# Research Interests

## Non-linear optics and quantum optics

Non-linear optical phenomena require high electro-magnetic fields and highly non-linear materials. The strongest optical non-linearities are non-linearities which can only exist in crystalline materials. Whispering gallery mode resonators made out of crystalline materials combine high quality factors with small mode volumes and are thus ideal systems to study non-linear optics.

We are working together with the QIV group at the MPL on studying the quantum properties of the emitted light from parametrically down converted light in a lithium niobate WGM resonator. A green pump photon splits into two highly tunable infra red photons and allows for heralded single photons of a single mode ArXiV (2014). In order to determine the exact modal parameters we have devised a method to clearly identify each mode ArXiV 1408.5071 (2014).

## Theoretical aspects of WGM resonators

Although the subject is already around for a while there are still many fascinating open questions. Such as a rather simple analytical description of the modal profile in a disk shaped WGM resonator Opt. Express (2013). If a asymmetrical small scatterer, it could be a plasmonic scatterer, is placed close to a WGM resonator then the symmetry is broken and fully three dimensional numerical methods are needed Opt. Express (2013). We published the COMSOL script to this article.

### Sensing with crystalline MgF2 WGM resonators

Besides non-linear optics and frequency stabilization, WGM resonators find also a broad range applications in the field of biological and chemical sensing. The long photon lifetime in high Q-resonators and the small line width of the resonances enables both high sensitivity and high measurement accuracy in such applications. Well established systems for sensing applications are microspheres made of fused silica, silica microtoroids and polystyrene beads. All this systems have an isotropic geometry and refractive index of about 1.45 or higher in common. In contrast, MgF2 is a birefringent crystal with a refractive index of n_e =1.387 and n_o=1.3751. The small index gap between a resonator made of MgF2 and water provides a long evanescent field at the surface of the resonator and thus a high sensitivity towards changes in the refractive index of the surrounding medium. We measured a sensitivity towards refractive index changes of the surrounding medium in a MgF2 resonator that is enhanced by nearly half an order of magnitude in comparison to a silica sphere of the same size. The intrinsic Q-factors achieved in aqueous environments are easily higher than 108 and so competitive with Q- values that are frequently reported for fused silica spheres in water ArXiv (2014).

## Polarization properties of crystalline WGM resonators

Currently most WGM resonators are fabricated fully symmetric to their rotational axis. In WGM resonators fabricated from uniaxial crystals this symmetry axis then coincides with the optic axis, such that the modes are either parallel or perpendicular polarized. If the optic axis is however tilted with respect to the symmetry axis the polarization of the modes changes dramatically. A complex type of mode is observed that can be fully coupled (decoupled) with a right (left) hand circular polarized beam of light. Furthermore, the polarization properties at different outcoupling positions, determined via full Stokes measurements, are recorded and show a continuous complex change in ellipticity. We present the experimental results. Understanding the polarization behavior in an off-axis, birefringent WGM resonator may offer a new way for phase-matching in non-linear materials ArXiv (2013), Opt. Express (2013) .

## Sub-kHz linewidth laser

Standard fiber ring lasers are cheap, but suffer from unstable lasing behavior and a relative large linewidth. Utilizing a millimeter sized diamond turned CaF2 WGM resonator as a passive filtering element in an erbium-doped fiber ring laser we achieve single mode lasing. This system sustains single mode lasing without the usage of active stabilization techniques which we characterized with a three-cornered-hat measurement to have a linewidth below 13kHz, Optics Letters (2010). These measurements were limited by the reference lasers used. Currently we have build an identical WGM system and together with a commercial system have measures the relative frequency stability to be below a 700 Hz ArXiV (2012) and Optics Express (2014).

## Microcavity stabilized Fiber Ring Laser

In an earlier experiment we utilized a quartz microsphere of 100 μm diameter. This sphere was molten by a CO_{2} laser and featured Q factors around 10^{7}. Evanescent coupling to the sphere was achieved by a tapered fiber and the out-coupling via an angle polished fiber. The setup was not as stable as the prism setup but nevertheless reduced the linewidth by five orders of magnitude to just below 170 kHz, Optics Letters (2009).

## Coupled Microresonators and Emission Properties in the THz domain

Single dielectric whispering gallery mode resonators have been thoroughly studied. They have an interesting mode spectrum, quite similar to the energy levels of an single atom. Bringing two atoms close to each other, perturbs their mode-field and induces due to the symmetry breaking a mode-splitting. Up to now such a mode splitting had not been observed on two identical whispering gallery mode resonators in the optical domain, as the requirements on the shape are stringent. We have fabricated two sets of identical resonators in the THz regime, which due to the wavelength of THz radiation (30 mu - 3 mm), was possible. Clear mode splitting was observed and reported in Optics Express (2008).

Furthermore we study the emission directionality of polymer WGM resonators with finite scatterers, yielding surprisingly high Q factors and directional emission properties ArXiV (2013)

## Wave-chaos in Microresonators

Wave-chaos studies the behavior of systems, with a chaotic ray-dynamics in the short wavelength limit. We have studied the emission properties of slightly deformed polymer microcavity lasers and found that the lasing directionality was in perfect agreement with the short time properties of the phase space flow in ray picture. This flow is given by the unstable manifolds of the unstable fixed-points in the ray-dynamical map and we were able to directly relate it to experimental near and farfield data. This work has been published in JOSA (2004)

## Numerical methods for dielectric resonators

Finding resonances in open, dielectric resonators is time and memory consuming with the standard FDTD approach, which has to discretize the whole space. Boundary methods avoid such problems and only need to discretize the problem on the boundary, lead however to a complex root search. We have devised a method of formulating the equations in term of an eigenvalue problem and by observing the behavior of the eigenvalues with respect to small changes of the wavenumber, we have devised an efficient root-search algorithm. I have worked on this with close collaboration with Hakan Türeci at the ETH Zürich. Recently I started a collaboration with Chris Poulton at the UTS in Australia to investigate multiple randomly positioned dielectric discs, recently published in Optics Express (2009).

## Goos-Hänchen Shift

I am interested in the fundamental properties of the reflection of light at a dielectric interface. When light from a denser dielectric material impinges on a less dense material, there is an angle beyond which light is totally internally reflected. Newton already proposed in his *Opticks* (1704) that light impinging under such an angle would show a shift with respect to the specularly reflected light. In 1947, Goos and Hänchen were the first to measure this shift. However, as the shift is only of the order of the wavelength, they used multiple reflections to obtain a result they could measure.

Our group has devised an experiment that allows the shift to be directly measured in the optical regime after only one reflection following an idea similar to the one behind Goos and Hänchen's original work, and we have published it in Optics Letters (2008), you can also get this pdf.

Further experiments will investigate the reflection properties of a non-linear medium instead of air.