WO2016066998A1 - Methods and devices incorporating surface nanoscale axial photonics - Google Patents

Abstract

Embodiment of the invention relate to the application of the Surface Nanoscale Axial Photonics (SNAP) technological platform in a microscale optical buffer; optomechanical phononic tweezers and signal processors in nonlinear optics; reconfigurable integrated circuits in microphotonics; and miniature sensors and manipulators suitable for use in microfluidics, An optical buffer comprises an actuator arranged to selectively introduce a deformation in a microresonator to switch it between a closed state for retaining a whispering gallery mode (WGM) optical signal and an open state for receiving or releasing the WGM optical signal. An optical integrated circuit includes a configuration actuator operable to adjust a position of similar deformation in a optical fibre. Phononic tweezers comprise a microresonator section for retaining first and. second WGM optical signals which are offset to excite a WGM phonon signal in the microresonator section.

Description

METHODS AND DEVICES INCORPORATING SURFACE NANOSCALE AXIAL PHOTONICS

FIELD OF THE INVENTION

The invention relates to applications for the Surface Nanoscale Axial Photonics (SNAP) technological platform.

BACKGROUND TO THE INVENTION

It is conventional to consider optical fibres as means for transmission of light over very long distances. In contrast, this disclosure relates to the utilization of light that circulates along the transverse direction of a fibre segment experiencing the total internal reflection from its surface. This light is called slow light because its speed of propagation along the fibre axis is small. Recently, the inventors discovered that the axial propagation of such slow light can be fully controlled by nanometre-scale variation of the fibre radius [1]. This dramatically small variation allows the creation of miniature integrated photonic circuits at the surface of an optical fibre with unprecedentedly high

precision and low loss [2-6] . The new technological platform was named "Surface Nanoscale Axial Photonics", or SNAP, emphasizing its simple, quick, inexpensive, and reproducible nature .

The present disclosure discusses various developments of SNAP from the recent proof of concept towards a powerful technological platform and demonstrates the revolutionary multi-disciplinary applications of the new technology in nonlinear optics, optomechanics, microfluidics, and integrated microphotonics . Specifically, the disclosure discusses breakthrough SNAP photonic devices _:and structures which were not possible previously due to insufficient fabrication precision, design limitations, and propagation losses.

In particular the present disclosure outlines the use of SNAP devices in: (i) a raicroscale optical buffer;

(ii) optomechanical phononic tweezers and signal

processors in nonlinear optics;

(iii) reconfigurable integrated circuits in microphotonics; and

(iv) miniature sensors and manipulators suitable for use in microfluidics.

Microscale optical buffer

According to this aspect of the present disclosure, there may be provided an optical buffer comprising: an optical fibre having an optical axis, the optical fibre having a

microresonator section configured to support optical radiation in a whispering gallery mode (WGM) ; an optical input coupled to the optical fibre to introduce a WGM optical signal to the microresonator section; and an actuator arranged to

selectively introduce a deformation in the microresonator section to switch the microresonator section between a closed state for retaining the WGM optical signal and an open state for receiving or releasing the WGM optical signal, wherein, in the closed state, the microresonator section has a geometry that forms a potential well which preserves the WGM optical signal. Thus, this aspect present switchable SNAP structure that can controllably admit and release an information

carrying WGM optical signal.

The geometry of the potential well may be selected from a class of potential wells which preserve a period of captured oscillations independently of amplitude. For example, the geometry may comprise a parabolic outer surface. Thus, the microresonator section may be a bottle resonator formed by a parabolic bulge in an outer diameter of the optical fibre.

The parabolic bulge may be formed on only one side of the optical fibre, i.e. it may be asymmetric with respect to the optical axis. The geometry may have a nanoscale magnitude, e.g. the parabolic bulge may project from the local fibre surface by less than 100 nm, preferably less than 10 nm.

The introduced deformation may comprise a physical variation in the effective radius of the optical fibre in the microresonator section. The deformation in this case may be a further variation in the parabolic bulge, e.g. a perturbation thereof. A magnitude of the physical variation may be less than 100 nm, preferably less than 5 nm. In some case, the magnitude of the physical variation may be less than

(i.e. less than 10^-10 m) .

The actuator may comprise any suitable device for delivering energy to the optical fibre to cause the

deformation. The energy may be thermal or electrical. For example, the actuator may comprise a laser for delivering a pulse of energy to deform, e.g. thermally deform, the

microresonator section. In another example, the actuator may comprises an voltage source for generating an electric field across the microresonator section. The electric field may cause the deform by electrostriction. Alternatively, the optical fibre may include a piezoelectric element in the microresonator section, whereby the deformation is caused by a reverse piezoelectric effect. The piezoelectric element may be a core of the optical fibre.

The optical input may be any device suitable for coupled optical energy into a WGM mode in the microresonator section. For example, the optical input may be a waveguide, e.g.

optical microfiber, mounted transversely to the optical axis.

Optomechanical phonon tweezers and processors

At its most general, this aspect of the present

disclosure provides an optical device for holding information as phononic WGM signals, i.e. acoustic-type lattice vibrations which travel around the surface of an optical fibre in a direction transverse to the optical axis. The optical device may be part of an optical computer or photonic integrated circuit, e.g. as a means of receiving an optical signal and transferring the information contained therein to a phononic WGM signal . The optical device may be used as an optical buffer or the like.

According to this aspect, there may be provided an optical device for confining phonons, the device comprising: an optical fibre having an optical axis, the optical fibre having a microresonator section configured to support optical radiation in a whispering gallery mode (WGM) ; and an optical input coupled to the optical fibre to introduce to the microresonator section a first WGM optical signal having a first frequency and wave vector and a second WGM optical signal having a second frequency and wave vector, the first frequency and wave vector being offset from the second frequency and wave vector, wherein the microresonator section has a geometry that forms a potential well which preserves both the first WGM optical signal and the second WGM optical signal, wherein the offset is arranged to excite a WGM acoustic (phonon) signal in the microresonator section. The WGM acoustic signal may be generated due to non-linear effects in the variance of refractive index in the microresonator section causing "beating" of the first and second WGM signals, whereby the frequency of the beating corresponds to the offset. The WGM phonon signal can subsequently be accessed, either by coupling it directly out of the microresonator section or transferring it back into a photon signal (e.g. by coupling the WGM phonon signal into an optical signal present in the optical fibre) .

The microresonator section of the optical fibre may be located between a pair of adjacent optical fibre portions, wherein an effective radius of the microresonator section is different from an effective radius of each of the pair of adjacent optical fibre portions. For example, the

microresonator section may comprise a physical variation, e.g. an asymmetric variation, in the effective radius of the optical fibre. As described above, a magnitude of the physical variation may be less than 100 nm, preferably less than 5 nm. In some case, the magnitude of the physical variation may be less than 1 A (i.e. less than 10^-10 m) . The geometry of the microresonator section may comprise a

parabolic shape formed on one side of the optical fibre.

The device may include an actuator arranged to

selectively introduce a deformation in the microresonator section to switch the microresonator section between a closed state for retaining the WGM acoustic signal and an open state for releasing the WGM acoustic signal.

The optical input may be arranged to phase match the first WGM optical signal and the second WGM optical signal. For example, the offset of optical WGM frequencies and wave vectors may be chose to be equal to an eigenfrequency and eigenvector of a resonant phonon state. The offset in frequency may be in the MHz to GHz order range. The actual value of the offset can be determined by the chosen acoustic (phonon) eigenstate of the fibre or the

Brillouin frequency shift of the fibre material.

The optical fibre may include a piezoelectric element in the microresonator section and the device includes a voltage source for generating an electric field across the

piezoelectric element. The electric field may cause the optical fibre to locally deform e.g. by the reverse

piezoelectric effect. The deformation may create the

microresonator geometry, or may be used to open/close the microresonator to allow optical signals to be coupled into or out of it. The -piezoelectric element may be a core of the optical fibre.

The optical input may be a waveguide (or a plurality of waveguides) mounted transversely to the optical axis. The (or each) waveguide may be an optical microfiber.

Reconfigurable photonic integrated circuit

In another aspect, the present disclosure provides a photonic integrated circuit comprising an asymmetric optical fibre arranged to support photon propagation in a localised whispering gallery mode (WGM) , and an optical fibre deforming means arranged to controllably cause one or more localised nanometre-scale variations in a radius of the optical fibre. The asymmetric optical fibre may comprise one or more SNAP circuit elements, wherein the optical fibre deforming means may be arranged to switch these circuit elements into and/or out of the optical fibre. The photonic integrated circuit may thus be adaptable in real time. The variations may be created, altered, and fully removed by the appropriate external and internal current and voltage distributions in background electric circuits.

The optical fibre deforming means may utilise any one or more of local heating, electrostriction [36], or local electric field (with a piezoelectric fibre core) .

The photonic integrated circuit may comprise a planar matrix of optical fibres that are in optical communication with one another. Thus, according to this aspect there may be provided a photonic integrated circuit for performing one or more photonic functions on optical signals that travel on photonic signal paths therethrough, the circuit comprising: an optical fibre for supporting optical radiation in a transverse whispering gallery mode (WGM) , the optical fibre having an optical axis oriented to intersect with a photonic signal path; and a configuration actuator arranged to selectively introduce a localised deformation in the optical fibre at a position where it intersects with the photonic signal path, wherein the localised deformation has a geometry that supports optical radiation in a whispering gallery mode (WGM) , and wherein the configuration actuator is operable to adjust the position of the localised deformation on the optical fibre. The optical fibre may be capable of intersecting a plurality of photonic signal paths in the circuit, whereby the

configuration actuator is capable of introduces a localised deformation (which may function as a SNAP circuit element) at each intersection. The optical fibre is thus reconfigurable according to the architecture of the photonic signal paths.

The optical fibre may be part of a two-dimensional array of parallel aligned optical fibres, each optical fibre in the two-dimensional array being optically coupled to its nearest neighbours, wherein the configuration actuator is arranged to selectively introduce one or more localised deformations in each of a plurality of optical fibres in the two-dimensional array to set a configuration for the two-dimensional array, and wherein the configuration actuator is operable to adjust the configuration for the two-dimensional array.

The circuit may include an optical input (e.g. a planar photonic waveguide) coupled to the two-dimensional array to introduce a WGM optical signal to the plurality of localised deformations in the two-dimensional array.

As described above, each localised deformation may comprise an asymmetric variation in the effective radius of the optical fibre. The asymmetric variation may have a magnitude less than 100 nm, preferably less than 5 nm. In some case, the magnitude of the physical variation may be less than 1 A (i.e. less than 10^-10 m) . Each localised deformation may form a potential well which preserves a WGM optical signal. Alternatively, a plurality of localised deformations may formed a series of coupled potential wells or more complex variations of the effective fibre radius.

The configuration actuator may be any suitable device for delivering energy to cause the local deformation. For example, the configuration actuator may comprise a laser having a controllable laser beam for creating the localised deformation by exciting the optical fibre using thermal, electrostrictive, non-linear Kerr, or piezoelectric effects. In another example, the configuration actuator may comprise a background electronic circuit arranged to selectively apply a local voltage across the optical fibre. In this arrangement the localised deformation may be created by electrostriction. Alternatively, the optical fibre may include a piezoelectric element, whereby the localised deformation is created by the reverse piezoelectric effect. The piezoelectric element may be a core of the optical fibre.

The configuration actuator may be operable to adjust the position of the localised deformation on the optical fibre rapidly, e.g. within a time window in the millisecond order for thermal deformation and down to nanosecond order for electrostrictive and piezoelectric deformations.

Slow light optofluidics At its most general, this aspect of the disclosure provides a SNAP element in the body of a microcapillary, whereby a microfluid in the microcapillary can be monitored or manipulated through an interaction with an evanescent field of a WGM optical signal in the SNAP element.

Thus, according to this aspect there may be provided a microfluidic device comprising: a microcapillary that defines a passage for conveying a microfluid, the microcapillary comprising a microresonator section configured to support optical radiation in a whispering gallery mode (WGM) around the passage; an optical input coupled to the microcapillary to introduce a WGM optical signal to the microresonator section; and a detector arranged to determine a transmission amplitude and/or phase of the optical input to monitor an interaction between an evanescent field of the WGM optical signal and matter contained in the passage. The microcapillary may comprise a tube-like structure with the passage formed through it. The passage may be radially offset from the centre of the tube-like structure so that it lies closer to the outer edge of the microcapillary on one side thereof. This may provide more control over the interaction between the evanescent field of the WGM optical signal and material in the passage. The passage may have a diameter of 10 μs ar less.

The microcapillary may be made from silica or any other suitable material that permits propagation of optical

radiation. In particular, the internal surface of

microcapillary can be coated with metal micro/nanoparticles enhancing the local electromagnetic field and thereby the sensitivity of the device. The internal surface can be also coated with nanolayers of material with enhanced sensitivity to certain microfluidic components.

This aspect of the disclosure may also be expressed as a microfluidic device comprising: a microcapillary that defines a passage for conveying a microfluid, the microcapillary comprising a microresonator section configured to support optical radiation in a whispering gallery mode (WGM) around the passage; an optical input coupled to the microcapillary to introduce a WGM optical signal to the microresonator section, whereby an evanescent field of the WGM optical is arranged to capture a microparticle in the passage; and a controller arranged to control the WGM optical signal to manipulate the captured microparticle. Herein, manipulation of the

microparticle may include trapping or moving the

microparticle. The microparticle may be attracted to the evanescent field, whereby suitable control of the evanescent field can constrain the position of the microparticle.

In one example, the microresonator section may be arranged to support a plurality of WGM eigenmodes. Each eigenmode may have a unique distribution of evanescent field within the passage. By appropriate selection of one or more of the eigenmodes, the controller may manipulate the

microparticle. The optical input may include a filter arranged to launch one or more of the plurality of eigenmodes into the microresonator section, e.g. under the control of controller.

As mentioned above, the microresonator section may comprise a localised deformation in an outer diameter of the microcapillary. The localised deformation may be an asymmetric variation in the effective radius of the

microcapillary. A magnitude of the physical variation may be less than 100 nm, preferably less than 5 nm. In some case, the magnitude of the physical variation may be less than 1 A (i.e. less than 10^-10 m) .

In one example, the microresonator section may comprise a triangle bottle resonator.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure herein refers to the accompanying

drawings, in which:

Fig. 1 shows images and illustrations of (a) a coupled ring resonator structure [7] , (b) and (c) coupled photonic crystal cavity structures [10], (d) microsphere resonator [11,

12], (e) micro-toroid resonator [11], and (f) ring resonator engraved at the optical cylinder surface [13];

Fig. 2 shows a comparison of fabrication precision demonstrated for the state of the art silicon photonics technology and SNAP. Fig. 2(a) is a SEM image (top) and transmission spectra of 28 coupled ring resonators (bottom) demonstrated in [7] with fabrication precision of 3 nm. Fig. 2(b) is an illustration of 30 coupled SNAP ring resonators (top) and surface plots of experimental and theoretical transmission spectra of these resonators demonstrated in [5] with fabrication precision of 0.07 nm. White line (right axis) at the bottom plot determines the introduced fibre radius oscillations having the magnitude of 2.6 nm. Fig. 2(c) shows the state of the art fabrication precision of silicon

photonics (3 nm) [7] vs. the precision of SNAP (0.07 nm) demonstrated in [5] ;

Fig. 3 is an illustration of propagation of WGMs along the surface of a SNAP fibre;

Fig. 4(a) is an illustration of a nanobump at the surface of an optical fibre;

Fig. 4(b) shows a cross-section of the fibre along the closed geodesic (the nanobump height is usually much smaller than the original axial asymmetry of the fibre (not to scale on the figure) ) ;

Fig. 5 is an illustration of azimuthal and axial

resonances of a SNAP bottle resonator; Fig. 6(a) is an illustration of a nanoscale radius variation of a parabolic bottle resonator that is an

embodiment of the invention;

Fig. 6(b) shows the resonator of Fig. 6(a) opened by the nanoscale variation of the effective fibre radius to let the input pulse in;

Fig. 6(c) shows the resonator of Fig. 6(a) after the variation is released, where the captured optical pulse bounces inside the parabolic resonator;

Fig. 6(d) shows the resonator of Fig. 6(a) where the captured pulse is coupled out by application of the same nanoscale deformation;

Figs. 7(a), 7(c), and 7(e) show a profile of an effective radius variation (left axis) rescaled to a refractive index variation (right axis) for three different bottle resonators;

Figs. 7(b), 7(d), and 7(f) show evolution of a 100 ps light pulse in the resonator of Figs. 7(a), 7(c), and 7(e), respectively;

Fig. 8(a) illustrates asymmetric nanoscale deformation of the fibre with a directed CO2 laser beam in which the right hand side part illustrates the characteristic fibre cross- section (not to scale) ;

Fig. 8 (b) illustrates asymmetric nanoscale deformation of the fibre with the electric field generated by the voltage between a metal strip and metal fibre core;

Fig. 9 is a schematic illustration of a 2D SNAP circuit; Figs. 10(a) and 10(b) illustrates a SNAP structure created at a fibre surface and capillary surface respectively, each coupled to an input-output microfiber;

Fig. 10(c) illustrates a SNAP structure created at a surface of a fibre have a capillary asymmetrically positioned within it; and

Fig. 11(a) shows a capillary with an introduced

triangular SNAP bottle resonator coupled to a transverse input-output microfiber;

Fig. 11(b) shows a 2D plot of the resonant evanescent field calculated at the capillary surface as a function of axial coordinate and wavelength;

Fig. 11(c) shows a numerically calculated resonant transmission spectrum of the SNAP structure shown in Fig.

11(a) as a function of the axial coordinate of the microparticle moving along the internal capillary surface and wavelength;

Fig. 12(a) illustrates a distribution of a driving field localized at an axial position defined by a vertical axis coordinate as a function of a horizontal axis coordinate; and

Fig. 12(b) illustrates a distribution of the driving field localized at two axial positions defined by the vertical coordinate as a function of the horizontal axis coordinate. DETAILED DESCRIPTION; FURTHER OPTIONS AMD PREFERENCES.

Introduction

One of the important objectives of the modern photonics is minimizing the size and power consumption of photonic devices. It is commonly envisioned that this objective can be achieved by employing miniature slow light devices engineered of optical microresonators such as ring microresonators [7-9] (Fig. 1 (a) ), photonic crystal (PC) micro-cavities [10] (Fig. 1(b) and (c) , and microsphere and micro-toroid resonators (Fig l.(d), (e) and (f) ) [11-13]. Both PC micro-cavities and ring microresonators can be integrated into photonic circuits to form a chain of coupled resonators (Fig. 1(a)) [7] and more complex resonant photonic circuits. While the resonators shown in Fig. 1(d) -(f) possess the record-high Q-factors, they are fabricated by melting or mechanical polishing with relatively low precision (several tens of nra) . Generally, these

resonators do not permit integration and flexible design of their spectral characteristics. On the other hand, the characteristic Q-factor of microresonators fabricated with much more design-flexible photonic integrated circuit (PIC) technologies is two orders of magnitude lower than that of a silica microsphere. In addition, the fabrication precision of microscopic photonic elements, which can be as small as a 3 nm [7], is still not sufficient for the creation of miniature

PICs since it causes strong random oscillations of the transmission spectrum (Fig. 2(a)). Due to the insufficient fabrication precision and surface roughness, the

characteristic attenuation of PIC miniature multi-bit slow light delay is measured in the range of 10-100 dB per nanosecond [14] and is insufficient for practical

applications .

A need for much higher fabrication precision and low attenuation of photonic circuits and devices exists in several other branches of modern photonics, e.g., in nonlinear optics and optomechanics . For example, the achieved fabrication precision of ultrahigh-Q micro-cavities with the dramatically narrow linewidths is far below the precision required to accurately support phase matching among the interacting optical waves in four wave mixing, optical frequency comb generation, and interacting optical and sonic modes in optomechanics .

Having a much higher fabrication precision and much smaller attenuation of light, SNAP may enable ground breaking advances in enhancing the functionalities of photonic

structures and devices, such as miniature delay lines, all- optical switches, and frequency comb generators. Moreover, the SNAP platform enables creation of conceptually new photonic devices and structures not possible previously with the existing technologies.

For example, as discussed below, the SNAP platform may realise the first-ever fully reconfigurable photonic circuits, which are now feasible due to nanoscale variation of the fibre radius in SNAP structures that can be temporarily introduced and removed. Moreover, the SNAP platform may realise advanced microfluidic sensors and manipulators, which became possible due to ultraprecise nanoscale fibre radius variation and characteristic cylindrical shape of SNAP structures. This device will solve a challenging problem of simultaneous characterisation and manipulation of liquid and gas species in micro-channels critical in multi-disciplinary applications.

The idea of the SNAP platform is illustrated in Fig. 3. A whispering gallery mode (WGM) is excited in the optical fibre with a transverse micron-thin waist of a bi-conical fibre taper connected to the light source and detector. The

direction of propagation of the excited resonant light is primarily transverse to the optical fibre axis. The idea of SNAP is to explore WGMs that circulate along the fibre surface and propagate very slowly along the fibre axis. The

propagation constant of these modes is so small that it can be fully controlled by extremely small nanoscale variation of the fibre radius [1] . Remarkably, the behaviour of these WGMs can be described by a one-dimensional wave equation with this propagation constant varying along the fibre axis. Thus, the nanoscale variation of the optical fibre radius enables creation of complex photonic structures (e.g., complex-shaped bottle resonators and series of coupled microresonators) at the fibre surface. Due to the extremely small attenuation of light in silica and excellent uniformity of drawn optical fibres, the propagation loss in these structures is very small. Crucially, it has been shown that these structures can be fabricated with unprecedented precision exceeding the precision of the state of the art photonics technologies by two orders of magnitude. This outstanding precision was demonstrated based on a local annealing of optical fibres with a focused CO₂ laser beam [2-6] . The comparison of the state of the art precision achieved in silicon photonics (3 nm) and demonstrated precision of SNAP (0.07 nm) is given in Fig. 2. As another example, the inventor recently demonstrated a ground breaking miniature slow light device in the form of a SNAP bottle semi-parabolic bottle resonator fabricated which sub-angstrom precision [6] . The attenuation of light in this device surpasses the previous demonstrations by tens of decibels. These preliminary demonstrations suggest that a new photonic technology with unprecedentedly high fabrication precision and low loss, which promises revolutionary

applications in several fundamental and applied fields of optics and microphotonics, has been born.

The preliminary demonstrations of SNAP discussed above show great potential [2-6] . The present invention concerns further advances of the SNAP platform. It is anticipated that the SNAP platform will revolutionize nonlinear optics, integrated microphotonics, microfluidics, and initiate numerous applications of SNAP in other areas of fundamental and applied research ranging from cavity quantum

electrodynamics and quantum processing to optical

communications, sensing, and ultraprecise metrology.

The anticipated broad range of applications of SNAP pushes for the establishment of the advanced SNAP technology with ultrahigh precision and ultralow loss. It may be based on the various types of linear, nonlinear and multi-material fibres including commercially available fibres as well as fibres fabricated from special amorphous and crystalline materials. The preliminary demonstrations [1-6] were based on pure silica fibres which are very uniform and low loss. The advanced SNAP technology may utilize highly nonlinear and active fibres, high refractive index soft material fibres, as well as non-conventional crystalline fibres fabricated of silicon, lithium niobate, calcium fluoride and other

materials. For several applications we will use multi-material fibres, in particular the fibre with metal and piezoelectric cores. The feasibility of realization of many of these fibres is supported by previous demonstrations. By combining

developed methods for creation of ultra-uniform advanced material optical fibres with developed methods for

ultraprecise introduction of nanoscale variation of the radius of these fibres, it is possible to push the fabrication precision and reproducibility of the SNAP platform to the experimental limit aiming at the 0.01 nm precision in the introduced effective fibre radius variation.

The breakthrough applications presented herein are concerned with nonlinear and transient phenomena in SNAP structures based on special optical fibres, fibre capillaries, and fibre matrices. In other words, the invention may be based on application of the SNAP principles to nonlinear fibres and also fibre segments fabricated of special amorphous and crystalline materials, e.g. to create ultraprecise, ultralow loss, nonlinear, tuneable SNAP technology based on the specialty fibre segments.

So far, the fibres demonstrated for SNAP applications were silica fibres [2-6] . These fibres are originally very uniform and have a low loss. The advanced SNAP technology discussed herein utilizes fibre segments fabricated of different materials, both amorphous and crystalline. For example, conventional highly nonlinear and active erbium doped fibres, high refractive index fibres drawn from soft

materials, as well as nonconventional crystalline fibres fabricated of silicon, lithium niobate, calcium fluoride, and other materials may be used. The feasibility of realization of crystalline fibres is supported by previous demonstrations of their fabrication from different materials, e.g., from silicon [27] and lithium niobate [28]. Crucially, employment of silicon fibres will allow us to use planar silicon photonics waveguides for direct excitation of SNAP structures. We anticipate the successful fabrication of crystalline fibres by application of the polishing technique developed in [29] . For several applications described below multi-material fibres may be used, in particular fibre with metal and piezoelectric cores. The preliminary technology for fabrication of such fibres was demonstrated previously [30, 31] .

The ultraprecise SNAP fabrication technique consists in nanoscale variation of the silica fibre radius with a CO₂ laser caused by local relaxation of originally frozen-in stresses

[2-6] . The achieved fabrication precision was less than 1 angstrom in effective fibre radius variation. For

photosensitive fibres, SNAP structures can be introduced with a UV laser with similar precision [32] . To arrive at the most flexible, precise, and reproducible fabrication of SNAP structures, the techniques disclosed herein may: explore alternative lasers, e.g., a femtosecond laser, for local nanoscale radius deformations; pre-introduce frozen-in

stresses in fibres by the heating and fast cooling technique; improve and optimize the fabrication setup and programs. By combining the best advanced material optical fibres and the developed advanced SNAP technology, the present invention may improve the fabrication precision and reproducibility of the SNAP platform to the experimental limit which is expected to be comparable to 0.01 angstrom in effective fibre radius variation.

The theory of nonlinear and active slow WGM mode

propagation along the surface of an optical fibre with

nanoscale effective radius variation may be developed starting from the 3D electromagnetic wave equation for nonlinear and active media [33] . This equation can be reduced to the ID equation under the assumption of slow propagation of resonant WGMs. It is expected that the reduction of 3D wave equation to the ID equation will be similar to that in the linear SNAP theory [4] . The resulting basic mathematical equations of nonlinear and active SNAP can be applied to describe the fundamental nonlinear phenomena in SNAP structures such as four wave mixing, parametric amplification, and frequency comb generation.

It is common for various applications (e.g., for tuneable and microfluidic devices) that the characteristic time of variation of the SNAP structure parameters is much longer than the resonance dwell time of light. To describe these

structures, it may be useful to model SNAP devices with adiabatically changing parameters. The relation between the observed resonance spectra and the distribution of the time- dependent refractive index along the SNAP fibre can be determined. Thus, situations when the 3D geometry and refractive index variation is caused by the electrostrictive deformations as well as by varying microfluidic parameters can be understood and utilised. The model of moving microparticles

[18] can be generalized to arbitrary variation of refractive index variation of microfluid. Both the direct and inverse problems of relation between the observed spectra and

refractive index distribution can be addressed.

The state of the art fabrication technology of optical fibres makes them extraordinary uniform and low loss. While the cross-sectional asymmetry of conventional

telecommunication fibres is usually ~1%, i.e., around a micron, their translation symmetry can be exceptional: the effective fibre radius variation can be less than an angstrom over a centimetre of the fibre length [42] . The original translation rather than axial symmetry of the optical fibre is a critical prerequisite for the surface nanoscale axial- photonics (SNAP) platform for ultraprecise fabrication of miniature ultralow-loss resonant photonic circuits at the surface of an optical fibre [2,5,6,11]. This platform is based on controlling the slow whispering gallery mode (WGM)

propagation along the fibre axis by nanoscale variation of the effective fibre radius with the unprecedented sub-angstrom precision [5,6].

An important experimental finding that supports the SNAP platform is illustrated in Fig. 4. It has been shown

experimentally that the unidirectional annealing of the fibre with a transverse focused CO₂ laser beam causes a local nanoscale change in the effective fibre radius and creation of a SNAP microresonator [2] . Since only one side of the fibre surface is primarily heated by the laser, the introduced nanobump is asymmetric, as shown in Fig. 4(a). Usually the nanobump height, which has an order of 10 nm, is much smaller than the original cross-sectional asymmetry of the fibre, which is typically equal to several hundred nanometres, as shown in Fig. 4(b). The underlying theory of operation for a WGM nanobump microresonator (NBMR) that operates on this principle can be determined based on the mathematical theory of diffraction, specifically the theory of WGMs localized in 3D near a closed and stable geodesic [43] . The condition when an NBMR exists is directly related to the condition of stability of the closed optical ray (geodesic) in the vicinity of which the WGMs confined by the NBMR are situated (Fig. 4) .

Similar to those in spherical, ellipsoidal_/ and toroidal microresonators, the WGMs with small transverse (axial) quantum numbers in an NBMR are localized near a closed optical ray (geodesic) at the resonator surface can be defined by equations

(indicated by the solid curve 401 in Fig. 4), where are cylindrical coordinates. In

the vicinity of this ray, the NBMR surface has the profile

with local axial radius

A comparison of an axially symmetric SNAP

microresonator having an parabolic axial profile and an NBMR determined by surface profile resembling a Maxwell's fish-eye potential permits one to derive simple and physically clear relationships between the NBMR parameters and the axial width of WGMs localized by this microresonator. Such a comparison also demonstrates a dramatically weak dependence of the WGM width on the height of the NBMR. Accordingly, a completely asymmetric nanoscale bump at the fibre surface can form a high

Q-factor microresonator that strongly confines WGMs.

The following sections set out various applications of the SNAP platform contemplated herein. All of them are feasible thanks to the outstanding features of SNAP: ultralow loss, nanoscale fabrication with unprecedented precision, and

3D cylindrical geometry of substrate fibres.

Low repetition rate octave spanning frequency comb generator There has been a tremendous recent progress in the demonstration of optical frequency combs using ultrahigh Q- factor microresonators, which are suggested as miniaturized alternative to the most popular mode-locked lasers [15-17] . These resonators have series of modes with almost equally- spaced frequencies. However, these frequencies are not exactly equally spaced due to dispersion. Furthermore, the available geometrical shapes of microresonators do not permit to arrive at a miniature resonator having the octave spanning combs with arbitrary low repetition rate, which is critical for several applications, e.g., in ultraprecise metrology.

While the four-wave mixing effect can create and stabilize a perfect frequency comb in such structures, it is critical to reduce and control the dispersion of a

microresonator [15-17] . In addition, the problem of dispersion significantly limits the range of available central

frequencies of combs [16], while the reduction of repetition rate requires the proportional increase in resonator

dimensions. For relatively small repetition rate, the

corresponding resonator size becomes impractical. To solve the dispersion problem, the authors of [16] suggest to use a bottle resonator (introduced by the inventor in 2004 [35]) which shape can be designed to produce the required

dispersion. However, to date the SNAP platform is the only one that enables the actual realization of such resonator fabricated with the ground breaking precision. The SNAP technology discussed can be used to advance the nonlinear science by demonstration of a ground breaking bottle resonator frequency comb generator. The resonator can exhibit

unprecedentedly precise dispersion and generate predetermined combs with arbitrary central frequency and arbitrary small repetition rate. The design idea of this resonator is

illustrated in Fig. 5. In order to support the generation of combs with low repetition rate without increasing the

resonator size, we will follow the idea of [16]: In addition to large free spectral range (FSR) azimuthal resonances usually employed for the frequency comb generation [15], we will employ the low FSR axial resonances (Fig. 5) attributed to the SNAP bottle resonators and control their dispersion with unprecedented precision. The feasibility of creation of such microresonator is supported by (a) its preliminary demonstration in [16], which was performed without precise realization of the required geometric profile, and (b) demonstration of an ultraprecise SNAP parabolic bottle resonator with equidistance spectrum in [6] .

Microscale optical buffer The following section describes a tunable bottle microresonator capable of trapping an optical pulse of the given spectral width, holding it as long as the material losses permit, and releasing it without distortion.

A microscale optical buffer (MOB) is proposed as one of the key components of the future optical signal processors on the chip [44, 45] . A MOB traps the input pulse, holds it over the predetermined period of time, and eventually releases without distortion. Combination of the smallest possible dimensions of the buffer with the required delay times suggests that light residing in an MOB experiences multiple reflections or rotations before it is finally released. This causes distortion of the pulse due to dispersion, multiple self-interferences, and attenuation. While the direct coiling of photonic waveguides allows one to come up with compact- and broadband delay lines [46, 47], much smaller MOBs can be fabricated based on optical microresonators and photonic crystals. The latter structures though suffer from the bandwidth-delay time limitation [44, 45] . A way to overcome this limitation suggested in [48] consists in creation of a MOB by adiabatic compression of the transmission band of a coupled resonator optical waveguide (CROW) . Ideally this CROW MOB enables slowing down and stopping of a light pulse with the predetermined spectral width. However, significant practical barriers, such as insufficient precision of modern photonics technologies and attenuation of light, remain in the way of fabrication of such MOBs.

In this embodiment, an alternative feasible MOB is proposed and demonstrated theoretically. In contrast to the previously suggested MOBs based on microresonators and photonic crystals [44-46], the device considered here is a specially designed tunable bottle resonator illustrated in Fig. 6. The effective radius variation of this resonator is dramatically small and has a parabolic shape of a few

nanometres height only. This variation can be introduced along an optical fibre with unprecedented sub-angstrom precision using the Surface Nanoscale Axial Photonics (SNAP) platform [6, 34] . The device proposed here is a tunable generalization of the record small and low loss bottle resonator delay line experimentally demonstrated in [6] . It is shown that the shape of optical pulse bouncing along the axis of a bottle resonator with parabolic radius variation changes periodically and, thus, is fully recovered after a roundtrip without distortion. Based on this fact, the appropriate nanoscale temporal and spatial tuning of the effective radius of this resonator allows to trap, hold, and release a telecommunication pulse without distortion for the period of time limited by the material losses only.

The bottle resonator considered below is an optical fibre segment with nanoscale effective radius variation illustrated in Fig. 6(a). Light is coupled in and out of this resonator through a transverse waveguide (microfiber taper) . The

buffering process includes: opening the bottle resonator by nanoscale variation of its effective radius (refractive index) and entering the optical pulse (Fig. 6(b)); closing the resonator when the pulse is completely inside it and holding the pulse in the parabolic bottle resonator for the duration of the required time delay (Fig. 6(c)); and releasing the pulse by reversing the deformation illustrated in Fig. 6(b) (Fig. 6(d)).

Due to the very small and smooth effective radius variation inside the bottle resonator considered, the

propagation of a whispering gallery mode (WGM) can be fully described by its amplitude variation

along the fibre axis z. The equation that describes this propagation has the form of the one-dimensional Schrodinger equation [6, 34] . For the non- stationary case under consideration this equation takes the form:

Here are defined

through the radiation wavelength λ of the transmission channel, refractive index n and bulk propagation constant

of the bottle resonator material, speed of light in vacuum c, and the nanoscale effective variation of the fibre radius

Fig. 7 illustrates pulse propagation in three bottle resonators. The bottle resonator in Fig. 7(a) has a rectangular shape. The bottle resonator in Fig. 7(c) has parabolic shape, and is an embodiment of the invention. The bottle resonator in Fig. 7(e) has a perturbed parabolic shape.

We first consider the propagation of a telecommunication pulse launched in the middle of the rectangular bottle

resonator having the height nm and length 2 mm (Fig.

7(a)). Here and below, we consider the propagation of a 100 ps pulse and set the fibre radius refractive index n =

1.5, and wavelength A = 1.5 um. The surface plot describing the evolution of this pulse along the fibre axis z as a function of time is shown in Fig. 7(b).

It is seen that the pulse experiences significant corruption in the process of bouncing caused by both

dispersion and self-interference. As the result, the original shape of the pulse is completely lost in a few nanoseconds.

On the contrary, multi-period bouncing of an optical pulse in a bottle resonator with a parabolic effective radius variation does not cause irreversible deformation of the pulse. This fact follows from the periodicity of motion of a wave packet described by the Schrodinger equation (1) with a parabolic potential [49] . The process warranting full

restoration of the input pulse after multiple bouncing in the bottle resonator is illustrated in Figs. 7(c) and 7(d). The original bottle resonator with 2 nm height (curve labelled 701 in the drawings) is opened by the introduced deformation ~ 3 nm (or refractive index variation ~3x10^-1) to enter the 100 ps pulse shown on the bottom of Fig. 7(d). The deformed resonator has a semi-parabolic shape, which allows us to avoid the pulse dispersion during the entering, exiting, and switching periods [6] . The deformation is gradually released without perturbing the pulse during the time period 1 ns to 2 ns when the pulse is situated near the right hand side of the resonator. After the switching process is finished, the pulse is forced to bounce inside the resonator as long as the resonator is closed (the middle part of Fig. 7(d)). Finally, the resonator is gradually opened during the time between 13 ns and 15 ns to completely release the pulse. Comparison of the shapes of the input and output pulses shows no distortion.

It is instructive to investigate the effect of finite perturbation of the parabolic radius profile on the performance of this MOB. To this end the parabolic variation (curve 701 in Fig. 7(c)) is perturbed by a 0.5 nm high and 0.5 mm FWHM Gaussian bump (curve 702 in Fig. 7(e)). It is seen from Fig. 7(f) that the evolution of the pulse changes noticeably after several oscillations and the output pulse experiences significant deformation. In practice, the sub- angstrom precision achieved in fabrication of parabolic resonators [6], allows to reduce the magnitude of this perturbation by an order of magnitude and eliminate the distortion. Importantly, similar perturbation introduced to the effective radius variation in the process of switching is much less destructive due to the relatively short switching time.

The discussion above demonstrates that a few nanometres tuning of a bottle resonator effective radius (equivalent to a variation in its refractive index of ~10^-4) is sufficient to trap, hold, and release telecommunication optical pulses over the time period of tens of nanoseconds or longer, while the delay time is limited by the material losses only. The dimensions of the MOB are determined by the footprint of the bottle resonator (0.08 mm² for the model considered; each oscillation of pulse in this resonator delays light by 3.5 ns) . The switching function of the proposed MOB can be realized by tuning the nanoscale deformation (refractive index) of the bottle resonator with a piezoelectric transducer attached to the fibre or coating it in the vicinity of the bottle resonator. This deformation can also be introduced by a nanosecond laser pulse which intensity is appropriately distributed along the fibre length. The power of the switching pulse can be enhanced dramatically if this pulse is resonantly coupled into the fibre WGM [50] . Since the required spatial distribution of the switching deformation is smooth (Fig. 7 (c) ) , the corresponding intensity variation is feasible.

Alternatively, the required nanoscale temporal and spatial variation can be introduced by in the fibre fabricated of a low loss piezoelectric or electrostrictive material, polled silica fibre, the silica fibre with a piezoelectric or electrostrictive core [31], and external acousto-optic or electro-optics by application of laser or electric pulses. Remarkably, the parabolic profile of the bottle resonator is not the unique profile which allows to hold the light pulse without distortion. In fact, there exists a wide family of potential wells in which the period of classical oscillations does not depend on its amplitude [51] . Using the bottle profiles determined by these generalized potentials allows us to make the design of MOBs more flexible. In addition, the advanced manipulation of optical pulses by complex deformation of the bottle resonator in the process of delay is of special interest. Optomechanical phonon tweezers and processors

Nanoengineering of slow propagation of interacting light and sound is a novel development in cavity optomechanics . The frequency of acoustic waves is five orders of magnitude smaller than that of optical waves. However, their wavelengths can be comparable. The axial localization of WGM in SNAP depends on their wavelength but is independent of their frequency [34] . Therefore, similar to SNAP, the spatial distribution of acoustic WGMs propagating along the fibre axis can be controlled with nanoscaie variation of the fibre radius. Consequently, in analogy to SNAP (Surface Nanoscaie Axial Photonics), the concept of SNAM (Surface Nanoscaie Axial Mechanics) may be introduced, and with it the creation of a theory of interaction between the axially confined and/or propagating SNAP and SNAM modes. This concept may be

applicable to the field of ultrahigh Q-factor optomechanics [19-23] and, thus, pave the way to its new features and applications. For example, the conditions for effective coupling between SNAP and SNAM modes may be determined and the theory of generation, transport, and trapping of SNAP-assisted

SNAM pulses may be developed. Implementation of these concepts may enable the demonstration of the optomechanical tweezers of sound and breakthrough ultrafast phononic

processor discussed below. In microfluidic and gas sensing, the developed theory supports the detection and control of transient processes in the vicinity of the resonance structure surfaces outside and inside SNAP fibres and capillaries [18] . Alternatively, we will create fully reconfigurable SNAP circuits, which can relocate optical microresonators and therefore effectively act as nanomechanical tweezers of light. Based on the concept of optomechanical nanoengineering, the SNAP platform may be used to create the first-ever phonon tweezers, buffers, and processors enabling trapping and manipulation of phononic waves and pulses. These concepts may find use in novel optical, optomechanical, and phononic buffers and processors with ultralow power consumption.

The SNAP platform discussed above allows us to

experimentally demonstrate optomechanical structures with unprecedented precision and flexibility while maintaining their record small losses and record large Q-factor.

Accordingly it is possible to reveal the mechanisms of the optomechanical interactions in fibres with specially designed SNAP structures. The advantage of sonic (phononic) pulses as compared to the optical pulses is that their lifetime is much longer and their storage within the same micro-scale

dimensions is easier [23] . Based on the developed SNAP optomechanical nanoengineering platform and recent

demonstrations of the excitation and manipulation of

mechanical modes and signals in micro-cavities [19-23], we can demonstrate the first-ever optical tweezers of phonons, phonon buffers, and processors.

To this end, the SNAM platform discussed above may be used to fully confine phononic modes by the nanoscale

variation of the fibre radius. In realization of the effective interaction between SNAP modes and mechanical modes, a broad range of mechanical excitations not necessarily limited to the SNAM modes may be considered. The excitation of mechanical modes by phase matching the series of equally spaced

frequencies of a SNAP resonator (such as that described above) with the mechanical mode frequency [22] may also be used. The predetermined positions and spacing between the optical frequencies of the SNAP resonator can be realized with unprecedented precision of -1 MHz. For creation, transport, and trapping of sonic pulses^ it is possible to create, vary, and remove the SNAP and SNAM resonators using the fibre electrostriction and also fibres with piezoelectric core material. In these fibres, the predetermined nanoscale variation of the local fibre radius can be introduced over the nanosecond-order time period by locally distributed voltage.

Fully reconfigurable microphotonics In contrast to the photonic integrated circuits

demonstrated to date, we show herein that the SNAP circuits can be introduced and removed during the nanosecond-order time scale. This is the first-ever demonstration of the fully reconfigurable microphotonic circuit, which is feasible due to dramatically small nanometre-scale variation of optical fibre radius in SNAP structures. These variations can be created, altered, and fully removed by the appropriate external and internal current and voltage distributions in the background electric circuits.

It is crucial that the full localization of WGMs along the fibre axis is achieved in SNAP technology by a small asymmetric rather than the axially symmetric deformation.

Furthermore, as illustrated in Fig. 8(a), usually the original axial asymmetry of the fibre is much larger than the

deformation introduced to create fully localized modes. This fact significantly enhances the ways the SNAP structures can be produced. For example, local heating by 100°C increases the effective radius of a 20 micron radius fibre (primarily through the refractive index variation) by ~2 nm, which is sufficient to introduce SNAP structures [2-6] . Similar variations can be introduced in fibres using their

electrostriction [36] (Fig. 8(b)) and by employing fibres with a piezoelectric core [31] under the locally applied voltage of a few tens of volts. Thus, in contrast to microphotonic circuits demonstrated to date, the SNAP circuits can be fully reconfigurable: a circuit with a certain configuration can be created, completely reconfigured, and removed by turning on the appropriate heat or voltage distribution. The advantage of electrostrictively/piezoelectrically reconfigurable circuits is that the corresponding transient time can approach the order of nanoseconds [37] as compared to the micro and millisecond time scale for thermally reconfigured circuits

[38].

In addition, a planar matrix of joined fibres may be used to create an advanced 2D reconfigurable photonic circuit. The reconfigurable circuits are of crucial importance in

reconfigurable computing, which allows to expedite signal processing by adapting the hardware during runtime. In other words, another advantage of the asymmetric fabrication is the feasibility of 2D SNAP (Fig. 9), where the circuit is

introduced with a focused CO₂ laser beam translated along the matrix of adjacent optical fibres. Accordingly it is possible to inscribe a 2D SNAP circuit along a matrix of silica fibres. This device may be developed into a fully reconfigurable 2D

SNAP circuits by placing the fibre matrix onto the specially designed metal wire chip, or matrix of fibres with

piezoelectric cores onto the specially designed metal wire chip. The chip will enable coupling of light into the SNAP fibres from the planar photonic waveguides based on the methods developed previously [39] .

Slow light microfluidics SNAP structures introduced at the surface of optical microcapillaries with micrometre-thin walls may be used to simultaneously characterise and control microfluidic phenomena in time and space [18] . The evanescent field of the resonant light, which circulates across the capillary and slowly propagates along its axis, can probe and manipulate the microfluidic components, while the optical spectra of these structures can characterize the microfluidic behaviour near the microcapillary surface. In addition, the microfluidic components can be manipulated by utilizing the optical forces introduced by this evanescent field.

The principle is illustrated in Fig. 10. As explained above, the SNAP platform enables fabrication of miniature, super-low-loss photonic circuits with unprecedented sub- angstrom precision. The new technology uses resonant light that circulates along the optical fibre surface and slowly propagates along the fibre axis. By varying the fibre radius by only a few nanometres, multifunctional SNAP devices can be created, e.g., complex-shaped bottle resonators including circuits of coupled resonators as shown in Fig. 10(a).

This aspect of the invention proposes the creation of

SNAP resonance structures at the surface of an optical capillary with a wavelength-scale thin wall. This structure allows one to extract both spatial and temporal dependences of physical and chemical characteristics of liquids in

microchannels as well as to manipulate the microfluidic processes with evanescent fields. In addition to the axially symmetric uniform capillary having a few micrometre-thin wall [Fig. 10(b)], one can consider the asymmetrically positioned capillary with a relatively small fraction having the

micrometre wall thickness [Fig. 10(c)]. In the latter case, the evanescent field is strongly localized along the azimuthal

(as well as the radial) direction and can perform sensing and manipulation of microfluids in a small micrometre/sub- micrometre cross-sectional area adjacent to the thinnest part of the capillary.

We now discuss how the spatial and temporal

characteristics of microfluids along the length of a specially designed SNAP structure within this cross-sectional area can be extracted from the spectrum of this structure.

One embodiment provides a theoretical demonstration of detection and manipulation of microparticles floating in a thin, highly transparent capillary with a SNAP triangular bottle resonator created along the capillary surface. It is shown that the positions of microparticles can be (i)

determined by monitoring the spectrum of a SNAP resonator, and (ii) manipulated by variation of the evanescent field of this resonator. For sensing applications, the applied resonant evanescent field should be small enough not to perturb the microfluid, while for microparticle manipulation, this field should be relatively large. Simultaneous sensing and

manipulation are possible provided they are performed at different frequencies.

The field distribution of a WGM slowly propagating along the axis z of an optical capillary containing spatially uniform microfluid can be written in the cylindrical coordinates r=

is defined by

the one-dimensional Schrödinger equation:

Here the azimuthal and radial quantum numbers, m and p, are omitted for brevity.

In equation (2), the energy is a linear

function of wavelength variation

.

The potential corresponds to

the uniformly filled capillary. Here is the fibre radius,

are the fibre radius and index variations,

is resonance wavelength, n-. is the refractive index of the fibre, and y determines the attenuation of light in the fibre.

Potential

in equation (2) is a function of z and parametric function of time t, which describes the processes in the microfluid adjacent to the internal capillary surface.

Generally, these processes are determined by the 3D

perturbation of the refractive index, caused by the

microfluidic spatial and temporal variations. Subsequently, the transmission amplitude

measured at the output of the microfiber coupled to the capillary (Fig. 10) is used to monitor the microfluidic processes in space and time.

Let us consider micrometre-size particles floating along the microfluidic capillary. After approaching the capillary surface, a microparticle can be captured by the evanescent field of the SNAP resonator and continue to move along the capillary surface. For the symmetric configuration [Fig.

10 (b) ] , a microparticle will drift in two (axial and

azimuthal) dimensions. For the asymmetric configuration [Fig.

10(c)], a microparticle will propagate along the line parallel to the capillary axis following the local maximum of the evanescent field.

Since the axial propagation of light in a SNAP structure is slow, the characteristic wavelength of the Schrodinger equation, equation (2) , is much greater than the radiation wavelength (typically, greater than 10 μιη) . Therefore, it is assumed here that the size of detected microparticles is much smaller than this characteristic wavelength. Then, the

microparticles can be modelled by equation (2) with the short- range potentials:

Here N is the number of microparticles,

is the delta function,

determines the axial coordinate of

microparticle, and

determines its detection contrast. The value of

is expressed through the 3D refractive index variation caused by the microparticle n:

where is the normalization factor of

In the derivation of this equation, it was assumed that

the characteristic size of the evanescent field along the azimuthal direction [Fig. 10(c)] is much greater than the microparticle size. This is always true for the axially symmetric capillary [Fig. 10(b)]. From equation (4), the contrast

rapidly grows with decreasing of the capillary wall thickness. However, thinning of the wall causes decrease of the resonance Q-factor. As opposed to the axially symmetric capillary [Fig. 10(b)], the micrometre-thin area in the asymmetric capillary [Fig. 10(c)] can be relatively small, and, thus, less affect the degradation of the Q factor.

The Green's function of equation (2) with short-range potentials determined by equation (3) can be analytically expressed through the Green's function of Eq. (2) with potential

in the absence of microparticles. Thus, the transmission amplitude of a capillary with floating

microparticles,

can also be determined. In this case, the solution of the inverse problem, which expressed and

through is reduced to the solution of a system of

2N algebraic equations at discrete

The high Q factor of the SNAP resonance structures enables highly accurate microfluidic sensing by monitoring the shifts of resonances (here s is the resonance number) .

For a relatively small variation of refractive indices

the shift is determined by the perturbation theory:

Here

is the coordinate of the microfiber and

is the resonator/microfiber coupling parameter, which

are usually independent of time t and can be determined experimentally. Functions

in equation (5) are the normalized eigenfunctions of the resonator determined from equation (2) . As an example, consider a mlcroparticle moving in the evanescent field of a triangle SNAP bottle resonator created at the surface of a silica capillary with radius r„ = 50 um and micrometre-thin wall [Fig. 11(a)]. The potential inside the triangular resonator is

The effective height of the triangle is

and its.: length is L = 0.5 mm [see inset in Fig. 11(a)]. The spectrum of the microcapillary sensor is measured using the microfiber positioned at the left edge of the resonator as shown in Fig.

11(a). The intrinsic Q-factor of the resonator is set to 10⁶.

The microfiber-resonator coupling parameters are assumed to be equal to those measured in [5] . The resonance wavelength is set to

Then, for a silica microcapillary with

we have κ = 8.31 um"¹.

Fig. 11(b) shows a 2D plot of the resonant evanescent field as a function of axial coordinate z and wavelength λ.

Calculations were performed by numerical solution of equation

(2) following theory [4]. It is seen that the resonator

possesses 10 axial eigenmodes. While the first eigenmode is localized in the vicinity of the left edge, the tenth mode is distributed along the whole length of the resonator. The axial dimension of modes grows linearly with their number.

The microparticle is modelled by the potential in

equation (2) corresponding to the effective refractive index variation with the Gaussian shape,

Here the refractive index maximum

is estimated from equation (4),

and, as noted above, strongly depends on the width of the capillary wall.

The preferable configuration for the detection of

microparticles is the asymmetric capillary [Fig. 10(c)], since it permits the enhancement of the microparticle-resonator coupling by thinning of a relatively small fraction of the capillary with minimum reduction of the resonator Q-factor. In addition, while the symmetric microcapillary [Fig. 10(b)] does not allow for the determination of the azirouthal coordinate of the microparticle φ, the asymmetric configuration allows for confinement of the microparticle positions at the fixed azimuthal angle.

In the numerical simulations shown in Fig. 11(c), the characteristic index variation is set to

and w - 0.6 um corresponds to the axial FWHM. of the microparticle equal to 1 um. This figure shows the numerically calculated surface plot of transmission amplitude as a function of microparticle position

and wavelength A. The trajectories of sharp spectral dips in this plot determine the variation of eigenvalues of the triangular resonator as a function of the microparticle position. The normalized eigenmodes of

triangular resonator can be approximately expressed through the Airy functions:

where

is the normalization factor,

1.245, etc. Comparison of rescaled

calculated from equation (8) for 5 = 1, 2,..., 5 (shown as dashed lines) with the trajectories of resonances at the surface plot of Fig. 11(c) demonstrates remarkably good accuracy of equation (8) . Nonlinear equations (5) and (8) can be used to determine the microparticle position and its contrast

as functions of time. Generally, these two unknowns can be determined from two equations of equation (5) corresponding to provided that eigenfunctions with numbers and

vary fast enough near the microparticle position. For example, one can use near the left-hand side

of the resonator. However, the inclusion of functions

with larger s is necessary to determine the microparticle position closer to the right-hand side, where

vanish. The plot in Fig. 11(c) can be used for detection of microparticles with an effective refractive index

different from the value 0.0005 assumed above. To this end, the amplitude of resonance trajectories in this figure should be rescaled by the factor

The resonant evanescent field of the SNAP structure created at the capillary surface can be used to control the microfluidic processes and, in particular, to manipulate the floating microparticles which are attracted to the capillary surface by this field. For the axially symmetric capillary

[Fig. 10(b)], the trapping field intensity is axially

symmetric and only the axial localization of the particle can be achieved. In contrast, the asymmetric configuration [Fig. 10(c)] enables the full axial and azimuthal localization.

The strongly localized driving field can be created using a multi-parametric, tunable filter positioned at the input of the microfiber. The filter launches light into the SNAP resonator at M eigenvalues

with the required partial powers and phases chosen so that the superposition of the excited modes is localized at the predetermined axial

position. Fig. 12 demonstrates this idea the for the

triangular bottle resonator considered above. In both Figs. 12 (a) and 12 (b) the input-output microfiber is positioned as indicated in Fig. 11.

In Fig. 12, the linear combinations of 10 complex-values axial distributions of the evanescent field calculated near the 10 resonant wavelengths [Fig. 1Kb)] are optimized to arrive at the single-maximum trapping field which can drive a microparticle within the axial dimensions of the resonator

[Fig. 12(a)] and the double-maxima trapping field which can independently and simultaneously drive two microparticles within the axial dimensions of the resonator [Fig. 12(b)]. In both cases, only real (field intensity) coefficients were optimized.

The characteristic spacing between eigenvalues of the SNAP resonator considered has a relatively small value: ~20 ps. This value grows with decreasing of the resonator length as L~² and is inversely proportional to the capillary radius r¾. For example, a two-time shorter resonator has the

characteristic resonance spacing ~0.1 run. Notice that the available axial length for sensing and manipulation of

microfluids can be increased by cascading the structures similar to that considered above. The embodiment discussed above shows that microfluidic processes can be detected and manipulated by monitoring the spectrum and varying the evanescent field of SNAP resonators in space and time. Tuning the input spectral distribution within a relatively narrow bandwidth of less than 1 nm allows one to program the axial distribution of the evanescent field and thereby manipulate the microfluidic components. The developed theory of sensing and manipulation of microparticles may be generalized to the case of a more complex distribution of refractive index and applied to investigate complex spatial and temporal processes in the vicinity of the capillary surface.

Similar theory may be applicable to the investigation of media adjacent to the outside surface of the SNAP fibre [Fig. 10(a)]. This is related to the processes in both liquids and gases. In particular, application of the developed approach to sensing and manipulation of clouds of cold atoms both outside and inside the SNAP structure may be of special interest. The practical realization of the proposed resonant slow light microfluidic sensor and manipulator can significantly advance the multi-disciplinary applications of optofluidics .

The SNAP structures described above operate along the surface of an optical microcapillary to characterise and manipulate microfluids. The microcapillaries with an ultrathin (few micron thick) walls will be fabricated following the previously developed method of HF etching suggested in [40] . The proposed device is a conceptually novel type of a slow light and resonant cavity sensor and manipulator that will allow us to simultaneously characterize and control the behaviour of microfluids in space and time [18] . The

evanescent field of SNAP structures penetrates into the microfluid and, thus, the spectrum of the resonant light is affected by the kinetics of liquid in a thin layer adjacent to the internal capillary surface. It has been shown previously that a resonant spectral peak of light excited in a uniform optical microcapillary shifts proportionally to the local change in refractive index of the microfluid and, therefore, can be used for its detection [40, 25] . It has also been shown that the evanescent field of optical waveguides and

microresonators can be used to move micro/nanoparticles [41]. The proposed device may thus enable detection and manipulations of micro/nanoparticles composed of different materials, including special physical, chemical and biological species, in time and space with specially designed SNAP resonators distributed along the microcapillary length. The spectral measurements will be performed with a high-resolution

OSA. Manipulation of microparticles can be performed using the Waveshaper, which will be used to generate the required linear combination of the SNAP structure eigenmodes (see preliminary calculations [18]) varying in time. This approach allows determination and control of a broad range of mechanical, physical, chemical, and biological parameters in microfluids. Beyond microfluidics, this approach can be applied in

molecular and atomic spectroscopy, sensing of gases, and quantum processing of cold atoms.

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Claims

1. An optical buffer comprising:

an optical fibre having an optical axis, the optical fibre having a microresonator section configured to support optical radiation in a whispering gallery mode (WGM) ;

an optical input coupled to the optical fibre to introduce a WGM optical signal to the microresonator section; and

an actuator arranged to selectively introduce a

deformation in the microresonator section to switch the microresonator section between a closed, state for retaining the WGM optical signal and an open state for receiving or releasing the WGM optical signal,

wherein, in the closed state, the microresonator section has a geometry that forms a potential well which preserves the WGM optical signal.

2. An optical buffer according to claim 1, wherein the geometry of the potential well is selected from a class of potential wells which preserve a period of captured

oscillations independently of amplitude.

3. An optical buffer according to claim 1 or 2, where the geometry comprises a parabolic outer surface.

4. An optical buffer according to claim 3, wherein the microresonator section is a bottle resonator formed by a parabolic bulge in an outer diameter of the optical fibre.

5. An optical buffer according to claim 4, wherein the parabolic bulge is formed on one side of the optical fibre.

6. An optical buffer according to any preceding claim, wherein the deformation comprises a physical variation in the effective radius of the optical fibre in the microresonator section.

7. An optical buffer according to claim 6, wherein a magnitude of the physical variation is less than 5 nm.

8. An optical buffer according to any preceding claim, wherein the actuator comprises a laser for delivering a pulse of energy to deform the microresonator section.

9. An optical buffer according to any one of claims 1 to 7, wherein the optical fibre includes a piezoelectric element in the microresonator section and the actuator

comprises an voltage source for generating an electric field across the piezoelectric element.

10. An optical buffer according to claim 9, wherein the piezoelectric element is a core of the optical fibre.

11. An optical buffer according to any preceding claim, wherein the optical input is a waveguide mounted transversely to the optical axis.

12. An optical buffer according to claim 11, wherein the waveguide is an optical microfiber.

13. An optical device for confining phonons, the device comprising:

an optical fibre having an optical axis, the optical fibre having a microresonator section configured to support optical radiation in a whispering gallery mode (WGM) ; and

an optical input coupled to the optical fibre to

introduce to the microresonator section a first WGM optical signal having a first frequency and a first wave vector and a second WGM optical signal having a second frequency and a second wave vector, the first frequency and first wave vector being offset from the second frequency and second wave vector, wherein the microresonator section has a geometry that forms a potential well which preserves both the first WGM optical signal and the second WGM optical signal,

wherein the offset is arranged to excite a WGM phonon signal in the microresonator section.

14. An optical device according to claim 13, wherein the microresonator section of the optical fibre is located between a pair of adjacent optical fibre portions, and wherein an effective radius of the microresonator section is different from an effective radius of each of the pair of adjacent optical fibre portions.

15. An optical device according to claim 14, wherein the microresonator section comprises a physical variation in the effective radius of the optical fibre.

16. An optical device according to claim 15, wherein a magnitude of the physical variation is less than 5 nm.

17. An optical device according to any one of claims 13 to 16, wherein the geometry of the microresonator section comprises a parabolic bulge formed on one side of the optical fibre .

18. An optical device according to any one of claims 13 to 17 including an actuator arranged to selectively introduce a deformation in the microresonator section to switch the microresonator section between a closed state for retaining the WGM acoustic signal and an open state for releasing the WGM acoustic signal.

19. An optical device according to any one of claims 13 to 18, wherein the optical input is arranged to phase match the first WGM optical signal and the second WGM optical signal.

20. An optical device according to any one of claims 13 to 18, wherein the offset of the first frequency and first wave vector from the second frequency and second wave vector is selected to be equal to an eigenfrequency and eigenvector of a resonant phonon state.

21. An optical device according to any one of claims 13 to 20, wherein the optical fibre includes a piezoelectric element in the microresonator section and the device includes a voltage source for generating an electric field across the piezoelectric element.

22. An optical device according to claim 21, wherein the piezoelectric element is a core of the optical fibre.

23. An optical device according to any one of claims 13 to 22, wherein the optical input is a waveguide mounted transversely to the optical axis.

24. An optical device according to claim 23, wherein the waveguide is an optical microfiber.

25. A photonic integrated circuit for performing one or more photonic functions on optical signals that travel on photonic signal paths therethrough, the circuit comprising: an optical fibre having an optical axis oriented

transversely to a photonic signal path; and

a configuration actuator arranged to selectively

introduce a localised deformation in the optical fibre at a position where it intersects with the photonic signal path, wherein the localised deformation has a geometry that supports optical radiation in a whispering gallery mode (WGM) , and

wherein the configuration actuator is operable to adjust the position of the localised deformation on the optical fibre.

26. A photonic integrated circuit according to claim 25, wherein the optical fibre is part of a two-dimensional array of parallel aligned optical fibres, each optical fibre in the two-dimensional array being optically coupled to its nearest neighbours, wherein the configuration actuator is arranged to selectively introduce a localised deformation in each of a plurality of optical fibres in the two-dimensional array to set a configuration for the two-dimensional array, and wherein the configuration actuator is operable to adjust the

configuration for the two-dimensional array.

27. A photonic integrated circuit according to claim 26? including an optical input coupled to the two-dimensional array to introduce a WGM optical signal to the plurality of localised deformations in the two-dimensional array.

28. A photonic integrated circuit according to claim 27, wherein the optical input is a planar photonic waveguide.

29. A photonic integrated circuit according to any one of claims 25 to 28, wherein the localised deformation

comprises an asymmetric variation in the effective radius of the optical fibre.

30. A photonic integrated circuit according to claim 29 wherein the asymmetric variation has a magnitude of 5 nm or less .

31. A photonic integrated circuit according to any one of claims 25 to 30, wherein the localised deformation forms a potential well which preserves a WGM optical signal.

32. A photonic integrated circuit according to any one of claims 25 to 31, wherein the configuration actuator comprises a laser having a controllable laser beam for creating the localised deformation by thermally exciting the optical fibre.

33. A photonic integrated circuit according to any one of claims 25 to 31, wherein the configuration actuator comprises a background electronic circuit arranged to

selectively apply a localised voltage across the optical fibre to create the localised deformation.

34. A photonic integrated circuit according to claim 33 wherein the optical fibre includes a piezoelectric element.

35. A photonic integrated circuit according to claim 34 wherein the piezoelectric element is a core of the optical fibre .

36. A photonic integrated circuit according to any one of claims 33 to 35, wherein the configuration actuator is operable to adjust the position of the localised deformation on the optical fibre within a time window less than 1 μs, preferably less than 100 ns.

37. A microfluidic device comprising: a microcapillary that defines a passage for conveying a microfluid, the microcapillary comprising a microresonator section configured to support optical radiation in a

whispering gallery mode (WGM) around the passage;

an optical input coupled to the microcapillary to introduce a WGM optical signal to the microresonator section; and

a detector arranged to determine a transmission amplitude of the optical input to monitor an interaction between an evanescent field of the WGM optical signal and matter

contained in the passage.

38. A microfluidic device comprising:

a microcapillary that defines a passage for conveying a microfluid, the microcapillary comprising a microresonator section configured to support optical radiation in a

whispering gallery mode (WGM) around the passage;

an optical input coupled to the microcapillary to introduce a WGM optical signal to the microresonator section, whereby an evanescent field of the WGM optical is arranged to capture a microparticle in the passage; and

a controller arranged to control the WGM optical signal to manipulate the captured microparticle.

39. A microfluidic device according to claim 38, wherein the passage is radially offset from a central axis through the microcapillary.

40. A microfluidic device according to claim 38 or 39, wherein the microresonator section is arranged to support a plurality of WGM eigenmodes, and wherein the optical input includes a filter arranged to launch one or more of the plurality of eigenmodes into the microresonator section.

41. A microfluidic device according to any one of claims 37 to 40, wherein the microresonator section comprises a localised deformation in an outer diameter of the

microcapillary.

42. A microfluidic device according to claim 41, wherein the localised deformation is an asymmetric variation in the effective radius of the microcapillary.

43. A microfluidic device according to claim 42, wherein the asymmetric variation has a magnitude of 5 nm or less.

44. A microfluidic device according to any one of claims 41 to 43, wherein microresonator section comprises a triangle bottle resonator.

45. A microfluidic device according to any one of claims 37 to 44, wherein the passage has diameter of 10 μs or less.