Remco Stoffer

Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters

In photonic crystals, light propagation is forbidden in a certain wavelength range, the bandgap. In a two-dimensional crystal composed of parallel high-refractive index rods in a low-index background a line defect can be formed by removing a row of these rods, which can act as a waveguide for frequencies in the bandgap of the crystal. In order to get more insight into the main features of such waveguides we have studied a number of properties, using simulation tools based on the finite difference time domain method and a finite element Helmholtz solver. We show conceptually simple methods for determining the bandgap of the crystal as well as the dispersion of a waveguide for wavelengths in this bandgap. For practical applications, it is also important to know how much light can be coupled into the waveguide. Therefore, the coupling of light from a dielectric slab waveguide into the photonic crystal waveguide has been examined, showing that a coupling efficiency of up to 83% can be obtained between a silicon oxide slab and a waveguide in a crystal of silicon rods. Finally, calculations on an ultra-compact filter based on reflectively terminated side-branches of waveguides (similar to tuned stubs in microwave engineering) are shown and discussed.

Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO2/Si3N4 system does not significantly affect the results. The existence of lossless Floquet-Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.

Integrated

Integrated Al(2)O(3):Er(3+) channel waveguide ring lasers were realized on thermally oxidized silicon substrates. High pump power coupling into and low laser output power coupling from the ring is achieved in a straightforward design. Output powers of up to 9.5 microW and slope efficiencies of up to 0.11% were measured while lasing was observed for a threshold diode-pump power as low as 6.4 mW for ring lasers with cavity lengths varying from 2.0 to 5.5 cm. Wavelength selection in the range 1530-1557 nm was demonstrated by varying the length of the output coupler from the ring.

Al_2O_3:Er^{3+}

We present a new class of low-loss integrated optical waveguide structures as CMOS-compatible industrial standard for photonic integration on silicon or glass. A TriPleXTM waveguide is basically formed by a -preferably rectangular- silicon nitride (Si3N4) shell filled with and encapsulated by silicon dioxide (SiO2). The constituent materials are low-cost stoichiometric LPVCD end products which are very stable in time. Modal characteristics, birefringence, footprint size and insertion loss are controlled by design of the geometry. Several examples of new applications will be presented to demonstrate its high potential for large-scale integrated optical circuits for telecommunications, sensing and visible light applications.

ring lasers on silicon with wide wavelength selectivity

Optical ring resonators are commonly discussed on the basis of a frequency‐domain model, that divides a resonator into coupler elements, ring cavity segments, and the straight port waveguides. We look at the assumptions underlying this model and at its implications, including remarks on reciprocity/symmetry arguments, the general power transfer characteristics, the resonance condition, the spectral distance and width of the resonances, the quantities that describe the resonator performance, and a few remarks about tuning. A survey of bend mode properties and a coupler description in terms of coupled mode theory fills the abstract notions of the model. As an example for devices that rely on a standing wave principle, in contrast to the traveling waves found in the microrings, we consider in less detail microresonators with square or rectangular cavity shapes. Also here a frequency domain coupled mode theory can be applied that opens up simple possibilities to characterize resonant configurations.

Large-scale integrated optics using TriPleX waveguide technology: from UV to IR

Passing across an abrupt junction from a thick vertically bimodal waveguide to a thinner single mode segment, guided light can undergo complete destructive interference, provided that the geometry and the phases of the modes in the initial segment are properly adjusted. We propose to employ this effect to realize a simple polarizer configuration, using a strip that is etched from a planar waveguide. A beam of light is made to pass the strip perpendicularly. The light enters from the single mode waveguide outside the strip into the strip segment, which is configured to support two modes. At the end of the strip, apart from reflections, the amount of power that is guided in the following lower segment depends on the local phases of the two modes. These phases are different for TE and TM light, hence we may expect a polarization dependent power transfer, resulting in polarizer performance for a properly selected geometry. The paper describes in detail the modeling of the device in terms of rigorous mode expansion. Design guidelines and tolerance requirements for geometric and material parameters are discussed. For typical Si3N4/SiO2 materials, our calculations predict a peak performance of 34 dB polarization discrimination and 0.3 dB insertion loss for a device with a total length of about 12 μm that selects TE polarization at a wavelength of 1.3 μm.

Analytical approaches to the description of optical microresonator devices

Whispering gallery modes supported by open circular dielectric cavities are embedded into a nonparametric two-dimensional frequency domain hybrid coupled mode theory framework. Regular aggregates of these cavities, including straight access channels, are investigated. The model enables convenient studies of the guided wave scattering process, the response of the circuit to guided wave excitation. Transmission resonances can be characterized directly in terms of resonance frequency and linewidth by computing supermodes of the entire composite circuits, comprising both cavities and bus waveguides. Examples of single ring and disk filters, a coupled-resonator optical waveguide, and a three-cavity photonic molecule in a reflector configuration allow the approach to be assessed.

Integrated optical cross strip polarizer concept

A combined planar lossless optical amplifier and 1 × 2 power splitter device has been realized in Al2O3:Er3+ on silicon. Net internal gain was measured over a wavelength range of 40 nm across the complete telecom C-band (1525-1565 nm). Calculations predict net gain in a combined amplifier and 1 × 4 power splitter device over the same wavelength range for a total injected pump power as low as 30 mW.

Interaction of whispering gallery modes in integrated optical micro-ring or -disk circuits: Hybrid CMT model

In order to model transmission scanning near-field optical microscopy (T-SNOM) experiments, we study the interaction between a nanosized atomic-force-microscopy-type probe and the optical field in a microcavity (MC) at or near resonance. Using a 2-D cross-sectional model of an experimentally studied photonic crystal MC, we have simulated the T-SNOM method by scanning a probe over the surface while monitoring the transmitted and reflected power. The simulations were performed for two probe materials: silicon and silicon nitride. From the probe-induced change in the transmission and reflection spectra, a wavelength shift was extracted. A shift almost proportional to the local field intensity was found if the resonator was excited just below a resonance wavelength. However, at the spots of highest interaction, we observed that besides the desired resonance wavelength shift, there was an increase in scattering. Furthermore, by moving the probe at such a spot in the vertical direction to a height of approximately 0.5, a 5% increase in transmission can be established because the antiresonant condition is satisfied. Finally, a 2-D top view simulation is presented of the experimentally studied T-SNOM method, which shows a remarkably good correspondence in intensity profile, except for the exact location of the high-interaction spots.

Integrated Al

A new 5-point finite difference operator is developed for integrated optics simulations. Interfaces are taken into account accurately. The eigenvalues of the discretization matrix converge rapidly, according to O(Δx4). Implementation of the operator in a beam propagator leads to a highly efficient computation scheme.