Whispering gallery mode resonators made from non-linear electro-optic materials are excellent platforms for frequency manipulation of electromagnetic radiation, allowing microwave up-conversion and the generation of frequency combs. By using an x-cut lithium niobate crystal to fabricate our WGM resonator, the resulting electro-optic coefficient varies around the circumference of the resonator, allowing for a simpler microwave geometry. We demonstrate a frequency comb with excellent repetition rate stability, and show results from dual combs with orthogonal polarisations. We measure the relative frequency stability of the dual combs, and find it to be 4 mHz, without any need for stabilisation or post processing. Besides these results at telecom frequencies, we will also show first results of a visible electro-optic frequency comb.
Dielectric whispering-gallery-mode (WGM) resonators can confine light via total internal reflection. Small perturbations in the local environment usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations and a theoretical model of strong frequency shifts that can be opposite and even exceed the contribution of the perturbations' polarizability [1]. We also report on a new, independent way of calibrating the prism distance based on Newton’s rings [2] and report on results from ultra-low threshold lasing from a titanium doped sapphire WGM resonator, showing that lasing as well as linewidth narrowing is possible [3].
[1] F. Azeem, …, and H.G.L. Schwefel, Opt. Lett. 46, 2477(2021).
[2] J. T. Christensen, …, and H. G. L. Schwefel, arXiv:2208.00667(2022).
[3] F. Azeem, …, and H.G.L. Schwefel, Adv. Optical Materials 10, 2102137(2022).
Whispering gallery mode resonators made from non-linear electro-optic materials are excellent platforms for frequency manipulation of electromagnetic radiation, allowing microwave up-conversion and the generation of frequency combs. By using an x-cut lithium niobate crystal to fabricate our WGM resonator, the resulting electro-optic coefficient varies around the circumference of the resonator, allowing for a simpler microwave geometry. We demonstrate a frequency comb with excellent repetition rate stability, and show results from dual combs with orthogonal polarisations. We measure the relative frequency stability of the dual combs, and find it to be 4 mHz, without any need for stabilisation or post processing.
Frequency combs are coherent light sources comprising multiple evenly spaced emission lines, allowing coherent sampling over a broad part of the optical spectrum. The addition of a second frequency comb results in a dual comb. Now, one comb can be used as a local oscillator frequency reference for the other, allowing spectroscopic measurement to take place at radio-frequencies. An important figure of merit is the relative frequency stability of the two combs. In this work we demonstrate efficient generation of ultrastable dual combs using an electro-optic whispering gallery mode resonator, with a relative comb line stability of order 1 mHz.
Dielectric whispering-gallery-mode resonators are a great tool to entrap electro-magnetic radiation throughout the dielectric’s transparency range[1]. I will discuss hybrid systems which are resonant for both microwave and optical fields and that allow for second order nonlinear effects.
In an efficient resonant system and for strong microwave and optical fields, sum- and difference frequency generation can cascade, leading to optical frequency combs[2]. For the limit of very weak microwaves and only sum frequency generation, coherent conversion of microwave signals allows the quantum state of individual microwave photons to be transferred into the optical domain[3], useful for connecting future superconducting-qubits-based quantum-networks.
1. D.V. Strekalov, C. Marquardt, A.B. Matsko, H.G.L. Schwefel, and G. Leuchs, Journal of Optics 18, 123002 (2016).
2. A. Rueda, ... and H.G.L. Schwefel, Nature 568, 378 (2019).
3. A. Rueda, ... and H.G.L. Schwefel, Optica 3, 597 (2016)
Through their small modal volumes and ultra-high finesse, optical microresonators are capable of exhibiting rich nonlinear behaviour, driven by pump powers in the milliwatt range. Microresonators with Kerr type non- linearities have been the focus of much research, resulting in the demonstration of chip-scale coherent optical frequency combs, underpinned by four-wave-mixing. Here, we consider a four-wave-mixing process in microresonators which generates widely-separated parametric sidebands, symmetrically spaced around the pump.
The strong confinement obtained in whispering gallery mode (WGM) resonators is highly conducive to nonlinear effects, due to both resonant enhancement of the fields and a large modal overlap. This confinement can, however, also lead to difficulties; it is difficult to efficiently pump the nonlinear interaction whilst also extracting the signal light, especially when very different wavelengths are involved.
The common coupling mechanisms to WGM resonators are all evanescent, and the coupling rates inherit the exponential decay of the evanescent field. The decay length of these fields is proportional to the wavelength, so longer wavelength modes will tend to couple more than their shorter counterparts. Experimentally this hinders efficiency and, by extension, observation of nonlinear processes.
Through the use of a birefringent prism, and the different phase-matching conditions it imposes on coupling orthogonally-polarized modes, we can independently control the coupling rates of a pump mode and its second harmonic in an x-cut lithium niobate resonator. We thereby critically couple pump and signal in kind, increasing the process’s efficiency fifteen-fold.
This selective coupling can easily be applied to birefringent resonators, where the birefringence is large enough, through use of a prism of the same material. This can also be used with isotropic media, if a suitable birefringent material can be found.
Lasing whispering gallery mode resonators, such as dye doped microspheres and microcapillaries, have shown tremendous potential for refractive index sensing and biosensing applications owning to the narrower resonances achieved upon lasing. This has enabled higher resolution on the determination of the resonance wavelength shift induced by a variation of the surrounding refractive index and as a consequence to reach lower detection limit compared with their fluorescent counterparts. The sensing procedure in both cases relies on tracking the wavelength shift of individual modes, therefore requiring high resolution spectral analysis. This stringent requirement not only prevents any viable commercial prospects due to high equipment cost but more importantly imposes a technological limit, related to the equipment spectral resolution, on the achievable detection limit.
In this paper, we show for the first time that the lasing threshold and eventually the resonances intensity can be used for inferring changes of refractive index around a 15 μm dye doped polystyrene instead of the mode tracking procedure. The sensing mechanism relies on the spoiling of the resonator Q factor upon change of refractive index which eventually increases the lasing threshold. In addition to allow free space excitation and collection, alleviating the need for phase matched prism or fiber taper, this novel approach promises to reach lower detection limit by suppressing the need of high resolution spectral analysis of the whispering gallery mode spectra but instead relying on cost effective and highly sensitive intensity measurements.
Long photon confinement and high optical fields require good optical resonators. Some of the best optical resonators with a small footprint are whispering gallery mode (WGM) resonators. Their principle is based on continuous total internal reflection at the interface of a round dielectric. 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. We report on high Q resonances in a slightly birefringent MgF2 WGM resonator, cut at an angle of 20° with respect to the optic axis. A novel 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 χ(2) materials.
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