Ring-resonator-based wavelength filters

Microring resonators (MR) represent a class of filters with characteristics very similar to those of Fabry–Perot filters. However, they offer the advantage that the injected and reflected signals are separated in individual waveguides, and in addition, their design does not require any facets or gratings and is thus particularly simple. MRs evolved from the fields of fibre optic ring resonators and micron scale droplets. Their inherently small size (with typical diameters in the range between several to tens of micrometres), their filter characteristics and their potential for being used in complex and flexible configurations make these devices particularly attractive for integrated optics or VLSI photonics applications.\ud MRs for filter applications, delay lines, as add/drop multiplexers, and modulators will be covered in detail in this chapter, while other applications such as in optical sensing, in spectroscopy or for coherent light generation (MR lasers) are outside the scope of this chapter.\ud This chapter focuses primarily on 4-port microrings, while 2-port devices will play a minor role here and are covered in more detail in Chap. 9. The present chapter starts with design considerations, the functional behaviour, and key characteristics of a single microring resonator and continues with the design of cascaded MRs allowing the implementation of higher order filters. Finally, complex devices like add-drop filters, tuneable dispersion compensators, all-optical wavelength converters, and tuneable cross-connects are treated.\u

High speed electro optic polymer micro-ring resonator

An electro-optic polymer micro-ring resonator for high speed modulation was designed, realized and characterized. The design of layer-stack and electrodes was done such that modulation frequencies up till 1 GHz should be possible. The device consists of a ridge waveguide, defined in a negative photoresist (SU8), with a poled electro-optic polymeric (PMMA-DR1) ring-resonator vertically coupled to it. The complete layerstack is sandwiched between electrodes to apply an electric field over the ringresonator in order to shift its resonance wavelength. Electro optic modulation was measured up to 50 MHz limited by weak modulation depth. Optimizing the polingprocess will increase the modulation efficiency thereby making modulation frequencies of 1 GHz measurable

High speed polymer E-O modulator consisting of a MZI with a microring resonator

A Mach-Zehnder interferometer with an polymer electro-optic micro-ring resonator on one of its branches is realized in a polymer layerstack and characterized. Electro-optic coefficients of 10 pm/V and modulation frequencies of 1 GHz were measured

Pricing Liquidity Risk with Heterogeneous Investment Horizons

We develop an asset pricing model with stochastic transaction costs and investors with heterogeneous horizons. Depending on their horizon, investors hold different sets of assets in equilibrium. This generates segmentation and spillover effects for expected returns, where the liquidity (risk) premium of illiquid assets is determined by investor horizons and the correlation between liquid and illiquid asset returns. We estimate our model for the cross-section of U.S. stock returns and find that it generates a good fit, mainly due to a combination of a substantial expected liquidity premium and segmentation effects, while the liquidity risk premium is small

Multimode waveguides of Photodefinable epoxy for optical backplane applications

We developed photodefined, multimode-fiber compatible waveguides based on epoxies. These waveguides will be embedded in backplane PCB’s for optical interconnect applications using 850 nm VCSELs as light sources. Apart from very low loss, the material selection took into account, PCB compatibility and low yellowing due to high temperature processing (for PCB lamination and soldering). The waveguides showed losses < 0.06 dB/cm at 832 nm and 633 nm. Their loss increase after aging (1 hr at 185 °C) was limited to 0.04 dB/cm at 850 nm. Waveguides realized on FR-4 (epoxyfiberglass)PCB material are demonstrated

Reduction of hydrogen-induced optical losses of plasma-enhanced chemical vapor deposition silicon oxynitride by phosphorus doping and heat treatment

Plasma enhanced chemical vapor deposition phosphoros-doped silicon oxynitride (SiON) layers with a refractive index of 1.505 were deposited from $N_{2}O$, 2% $SiH_{4}/N_{2}$, and 5% $PH_{3}/Ar$ gaseous mixtures. The $PH_{3}/Ar$ flow rate was varied to investigate the effect of the dopant to the layer properties. We studied the compositions and the chemical environment of phosphorus, silicon, oxygen, nitrogen and hydrogen in these layers by using x-ray photoelectron spectroscopy and Fourier transform infrared spectroscopy. The number of N-H and O-H bonds, which are responsible for optical losses around 1.55 and 1.3 μm, decreases in the as-deposited layers with increasing phosphorus concentration. Furthermore, the bonded hyrogen in all P-doped layers has been eliminated after annealing at a temperature significantly lower than required for undoped silicon oxynitride layers, that is so to say 1000°C instead of 1150°C. The resulting optical loss in the entire third telecommunication window was well below 0.2dB/cm, making P-doped SiON an attractive material for demanding integrated optics applications

Deposition and characterization of PECVD phosphorus doped silicon oxynitride layers for integrated optics applications

Phosphorus-doped silicon oxynitride layers have been deposited by a Plasma Enhanced Chemical Vapor Deposition process from $N_20$, 2% $SiH_4/N_2$ and 5% $PH_3/Ar$ gaseous mixtures. The $PH_3/Ar$ flow rate was varied to investigate the effect of the dopant to the layer properties. As deposited and annealed (600, 800, 900 and 1000 °C) layers were characterized by Fourier transform infrared spectroscopy, Rutherford backscattering spectroscopy and spectroscopic ellipsometry. In this way the refractive index could be determined as well as the amount of hydrogen that is responsible for enhanced absorption in the 3rd telecommunication window around 1550 nm. The N-H bonds concentration was found to decrease with the phosphorus concentration. Furthermore the bonded hydrogen in the entire P-doped layers have been eliminated after annealing at 1000 °C, while undoped SiON layers require annealing at 1150 °C

Silicon oxynitride based photonics

Silicon oxynitride is a very attractive material for integrated optics. Besides possessing excellent optical properties it can be deposited with refractive indices varying over a wide range by tuning the material composition. In this contribution we will summarize the key properties of this material class and discuss several application examples. Preliminary results on novel processes, which will lead to largely reduced hydrogen incorporation and enable reflow of SiON material, are being presented