Reduced cladding multi-mode fiber for generating a brillouin response, methods and systems thereof

Abstract

A method of generating a Brillouin signal resonance response by forward inter-modal Brillouin scattering with fundamental acoustic modes (FIM-FAM) using an RC-TMF, comprising the steps of: generating a first optical mode, wherein the first optical mode is a fundamental optical mode; generating a second optical mode, wherein the second optical mode is a higher-order optical mode; coupling through a mode selective coupler the first optical mode to the second optical mode to become combined optical modes; collimating the combined optical modes within an input two-mode optical fiber, wherein the combined optical modes are focused by one or more focusing lenses onto an input end of an RC-TMF as described herein; driving a fundamental acoustic mode in the RC-TMF as described herein, wherein the combined optical modes enter the RC-TMF through said input end; wherein a single Brillouin signal resonance response is generated within the RC-TMF.

Description

DOCKET NO: 1134-201 PCT TITLE REDUCED CLADDING MULTI-MODE FIBER FOR GENERATING A BRILLOUIN RESPONSE, METHODS AND SYSTEMS THEREOF

[0001] This invention was made with government support under ECCS-1943658 awarded by the National Science Foundation. The government has certain rights in the invention.

[0002] This application claims priority from U.S. Provisional App. No.63 / 586,559, filed September 29, 2023, which is incorporated herein by reference. FIELD

[0003] This application relates to the field of optomechanical interactions and, in particular, the generation of stimulated Brillouin scattering (SBS). BACKGROUND

[0004] Brillouin interactions date back 100 years with essential applications for lasers, delay lines, sensing, and fast, tunable and high resolution microwave photonic filters. In short, optical and acoustic waves couple through electrostrictive forces where a beat wave between two optical waves induces a density variation in the material which propagates at the speed of sound and modulates the refractive index which then reflects and Doppler shifts one optical tone to amplify the other optical tone. It is a lossless parametric interaction for which the interaction frequency is determined by simple energy and momentum conservation laws. In the standard configuration, the acoustic frequency is lower than the optical frequency by the ratio of the light speed to sound speed, giving ~10 GHz for most solids. The linewidth of the response is given by the decay rate of the acoustic waves which for this high frequency is ~40 MHz linewidth. Since the acoustic-wave parameters are fixed by the material, the linewidth response and the performance of devices based on previous interactions is fundamentally limited. SUMMARY

[0005] One aspect of the application relates a reduced cladding two-mode optical fiber (RC-TMF), comprising: an optical core layer having a core diameter, wherein said optical core layer has a refractive index nco, and wherein said core diameter is in a range of 2- 50 µm; a cladding layer, wherein said cladding layer has a cladding diameter and is overlaidaround the optical core layer and said cladding layer has a refractive index ^^^^^^^^ ^^^^, and said cladding diameter is in a range of 15-70 µm; wherein Δ ^^^^ = ^^^^^^^^ ^^^^− ^^^^^^^^ ^^^^is the difference between the refractive index of said optical core layer and the refractive index of said cladding layer and Δn is in a range of 0.001 – 0.03; and wherein said RC-TMF supports at least a fundamental spatial optical mode and a higher order spatial optical mode.

[0006] Another aspect of the application relates a system of generating a Brillouin signal resonance response by forward inter-modal Brillouin scattering with fundamental acoustic modes (FIM-FAM), comprising: an RC-TMF as described herein; and a plurality of polarization controllers optically connected to an input end of said RC-TMF.

[0007] Another aspect of the application relates to a method of generating a Brillouin signal resonance response by forward inter-modal Brillouin scattering with fundamental acoustic modes (FIM-FAM) using an RC-TMF, comprising the steps of: generating a first optical mode, wherein the first optical mode is a fundamental optical mode; generating a second optical mode, wherein the second optical mode is a higher-order optical mode; coupling through a mode selective coupler the first optical mode to the second optical mode to become combined optical modes; collimating the combined optical modes within an input two-mode optical fiber, wherein the combined optical modes are focused by one or more focusing lenses onto an input end of an RC-TMF as described herein; driving a fundamental acoustic mode in the RC-TMF as described herein, wherein the combined optical modes enter the RC-TMF through said input end; wherein a single Brillouin signal resonance response is generated within the RC-TMF.

[0008] Another aspect of the application relates to a method of manufacturing an RC- TMF as described herein, comprising the steps of: drawing an optical fiber; applying a cladding to said optical fiber using a coating dye. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] FIG.1 shows two counter propagating optical fields, pump and Stokes are coupled via a freely propagating longitudinal acoustic wave.

[0010] FIG.2 shows Backward Brillouin interaction. (Upper Panel) acoustic dispersion with the optical driving wavevector overlaid. The intersection point is the allowed interaction, where the phonon has an approximate wavevector magnitude of|^^^^|≈ 2 ^^^^^^^^. (Lower Panel) Measurements from the PI’s group of the standard high frequency 37-MHz response from an optical fiber.

[0011] FIG.3 shows Panel a) Phase matching and energy conservation diagrams for anti-Stokes scattering process. Panel b) Frequency response of a backward Brillouin system showing gain and loss bands created in the presence of a strong optical pump.

[0012] FIG.4 shows Forward Intermodal (FIM) Brillouin scattering. Panel a) Two co-propagating optical fields, pump and stokes, in different spatial optical modes are coupled either through a higher order guided acoustic mode (non-tunable FIM) or fundamental acoustic modes (FIM-FAM). Panel b) The acoustic dispersion diagram showing phase matching with higher-order acoustic modes for well-known non-tunable FIM processes and the proposed FIM-FAM interactions.

[0013] FIG.5 shows a taper-based FIM-FAM device. (Panel a) An illustration of the FIM-FAM process in a few-mode taper. Regions of the taper are labeled above each section. Pump ( ^^^^^^^^) and Stoke ( ^^^^^^^^) beams input respectively into the fundamental and higher-order spatial modes of the input fiber core couple through the transition region into the fundamental mode and higher-order mode family of the taper waist, where the pump light is optomechanically coupled to the Stokes field through the FIM-FAM process before being coupled out of the device in the two modes of the output fiber core through the second transition region. The phase-matching relations for the FIM-FAM interaction indicating the optical wavevector difference between the axial wavevector of the two participating optical modes, Δ ^^^^, must equal the acoustic wavevector, ^^^^, is inset below the device. (Panel b) The acoustic dispersion profiles for the modes of the taper waist. While the higher-order acoustic modes (magenta) have a fixed nonzero cutoff frequency at ^^^^ = 0, the fundamental mode frequencies (Ω) and wavevectors ( ^^^^) extend continuously to zero (cyan). Optomechanical interactions are possible at frequencies where the optical wavevector difference (Δ ^^^^) intersects the acoustic dispersion curves. In contrast to interactions with the higher-order modes, FIM-FAM interactions with the fundamental modes can be tuned in frequency by varying the optical wavevector difference, Δ ^^^^.

[0014] FIG.6 shows the wide new range of acoustic frequencies, lifetimes, and linewidths that can be accessed through FIM-FAM optomechanical interactions.

[0015] FIG.7 shows target Δ ^^^^ for the reduced cladding fiber design. The green region indicates the targeted two-mode design that is also compatible with fabrication. The orange dot indicates the initial design.

[0016] FIG.8 shows Panel a) The simulated fundamental and higher order optical mode in the reduced-cladding two-mode fiber (RC-TMF). Panel b) The simulated transversedisplacement field of the fundamental flexural acoustic modes. Panel c) Spatial mode coupling into the RC-TMF via a mode selective coupler (MSC), a standard step-index two- mode fiber, and a telescope.

[0017] FIG.9 shows measurements on the reduced cladding two-mode fiber. (Panel a) The cladding size of the fiber under the microscope. (Panel b) Far field infrared images of the output modes patterns from the fiber, when LP01 and LP11 modes were coupled into the fiber from the other end. (Panel c) Initial results of FIM-FAM measurements on different processed fiber samples, with various total lengths (Piece #1, top signal; Piece #2, middle signals; Piece #3, bottom signal).

[0018] FIG.10 shows in the (upper panel) a cross-section of a fiber with a core surrounded by a cladding layer and still having a jacket. The cladding diameter is marked. The (lower panel) shows a cross-section of a fiber with a core surrounded by a cladding layer with the jacket removed. The core diameter is marked. DETAILED DESCRIPTION

[0019] Reference will be made in detail to certain aspects and exemplary embodiments of the application, illustrating examples in the accompanying structures and figures. The aspects of the application will be described in conjunction with the exemplary embodiments, including methods, materials and examples, such description is non-limiting and the scope of the application is intended to encompass all equivalents, alternatives, and modifications, either generally known, or incorporated here. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. One of skill in the art will recognize many techniques and materials similar or equivalent to those described here, which could be used in the practice of the aspects and embodiments of the present application. The described aspects and embodiments of the application are not limited to the methods and materials described.

[0020] As used in this specification and the appended claims, the singular forms "a," "an" and "the" include plural referents unless the content clearly dictates otherwise.

[0021] Ranges may be expressed herein as from "about" one particular value, and / or to "about" another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent "about," it will be understood that the particular value forms another embodiment. It will be further understoodthat the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. It is also understood that there are a number of values disclosed herein, and that each value is also herein disclosed as "about" that particular value in addition to the value itself. For example, if the value "10" is disclosed, then "about 10" is also disclosed. It is also understood that when a value is disclosed that "less than or equal to" the value, "greater than or equal to the value" are also disclosed, as appropriately understood by the skilled artisan. For example, if the value "10" is disclosed, the "less than or equal to 10" and “greater or equal to 10” is also disclosed. When two or more value are disclosed, all possible ranges between any two values are disclosed. Brillouin Scattering

[0022] In Brillouin scattering, optical and acoustic waves couple through electrostrictive forces (materials become compressed in the presence of a strong electric field gradient). The beat wave between two counter-propagating optical waves with a small frequency difference induces a density variation in the material (Fig.1). For the appropriate difference frequency, the density variation will propagate at the speed of sound. This periodic density variation also modifies the refractive index with the same spatial period, which reflects and Doppler shifts the pump light to the frequency of the counter-propagating probe light. In other words, the two optical waves generate an acoustic wave, which then amplifies the probe light.

[0023] Brillouin has now been demonstrated in many systems, with useful devices developed in fiber and integrated waveguides. Brillouin has been proven effective for reversing atmospheric distortions in high power lasers, increasing spatial optical coherence, enabling ultranarrow laser sources, and creating optical delay lines. Brillouin is also a very effective sensor for strain and temperature and has more recently seen growing impact for a new form of elastic sensing in tissues. Finally, Brillouin scattering enables fast, tunable and high resolution optical filters that are well-suited for microwave photonic systems. Backward Brillouin Scattering

[0024] Energy and momentum conservation laws determine whether the interaction is allowed and if so, what the frequency will be. By understanding these simple conservation laws, it can be seen why the frequency of traditional backward interactions is fixed, and why FIM-FAM interactions are extremely flexible. Considering an optical pump wave with frequency ωp, and wavevector (or momentum) ^^^^^^^^, an optical probe (from now on calledStokes) wave with frequency ^^^^^^^^, and wavevector ^^^^^^^^, and an acoustic wave with frequency Ω^^^^, and wavevector ^^^^^^^^. The conservation equations can be written simply as: ^^^^^^^^= ^^^^^^^^+ Ω^^^^(1a)

[0025] In a waveguide these wavevectors are simplified to scalar quantities for the wavevector component along the waveguide axis. Generally, these two equations can be solved by plugging Eq.1a into 1b and solving for Ω^^^^. The resulting transcendental equation,using the optical wavevector difference, Δ ^^^^ = ^�^^⃗^ ^^^^ − ^�^^⃗^ ^^^^, is expressed as Δ ^^^^( ^^^^=^^^^(Ω^^^^). Because the acoustic dispersion can become complicated (e.g. in waveguides) it is convenient to solve this equation graphically by plotting the optical wavevector difference, Δ ^^^^( ^^^^ , on a plot of the acoustic dispersion, ^^^^(Ω^^^^), and identifying the allowed interactions as the points of intersection (e.g. Fig.2, upper panel).

[0026] In the traditional backward interaction, the optical pump and Stokes fields are counter-propagating, which can be represented by adding a negative sign to the counter-propagating Stokes wavevector. In this case Δ ^^^^( ^^^^=≈ 2 ^^^^^^^^( ^^^^^^^^). The Ω^^^^dependence is ignored because the acoustic frequency (~10 GHz) is orders of magnitude smaller than the optical frequencies (~200 THz). Energy and momentum conservation, Δ ^^^^( ^^^^^^^^,Ω^^^^) = ^^^^(Ω^^^^), for a fixed optical pump frequency ( ^^^^^^^^), now tell us that the acoustic wave accessed by the backward interaction simply has to satisfy ^^^^(Ω^^^^) = 2 ^^^^^^^^. The dispersion for freely propagating acoustic waves is ^^^^(Ω^^^^) =where ^^^^^^^^is the acoustic velocity. Graphically, this acoustic dispersion ( ^^^^(Ω^^^^)) line is plotted with slope ^^^^^^^^and the wavevector difference is plotted as a single value of ^^^^, at 2 ^^^^^^^^. The intersection point determines the allowed Brillouin interaction aswhere ^^^^ is the refractive index of the medium and ^^^^0is the optical wavelength of the pump.

[0027] The acoustic frequency for standard backward Brillouin interactions for most solids is ~10 GHz for near-infrared optical pumping. This backward interaction occurs with the most ubiquitous freely propagating acoustic waves, which also explains why this is the most common and well-studied interaction. The backward interaction also occurs in acoustic waveguides, but because the acoustic wavevector is so large, the waveguide does notsignificantly alter the response from the bulk case. An example response measured in the PI’s lab of the most common standard single-mode fiber yields a strong peak at 10.8 GHz, with several much weaker peaks from higher order acoustic modes (Fig.2, lower panel). The linewidth of the response given by the decay rate of the acoustic waves is largely determined by the frequency of the interaction, with higher frequencies giving broader linewidths. The 37 MHz linewidth from Fig.3, Panel b is representative of the high frequency backward interactions and corresponds to acoustic waves that are short lived, decaying after only 100 microns in the fiber. Since the acoustic-wave parameters are fixed by the material, the linewidth response and the performance of devices based on standard backward interactions is fundamentally limited by intrinsic material constraints. Overcoming The Limitations Of Backward Brillouin Scattering

[0028] The limitations of traditional backward Brillouin scattering can be overcome by engineering the momentum through appropriately designed optical and acoustic waveguides.

[0029] The Brillouin coupling strength is quantified by a gain coefficient, ^^^^0, which depends on system parameters including the optical wavelength, refractive index, speed of sound, density of the medium and its electrostrictive constant. The gain coefficient quantifies how much amplification the Stokes optical field will experience through ^^^^^^^^^^^^ ^^^^ ^^^^= ^^^^^^^^^^^^ ^^^^^^^^^^^^0 ^^^^ ^^^^ ^^^^, (2)

[0030] where ^^^^^^^^^^^^ ^^^^is the initial Stokes power, ^^^^^^^^^^^^ ^^^^ ^^^^is the final Stokes power, ^^^^^^^^is the pump power, and ^^^^ is the length of the Brillouin active medium. ^^^^0is in units ofsuch that the exponential’s power is unitless. The overall amplification is increased by increasing the pump power, ^^^^^^^^, the device length, ^^^^, or the intrinsic Brillouin gain, ^^^^0. Therefore, higher Brillouin coupling strength leads to comparable devices with shorter lengths and lower power requirements.

[0031] Note that energy flow in a Brillouin interaction is one-directional, from the pump to the Stokes field. It does not oscillate between the pump and Stokes optical fields, even if the pump is heavily depleted. The phonons generated through the Brillouin process have a finite lifetime typically much smaller than optical lifetimes. New pump photons can be only created when the Stokes photon absorbs a phonon to create a pump photon, thereby transferring energy into the pump field. Phonons generated through the Brillouin process arelost comparatively quickly and consequently, the pump field continually loses energy, even if it already is depleted.

[0032] In the Stokes processes described so far, energy is transferred from the optical pump to an acoustic wave and a redshifted optical Stokes tone. Alternatively, in the anti- Stokes process energy from an acoustic wave combines with energy from a pump to create a higher energy, blue-shifted (higher frequency) anti-Stokes optical tone. Importantly, the acoustic wave mediating the anti-Stokes process propagates in the opposite direction to that from the Stokes process (Fig.3). In the absence of any external acoustic waves, the anti- Stokes tone experiences exponential loss as it propagates, in contrast to exponential gain experienced by the Stokes tone, and its output power ( ^^^^^^^^^^^^^^^^^^^^ ^^^^) can be written as ^^^^^^^^^^^^^^^^^^^^ ^^^^= ^^^^^^^^^^^^^^^^^^^^^^^^− ^^^^0 ^^^^ ^^^^ ^^^^. (3)

[0033] Selecting between Stokes / anti-Stokes process forms the basis of Brillouin based applications including lasers, amplifiers, and filtes; anti-Stokes processes are well- suited to notch filtering applications.

[0034] With a single optical mode, pump and Stokes light propagating in the same direction can couple to guided acoustic waves, leading to so-called forward Intra-modal Brillouin interactions. While these interactions open up new frequencies and have enabled new devices, as described in more detail below, they are still limited in frequency, linewidth and coupling, but now by the device geometry. Forward Inter-modal Brillouin Scattering

[0035] With two optical modes with different effective indices much more flexibility becomes available for Brillouin interactions. For a pump propagating in a mode with refractive indexand the Stokes field propagating in another mode with refractive index ^^^^2, the optical wavevector difference becomes Δ ^^^^ = ^^^^^^^^− ^^^^^^^^≈(^^^^1− ^^^^2)^^^^0= ^^^^ ^^^^ ^^^^0, where ^^^^ ^^^^ is the difference in refractive index of the two optical modes. Let’s consider a two-mode waveguide for light and a solid cylinder for acoustic guidance (Fig.4, Panel a). To determine the available interactions, from the analysis above, the study looks at the dispersion of all of the acoustic modes (Fig.4, Panel b) and looks for all of the points where the single value of Δ ^^^^ (Fig.4, Panel b) intersects these curves.

[0036] Although this process uses the same acoustic higher order modes as intra- mdoal scattering (upper oval region in Fig.4), the Stokes and anti-Stokes process in inter- modal scattering uses acoustic waves traveling in opposite directions which is advantageous for applications requiring single-sideband responses. However, like the intramodalinteractions, intermodal interactions with the higher order modes are higher frequency with negligible tunability because the higher order modes do not vary in frequency with wavevector.

[0037] Using standard fiber geometries, the interaction strength of forward Brillouin is very weak because the light in the fiber core has a very small overlap with the acoustic mode extending out through the cladding. Forward Inter-modal Brillouin Scattering with Fundamental Acoustic Modes (FIM- FAM)

[0038] The fundamental acoustic modes exist at all frequencies in bulk and waveguide systems and do not have the lower frequency bound that limits the higher-order acoustic modes. Without a strong dependence of the frequency on the geometry, the fundamental acoustic modes offer a unique opportunity to decouple the frequency (and linewidth) from the confinement and therefore strength of the interaction. As can be seen from the vertical graph line in Fig.4, Panel b, the frequency of the interaction can be tuned (dots in Fig.4, Panel b) by the choice of relative effective indices of the participating optical modes (Δ ^^^^ = ^^^^ ^^^^ ^^^^0).

[0039] FIM-FAM is a coherent optomechanical process through which a fundamental acoustic mode with frequency Ω and wavevector ^^^^ mediates parametric coupling between two distinct optical spatial modes (pump with frequency ^^^^^^^^and wavevector ^^^^^^^^, and Stokes with frequency ^^^^^^^^and wavevector ^^^^^^^^). For coupling to occur, the interaction must satisfy phase matching (Δ ^^^^ = ^^^^^^^^− ^^^^^^^^= ^^^^) and energy conservation (Ω = ^^^^^^^^− ^^^^^^^^). These conditions can be succinctly expressed graphically by examining the acoustic dispersion lines ( ^^^^(Ω)) and the difference in optical wavevectors between the two optical modes, Δ ^^^^ (Fig.5, Panel b). In this picture, interactions are possible at the frequencies where these lines intersect. Intermodal Brillouin interactions of this type allow for stimulated gain, single- sideband amplification, and non-reciprocal processes because of distinct phonon modes mediating Stokes and anti-Stokes processes. In addition, because the interaction frequency is determined by Δ ^^^^, by engineering the differential effective index of the participating optical modes, Δ ^^^^, the frequency of the interaction, Ω, can be tuned. However, as illustrated in Fig. 5, Panel b, when changing Δ ^^^^ for the higher-order modes (Fig.5, Panel b) that are the subjectof previous studies of intermodal Brillouin scattering, the frequency remains close to its ^^^^ =0 value, which is fixed by the geometry. In contrast, with the fundamental acoustic modes(Fig.5, Panel b), there is no low-frequency cutoff, and all frequencies become available.FIM-FAM, therefore, offers a wide new window of opportunity for traveling-wave optomechanical interactions (see also Xu et al., Optica, Vol.10, No.2, pp.206-213, Feb. 2023, incorporated herein by reference).

[0040] Novel device design techniques are required to achieve strong confinement of acoustic waves with the long wavelengths needed for large acoustic lifetimes. However, if strong optical coupling can be achieved with the frequency-agile fundamental acoustic modes, this versatile optomechanical interaction can enable unprecedented access to simultaneous strong coupling and the narrow linewidths associated with lower frequency modes (Fig.6). A Reduced Cladding Two-mode fiber

[0041] An aspect of the application is a reduced cladding two-mode optical fiber (RC- TMF), comprising: an optical core layer having a core diameter, wherein said optical core layer has a refractive index ^^^^^^^^ ^^^^, and wherein said core diameter is in a range of 2-50 µm; a cladding layer, wherein said cladding layer has a cladding diameter and is overlaid around the optical core layer and said cladding layer has a refractive index ^^^^^^^^ ^^^^, and said cladding diameter is in a range of 15-70 µm; wherein Δ ^^^^ = ^^^^^^^^ ^^^^− ^^^^^^^^ ^^^^is the difference between the refractive index of said optical core layer and the refractive index of said cladding layer and Δ ^^^^ is in a range of 0.001 – 0.03; and wherein said RC-TMF supports at least a fundamental spatial optical mode and a higher order spatial optical mode.

[0042] In certain embodiments, said cladding layer has no jacket.

[0043] In certain embodiments, the optical core layer. is composed of a material selected from one of the group comprising: silicon dioxide, fluorozirconate, fluoroaluminate, chalcogenide, sapphire and silicon. A system of generating a Brillouin signal response

[0044] Another aspect of the application is a system of generating a Brillouin signal resonance response by forward inter-modal Brillouin scattering with fundamental acoustic modes (FIM-FAM), comprising: said RC-TMF as described herein; a plurality of polarization controllers optically connected to an input end of said RC-TMF.

[0045] In certain embodiments, further comprising: a mode selective coupler optically connected to said input end of said RC-TMF, wherein said mode selective coupler couples said fundamental spatial optical mode to said higher order spatial optical mode to become combined optical modes within said RC-TMF.

[0046] In certain embodiments, the mode selective coupler is selected from one of the group comprising: a mode converting device, a spatial light modulator, an on-chip mode splitter or a photonic lantern. A method of generating a Brillouin signal response

[0047] Another aspect of the application is a method of generating a Brillouin signal resonance response by forward inter-modal Brillouin scattering with fundamental acoustic modes (FIM-FAM) using an RC-TMF, comprising the steps of: generating a first optical mode, wherein the first optical mode is a fundamental optical mode; generating a second optical mode, wherein the second optical mode is a higher-order optical mode; coupling through a mode selective coupler the first optical mode to the second optical mode to become combined optical modes; collimating the combined optical modes within an input two-mode optical fiber, wherein the combined optical modes are focused by one or more focusing lenses onto an input end of said RC-TMF as described herein; driving a fundamental acoustic mode in said RC-TMF as described herein, wherein the combined optical modes enter the RC-TMF through said input end; wherein a single Brillouin signal resonance response is generated within said RC-TMF.

[0048] In certain embodiments, said RC-TMF has a glued input end and a glued output end.

[0049] In certain embodiments, said RC-TMF has a core radius of 7.5 µm, and a cladding radius of 20 µm, and a Δ ^^^^ is 0.005.

[0050] In certain embodiments, the fundamental acoustic mode is flexural.

[0051] In certain embodiments, the fundamental acoustic mode is torsional.

[0052] In certain embodiments, the fundamental acoustic mode is longitudinal.

[0053] In certain embodiments, the one or more focusing lenses are in a telescope.

[0054] In certain embodiments, said RC-TMF is suspended so that the RC-TMF has an air-cladding boundary along its length.

[0055] In certain embodiments, said RC-TMF transmits the first optical mode at greater than 90% and the second optical mode at greater than 65%. Manufacturing

[0056] Another aspect of the application is a method of manufacturing the RC-TMF as described herein, comprising the steps of: drawing an optical fiber; applying a cladding to said optical fiber using a coating dye.

[0057] In certain embodiments, the coating dye is a polytetrafluoroethylene dye.

[0058] In certain embodiments, the jacket is removed by use of acetone and edged instruments.

[0059] In certain embodiments, said RC-TMF is end-cleaved manually.

[0060] In certain embodiments, cladding is removed by a cladding stripper.

[0061] The present application is further illustrated by the following examples that should not be construed as limiting. The contents of all references, patents, and published patent applications cited throughout this application, as well as the Figures and Tables, are incorporated herein by reference. EXAMPLES Example 1

[0062] Higher performance FIM-FAM with narrower linewidths and high coupling can be achieved by coupling to lower frequency resonances, as described above. Lower frequencies can be achieved if the index contrast (Δk) between the two modes can be reduced. Small index contrasts are common in standard two-mode fibers, but FIM-FAM is not possible in standard fibers because the acoustic mode supported by the glass-air boundary of the cladding is much larger than the optical core, resulting in a very low overlap between them. However, if the optical core size is increased and the cladding size is decreased in so- called ‘reduced cladding fibers’, appreciable FIM-FAM coupling can be achieved with record low frequencies.

[0063] Higher performance FIM-FAM with narrower linewidths and high coupling can be achieved by coupling to lower frequency resonances, as described above. Lower frequencies can be achieved if the index contrast (Δ ^^^^) between the two modes can be reduced. Small index contrasts are common in standard two-mode fibers, but FIM-FAM is not possible in standard fibers because the acoustic mode supported by the glass-air boundary of the cladding is much larger than the optical core, resulting in a very low overlap between them. However, if the optical core size is increased and the cladding size is decreased in so- called ‘reduced cladding fibers’, appreciable FIM-FAM coupling can be achieved with record low frequencies.

[0064] The number of optical modes is determined by the normalized frequency ^^^^ =^^^^ the core radius, ^^^^^^^^ ^^^^the core refractive index and ^^^^^^^^ ^^^^the cladding refractive index. In practice, ^^^^^^^^ ^^^^is usually increased via doping from ^^^^^^^^ ^^^^during the fabrication process while ^^^^^^^^ ^^^^remains the same. The study analyzed variations of core radii and Δ ^^^^ = ^^^^^^^^ ^^^^− ^^^^^^^^ ^^^^for optimizing the two-mode fiber design. The minimum cladding radiuschosen to maintain physical stability is 20um. The fiber should only support the 1st( ^^^^ ^^^^11) and 2ndoptical mode families ( ^^^^ ^^^^01, ^^^^ ^^^^01and ^^^^ ^^^^21), while maximizing the core radius (Fig.7). To maximize the interaction while maintaining a lossless signal propagation, the study targets a reduced-cladding two-mode fiber with a core radius of 7.5um and cladding radius of 20um, with Δ ^^^^ = 0.005 (Fig.7).

[0065] In the targeted reduced-cladding two-mode fiber, in the FIM-FAM process the fundamental acoustic mode interacts with the fundamental optical mode and three possible higher-order modes (simulated in Fig 8 a-b), enabling very low frequencies around 500 kHz. The FIM-FAM gain is calculated as 5 × 10−3^^^^−1^^^^−1, with a conservatively assumed acoustic quality factor of 100. For these sub-MHz resonances, record-low acoustic linewidths at the kHz level are anticipated. This FIM-FAM response should be readily observable (SNR>10) with the highly sensitive FIM-FAM spectroscopy technique described above. The setup will be modified to incorporate the reduced cladding fiber using a mode selective coupler (MSC), a standard step-index two-mode fiber, and a telescope (Fig 8c). The MSC splits two single mode inputs into the respective modes of a standard two-mode fiber which isimaged into the reduced cladding fiber. Experimentally, the study already has achieved~90% transmission for the fundamental mode and ~65% transmission for the higher-ordermodes, which will be further optimized through this effort. FIM-FAM in reduced cladding fibers enables incredibly low frequency narrowband coupling, and because the fiber is coated, they can be very robust and developed at customized length scales. Reduced cladding FIM- FAM is a promising direction for the most robust, reproducible, and high-performance fiber- based devices. Example 2

[0066] Upon receiving a reduced fiber sample, the study confirmed the cladding diameter as designed under the microscope (Fig.9, Panel a). To safely strip the fiber jacket without breaking it, the study applied acetone at the fiber ends to separate it from the bare fiber. Then, the study used razor blades to remove short jacket sections carefully. The study repeated this process for the whole fiber for improved acoustic guidance. Manual fiber scribes were then used to cleave the fiber end repeatedly until it looked smooth and flat under a fiber microscope. Then, LP01 and LP11 modes were spatially coupled into the fiber, where the fiber was aligned to achieve maximum coupling at the output (corresponding mode transverse profiles measured in Fig.9, Panel b).

[0067] The study used a similar spectroscopy measurement setup to the one the study used for the fiber tapers. According to the simulation results based on typical fiber parameters, there should be a FIM-FAM resonance at around 500 kHz. Indeed a response was observed when the study measured the Brillouin response of piece #1 of the fiber with a 70 cm length (Fig.9, Panel c). Moreover, these resonances have a net linewidth of on the order of 10kHz which is remarkable narrow and demonstrates the key concept of FIM-FAM in reduced cladding fibers. To further investigate this, the study processed several sample pieces. Each fiber had a slight different Brillouin response in this frequency region, and the profiles of the multiple peaks also changed (Fig.9, Panel c), but each with ultra-narrow linewidths. In the same fiber also different input polarization states led to different signal behaviors. The study hypothesised that the response is from optical power coupling into fiber cladding modes, guided by the boundary between the fiber cladding and the air. As these cladding modes have slightly different effective refractive indices below the cladding index, the Brillouin interaction between various pairs of cladding modes would cause multi-peak responses. Two methods can remove the optical power guided by the fiber cladding: surface recoating with graphite paste [Talataisong, et al. Sci. Reports 202010110, 1–10 (2020)] and surface damage with the glass etcher [Li, et al. Appl. Opt. Vol.56, Issue 7, pp.1935-193956, 1935–1939 (2017)]. These techniques further enable a single resonance FIM-FAM response.

[0068] The methods described herein can be applied in any cases where there are at least two or more modes within the fiber described herein, up to the nthnumber of modes within the reduced cladding fiber; two or more modes within the fiber are then selected for producing a FIM-FAM response.

[0069] While various embodiments have been described above, it should be understood that such disclosures have been presented by way of example only and are not limiting. Thus, the breadth and scope of the subject compositions and methods should not be limited by any of the above-described exemplary embodiments but should be defined only in accordance with the following claims and their equivalents.

[0070] The above description is for the purpose of teaching the person of ordinary skill in the art how to practice the present invention, and it is not intended to detail all those obvious modifications and variations of it which will become apparent to the skilled worker upon reading the description. It is intended, however, that all such obvious modifications and variations be included within the scope of the present invention, which is defined by the following claims. The claims are intended to cover the components and steps in anysequence which is effective to meet the objectives there intended, unless the context specifically indicates the contrary.

Claims

WHAT IS CLAIMED IS:

1. A reduced cladding two-mode optical fiber (RC-TMF), comprising: an optical core layer having a core diameter, wherein said optical core layer has a refractive index ^^^^^^^^ ^^^^, and wherein said core diameter is in a range of 2-50 µm; a cladding layer, wherein said cladding layer has a cladding diameter and is overlaid around the optical core layer and said cladding layer has a refractive index ^^^^^^^^ ^^^^, and said cladding diameter is in a range of 15-70 µm; wherein Δ ^^^^ = ^^^^^^^^ ^^^^− ^^^^^^^^ ^^^^is the difference between the refractive index of said optical core layer and the refractive index of said cladding layer and Δ ^^^^ is in a range of 0.001 – 0.03; and wherein said RC-TMF supports at least a fundamental spatial optical mode and a higher order spatial optical mode.

2. The RC-TMF of Claim 1, wherein said cladding layer has no jacket.

3. The RC-TMF of any of Claims 1-2, wherein the optical core layer. is composed of a material selected from one of the group comprising: fluorozirconate, fluoroaluminate, chalcogenide, sapphire and silicon.

4. A system of generating a Brillouin signal resonance response by forward inter- modal Brillouin scattering with fundamental acoustic modes (FIM-FAM), comprising: said RC-TMF of Claims 1-3; and a plurality of polarization controllers optically connected to an input end of said RC- TMF.

5. The system of Claim 4, further comprising: a mode selective coupler optically connected to said input end of said RC-TMF, wherein said mode selective coupler combines said fundamental spatial optical mode to said higher order spatial optical mode to become combined optical modes within said RC-TMF.

6. The system of Claim 5, wherein the mode selective coupler is selected from one of the group comprising: a mode converting device, a spatial light modulator, an on-chip mode splitter and a photonic lantern.

7. A method of generating a Brillouin signal resonance response by forward inter- modal Brillouin scattering with fundamental acoustic modes (FIM-FAM) using an RC-TMF, comprising the steps of: generating a first optical mode, wherein the first optical mode is a fundamental optical mode;generating a second optical mode, wherein the second optical mode is a higher-order optical mode; coupling through a mode selective coupler the first optical mode to the second optical mode to become combined optical modes; collimating the combined optical modes within an input two-mode optical fiber, wherein the combined optical modes are focused by one or more focusing lenses onto an input end of said RC-TMF of any one of Claims 1-3; driving a fundamental acoustic mode in said RC-TMF any one of Claims 1-3, wherein the combined optical modes enter the RC-TMF through said input end; and wherein a single Brillouin signal resonance response is generated within said RC- TMF.

8. The method of Claim 7, wherein said RC-TMF has a glued input end and a glued output end.

9. The method of Claim 7, wherein said RC-TMF has a core radius of 7.5 µm, and a cladding radius of 20 µm, and a Δ ^^^^ is 0.

005.

10. The method of any one of Claims 7-9, wherein the fundamental acoustic mode is flexural.

11. The method of any one of Claims 7-9, wherein the fundamental acoustic mode is torsional.

12. The method of any one of Claims 7-9, wherein the fundamental acoustic mode is longitudinal.

13. The method of any one of Claims 7-12, wherein the one or more focusing lenses are in a telescope.

14. The method of any one of Claims 7-13, wherein said RC-TMF is suspended so that the RC-TMF has an air-cladding boundary along its length.

15. The method of any one of Claims 7-14, wherein said RC-TMF transmits the first optical mode at greater than 90% and the second optical mode at greater than 65%.

16. A method of manufacturing the RC-TMF of Claims 1-3, comprising the steps of: drawing an optical fiber; applying a cladding to said optical fiber using a coating dye.

17. The method of manufacturing of Claim 16, wherein the coating dye is a polytetrafluoroethylene dye.

18. The method of manufacturing of any one of Claims 16-17, wherein the jacket is removed by use of acetone and edged instruments.

19. The method of manufacturing of any one of Claims 16-18, wherein said RC-TMF is end-cleaved manually.

20. The method of manufacturing of any one of Claim 16-19, wherein cladding is removed by a cladding stripper.

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