geometry devices (i.e., VCSELs) differ from those of planar geometry devices (i.e., edge emitters).

Boundaryless finite-difference method for three-dimensional beam propagation

A two-dimensional optical field paraxial propagation scheme, in Cartesian and cylindrical coordinate systems, is proposed. This is achieved by extending the method originally proposed by Ladouceur [Opt. Lett. 21, 4 (1996)] for boundaryless beam propagation to two-dimensional optical wave fields. With this formulation the arbitrary choice of physical window size is avoided by mapping the infinite transverse dimensions into a finite-size domain with an appropriate change of variables, thus avoiding the energy loss through the artificial physical boundary that is usually required for the absorbing or the transparent boundary approach.

Quasi-vectorial analysis of the optical characteristics of rib waveguides and directional couplers based on InGaAs/InAlAs multiple quantum wells

A new three-dimensional quasi-vectorial beam propagation method based on the series expansion (SE-QV-BPM) is proposed for simulating the optical rib waveguide and directional coupler based on InGaAs/InAlAs multiple quantum wells. For the same etched-depth, the confinement of TM mode in horizontal direction is shown to be stronger than that of TE mode, and the singular behaviors for TM modes at the corners are clearly observed. For the same gap width, the coupling length of TM mode for directional coupler is larger than that of TE mode. The effective indices and modal profiles of the quasi-vectorial fundamental TE and TM modes for shallow- and deep-etched rib waveguides and directional couplers are obtained. Besides, the evolution of the injected field with propagation distance through the directional coupler is demonstrated. The calculation has good efficiency due to the small size of the resulting matrix, and the rib structures can be conveniently dealt with since the sinusoidal functions are selected as the basis functions. Moreover, the variable transformation is introduced to avoid the boundary truncation.

Fast-Fourier-based three-dimensional full-vectorial beam propagation method

An accurate and highly efficient fast-Fourier-based full-vectorial beam propagation method (BPM) with perfectly matched layer absorbing boundary conditions is presented. Full vectorial results obtained for highly guiding z-variant structures, such as a spot size converter and a Y-branch in rib technology, show that accurate results can be obtained with reduced computational effort, thus making this technique an interesting alternative to other existing BPM strategies.

Modeling, fabrication, and characterization of large aperture two-dimensional antiguided vertical-cavity surface-emitting laser arrays

We have investigated the modal behavior of two-dimensional (up to 400 elements) active-photonic-lattice-based antiguided vertical-cavity surface-emitting laser (VCSEL) arrays by both modeling and device characterization. A two-dimensional (2-D) model based on the effective index method has been constructed to analyze 2-D resonance and calculate array mode frequencies in rectangular geometry arrays. A more comprehensive three-dimensional bi-directional beam propagation code has also been developed to theoretically describe 2-D antiguided arrays with the VCSEL structure in the primary wave propagation direction. Gain spatial hole burning (GSHB) effects above laser threshold are applied to find conditions favorable for in-phase mode lasing and high intermodal discrimination. Three rectangular geometry array structures based on different interelement loss mechanisms have been designed and fabricated. Both far-field and spectral characterization were conducted on the devices to make detailed comparison with theoretical results. We found that introducing higher loss within the interelement region can allow the in-phase mode to exhibit the lowest threshold gain for a wide range of interelement widths around the in-phase resonance condition. A detailed spectral study of 5/spl times/5 arrays with the highest interelement loss design has demonstrated suppression of competing guided array modes and higher order leaky array modes at drive currents up to 10 times threshold.

Variable optical attenuator based on large-core single-mode polymer waveguide

To improve the reproducibility of passive alignment, large-core single-mode waveguides are demonstrated, which can be connected to thermally expanded core fibers with increased alignment tolerance. It is shown that polymer waveguides with a core dimension of 25 /spl times/25 /spl mu/m/sup 2/ and an index contrast less than 0.001 can satisfy single-mode condition. As a novel functional device incorporating the large-core waveguide, variable optical attenuators (VOAs) are designed and fabricated. For the fabrication of the thick core structure, a soft molding process is developed. Due to the small index contrast of the waveguide, efficient attenuation is expected for small electrical power consumption, which is confirmed by three-dimensional beam propagation method. From the fabricated VOA, more than 20 dB of attenuation is obtained by applying 20 mW.

Effect of mask thickness on the nanoscale sidewall roughness and optical scattering losses of deep-etched InP∕InGaAsP high mesa waveguides

Deep-etched mesa waveguide in InP∕InGaAsP heterostructures were fabricated using different thicknesses of NiCr etching mask in an inductively coupled plasma reactive ion etching system with Cl2-based plasmas. An atomic force microscope (AFM) loaded with a carbon nanotube tip was utilized to measure the sidewall roughness of the etched structures. The root-mean-square (rms) roughness values were calculated separately for the horizontal and vertical directions of the waveguide sidewall. As the NiCr mask thickness increased from 10 nm to 150 nm, the rms roughness value in the vertical direction of the waveguide sidewall decreased from 19.5 nm to 2.8 nm. On the other hand, the rms roughness value in the horizontal waveguiding direction increased from 2.5 nm to 4.0 nm. The correlation lengths along the horizontal direction for the etched waveguide structures were also extracted from the AFM roughness data. The rms roughness values and correlation lengths were used as parameters in three-dimensional beam propagation method to calculate the optical scattering loss. The calculated optical losses ranged from 1.2dB∕cm to 2.5dB∕cm.

Compact silicon-on-insulator-based multimode interference coupler with bilevel taper structure

A novel compact silicon-on-insulator- (SOI-)based multimode interference (MMI) coupler with bilevel taper structures was designed. The MMI section and the S-bend sections of the input-output waveguides are deeply etched. The input-output waveguides connecting to single-mode fibers or other photonic light circuits are etched shallowly to yield single-mode operation. A bilevel taper is introduced in the transition region between the shallowly and deeply etched regions. It is predicted theoretically that this design will not only improve the quality of the self-imaging in the MMI section but will also make the structure compact. Both the excess loss and the nonuniformity of the MMI coupler are reduced. By use of a three-dimensional beam propagation method, the performance of a 1 x 4 MMI coupler based on a SOI is simulated as a numerical example of the novel design. The simulated nonuniformity and the excess loss are approximately 0.0285 and 0.2 dB, respectively.

Singlemode and polarisation free conditions for small silicon-on-insulator waveguides

An analysis based on simulation of polarisation depedence and the singlemode condition for small and deeply etched silicon-on-insulator waveguide dimensions is presented. Examples of designs that satisfy both requirements simultaneously have been evaluated using the three-dimensional full vectorial beam propagation method.

Effect of Conductor Cladding on Dielectric Slab for Coupling with Side-Polished Fiber

The effect of planar waveguide with conductor cladding (PWGCC) on evanescent coupling with a side-polished fiber is investigated using the three-dimensional finite difference beam propagation method (3D FD-BPM). The coupling and propagation of light were found to depend on the relationship between the refractive index values of each structure and the configuration of the side-polished fiber used in the PWGCC.

Microfluidic interferometer

We present a class of compact, fluid-based, interferometric, tunable optical components: the single-beam microfluidic Mach–Zender interferometer. Phase delay is achieved through light propagation across a fluid–air interface (meniscus). The effect of meniscus curvature on the device transmission is considered using the three-dimensional beam propagation method and shown to be an important device parameter. We engineer the meniscus curvature using monomer surface chemistry, rendering it flat, and find that the experimental response corresponds well with simulation. The device has a resonance at 1.3μm with a 25dB extinction ratio; the latter can be adjusted by shifting the meniscus position.

Polarization-Independent, Thickness-Insensitive, and Refractive-Index-Difference-Independent Broad-Band Fluorinated Polyimide Waveguide Coupler

A statistically optimized design method is proposed for the construction of polarization-independent, thickness-insensitive, and refractive-index-difference-independent broad-band waveguide couplers. Using this method, a fluorinated polyimide waveguide 3-dB coupler for a 1490-1610-nm operation is designed through optimization of the polarization, variation in thickness of the waveguide core, and variation in refractive-index difference of the waveguide core and cladding. The performance of the design is verified through simulation based on the three-dimensional beam-propagation method (3-D-BPM). The two orthogonal polarizations of the final design have a coupling ratio of (50/spl plusmn/2.0)% for a bandwidth of 120 nm, a thickness fluctuation of 7-8 /spl mu/m, and a refractive-index-difference fluctuation of 0.24-0.30%.

Y-branch spot-size converter for a buried silica waveguide with large index difference.

Coupling loss occurs between a standard single-mode fiber and a silica waveguide when the difference between the refractive indices of the core and the cladding of the silica waveguide is high. We designed a Y-branch structure for use as a spot-size converter to reduce this coupling loss. The structure was tested with a three-dimensional beam-propagation method and was shown to exhibit a significantly reduced coupling loss, a low polarization-dependent loss, and a good tolerance of imprecision in fabrication. No additional fabrication steps are required for this proposed spot-size converter.

Three-dimensional beam propagation method based on the variable transformed Galerkin?s method

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin’s method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.

Design of a highly nonlinear dispersion-shifted fiber with a small effective area by use of the beam propagation method with the Gaussian approximation method

A new design of a highly nonlinear dispersion-shifted fiber (HNDSF) with an effective area of 9.3 microm2 is presented. The three-dimensional beam propagation method combined with the Gaussian approximation method is used to analyze the new HNDSF. This innovative HNDSF has a unique triple-cladding structure that can offer not only a large nonlinear coefficient but also low attenuation, low splicing, and bending losses. It is a suitable candidate to implement an all-fiber wavelength converter by four-wave mixing.