SNAP microwave optical filters.

If the originally flat bottom of a wide quantum well with multiple eigenstates is periodically modulated, its eigenvalues rearrange into denser groups separated by wider gaps. We show that this effect, if implemented in an elongated bottle microresonator [also called a surface nanoscale axial photonics (SNAP) microresonator] allows us to design microwave photonic tunable filters with an outstanding performance.

Enhancing the impedance matched bandwidth of bottle microresonator signal processing devices.

Light pulses entering an elongated bottle microresonator (BMR) from a transversely oriented input-output waveguide (microfiber) slowly propagate along the BMR length and bounce between turning points at its constricting edges. To avoid insertion losses and processing errors, a pulse should completely transfer from the waveguide into the BMR and, after being processed, completely return back into the waveguide. For this purpose, the waveguide and BMR should be impedance matched along the pulse bandwidth. Here we show how to enhance the impedance matched bandwidth by optimization of the BMR effective radius variation in a small vicinity of the input-output waveguide.

Fundamental limit of microresonator field uniformity and slow light enabled ultraprecise displacement metrology.

We determine the fundamental limit of microresonator field uniformity. It can be achieved in a specially designed microresonator, called a bat microresonator, fabricated at the optical fiber surface. We show that the relative nonuniformity of an eigenmode amplitude along the axial length L of an ideal bat microresonator cannot be smaller than 13π2n4λ-4Q-2L4, where n,λ, and Q are its refractive index, eigenmode wavelength, and Q-factor, respectively. For a silica microresonator with Q=108, this eigenmode has axial speed ∼10-4c, where c is the speed of light in vacuum, and its nonuniformity along length L=100\unicode{x00B5}m at wavelength λ=1.5µm is ∼10-7. For a realistic fiber with diameter 100 µm and surface roughness 0.2 nm, the smallest eigenmode nonuniformity is ∼0.0003. As an application, we consider a bat microresonator evanescently coupled to high Q-factor silica microspheres, which serves as a reference supporting ultraprecise straight-line translation.

Microresonator devices lithographically introduced at the optical fiber surface.

We present a simple lithographic method for fabrication of microresonator devices at the optical fiber surface. First, we undress the predetermined surface areas of a fiber segment from the polymer coating with a focused CO2 laser beam. Next, using the remaining coating as a mask, we etch the fiber in a hydrofluoric acid solution. Finally, we completely undress the fiber segment from coating to create a chain of silica bottle microresonators with nanoscale radius variation [surface nanoscale axial photonics (SNAP) microresonators]. We demonstrate the developed method by fabrication of a chain of five 1 mm long and 30 nm high microresonators at the surface of a 125 µm diameter optical fiber and a single 0.5 mm long and 291 nm high microresonator at the surface of a 38 µm diameter fiber. As another application, we fabricate a rectangular 5 mm long SNAP microresonator at the surface of a 38 µm diameter fiber and investigate its performance as a miniature delay line. The propagation of a 100 ps pulse with 1 ns delay, 0.035c velocity, and negligible dispersion is demonstrated. In contrast to previously developed approaches in SNAP technology, the developed method allows the introduction of much larger fiber radius variation ranging from nanoscale to microscale.

Coupling between waveguides and microresonators: the local approach.

Coupling between optical microresonators and waveguides is a critical characteristic of resonant photonic devices that has complex behavior that is not well understood. When the characteristic variation length of the microresonator modes is much larger than the waveguide width, local coupling parameters emerge that are independent of the resonator mode distributions and offer a simplified description of coupling behavior. We develop a robust numerical-fitting-based methodology for experimental determination of the local coupling parameters in all coupling regimes and demonstrate their characterization along a microfiber waveguide coupled to an elongated bottle microresonator.

Optical bottle microresonators with axially uniform eigenmode field distribution.

We show that the fundamental eigenmode of a shallow optical bottle microresonator (also called a SNAP microresonator) can be made exceptionally uniform along its axial length. The introduced microresonator has effective radius variation resembling the contour of a bat with ears and wings. Remarkably, reduction of the axial size of this microresonator achieved by cutting the wings does not alter the uniformity of its fundamental eigenmode. Being of general interest, our findings pave a way for improving the perceptibility of micro/nanoparticle sensing. These results also suggest a bottle microresonator suitable for accurate assembling of quantum emitters near the maximum of its eigenmode to be important in cavity quantum electrodynamics.

In situ observation of slow and tunnelling light at the cutoff wavelength of an optical fiber.

Slow waves and tunneling waves can meet at the cutoff wavelengths and/or the transmission band edges of optical and quantum mechanical waveguides. The experimental investigation of this phenomenon, previously performed using various optical microstructures, is challenged by fabrication imperfections and material losses. Here, we demonstrate this phenomenon in situ for whispering gallery modes slowly propagating along a standard optical fiber, which possesses a record uniformity and exceptionally small transmission losses. The slow axial propagation dramatically increases the longitudinal wavelength of light and allows us to measure nanosecond-long tunneling times along tunable potential barriers having the width of hundreds of micrometers. This demonstration paves a simple and versatile way to investigate and employ the interplaying slow and tunneling light.

Surface nanoscale axial photonics at a capillary fiber: publisher's note.

This publisher's note corrects the surname of one of the authors of Opt. Lett.42, 3060 (2017)OPLEDP0146-959210.1364/OL.42.003060.

Surface nanoscale axial photonics at a capillary fiber.

We present the theory and first experimental demonstration, to the best of our knowledge, of a sensing platform based on surface nanoscale axial photonics (SNAP) at a capillary fiber. The platform explores optical whispering gallery modes, which circulate inside the wall of a capillary and slowly propagate along its axis. Due to the small thickness of the capillary wall, these modes are sensitive to spatial and temporal variations of the refractive index of the media adjacent to the internal capillary surface. In particular, the developed theory allows us to determine the internal effective radius variation of the capillary from the measured mode spectra. Experimentally, a SNAP resonator is created by local annealing of the capillary with a focused CO2 laser followed by internal etching with hydrofluoric acid. The comparison of the spectra of this resonator in the cases when it is empty and filled with water allows us to determine the internal surface nonuniformity introduced by etching. The results obtained pave the way for a novel advanced approach in sensing of media adjacent to the internal capillary surface and, in particular, in microfluidic sensing.

Optical frequency combs generated mechanically.

An elongated bottle microresonator with nanoscale parabolic effective radius variation can possess a series of dense equally spaced optical eigenfrequencies whose separation can match the eigenfrequency of its axially symmetric acoustic mode. It is shown that this acoustic mode can parametrically excite optical modes and give rise to a highly equidistant and moderately broadband optical frequency comb with the teeth spacing independent of the input laser power and the amplitude of mechanical vibrations.

Optical bottle versus acoustic bottle and antibottle resonators.

The theory of slow acoustic modes propagating along the optical fiber and being controlled by the nanoscale variation of the effective fiber radius (analogous to the theory of slow optical whispering gallery modes) is developed. Surprisingly, it is shown that, in addition to acoustic bottle resonators (which are similar to optical bottle resonators), there exist antibottle resonators, the neck-shaped deformations of the fiber that can fully confine acoustic modes. It is also shown that an eigenfrequency of the mechanical vibrations of a silica parabolic bottle resonator can match the separation between the eigenfrequencies of a series of its optical modes, thereby enabling the resonant mechanical excitation of these series. The developed theory paves the groundwork for slow-mode optomechanics in an optical fiber.

Bottle microresonator broadband and low-repetition-rate frequency comb generator.

We propose a new type of broadband and low repetition rate (RR) frequency comb generator that has the shape of an elongated and nanoscale-shallow optical bottle microresonator created at the surface of an optical fiber. The free spectral range (FSR) of the broadband azimuthal eigenfrequency series of this resonator is the exact multiple of the FSR of the dense and narrowband axial series. The effective radius variation of the microresonator is close to a parabola with a nanoscale height that is greater or equal to λ/2πn0. (Here λ is the characteristic radiation wavelength and n0 is the refractive index of the microresonator material.) Overall, the microresonator possesses a broadband, small FSR and accurately equidistant spectrum convenient for the generation of a broadband and low RR optical frequency comb. It is shown that this comb can be generated by pumping with a cw laser, with a radiation frequency that matches a single axial eigenfrequency of the microresonator or, alternatively, by pumping with a mode-locked laser, which generates a narrowband low RR comb matching a series of equidistant axial eigenfrequencies situated between adjacent azimuthal eigenfrequencies.

Precise optical characterization of SNAP structures with a reference fiber.

A method of precise characterization of surface nanoscale axial photonics (SNAP) structures with a reference fiber is proposed, analyzed, and demonstrated experimentally. The method is based on simultaneous coupling of a microfiber to a SNAP structure under test and to a reference optical fiber. Significant reduction of measurement errors associated with the environmental temperature variations and technical noise of the spectrum analyzer is demonstrated. The achieved measurement precision of the effective radius variation of the SNAP structure is 0.2 Å.

Fabrication of surface nanoscale axial photonics structures with a femtosecond laser.

Surface nanoscale axial photonics (SNAP) structures are fabricated with a femtosecond laser for the first time, to the best of our knowledge. The inscriptions introduced by the laser pressurize the fiber and cause its nanoscale effective radius variation. We demonstrate the subangstrom precise fabrication of individual and coupled SNAP microresonators having the effective radius variation of several nanometers. Our results pave the way to a novel ultraprecise SNAP fabrication technology based on the femtosecond laser inscription.

Tunable photonic elements at the surface of an optical fiber with piezoelectric core.

Tunable photonic elements at the surface of an optical fiber with piezoelectric core are proposed and analyzed theoretically. These elements are based on whispering gallery modes whose propagation along the fiber is fully controlled by nanoscale variation of the effective fiber radius, which can be tuned by means of a piezoelectric actuator embedded into the core. The developed theory allows one to express the introduced effective radius variation through the shape of the actuator and the voltage applied to it. In particular, the designs of a miniature tunable optical delay line and a miniature tunable dispersion compensator are presented. The potential application of the suggested model to the design of a miniature optical buffer is also discussed.

Permanent matching of coupled optical bottle resonators with better than 0.16 GHz precision.

The fabrication precision is one of the most critical challenges to the creation of practical photonic circuits composed of coupled high Q-factor microresonators. While very accurate transient tuning of microresonators based on local heating has been reported, the record precision of permanent resonance positioning achieved by post-processing is still within 1 and 5 GHz. Here we demonstrate two coupled bottle microresonators fabricated at the fiber surface with resonances that are matched with a better than 0.16 GHz precision. This corresponds to a better than 0.17 Å precision in the effective fiber radius variation. The achieved fabrication precision is only limited by the resolution of our optical spectrum analyzer and can be potentially improved by an order of magnitude.

Microscopic optical buffering in a harmonic potential.

In the early days of quantum mechanics, Schrödinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been created artificially. However, an optical pulse propagating in a bottle microresonator (a dielectric cylinder with a nanoscale-high bump of the effective radius) can exactly imitate a quantum wave packet in the harmonic potential. Here, we propose a tuneable microresonator that can trap an optical pulse completely, hold it as long as the material losses permit, and release it without distortion. This result suggests the solution of the long standing problem of creating a microscopic optical buffer, the key element of the future optical signal processing devices.

Kerr nonlinear switching in a hybrid silica-silicon microspherical resonator.

A hybrid silicon-core, silica-clad microspherical resonator has been fabricated from the semiconductor core fiber platform. Linear and nonlinear characterization of the resonator properties have shown it to exhibit advantageous properties associated with both materials, with the low loss cladding supporting high quality (Q) factor whispering gallery modes which can be tuned through the nonlinear response of the crystalline core. By exploiting the large wavelength shift associated with the Kerr nonlinearity, we have demonstrated all-optical modulation of a weak probe on the timescale of the femtosecond pump pulse. This novel geometry offers a route to ultra-low loss, high-Q silica-based resonators with enhanced functionality.

Nanobump microresonator.

We introduce a whispering gallery-mode (WGM) nanobump microresonator (NBMR) and develop its theory. This microresonator is formed by an asymmetric nanoscale-high deformation of the translationally symmetric optical fiber surface, which is employed in fabrication of surface nanoscale axial photonics (SNAP) structures. It is shown that an NBMR causes strong localization of WGMs near a closed ray (geodesic) at the fiber surface, provided that this ray is stable. Our theory explains and describes the experimentally observed localization of WGMs by NBMRs and is useful for the design and fabrication of SNAP devices.

Slow light optofluidics: a proposal.

The resonant slow light structures created along a thin-walled optical capillary by nanoscale deformation of its surface can perform comprehensive simultaneous detection and manipulation of microfluidic components. This concept is illustrated with a model of a 0.5 mm long, 5 nm high, triangular bottle resonator created at a 50 µm radius silica capillary containing floating microparticles. The developed theory shows that the microparticle positions can be determined from the bottle resonator spectrum. In addition, the microparticles can be driven and simultaneously positioned at predetermined locations by the localized electromagnetic field created by the optimized superposition of eigenstates of this resonator, thus exhibiting a multicomponent, near-field optical tweezer.