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We investigate the frequency-resolved intensity noise spectrum of an Yb-doped fiber amplifier down to the fundamental limit of quantum noise. We focus on the kHz and low MHz frequency regime with special interest in the region between 1 and 10 kHz. Intensity noise levels up to $$\ge$$ ≥ 60 dB above the shot noise limit are found, revealing great optimization potential. Additionally, two seed lasers with different noise characteristics were amplified, showing that the seed source has a significant impact and should be considered in the design of high power fiber amplifiers.

In this paper we present a room temperature radiometer that can eliminate the need of using cryostats in satellite payload reducing its weight and improving reliability. The proposed radiometer is based on an electro-optic upconverter that boosts up microwave photons energy by upconverting them into an optical domain what makes them immune to thermal noise even if operating at room temperature. The converter uses a high-quality factor whispering gallery mode (WGM) resonator providing naturally narrow bandwidth and therefore might be useful for applications like microwave hyperspectral sensing. The upconversion process is explained by providing essential information about photon conversion efficiency and sensitivity. To prove the concept, we describe an experiment which shows state-of-the-art photon conversion efficiency $\eta =10^{-5}$ per mW of pump power at the frequency of 80 GHz.

Coherent beam combining refers to the process of generating a bright output beam by merging independent input beams of individually diffusing relative phases by locking them to each other. We report the first quantum mechanical noise limit calculations for coherent beam combining and compare our results to quantum-limited amplification. Our coherent beam combining scheme is based on an optical Fourier transformation which renders the scheme compatible with integrated optics combined with feed-back stabilization of the relative phases. The scheme can be layed out for an arbitrary number of input beams and approaches the shot noise limit for a large number of inputs.

Optical frequency combs (OFCs) are light sources whose spectra consists of equally spaced frequency lines in the optical domain [1]. They have great potential for improving high-capacity data transfer, all-optical atomic clocks, spectroscopy, and high-precision measurements [2].

Quantum repeaters rely on an interfacing of flying qubits with quantum memories. The most common implementations include a narrowband single photon matched in bandwidth and central frequency to an atomic system. Previously, we demonstrated the compatibility of our versatile source of heralded single photons, which is based on parametric down-conversion in a triply-resonant whispering-gallery mode resonator, with alkaline transitions [Schunk et al., Optica 2, 773 (2015)]. In this paper, we analyze our source in terms of phase matching, available wavelength-tuning mechanisms, and applications to narrow-band atomic systems. We resonantly address the D1 transitions of cesium and rubidium with this optical parametric oscillator pumped above its oscillation threshold. Below threshold, the efficient coupling of single photons to atomic transitions heralded by single telecom-band photons is demonstrated. Finally, we present an accurate analytical description of our observations. Providing the demonstrated flexibility in connecting various atomic transitions with telecom wavelengths, we show a promising approach to realize an essential building block for quantum repeaters.

We demonstrate electro-optic frequency comb generation using a doubly resonant system comprising a whispering gallery mode disk resonator made of lithium niobate mounted inside a three dimensional copper cavity. We observe 180 sidebands centred at 1550 nm.

High speed optical telecommunication is enabled by wavelength division multiplexing, whereby hundreds of individually stabilized lasers encode the information within a single mode optical fiber. In the seek for larger bandwidth the optical power sent into the fiber is limited by optical non-linearities within the fiber and energy consumption of the light sources starts to become a significant cost factor. Optical frequency combs have been suggested to remedy this problem by generating multiple laser lines within a monolithic device, their current stability and coherence lets them operate only in small parameter ranges. Here we show that a broadband frequency comb realized through the electro-optic effect within a high quality whispering gallery mode resonator can operate at low microwave and optical powers. Contrary to the usual third order Kerr non-linear optical frequency combs we rely on the second order non-linear effect which is much more efficient. Our result uses a fixed microwave signal which is mixed with an optical pump signal to generate a coherent frequency comb with a precisely determined carrier separation. The resonant enhancement enables us to operate with microwave powers three order magnitude smaller than in commercially available devices. We can expect the implementation into the next generation long distance telecommunication which relies on coherent emission and detection schemes to allow for operation with higher optical powers and at reduced cost.

Graphene and liquid crystals (LC) as emerging materials for the THz region are reviewed together with whispering gallery mode (WGM) resonators as fundamental building blocks for future THz applications. Whispering gallery mode resonators can confine optical as well as THz radiation. The fundamental properties of resonators and, in particular, WGM resonators are discussed and applied to different experimental realizations of coupled resonators. Furthermore, an outlook on the very promising task of nonlinear frequency conversion between THz and optical light is given. Liquid crystals are promising tunable materials for THz applications. The fundamental physical and electrical properties of nematic LCs in terms of molecule interaction, alignment, and tuning techniques are presented. Then, different characterization methods for the broad region of microwave to THz frequencies are reviewed for this emerging material class. Finally, possible applications based on LC material are described. Graphene is another very promising material for THz applications. Its properties are introduced theoretically, highlighting exceptional effects such as Dirac-like behavior of the charge carriers, extremely high carrier mobility, and carrier-density-dependent THz transmission properties. Several examples of promising applications, such as graphene-based field effect transistors, switchable THz filters, and modulators are discussed.

Coherent beam combining refers to the process of generating a bright output beam by merging independent input beams with locked relative phases. We report the first quantum mechanical noise limit calculations for coherent beam combining and compare our results to quantum-limited amplification. We highlight a favourable noise scaling for both pure and noisy input states.

We present the current state of nonlinear and quantum optics within WGM resonators with particular emphasis on frequency conversion. This includes electro-optic microwave to optics transduction as well as parametric photon triplet generation.

We propose a dielectric rod waveguide antenna (DRW) integrated with a photomixer as a THz emitter. This represents a different approach as opposed to the classical solution of a substrate lens. Main goals are an inexpensive alternative to substrate lenses, reduction of both reflections on the semiconductor-air interface and scattering of terahertz-generated power into the substrate. A radiation pattern measured at 137 GHz is shown as a proof-of-concept. In order to increase radiated power, the improvement of the rod antenna is discussed. Finally, as an application example, evanescent coupling of the DRW into a high index whispering gallery mode resonator is shown.

In this paper, the coupling mechanism of a free-space Gaussian beam into a whispering-gallery mode resonator through a dielectric lens is mathematically modeled and numerically solved by means of the Schelkunoff-Waterman method (the so called T-matrix method). This approach allows in principle, to quickly analyze the performance of different near-field coupling mechanisms with arbitrary excitations. The aim is to efficiently excite a WGM into a nonlinear dielectric resonator in order to detect the weak mm-wave radiation from the cosmic microwave background (CMB) by up-converting the signal into the optical domain via the nonlinearity of the medium.

In this paper, a scheme for coupling free-space THz radiation into a nonlinear whispering-gallery mode (WGM) resonator is presented. The purpose is to detect the weak THz radiation from the cosmic microwave background (CMB) by up-converting the signal into the optical domain via the nonlinearity of the medium. Such high-sensitivity receiver has theoretically shown capabilities towards photon counting at room temperature, however, it is critical to efficiently couple the THz radiation into the resonator. Therefore, by using the Schelkunoff-Waterman method (the so called T-matrix method) we perform an analytical evaluation of two different free-space coupling techniques: a frees-pace Gaussian beam, and a Gaussian beam incident in a silicon lens under total internal reflection. By comparing the excited modes in the resonator, the optimal parameters for each case are given.

We report on experiments on refractrometric sensing with crystalline Whispering Gallery Mode (WGM) resonators made of magnesium fluoride, which has a refractive index that is only slightly larger than that of water (Δn ≈ 0.05). The resulting evanescent field of a WGM resonator placed in an aqueous environment penetrates therefore deep into the surrounding medium, which makes it a promising candidate for sensing applications. We measured a bulk index sensitivity of 1.09 nm/RIU (refractive index unit) in a resonator with a radius of R = 2.91 mm and intrinsic Q-factors of more than 108 in aqueous environments. Furthermore, we describe the fabrication process of crystalline WGM resonators.

Change history: In the Methods section of this Letter, there were formatting errors to the equations of motion using the Heisenberg picture; see accompanying Amendment for further details. This has been corrected online.

Whispering gallery mode (WGM) resonators are an important platform for linear, nonlinear and quantum optical experiments. In such experiments, independent control of in- and out-coupling rates to different modes can lead to higher conversion efficiencies and greater flexibility in the generation of non-classical states based on parametric down conversion. In this work, we introduce a scheme that enables selective out-coupling of WGMs belonging to a specific polarization family, while the orthogonally polarized modes remain largely unperturbed. Our technique utilizes material birefringence in both the resonator and the coupler such that a negative (positive) birefringence allows for polarization-selective coupling to TE (TM) WGMs. We formulate a new coupling condition suitable for describing the case where the refractive indices of the resonator and the coupler are almost the same, from which we derive a criterion for polarization-selective coupling. Finally, we experimentally demonstrate our proposed method using a lithium niobate disk resonator coupled to a lithium niobate prism, where we show a \SI{22}{dB} suppression of coupling to TM modes relative to TE modes.

We present results on nonlinear electro-optical conversion of microwave radiation into the optical telecommunication band with more than 0.1% photon number conversion efficiency with MHz bandwidth, in a crystalline whispering gallery mode resonator.

We show that broadband second harmonic generation within birefringent whispering gallery mode resonators can be significantly enhanced by polarization selective out-coupling.

In this paper, a detailed description of the optical coupling into a Whispering Gallery Mode (WGM) resonator through a prism via frustrated total internal reflection (FTIR) is presented. The problem is modeled as three media with planar interfaces and closed expressions for FTIR are given. Then, the curvature of the resonator is taken into account and the mode overlap is theoretically studied. A new analytical expression giving the optimal geometry of a disc-shaped or ring-shaped resonator for maximizing the intra-cavity circulating power is presented. Such expression takes into consideration the spatial distribution of the WGM at the surface of the resonator, thus being more accurate than the currently used expressions. It also takes into account the geometry of the prism. It is shown an improvement in the geometry values used with the current expressions of about 30%. The reason why the pump laser signal can be seen in experiments under critical coupling is explained on this basis. Then, the conditions required for exciting the highest possible optical power inside the resonator are obtained. The aim is to achieve a highly-efficient up-conversion of a THz signal into the optical domain via the second-order nonlinearity of the resonator material. This work has been financially supported by "DiDaCTIC: Desarrollo de un sistema de comunicaciones inalámbrico en rango THz integrado de alta tasa de datos", TEC2013-47753-C3, CAM S2013/ICE-3004 "DIFRAGEOS" projects, "Proyecto realizado con la Ayuda Fundación BBVA a Investigadores y Creadores Culturales 2016" and "Estancias de movilidad de profesores PRX16/00021".

Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme, this is impossible because both up- and down-converted sidebands are necessarily present. Here, we demonstrate true single-sideband up- or down-conversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a 3 orders of magnitude improvement of the electro-optical conversion efficiency, reaching 0.1% photon number conversion for a 10 GHz microwave tone at 0.42 mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for nonclassical state conversion and communication. Our conversion bandwidth is larger than 1 MHz and is not fundamentally limited.

We present a coherent microwave to telecom signal converter based on the electro-optical effect using a crystalline WGM-resonator coupled to a 3D microwave cavity, achieving high photon conversion efficiency of 0.1% with MHz bandwidth.

In this paper, a general scheme for a sub-THz photon counting receiver working at room temperature is presented. Its working principle is based on nonlinear up-conversion of the sub-THz signal into the optical domain. For that, a lithium niobate (LiNbO3) WGM resonator is used in a double-resonant configuration. This system has theoretically shown capabilities towards photon counting. The concept is evaluated and is shown to be suitable for cosmic microwave background polarization measurements. Then, a practical configuration of several receivers is engineered for that purpose. The general receiver scheme is tested and experimental results are given.

Conventional ultra-high sensitivity detectors in the millimeter-wave range are usually cooled as their own thermal noise at room temperature would mask the weak received radiation. The need for cryogenic systems increases the cost and complexity of the instruments, hindering the development of, among others, airborne and space applications. In this work, the nonlinear parametric upconversion of millimeter-wave radiation to the optical domain inside high-quality (Q) lithium niobate whispering-gallery mode (WGM) resonators is proposed for ultra-low noise detection. We experimentally demonstrate coherent upconversion of millimeter-wave signals to a 1550 nm telecom carrier, with a photon conversion efficiency surpassing the state-of-the-art by 2 orders of magnitude. Moreover, a theoretical model shows that the thermal equilibrium of counterpropagating WGMs is broken by overcoupling the millimeter-wave WGM, effectively cooling the upconverted mode and allowing ultra-low noise detection. By theoretically estimating the sensitivity of a correlation radiometer based on the presented scheme, it is found that room-temperature radiometers with better sensitivity than state-of-the-art high-electron-mobility transistor (HEMT)-based radiometers can be designed. This detection paradigm can be used to develop room-temperature instrumentation for radio astronomy, earth observation, planetary missions, and imaging systems. Ministerio de Economía y Competitividad (MINECO) (TEC2013-47753-C3); Comunidad de Madrid (S2013/ICE-3004); Banco Santander (TEC2016-76997-C3-2-R); Banco Bilbao Vizcaya Argentaria (BBVA) (IN[16]_TIC_TIC_0040); 2017 UC3M-Santander Chair of Excellence.

We study a calibration scheme for terahertz wave nonlinear-optical detectors based on spontaneous parametric down-conversion. Contrary to the usual low wavelength pump in the green, we report here on the observation of spontaneous parametric down-conversion originating from an in-growth poled lithium niobate crystal pumped with a continuous wave 50 mW, 795 nm diode laser system, phase-matched to a terahertz frequency idler wave. Such a system is more compact and allows for longer poling periods as well as lower losses in the crystal. Filtering the pump radiation by a rubidium-87 vapor cell allowed the frequency-angular spectra to be obtained down to ∼0.5 THz or ∼1 nm shift from the pump radiation line. The presence of an amplified spontaneous emission “pedestal” in the diode laser radiation spectrum significantly hampers the observation of spontaneous parametric down-conversion spectra, in contrast to conventional narrowband gas lasers. Benefits of switching to longer pump wavelengths are pointed out, such as collinear optical-terahertz phase-matching in bulk crystals.

Nonlinear electro-optical conversion of microwave radiation into the optical telecommunication band is achieved within a crystalline whispering gallery mode resonator, reaching 0.1% photon number conversion efficiency with MHz bandwidth.

Down-converted photons from counterpropagating whispering gallery modes can be used to generate two-photon interference. We present our experimental scheme and discuss the interference visibility in case of backscattering.

We present efficient up-conversion of 80 GHz signals into the optical regime utilizing a high-Q dielectric resonator. Since the system is all-resonant and phase-matched, we reach a record power conversion of 6%.

We successfully demonstrate squeezing of nanosecond pulses via self-induced transparency in a system of mercury vapor confined in a hollow core kagome-style fiber.

Third harmonic and its reverse process of photon triplet generation are of particular interest for quantum communication and computing tasks. We present crystal classes and their necessary geometries to generate such triplets in WGM resonators.

We report a highly efficient source of narrow-band photon pairs based on parametric down-conversion in a crystalline whispering-gallery-mode resonator. Remarkably, each photon of a pair is detected in a single spatial and temporal mode, as witnessed by Glauber's autocorrelation function. We explore the phase-matching conditions in spherical geometries, and determine the requirements for single-mode operation. Understanding these conditions has allowed us to experimentally demonstrate a single-mode pair-detection efficiency of $1.13\ifmmode\times\else\texttimes\fi{}{10}^{6}$ pairs/s per mW pump power per 26.8 MHz bandwidth.

Quantum information technology strongly relies on coupling of optical photons with narrowband quantum systems, such as quantum dots, color centers, and atomic systems. This coupling requires matching the optical wavelength and bandwidth to the desired system, which presents a considerable problem for most available sources of quantum light. Here we demonstrate coupling of alkali dipole transitions with a tunable source of photon pairs. Our source is based on spontaneous parametric down-conversion in a triply-resonant whispering-gallery mode resonator. For this, we have developed novel wavelength tuning mechanisms, which allow for a coarse tuning to either cesium or rubidium wavelength with subsequent continuous fine-tuning to the desired transition. As a demonstration of the functionality of the source, we performed a heralded single photon measurement of the atomic decay. We present a major advance in controlling the spontaneous down-conversion process, which makes our bright source of single photons now compatible with a plethora of narrow-band resonant systems., 8 pages, 5 figures

Coherent detection of very weak THz signals is important in astronomy, spectroscopy, and communications. We report on coherent up-conversion of THz radiation into the optical telecommunication range. All resonant phase-matched conversion can be achieved in a whispering gallery mode (WGM) resonator. Furthermore we present first results on WGM resonators that can be coupled to both THz radiation as well as optical fields allowing the study of non-linear interactions between the two frequency domains.

Whispering gallery mode (WGM) resonators have high Q factors and small modal volumes and can thus show strong non-linear interactions. Most of the interesting non-linear materials are crystalline and feature high refractive indices such that efficient coupling to the resonator is challenging. We present a study on high refractive index WGM resonators and show that coupling via a crystalline dielectric rod waveguide is possible.

We report on a refractometric sensor based on crystalline MgF2 Whispering Gallery Mode resonators. High sensitivity, small resonance line widths and good thermal stability provide a limit of detection of 4×10−6 refractive index units.

We demonstrate a method to perform spectroscopy of near-infrared single photons without the need of dispersive elements. This method is based on a photon energy resolving transition edge sensor and is applied for the characterization of widely wavelength tunable narrow-band single photons emitted from a crystalline whispering gallery mode resonator. We measure the emission wavelength of the generated signal and idler photons with an uncertainty of up to 2 nm., Comment: 4 pages, 4 figures

Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) is important for tailoring them to experimental needs. Here we report on a novel experimental mode analysis technique based on the combination of frequency analysis and far-field imaging for high mode numbers of large WGMRs. The radial mode numbers q and the angular mode numbers p=$\ell$-m are identified and labeled via far-field imaging. The polar mode numbers $\ell$ are determined unambiguously by fitting the frequency differences between individual whispering gallery modes (WGMs). This allows for the accurate determination of the geometry and the refractive index at different temperatures of the WGMR. For future applications in classical and quantum optics, this mode analysis enables one to control the narrow-band phase-matching conditions in nonlinear processes such as second-harmonic generation or parametric down-conversion., Comment: 12 pages, 6 figures

The usual configuration of uniaxial whispering gallery mode resonators is a disk shaped geometry where the optic axis points along the symmetry axis, a so called z-cut resonator. Recently x-cut resonators, where the optic axis lies in the equatorial plane, became of interest as they enable extremely broadband second harmonic generation. In this paper we report on the properties of a more generalized system, the so called angle-cut resonator, where the optic axis exhibits an arbitrary angle against the symmetry axis. We show experimentally that the modal structure and quality factors are similar to common resonators but that the polarization properties differ quite significantly: due to the asymmetry the polarization depends on the equatorial position and is, in general, elliptical.

We present a spectroscopy technique on the single photon level by combining a widely wavelength tunable single photon source based on a crystalline whispering gallery mode resonator with an energy resolving transition edge sensor.

Birefringent crystals like lithium niobate show a very strong χ(2) non-linear response and have thus been used in a whispering galley mode (WGM) supporting geometry to achieve extremely high conversion efficiencies[1,2]. In a uniaxial crystal, light is split into two different eigenpolarizations showing different phase velocities. Usually the WGM resonators are fabricated such that the optic axis is parallel to the symmetry axis, such that there are still two mode families of parallel (perpendicular) polarization with respect to the optic axis, namely TE (TM) modes, which “feel” the extraordinary (ordinary) index of refraction of the material respectively. The dispersion between these two types of modes can be exploited to achieve phasematching in nonlinear processes.

Long photon con nement and high optical elds require good optical resonators. Some of the best opticalresonators with a small footprint are whispering gallery mode (WGM) resonators. Their principle is basedon continuous total internal reection at the interface of a round dielectric. Currently most WGM resonatorsare fabricated fully symmetric to their rotational axis. In WGM resonators fabricated from uniaxial crystalsthis symmetry axis then coincides with the optic axis, such that the modes are either parallel or perpendicularpolarized. If the optic axis is however tilted with respect to the symmetry axis the polarization of the modeschanges dramatically. We report on high Q resonances in a slightly birefringent MgF 2 WGM resonator, cutat 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 propertiesat di erent outcoupling positions, determined via full Stokes measurements, are recorded and show a continuouscomplex change in ellipticity. We present the experimental results. Understanding the polarization behavior inan o -axis, birefringent WGM resonator may o er a new way for phase-matching in non-linear

Optical whispering gallery modes (WGMs) of mm-sized axisymmetric resonators are well localized at the equator. Employing this distinctive feature, we obtain simple analytical relations for the frequencies and eigenfunctions of WGMs which include the major radius of the resonator and the curvature radius of the rim. Being compared with results of finite-element simulations, these relations show a high accuracy and practicability. High-precision free-spectral-range measurements with a millimeter-sized disc resonator made of MgF(2) allow us to identify the WGMs and confirm the applicability of our analytical description.

Optical whispering gallery mode (WGM) resonators are a powerful and versatile tool used in many branches of science. Fine tuning of the central frequency and line width of individual resonances is however desirable in a number of applications including frequency conversion, optical communications and efficient light-matter coupling. To this end we present a detailed theoretical analysis of dielectric tuning of WGMs supported in axisymmetric resonators. Using the Bethe-Schwinger equation and adopting an angular spectrum field representation we study the resonance shift and mode broadening of high $Q$ WGMs when a planar dielectric substrate is brought close to the resonator. Particular focus is given to use of a uniaxial substrate with an arbitrarily aligned optic axis. Competing red and blue resonance shifts ($\sim 30$ MHz), deriving from generation of a near field material polarisation and back action from the radiation continuum respectively, are found. Anomalous resonance shifts can hence be observed depending on the substrate material, whereas mode broadening on the order of $\sim 50$ MHz can also be simply realised. Furthermore, polarisation selective coupling with extinction ratios of $> 10^4$ can be achieved when the resonator and substrate are of the same composition and their optic axes are chosen correctly. Double refraction and properties of out-coupled beams are also discussed.

Detection of weak THz signals is very challenging due to the extremely low energy of one THz photon (temperature equivalent of 48K). Frequency up-conversion to the near infra-red (NIR) and subsequent detection of the up-converted photon with sensitive, low-noise detectors is one way to achieve this task, albeit suffering form extremely poor conversion rates. Whispering gallery mode resonators (WGMRs), however, support well confined modes with high quality factors (Q) and extremely high field intensities inside the resonator, thus allowing efficient non-linear conversion rates.

We report on efficient up-conversion of THz signals into the optical domain using a high-Q dielectric resonator. Since the system is all-resonant and phase-matched, we present a record photon number conversion of 2.5×10−5 around 100 GHz.

We report on a compact and stable optical parametric oscillator in a whispering gallery mode resonator, that combines very low pump thresholds with versatile tunability.