arXiv subjects

Harald G. L. Schwefel

Publications and source records attributed to Harald G. L. Schwefel.

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear and Quantum Optics with Whispering Gallery Resonators Revisited

In 2016 we published a review paper "Nonlinear and Quantum Optics with Whispering Gallery Resonators" (1). While writing this review, we found it often necessary to defer addressing many challenges of the field to the future. At the same time, many potential benefits offered by nonlinear optical resonators were also deferred to the future pending the underlying technology development. The past ten years have seen a great deal of such development, including in the field of resonator optics. We feel that an update to our 2016 review is in order. In this new review we focus on the most significant developments in the field that took place in past ten years.

physics.optics↗

arXiv2025

Spatial mapping and tuning of terahertz modes in a silicon whispering gallery mode resonator

Identification and subsequent manipulation of resonant modes typically relies on comparison with calculations which require precise knowledge of material parameters and dimensions. For millimetre-sized resonators that support millimetre-wave modes, this is particularly challenging due to the poorly determined physical parameters and additional perturbative effects of nearby dielectric or metallic substrates in experimental setups. Here, we use perturbation from a metal needle to experimentally map the spatial distribution of terahertz modes in a silicon disc resonator. We then use this information to design a patterned structure to manipulate specific modes in the system, a technique that could be useful for targeted tuning of such modes.

physics.optics↗

arXiv2024

Cascaded Raman lasing in a lithium tetraborate (LB4) whispering gallery mode resonator

Lithium tetraborate (LB4) is a lithium borate compound and recently has shown renewed interest due to its exceptional linear and nonlinear optical properties. Its wide transparency range, spanning from 0.16$μm$ to 3.5$μm$, and low loss in the visible range make LB4 highly popular in applications of harmonics generation and deep ultraviolet radiation. Also, LB4 is a good Raman-active material due to its high Raman gain. Here, a millimeter sized LB4 whispering gallery mode resonator (WGMR) is machined using single point diamond cutting, which has, to the best of our knowledge, the highest reported quality ($Q$) factor of $2.0 \times 10^9$ at 517 nm. Then, stimulated Raman scattering (SRS) was investigated in this LB4 WGMR. When pumped with about 7 mW at 517 nm, four cascaded SRS peaks with wavelengths ranging from 537 nm to 608 nm are demonstrated, which can be clearly observed using an optical grating. Among them, the first order SRS is characterized and has a threshold of 0.69 mW with a slope efficiency of 7.2 %. This is the first implementation of a LB4 whispering gallery mode Raman laser, which will facilitate usages of LB4 WGMR as compact Raman lasing source in future.

physics.optics↗

arXiv2024

Single-point-diamond-turned GaAs disk resonator with over a million optical quality factor

Gallium arsenide optical resonators have been identified as platforms for light-matter interactions ranging from optomechanics to quantum electrodynamics involving nonlinear optics. Here, we present a 5-mm-diameter whispering gallery mode resonator made of undoped gallium arsenide. The fabrication was done using single-point diamond turning followed by polishing with diamond solutions of varying grain size. The resulting resonator was optically characterized to have a quality factor of more than a million.

physics.optics↗

arXiv2023

Gallium arsenide whispering gallery mode resonators for terahertz photonics

As the field of terahertz (THz) photonics advances, we present a monolithic gallium arsenide (GaAs) disk-shaped whispering gallery mode resonator that has potential as a component in THz nonlinear optics. GaAs is a material with significant optical nonlinearity which can be enhanced when the crystal is shaped into a microdisk resonator. A 4-mm-disk-resonator was fabricated using single-point diamond turning and was characterised to obtain a quality (Q) factor of 2.2k at ~150 GHz and 1.4k at ~300 GHz. We also demonstrated the blue-shifting of up to ~0.3 GHz of the THz modes using a block of metal. This post-fabrication degree of freedom could be useful for phase-matching requirements for nonlinear optical processes, such as detection based on optical up-conversion of THz radiation. Such a compact, tunable and efficient device could be integrated into nonlinear photonic platforms for THz generation, manipulation and detection.

physics.optics↗

arXiv2022

Microwave-optical double resonance in a erbium-doped whispering-gallery-mode resonator

We showcase an erbium-doped whispering-gallery-mode resonator with optical modes that display intrinsic quality factors better than $10^8$ (linewidths less than 2 MHz), and coupling strengths to collective erbium transitions of up to 2$π\times$1.2 GHz - enough to reach the ensemble strong coupling regime. Our optical cavity sits inside a microwave resonator, allowing us to probe the spin transition which is tuned by an external magnetic field. We show a modified optically detected magnetic resonance measurement that measures population transfer by a change in coupling strength rather than absorption coefficient. This modification was enabled by the strong coupling to our modes, and allows us to optically probe the spin transition detuned by more than the inhomogeneous linewidth. We contrast this measurement with electron paramagnetic resonance to experimentally show that our optical modes are confined in a region of large microwave magnetic field and we explore how such a geometry could be used for coherent microwave-optical transduction.

quant-ph↗

arXiv2022

Distance calibration via Newton's rings in yttrium lithium fluoride whispering gallery mode resonators

In this work, we analyze the first whispering gallery mode resonator (WGMR) made from monocrystalline yttrium lithium fluoride (YLF). The disc-shaped resonator is fabricated using single-point diamond turning and exhibits a high intrinsic quality factor ($Q$) on the order of $10^9$. Moreover, we employ a novel method based on microscopic imaging of Newton's rings through the back of a trapezoidal prism. This method can be used to evanescently couple light in to a WGMR and monitor the separation between the cavity and the coupling prism. Accurately calibrating the distance between a coupling prism and a WGMR is desirable as it can be used to improve experimental control and conditions, i.e., accurate coupler gap calibration can aid in tuning into desired coupling regimes and can be used to avoid potential damage caused by collisions between the coupling prism and the WGMR. Here, we use two different trapezoidal prisms together with the high-$Q$ YLF WGMR to demonstrate and discuss this method.

physics.optics↗

arXiv2021

Soliton linear-wave scattering in a Kerr microresonator

The nonlinear scattering of a linear optical wave from a conservative soliton has been widely studied in optical fibers as a mechanism for nonlinear frequency conversion. Here we extend this analysis to consider the scattering of an externally injected probe wave from a dissipative Kerr cavity soliton circulating in a Kerr microresonator. We demonstrate, both theoretically and experimentally, that this nonlinear interaction can be harnessed for useful expansion of the soliton frequency comb via the formation of a secondary idler comb. We explore the physics of the process, showing that the phase detuning of the injected probe from a cavity resonance plays a key role in setting the central frequency of the idler comb, thus providing a convenient parameter through which to control the spectral envelope of that comb. Our results elucidate the dynamics that govern the interactions between dissipative Kerr cavity solitons and externally injected probe waves, and could prove useful in the design of future Kerr frequency comb systems by enabling the possibility to provide high-power comb lines in a specified spectral region simply through the injection of a suitably chosen probe.

physics.optics↗

arXiv2021

Ultra-low Threshold Titanium doped sapphire Whispering-gallery Laser

Titanium doped sapphire (Ti:sapphire) is a laser gain material with broad gain bandwidth benefiting from the material stability of sapphire. These favorable characteristics of Ti:sapphire have given rise to femtosecond lasers and optical frequency combs. Shaping a single Ti:sapphire crystal into a millimeter sized high quality whispering gallery mode resonator ($Q\sim10^8$) reduces the lasing threshold to 14.2 mW and increases the laser slope efficiency to 34%. The observed lasing can be both multi-mode and single-mode. This is the first demonstration of a Ti:sapphire whispering-gallery laser. Furthermore, a novel method of evaluating the gain in Ti:sapphire in the near infrared region is demonstrated by introducing a probe laser with a central wavelength of 795 nm. This method results in decreasing linewidth of the modes excited with the probe laser, consequently increasing their $Q$. These findings open avenues for the usage of whispering gallery mode resonators as cavities for the implementation of compact Ti:sapphire lasers. Moreover, Ti:sapphire can also be utilized as an amplifier inside its gain bandwidth by implementing a pump-probe configuration.

physics.optics↗

arXiv2020

Dielectric perturbations: anomalous resonance frequency shifts in optical resonators

Small perturbations in the dielectric environment around a high quality whispering gallery mode resonator usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations of strong frequency shifts that can be opposite and even exceed the contribution of the perturbations' polarizability. The mode frequencies of a lithium niobate whispering gallery mode resonator are shifted using substrates of refractive indices ranging from 1.50 to 4.22. Both blue- and red-shifts are observed, as well as an increase in mode linewidth, when substrates are moved into the evanescent field of the whispering gallery mode. We compare the experimental results to a theoretical model by Foreman et al. and provide an additional intuitive explanation based on the Goos-Hänchen shift for the optical domain.

physics.optics↗

arXiv2020

Thermal Noise in Electro-Optic Devices at Cryogenic Temperatures

The quantum bits (qubits) on which superconducting quantum computers are based have energy scales corresponding to photons with GHz frequencies. The energy of photons in the gigahertz domain is too low to allow transmission through the noisy room-temperature environment, where the signal would be lost in thermal noise. Optical photons, on the other hand, have much higher energies, and signals can be detected using highly efficient single-photon detectors. Transduction from microwave to optical frequencies is therefore a potential enabling technology for quantum devices. However, in such a device the optical pump can be a source of thermal noise and thus degrade the fidelity; the similarity of input microwave state to the output optical state. In order to investigate the magnitude of this effect we model the sub-Kelvin thermal behavior of an electro-optic transducer based on a lithium niobate whispering gallery mode resonator. We find that there is an optimum power level for a continuous pump, whilst pulsed operation of the pump increases the fidelity of the conversion.

quant-ph↗

arXiv2020

Cavity quantum electro-optics: Microwave-telecom conversion in the quantum ground state

Fiber optic communication is the backbone of our modern information society, offering high bandwidth, low loss, weight, size and cost, as well as an immunity to electromagnetic interference. Microwave photonics lends these advantages to electronic sensing and communication systems, but - unlike the field of nonlinear optics - electro-optic devices so far require classical modulation fields whose variance is dominated by electronic or thermal noise rather than quantum fluctuations. Here we present a cavity electro-optic transceiver operating in a millikelvin environment with a mode occupancy as low as 0.025 $\pm$ 0.005 noise photons. Our system is based on a lithium niobate whispering gallery mode resonator, resonantly coupled to a superconducting microwave cavity via the Pockels effect. For the highest continuous wave pump power of 1.48 mW we demonstrate bidirectional single-sideband conversion of X band microwave to C band telecom light with a total (internal) efficiency of 0.03 % (0.7 %) and an added output conversion noise of 5.5 photons. The high bandwidth of 10.7 MHz combined with the observed very slow heating rate of 1.1 noise photons s$^{-1}$ puts quantum limited pulsed microwave-optics conversion within reach. The presented device is versatile and compatible with superconducting qubits, which might open the way for fast and deterministic entanglement distribution between microwave and optical fields, for optically mediated remote entanglement of superconducting qubits, and for new multiplexed cryogenic circuit control and readout strategies.

quant-ph↗

arXiv2020

Nonlinear power dependence of the spectral properties of an optical parametric oscillator below threshold in the quantum regime

Photon pairs and heralded single photons, obtained from cavity-assisted parametric down-conversion (PDC), play an important role in quantum communications and technology. This motivated a thorough study of the spectral and temporal properties of parametric light, both above the Optical Parametric Oscillator (OPO) threshold, where the semiclassical approach is justified, and deeply below it, where the linear cavity approximation is applicable. The pursuit of a higher two-photon emission rate leads into an interesting intermediate regime where the OPO still operates considerably below the threshold but the nonlinear cavity phenomena cannot be neglected anymore. Here, we investigate this intermediate regime and show that the spectral and temporal properties of the photon pairs, as well as their emission rate, may significantly differ from the widely accepted linear model. The observed phenomena include frequency pulling and broadening in the temporal correlation for the down-converted optical fields. These factors need to be taken into account when devising practical applications of the high-rate cavity-assisted SPDC sources.

physics.optics↗

arXiv2019

Experimental observation of internally-pumped parametric oscillation and quadratic comb generation in a $χ^{(2)}$ whispering-gallery-mode microresonator

We report on the experimental observation of internally-pumped parametric oscillation in a high-Q lithium niobate microresonator under conditions of natural phase-matching. Specifically, launching near-infrared pump light around 1060 nm into a $z$-cut congruent lithium niobate microresonator, we observe the generation of optical sidebands around the input pump under conditions where second-harmonic generation is close to natural phase-matching. We find that a wide range of different sideband frequency shifts can be generated by varying the experimental parameters. Under particular conditions, we observe the cascaded generation of several equally-spaced sidebands around the pump -- the first steps of optical frequency comb generation via cavity-enhanced second-harmonic generation.

physics.optics↗

arXiv2019

Squeezed vacuum states from a whispering gallery mode resonator

Squeezed vacuum states enable optical measurements below the quantum limit and hence are a valuable resource for applications in quantum metrology and also quantum communication. However, most available sources require high pump powers in the milliwatt range and large setups, which hinders real world applications. Furthermore, degenerate operation of such systems presents a challenge. Here, we use a compact crystalline whispering gallery mode resonator made of lithium niobate as a degenerate parametric oscillator. We demonstrate about 1.4 dB noise reduction below the shot noise level for only 300 $μ\text{W}$ of pump power in degenerate single mode operation. Furthermore, we report a record pump threshold as low as 1.35 $μ\text{W}$. Our results show that the whispering gallery based approach presents a promising platform for a compact and efficient source for nonclassical light.

quant-ph↗

arXiv2019

Steady states, squeezing, and entanglement in intracavity triplet down conversion

Triplet down conversion, the process of converting one high-energy photon into three low-energy photons, may soon be experimentally feasible due to advances in optical resonator technology. We use quantum phase-space techniques to analyse the process of degenerate intracavity triplet down conversion by solving stochastic differential equations within the truncated positive-P representation. The time evolution of both intracavity mode populations are simulated, and the resulting steady-states are examined as a function of the pump intensity. Quantum effects are most pronounced in the region immediately above the semi-classical pumping threshold, where our numerical results differ significantly from semi-classical predictions. Regimes of measurable squeezing and bipartite entanglement are identified from steady-state spectra of the cavity output fields. We validate the truncated positive-P description against Monte Carlo wave function simulations, finding good agreement for low mode populations.

quant-ph↗

arXiv2019

Coherent conversion between microwave and optical photons -- an overview of physical implementations

Quantum information technology based on solid state qubits has created much interest in converting quantum states from the microwave to the optical domain. Optical photons, unlike microwave photons, can be transmitted by fiber, making them suitable for long distance quantum communication. Moreover, the optical domain offers access to a large set of very well developed quantum optical tools, such as highly efficient single-photon detectors and long-lived quantum memories. For a high fidelity microwave to optical transducer, efficient conversion at single photon level and low added noise is needed. Currently, the most promising approaches to build such systems are based on second order nonlinear phenomena such as optomechanical and electro-optic interactions. Alternative approaches, although not yet as efficient, include magneto-optical coupling and schemes based on isolated quantum systems like atoms, ions or quantum dots. In this Progress Report, we provide the necessary theoretical foundations for the most important microwave-to-optical conversion experiments, describe their implementations and discuss current limitations and future prospects.

physics.optics↗

arXiv2019

Octave-spanning tunable parametric oscillation in crystalline Kerr microresonators

Parametric nonlinear optical processes allow for the generation of new wavelengths of coherent electromagnetic radiation. Their ability to create radiation that is widely tunable in wavelength is particularly appealing, with applications ranging from spectroscopy to quantum information processing. Unfortunately, existing tunable parametric sources are marred by deficiencies that obstruct their widespread adoption. Here we show that ultrahigh-Q crystalline microresonators made of magnesium fluoride can overcome these limitations, enabling compact and power-efficient devices capable of generating clean and widely-tunable sidebands. We consider several different resonators with carefully engineered dispersion profiles, achieving hundreds of nanometers of sideband tunability in each device when driven with a standard low-power laser at 1550 nm. In addition to direct observations of discrete tunability over an entire optical octave from 1083 nm to 2670 nm, we record signatures of mid-infrared sidebands at almost 4000 nm. The simplicity of the devices considered -- compounded by their remarkable tunability -- paves the way for low-cost, widely-tunable sources of electromagnetic radiation.

physics.optics↗