Method and system of filtering using inter-modal brillouin scattering

Abstract

A system of filtering using inter-modal Brillouin scattering, comprising: a first probe light source that generates a probe optical field having a first optical signal in a first optical waveguide; a first phase modulator that modulates the first optical signal by broadband radiofrequency (RF) data containing a first carrier to produce a phase modulated first optical signal; a first Brillouin pump light source that generates a second optical field having a second optical signal in a second optical waveguide; a mode combiner that is input connected to the first optical waveguide and the second optical waveguide, and output connected to a multi-mode third optical waveguide; an inter-modal Brillouin device connected to the mode combiner via the multi-mode third optical waveguide at its input, and having a multi-mode fourth optical waveguide at its output; a mode splitter input connected to the inter-modal Brillouin device via the multi-mode fourth optical waveguide and is output connected to a fifth optical waveguide; and a first photodetector, wherein the photodetector is input connected by a fifth optical waveguide to the mode splitter.

Description

DOCKET NO: 1134-204 PCT TITLE METHOD AND SYSTEM OF FILTERING USING INTER-MODAL BRILLOUIN SCATTERING

[0001] This invention was made with government support under ECCS-1943658 awarded by the National Science Foundation and N00014-23-1-2704 awarded by the Office of Naval Research. The government has certain rights in the invention.

[0002] This application claims priority from U.S. Provisional Application No. 63 / 586,611, 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 to a method of filtering using inter-modal Brillouin scattering, comprising a stage of: generating by a first probe light source an optical field having a first optical signal in a first optical waveguide; phase modulating via a first phase modulator the first optical signal by broadband radiofrequency (RF) data containing a first carrier to produce a phase modulated first optical signal; producing an input higher frequency optical sideband and an input lower frequency optical sideband on either side of the phase modulated first optical signal; generating by a first Brillouin pump light source asecond optical field having a second optical signal in a second optical waveguide; coupling through a mode combiner the phase modulated first optical signal to the second optical signal, so that the first optical signal and second optical signal become a first set of coupled optical signals within a multi-mode third optical waveguide, and the first optical signal and the second optical signal have different spatial optical modes; connecting via the multi-mode third optical waveguide the mode combiner to an inter-modal Brillouin device; receiving the first set of coupled optical signals in the inter-modal Brillouin device; driving an acoustic mode in the inter-modal Brillouin device, wherein gain and loss bands are created by the second optical signal on the phase modulated first optical signal through inter-modal Brillouin scattering; receiving through a mode splitter connected to the inter-modal Brillouin device the first set of coupled optical signals exiting the inter-modal Brillouin device, wherein the mode splitter removes the second optical signal, and the phase-modulated first optical signal with gain and loss sidebands remains as a first exit signal; receiving the first exit signal on a first photodetector, wherein the first exit signal is passed through the first photodetector; outputting an RF signal from the first exit signal passed through the first photodetector.

[0006] Another aspect of the application relates to an embodiment further comprising a second stage of: generating by a second probe light source an optical field having a third optical signal in a fourth optical waveguide; phase modulating via a second phase modulator the third optical signal by the RF signal of a prior stage for a second filtering frequency band to form a phase modulated third optical signal, wherein said second carrier is different from the first carrier; producing a first pair of higher frequency optical sidebands, wherein the first pair comprises a first higher frequency optical passband and a second higher frequency optical passband, and a second pair of lower frequency optical sidebands, wherein the second pair comprises a first lower frequency optical passband and a second lower frequency optical passband, wherein said first pair and said second pair on either side of the phase modulated third optical signal; generating by a second pump light source an optical field having a fourth optical signal in a fifth optical waveguide, wherein the frequency of the fourth optical signal is selected so as to increase or decrease the power on any one of the optical passbands on either side of the phase modulated third optical signal; coupling through a mode combiner the phase modulated third optical signal to the fourth optical signal to become a second set of coupled optical modes within a shared waveguide, and the third optical signal and the fourth optical signal have different spatial optical modes; receiving through a frequency filter device the second set of coupled optical modes; receiving through a mode splitter connected to thefrequency filter device the second set of coupled optical modes exiting the frequency filter device, wherein the mode splitter removes the fourth optical signal and the phase-modulated third optical signal remains as a second exit signal; receiving the second exit signal through a second photodetector, wherein the second exit signal is passed through the second photodetector; outputting an RF signal from the second exit signal passed through the second photodetector.

[0007] Another aspect of the application relates to an embodiment further comprising a third stage of: generating an fifth optical signal with a probe light source; passing the fifth optical signal through an optical delay line; modulating the fifth optical signal with an intensity modulator to get the third exit signal; receiving the third exist signal on the second photodetector, with a 180 degree phase difference compared to the received second exist signal in the RF domain; outputting an RF signal from the mixed second and third exit signals passed through the second photodetector.

[0008] Another aspect of the application relates to a system of filtering using inter- modal Brillouin scattering, comprising: a first probe light source that generates a probe optical field having a first optical signal in a first optical waveguide; a first phase modulator that modulates the first optical signal by broadband radiofrequency (RF) data containing a first carrier to produce a phase modulated first optical signal; a first Brillouin pump light source that generates a second optical field having a second optical signal in a second optical waveguide; a mode combiner that is input connected to the first optical waveguide and the second optical waveguide, and output connected to a multi-mode third optical waveguide; an inter-modal Brillouin device connected to the mode combiner via the multi-mode third optical waveguide at its input, and having a multi-mode fourth optical waveguide at its output; a mode splitter input connected to the inter-modal Brillouin device via the multi- mode fourth optical waveguide and is output connected to a fifth optical waveguide; and a first photodetector, wherein the photodetector is input connected by a fifth optical waveguide to the mode splitter.

[0009] Another aspect of the application is a filter system for inter-modal Brillouin scattering, comprising: a phase modulator; a mode combiner, connected to the phase modulator by at least one optical waveguide; a frequency filtering device connected to the mode combiner by a multi-mode optical waveguide; a mode splitter connected to the frequency filtering device by a multi-mode optical waveguide; a photodetector connected to the mode splitter by a single mode optical waveguide.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG.1 shows two counter propagating optical fields, pump and Stokes are coupled via a freely propagating longitudinal acoustic wave.

[0011] FIG.2 shows Backward Brillouin interaction. (Upper Panel) acoustic dispersion with the optical driving wavevector overlaid. The intersection point is the allowedinteraction, 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.

[0012] 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.

[0013] 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.

[0014] 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 acousticmodes (magenta) have a fixed nonzero cutoff frequency at ^^^^ = 0, the fundamental modefrequencies (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-ordermodes, FIM-FAM interactions with the fundamental modes can be tuned in frequency by varying the optical wavevector difference, Δ^^^^.

[0015] FIG.6 shows the wide new range of acoustic frequencies, lifetimes, and linewidths that can be accessed through FIM-FAM optomechanical interactions.

[0016] FIG.7 shows a simple illustration of FIM-FAM gain and loss for filtering applications.

[0017] FIG.8 shows experiment demonstrating the frequency agility of FIM-FAM filters. (Panel a) In the proposed setup, the upshifted sideband of a phase modulated carrier is selectively amplified by a frequency shifted pump. The imbalance in the sideband amplitudes is measured by the photodetector (PD). PM: Phase modulator, MSC: mode-selective coupler. (Panel b) Tunability is achieved by optically tuning the Brillouin pump, which translates to a Lorentzian pass-band response which will be tuned over 20 GHz of electrical frequency.

[0018] FIG.9 shows simple FIM-FAM notch filter. The RF data is modulated onto an optical carrier through single side-band modulation. The Brillouin pump is redshifted from the frequency band of interest by the resonant frequency. This creates a loss band at the frequency of interest, attenuating a narrow band within the RF data.

[0019] FIG.10 shows FIM-FAM based bandpass filter. A phase modulator is used to modulate data onto a carrier. The FIM-FAM process enabled by a blue-shifted pump is used to selectively amplify a narrow spectral band. The interference of the two sidebands on the photodetector (PD) yields the required narrow bandpass response.

[0020] FIG.11 shows ultra-high rejection tunable FIM-FAM notch filters. An IQ modulator is used to modulate data onto a carrier such that there is a slight imbalance in the amplitudes of the two sidebands. The FIM-FAM process enabled by a tunable pump equalizes the amplitudes of the two sidebands within a narrow spectral band. The interference of the two sidebands on the photodetector (PD) yields a notch filter.

[0021] FIG.12 shows (Panel a) Broad-bandwidth two-stage filter explained through separate diagrams for the (Panel b) first stage going to the right and the (Panel c) second stage going to the left. (Panel b) Laser 1 is phase modulated by the broadband RF data. In the FIM-FAM device, the higher frequency phase-modulated sideband is modulated by the Brillouin pump 1 coupled from port 2 of the MSC1. After the Brillouin pump 1 is removed with MSC2, photodetector PD1receives a RF signal with only two passbands separated by two times the FIM-FAM frequency, with FIM-FAM determined linewidths. (Panel c) In the second stage laser 2 is phase modulated by the RF signal from the first stage. In the FIM- FAM device again, the lower frequency phase-modulated sideband experiences power lossfrom another Brillouin pump 2 coupled from port 2 of the MSC2. After the Brillouin pump 2 is removed with MSC1, photodetector PD2receives a single band RF signal, with FIM-FAM determined linewidths. Only the RF data in this frequency band is preserved and filtered out from the original broadband RF data.

[0022] FIG.13 shows ultra-high rejection tunable FIM-FAM notch filters.

[0023] FIG.14 shows full filter simulations. Single stage simulated filtering performance as a function of the pump power and the detector power, with 4V half-wave voltages. (left panel) system link gain; (center panel) system noise figure; (right panel) at the designed detector power, the change of noise sources as a function of the pump power on the final detector. Circles indicate the proposed working point.

[0024] FIG.15 shows ultranarrow and broad instantaneous bandwidth FIM-FAM notch filters.

[0025] FIG.16 shows dual-stage large instantaneous bandwidth FIM-FAM microwave photonic bandpass filter. The small 500 MHz instantaneous bandwidth RF filtering response, measured by the first photodetector PD1, is sent to a fiber-based backward Brillouin microwave photonic filter to increase the instantaneous bandwidth to be over 20 GHz.

[0026] FIG.17 shows demonstration of a large instantaneous bandwidth bandpass filter centering at 9 GHz. The suppression of the background is >18 dB over 1-19 GHz. With further optimized suppression on the RF signal from the pump leakage from both stages, >38 dB suppression over 20 GHz can be readily achieved.

[0027] FIG.18 shows design of the bandpass filtering system. (Panel a) The RF data is modulated onto the optical carrier (f_c), then part of the carrier sideband will be selectively amplified according to the FIM-FAM frequency f_B, by the Brillouin pump (f_p) with a 3- dB amplification bandwidth, Δf. (Panel b) The bandpass filtering response determined by the FIM-FAM process (linewidth Δf_B), with a central frequency f_0 and the bandwidth Δf proportional to Δf_B. (Panel c) A single-frequency RF signal (f_RF) sweeps through the frequency region to demonstrate the filter response. Panel d) The experimental setup of the full filter system. EDFA, erbium-doped fiber amplifier; PM, phase modulator; PC, polarization controller; MSC, mode selective coupler; PD, photodetector; and SA, spectrum analyzer.

[0028] FIG.19 shows ultranarrow filter measurements over >10GHz. Panel a) The wideband RF response of the bandpass filter centered at 13 GHz, with a 3-dB bandwidth of 275 kHz and 29 dB out-of-band rejection over 500MHz, limited by undesirable high-orderoptical modes. Panel b) The RF filtering response with the central frequency of the passband varying from 7 GHz to 19 GHz in 2 GHz intervals, each plotted over an 80MHz range. The 3-dB filter bandwidth is labeled on each plot. DETAILED DESCRIPTION

[0029] 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.

[0030] 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.

[0031] 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 understood that 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

[0032] 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.

[0033] 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

[0034] 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 called Stokes) wave with frequency ^^^^^^^^, and wavevector ^^^^^^^^, and an acoustic wave with frequency Ω^^^^, and wavevector ^^^^^^^^. The conservation equations can be written simply as: ^^^^^^^^ = ^^^^^^^^ + Ω^^^^ (1a)

[0035] 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).

[0036] 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=≈ 2^^^^^^^^(^^^^^^^^). The Ω^^^^ dependence is ignored because the acousticfrequency (~10 GHz) is orders of magnitude smaller than the optical frequencies(~200 THz). Energy and momentum conservation,= ^^^^(Ω^^^^), for a fixedoptical pump frequency (^^^^^^^^), now tell us that the acoustic wave accessed by the backwardinteraction simply has to satisfy ^^^^(Ω^^^^) = 2^^^^^^^^. The dispersion for freely propagatingacoustic waves is ^^^^(Ω^^^^) =, ^^^^^^^^ is the acoustic velocity. Graphically, thisacoustic 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 allowedBrillouin interaction as,^^^^0, where ^^^^ is the refractive index of the medium and ^^^^0is the optical wavelength of the pump.

[0037] 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 not significantly 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.3b 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

[0038] The limitations of traditional backward Brillouin scattering can be overcome by engineering the momentum through appropriately designed optical and acoustic waveguides.

[0039] 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 ^^^^ ,

[0040] where ^^^^^^^^^^^^^^^^is the initial Stokes power, ^^^^^^^^^^^^^^^^^^^^is the final Stokes power, ^^^^^^^^is thepump power, and ^^^^ is the length of the Brillouin active medium. ^^^^0is in units of such 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.

[0041] 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 are lost comparatively quickly and consequently, the pump field continually loses energy, even if it already is depleted.

[0042] 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)

[0043] 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.

[0044] 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

[0045] 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 our analysis above, we look at the dispersion of all of the acoustic modes (Fig.4b) and look for all of the points where the single value of Δ^^^^ (Fig.4, Panel b) intersects these curves.

[0046] Although this process uses the same acoustic higher order modes as intra- mdoal scattering (upper oval region in Fig.4, Panel b), 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 intramodal interactions, 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.

[0047] 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)

[0048] 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, thefundamental 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 opticalmodes (Δ^^^^ = ^^^^^^^^^^^^0).

[0049] 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 satisfyphase matching (Δ^^^^ = ^^^^^^^^ − ^^^^^^^^ = ^^^^) and energy conservation (Ω = ^^^^^^^^ − ^^^^^^^^). Theseconditions 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).

[0050] 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 FIM-FAM Optical filter

[0051] Brillouin interactions are well-suited for filtering tasks. In microwave photonic systems, such as for radio-over-fiber, microwave signals processed in the optical domain depend on optical spectral filters. Using multiple optical paths with different delays and attenuation is complex and leads to undesirably periodic frequency responses. Brillouin based filtering enables a better filter with a selective single frequency response. The center frequency can be tuned with a variable local oscillator, but the resolution of the filter is limited by the restricted linewidth of the Brillouin resonance which can be dramatically improved with the FIM-FAM interactions described here.

[0052] Brillouin processes excel at photonic signal processing because of the frequency selective gain or loss which occurs when a strong pump is detuned from the signal of interest by the resonant frequency (Fig.7). The ability to tune this gain / loss band by tuning the frequency of the pump field underlies the versatility of Brillouin-based processes for low- loss tunable photonic microwave filters. Beyond offering unprecedented filter resolutions FIM-FAM processes also offer the opportunity to make reconfigurable filters, where the filter linewidth, filter shape and central frequency can be continuously tuned by altering the pump spectrum.

[0053] 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: Simple bandpass filter over a broad instantaneous bandwidth

[0054] The first system will demonstrate the broadband frequency tunabilty of FIM- FAM-based narrow-linewidth filters. The system (Fig.8, Panel a) consists of modulating a laser with optical frequency ^^^^^^^^using an electrooptic phase modulator driven by an RF signal at frequency Ω^^^^^^^^, tunable from 0-20 GHz. The phase modulator creates an upper and lower sideband shifted by Ω^^^^^^^^, equal in amplitude but out of phase relative to the carrier (denoted as 0 and ^^^^). This modulated signal is injected into the fundamental port (LP01) of a mode selective coupler (MSC). In parallel, a frequency tunable Brillouin pump (^^^^^^^^) blue shifted from the optical sideband by a tunable frequency Ω is coupled into the higher order mode (LP11) of the MSC. The two optical fields in their respective spatial modes are coupled into a FIM-FAM device. FIM-FAM couples power from the pump to the blue-shifted opticalsideband when the detuning (Ω) is within the Brillouin gain band. A spatial mode filter (e.g. a single mode fiber) is used to reject the excess pump and the filtered signal is incident on a highspeed photodetector (PD) and the power of the beat tone (^^^^^^^^^^^^) between the carrier and the amplified sideband at Ω^^^^^^^^is measured as a function of Ωrf. The imbalance in the sideband amplitudes appears as a single RF tone on the detector.

[0055] To demonstrate the frequency tunability the study reproduces the FIM-FAM response at different values of Ω^^^^^^^^ranging from 0-20 GHz (Fig.8, Panel b). For each value of Ω^^^^^^^^the Brillouin pump frequency is swept such that the sideband is swept through the resonance and consequently its associated gain band is also tuned (Fig.8, Panel b). In the electrical domain this translates to a Lorentzian shaped pass-band response with the narrow linewidth tunable over 20 GHz of electrical frequency (Fig.8, Panel b), demonstrating the high-resolution frequency versatility offered by FIM-FAM devices. Example 2: Conventional notch filter based on anti-Stokes Brillouin loss

[0056] The second system demosntrates a simple notch filter based on FIM-FAM using the anti-Stokes sideband to selectively attenuate a desired frequency band. Whileanalogous demonstrations based on backward Brillouin scattering have linewidths of ~10 −30 ^^^^^^^^^^^^ FIM-FAM based devices can achieve >500x narrower linewidths while retaining the reconfigurability of prior devices. In this demonstration broadband RF data will be added to the carrier for notch filtering (Fig.9). The RF data is modulated onto a carrier (^^^^^^^^) using a single sideband modulator (SSB-MZM), which selectively modulates an upper sideband while suppressing the conjugate redshifted sideband. A Brillouin pump laser is red shifted from the region of interest by the Brillouin resonant frequency (Ω^^^^). This creates a loss band in the region of interest, where the filter depth is determined by the Brillouin gain (^^^^0^^^^^^^^) and the width is determined by the FIM-FAM linewidth. This system makes for a desirable demonstration of FIM-FAM notch filtering because is very simple to implement and requires minimal optimization. The simplicity of the device would also allow for studies on other practical aspects of the FIM-FAM filters including the long-time stability of devices. However, this setup requires large Brillouin gains for appreciable modulation depth notch filters, which may be sufficient but can nonetheless be avoided using the 4thapproach described below. Example 3: FIM-FAM-based bandpass filter with a modulated signal

[0057] To demonstrate the full suite of photonic processing functionalities possible with a FIM-FAM device, the next system demonstrates a narrow Brillouin based bandpassfilter. The architecture of this proposed experiment is similar to previous demonstrations which utilized backward Brillouin scattering. The setup (Fig.10) consists of modulating broadband data onto an optical carrier using an electrooptic phase modulator. Similar to other schemes described, a Brillouin pump is blue shifted from the frequency band intended to be filtered by the Brillouin resonant frequency Ω^^^^. This causes a small spectral band within the data to be selectively amplified, causing the amplitudes of the two sidebands to now be unequal. Excess pump is rejected by a mode filter and detected on a photodetector. The interference between the two unequal sideband on the photodetector yields the required signal within the bandpass. The width of the bandpass filter is determined by the FIM-FAM linewidth; this can also be broadened with multiple closely spaced pump tones. Additionally, multiple pump tones can be used to created multiple pass bands. FIM-FAM devices enable highly tailorable bandpass filters with unprecedented spectral resolution. Example 4: Interference-based FIM-FAM notch filter with improved rejection and notch depth

[0058] The fourth design implements a state-of-the-art interference-based notch filter optimized for maximizing notch depth with low Brillouin gains. This technique with backward Brillouin systems have been shown to achieve ultra-high rejection (~70 dB) of notch depth. Such systems could form the basis for next generation of microwave photonic filters with performance exceeding current systems by 2-3 orders of magnitude. In this design (Fig.11) RF data is modulated onto an optical carrier by using a Dual-Parallel Mach Zehnder Modulator (DPMZM, also known as an IQ modulator). The modulator is biased such that the two sidebands modulated on the carrier are of unequal amplitudes but opposite in phase. A frequency tuned Brillouin pump induces gain / loss in the spectral band of interest. The power of the Brillouin pump and the resulting gain / loss is optimized such that it equalizes the amplitudes of the two sidebands within a narrow spectral band of interest. On detecting the signal on a photodetector, the two sidebands destructively interfere within the narrow band of interest (where their amplitudes have been equalized) to create a strong notch filter. The notch depth depends on the contrast of destructive interference controlled through the Brillouin gain and the relative phase of the two sidebands. The width of this notch filter isgiven by

[0024] Δ^^^^ = Γ�^^^^ / ln(.5(^^^^^^^^ + 1)) − 1, which for a loss of 4 dB gives Δ^^^^ = 0.6Γ.Interestingly, the width of the notch through this technique can be made smaller than the natural Brillouin linewidth.

[0059] This study showed narrowing by a factor of ½ with a gain of 11 dB and obtained notch depths exceeding 50 dB with linewidths of ~32 MHz.

[0060] FIM-FAM based filters of this type could yield notch filters with linewidths as much as 500x narrower with 70 dB rejection ratios with lower pump requirements and shorter lengths because of the large gain afforded by the FIM-FAM process. Example 5: Novel Filter design for either FIM-FAM or any other Brillouin device

[0061] This design extends the instantaneous bandwidth of FIM-FAM bandpass filters. This filter consists of two stages (Fig.12, Panel a). In the first stage (Fig.12, Panel b), the laser phase modulated by the RF signal travels through the FIM-FAM device to the right, and the first photodetector PD1 receives a dual-band bandpass filter response, where the central frequencies of those two bands are separated by twice the FIM-FAM resonant frequency determined by the device. In the second stage (Fig.12, Panel c), another laser with a different wavelength is phase modulated by the dual-band response then travels through the FIM-FAM device to the left, received by the second photodetector PD2. A single-band bandpass filtering response with arbitrary central frequency can be realized at the photodetector output.

[0062] In more detail, in the first stage (Fig.12, Panel b), for a targeted central filter frequency of Ω^^^^, the provided broadband RF signal is modulated onto the optical carrier (carrier 1, blue) with frequency ^^^^^^^^1using an electrooptic phase modulator (PM1). Two optical sidebands on both sides of ^^^^^^^^1on the optical spectrum will be created, with the same amplitude but out of phase. Compared to the carrier, the higher frequency sideband has the same phase, while the lower frequency sideband has a relative ^^^^ phase difference. At the mode selective coupler (MSC1), the Brillouin pump (pump 1, cyan) at a frequency ^^^^^^^^1islaunched into the higher-order mode. Here, ^^^^^^^^1 = ^^^^^^^^1 + Ω^^^^ − Ω^^^^1, where Ω^^^^1 is the FIM-FAM frequency at an optical frequency ^^^^^^^^1. Pump 1 can be derived from the carrier 1 with a null-biased intensity modulator and optical bandpass filters. Then in the FIM-FAM device, pump 1 creates gain and loss bands on the modulated carrier 1 in the fundamental opticalmode through the FIM-FAM process, at optical frequencies ^^^^^^^^1 − Ω^^^^1respectively. Pump 1 is removed from the system after the second mode selective coupler (MSC2). The remaining signal reaches the first photodetector PD1. Throughout the whole signal spectrum, most of the signal cancels out through interference between the lower and higher frequency sidebands, except at those gain / loss bands created by the FIM-FAMprocess. A new RF signal is generated, with only two frequency bands at Ω^^^^ − 2Ω^^^^1 (=^^^^^^^^1 − Ω^^^^1 − ^^^^^^^^1) and Ω^^^^ (= ^^^^^^^^1 + Ω^^^^1 − ^^^^^^^^1), and with linewidths determined by theFIM-FAM acoustic linewidth.

[0063] For the second stage with more detail (Fig.12, Panel c), the output RF signal from the first stage (amplified first if needed) is sent to the phase modulator PM2, modulating another carrier (carrier 2, purple) with frequency ^^^^^^^^2(this must be >1nm from the other laser to avoid phonon interactions between the two stages). There are four dominant frequencysidebands in the modulated signal, two lower frequency sidebands at ω^^^^1 − Ω^^^^ and ω^^^^1 −Ω^^^^ + 2Ω^^^^1, two higher frequency sidebands at ω^^^^1 + Ω^^^^ − 2Ω^^^^1 and ω^^^^1 + Ω^^^^. Through acirculator, the modulated carrier 2 is sent back into the fundamental mode of the FIM-FAM device from the mode selective coupler MSC2, along with another Brillouin pump (pump 2, green) in the higher-order optical mode. The frequency of this Brillouin pump is designatedat ^^^^^^^^2 = ^^^^^^^^2 −− Ω^^^^2, so that it will only decrease the power on the lowest frequencysideband in the signal through the FIM-FAM interaction. Here, Ω^^^^2is the FIM-FAM frequency in this stage, which differs from Ω^^^^1because of the laser wavelength dependence of the FIM-FAM frequency. The modulated signal is then collected from the mode selective coupler MSC1, and sent into the photodetector PD2. The output of the photodetector will bean RF passband filter centered at the frequency Ω^^^^ = ^^^^^^^^2 − (^^^^^^^^2 − Ω^^^^).

[0064] This design ultimately leads to unprecedented ultra-narrow filter bandwidths with modulator limited instantaneous bandwidth (i.e. >10GHz) and flexible control over the RF vs. optical power requirements. This study investigates each of these designs with the fiber FIM-FAM devices described above to determine performance and quantitative system requirements. Example 6: Single-stage Notch-filter demonstrating ultranarrow linewidth and minimal noise

[0065] A representative single-stage design is a state-of-the-art interference-based notch filter optimized for maximizing control of the Brillouin-based notch depth. This technique with backward Brillouin systems have been shown to achieve ultra-high rejection (>60 dB) of notch depth. A FIM-FAM version could form the basis for next generation microwave photonic filters with performance exceeding current systems by 2-3 orders of magnitude. In this design (Fig.13), RF data is modulated onto an optical carrier by using a Dual-Parallel Mach Zehnder Modulator (DP-MZM). The modulator is properly biased with three input DC voltages, so that the relative phases and amplitudes among the carrier and two sidebands can be flexibly controlled. To achieve the targeted notch filtering, the twosidebands modulated on the carrier are biased to be of unequal amplitudes but opposite in phase. A frequency tuned Brillouin pump induces gain in the spectral band of interest, and induces loss in another spectral band, distanced from the previous one by double the FIM- FAM frequency. The gain band will have a narrower 3-dB bandwidth compared to the FIM- FAM linewidth, where the loss band bandwidth will be wider than the FIM-FAM linewidth. This is because the ratio between the filter bandwidth and the FIM-FAM linewidth is sqrt(G / ln(0.5(exp(G)+1))-1), which will be smaller than 1 with positive G (gain band) and larger than 1 with a negative G (loss band). The power of the Brillouin pump and the resulting gain is optimized such that it equalizes the amplitudes of the two sidebands within a narrow spectral band of interest. Before the photodetector, the pump is completely separated from the probe signal via an output mode selective coupler. As any residual power from the pump will deteriorate the performance of the final RF filter, this mode coupler together with the following waveguide will be refined during fabrication rounds to minimize the pump leakage. On detecting the signal on a photodetector, the two sidebands destructively interfere within the narrow band of interest to create a strong notch filter. The notch depth depends on destructive interference of the two sidebands. The remaining part of the RF spectrum partially destructively interferes and remains undistorted in the RF domain, except near the region where the extra FIM-FAM introduced signal loss is located. This extra distortion is <0.1 dB with the large FIM-FAM enabled gain.

[0066] One key advantage of the FIM-FAM based filters, compared to filters based on other types of Brillouin scattering including the backward and forward intramodal ones, is the much narrower achievable filter bandwidth. For the interference-based Brillouin RF filters, the filter bandwidth Δ^^^^ is proportional to the Brillouin acoustic linewidth Γ. In the gain-based FIM-FAM notch filter, as illustrated in Fig.13, the lower frequency sidebandcreating the final notch experiences an amplification, and the total gain ^^^^ = ^^^^^^^^^^^^^^^^^^^^, where^^^^^^^^is the Brillouin gain in the unit of ^^^^−1^^^^−1, ^^^^^^^^is the pump power, and ^^^^ is the length of the Brillouin active waveguide. In a loss-based notch filter utilizing the higher frequencysideband, ^^^^ = −^^^^^^^^^^^^^^^^^^^^ instead. As a result, the gain-based filter bandwidth will be narrowerwith a stronger Brillouin interaction, while the loss-based filter bandwidth will be wider with a stronger interaction. The narrower acoustic linewidth in the proposed FIM-FAM process, which can be several orders of magnitudes smaller compared to other well-established Brillouin processes, also brings down the filter bandwidth from at least ~10MHz all the way down into the kHz regime with a proper waveguide design. In addition, the huge Brillouingain ^^^^^^^^also eases the requirements on ^^^^^^^^^^^^, beneficial for the filter system with lower power consumption, less optical power handing issues, and smaller waveguide footprints.

[0067] In microwave photonic filters, the two most prominent performance parameters are the link gain and the noise figure. Link gain describe the RF output power from the final detector compared to the input RF power to the system.0 dB link gain, representing a situation where the RF amplitude remains unaffected, can be achieved with large signal gain in the FIM-FAM process. This gain is usually enhanced by increasing the pump power in a physically built waveguide, which also means that the relative amplitude between two sidebands will be more drastic. Ultimately, the relative amplitude will be capped due to the imperfectness of the real modulator and the accuracy and stability of the voltage supplies.

[0068] Another important factor is the noise figure, calculated with the total noise power in the system and the link gain value. In this notch filter system, the noise sources to consider include the thermal noise and the shot noise on the detector, the RIN noise from the probe and pump lasers, the ASE amplification noise from the possible fiber amplifiers in the system, and the Brillouin thermal noise from the FIM-FAM process. As a result, noise in the filtering system will be influenced by multiple factors including the required pump power and the optical power on the photodetector. Targeting 0 dB out-of-notch link gain, <20 dB noise figure can be achieved with commercially available components, including low RIN-noise, high-power lasers, a low ^^^^^^^^modulator, and a large power tolerance photodetector. Specifically, with a 120-mW probe laser with -165 dB / Hz RIN noise, a DP-MZM with a 4 V half-wave voltage at the target RF frequency, an on-chip pump power at 90 mW, a detector power of 5 mW, the system noise figure is anticipated to be around 16 dB in the out-of-notch frequency bands far away from the notch center (Fig.14). The half-wave voltage of the DP- MZM is the limiting factor, and if it can be further reduced to 0.1 V, a notch filter with 90 mW on-chip pump power and 200 μW detector power offers ~5 dB noise figure with 0 dB link gain. The noise figure will be higher near the notch, and near another RF frequency lower than the notch by twice the FIM-FAM frequency, primarily due to the Brillouin thermal noise that experienced the high FIM-FAM gain; the bandwidth of the noise will be narrow, however, due to the narrow linewidth of the FIM-FAM interaction.

[0069] The DC bias drifts, power fluctuations from the amplified lasers, and the Brillouin thermal noise at the notch frequency can limit the notch suppression ratio. Commercial DC biases with 1 mV resolution and amplifiers with short-term output power stability better than 0.05 dB are more than enough to achieve >60 dB suppression ratio withproper active feedback controls. With the proposed system parameters, Brillouin thermal noise will not be the limit with a reasonable RF input power. FIM-FAM therefore improves on the state-of-the-art techniques by orders of magnitude with low pump requirements and small PIC devices. Example 6: Dual-stage Notch-filter demonstrating ultranarrow linewidth and wide instantaneous bandwidth

[0070] The instantaneous bandwidth over which there is zero distortion from the unused Brillouin sideband can be extended with a dual-stage notch-filter design (Fig.15). The first stage contains a phase modulator, which generates two sidebands with the same amplitude but opposite phase. After a left-to-right FIM-FAM interaction, a gain band and a loss band appear on the optical sideband spectrum around the pump frequency. At the first photodetector, the uninfluenced RF signal will perfectly destructively interfere with zero RF output amplitude, yet the gain and loss bands will only partially interfere with the other sideband, leading to two passbands at the detector output, separated by twice the FIM-FAM frequency. In this first stage, with a 120-mW probe laser with -165 dB / Hz RIN noise, and a phase modulator with a 4 V half-wave voltage, a noise figure of only 1 dB can be achieved with ~120 mW pump power, 400 μW detector power at a 10 dB link gain.

[0071] In the second stage, after reloading the RF output onto another phase modulator, a right-to-left FIM-FAM interaction, or other types of photonic bandpass filtering with bandwidth much smaller than twice the FIM-FAM frequency will be suitable to filter out one of the passbands from the first stage, creating a single-band bandpass filtering response. Here we demonstrate this with a right-to-left FIM-FAM interaction, and this probe laser will be tuned at a different wavelength compared to the first probe laser, so that they do not interfere either optically or acoustically inside the FIM-FAM waveguide. The signal will then be received by the second photodetector as a single-band bandpass filtering in the RF domain. To convert the bandpass response into a notch response, another optical signal will be generated with the first probe laser and an intensity modulator modulated after with the RF data, which is then also received by the same photodetector. Due to the large wavelength separation between two probe lasers, it will not interact with the bandpass RF response. An optical delay line (ODL) is used to control the time difference between these two RF signals, so that they can have a ^^^^ phase difference in the RF domain to cancal out with each other. By matching their amplitudes at the passband, the cancellation yielding a notch response can be generated. The second stage is designed to have -10 dB link gain for the out-of-notch signal, so that the system link gain remains as the targeted 0 dB.

[0072] With a 120-mW probe laser with -165 dB / Hz RIN noise, a phase modulator and a intensity modulator both with 4 V half-wave voltages at the target RF frequency, an on- chip pump power at only 30 mW, a detector power of 3 mW, the second stage noise figure is anticipated to be around 23 dB in the out-of-notch frequency bands far away from the notch center, resulting in a total noise figure around 24 dB. Like the first notch filter, if the half- wave voltages can be further reduced to 0.1 V, a second stage with ~20 mW on-chip pump power and 300 μW detector power offers ~5 dB system noise figure with 0 dB link gain.

[0073] In this single notch filter, the major limiting factors of the suppression ratio will be the DC bias drift on the intensity modulators, power fluctuations from the amplified lasers, the Brillouin thermal noise that peaks at the notch frequency, and the precision of the optical delay line. With carefully designed feedback loops to control optical powers, DC voltages and stage movements, commercial components will be enough to achieve >60 dB suppression ratio with all four factors considered. The dual stage FIM-FAM notch filter offers broad instantaneous bandwidth limited only by the bandwidth of RF modulators. Example 7: Dual Stage Filter

[0074] The instantaneous bandwidth of the simple single-stage bandpass filter based on sub-MHz taper FIM-FAM is limited by the pump signal leaking into the detector as well as the other Brillouin sideband from the Stokes-Anti-Stokes pair. The instantaneous bandwidth of the demonstrated single-stage filter was therefore limited to ~ 500 MHz. To overcome this limitation, a second bandpass filtering stage can be used to further suppress the unwanted microwave signal to expand the instantaneous bandwidth of the whole filtering system. To demonstrate this idea, a second bandpass filtering stage based on the same destructive-interference approach, but with backward Brillouin scattering in a standard single-mode fiber with ~10 MHz 3-dB bandwidth (Fig.16). In the second filtering stage, the RF output signal from the previous small instantaneous bandwidth RF filter system is sent to a phase modulator to modulate the optical carrier, which then propagates through a standard single mode fiber. MetroCor fiber is used here with opposite dispersion than the SMF-28 fiber used in the remaining part of the system to maximize the background suppression of the whole filter. Backward Brillouin scattering happens in the 100-meter MetroCor fiber at ~10.5 GHz with the strong Brillouin pump propagating in the opposite direction as the carrier. When the frequency separation between the carrier and the pump is at the phase-matched condition, one of the carrier sidebands generated by the phase modulation is amplified or reduced by the Brillouin pump. Here, the pump frequency is placed higher than the carrier exactly by the designed filtering frequency plus the resonant frequency of the MetroCor fiber,so that the RF signal originated from the pump leakage and the other Brillouin sideband from the first filtering stage can be suppressed for a higher instantaneous bandwidth of the whole system.

[0075] Initial results without thorough optimizations have already revealed >18 dB background suppression within the components-limited frequency range from 1-19 GHz with the central frequency at 9 GHz (Fig.17). The filtering response from the second stage itself comes from the backward Brillouin response of the MetroCor fiber, and several peaks are anticipated. The highest RF response comes from point A at the designed filter central frequency, and the RF signal at the point B comes from the pump leakage at the first stage, ~250 MHz away from point A. The RF signal at the point C comes from the other undesired FIM-FAM sideband at the first stage, ~ 500 MHz away from point A. The RF signal at the point D comes from the other weaker Brillouin responses from the MetroCor fiber in the second stage other than the major peak, also ~ 500 MHz away from point A. The pump leakage can be further reduced by fine-tuning the polarization state of the optical modes throughout the taper and optimizing the mode selective couplers as well as the transmission of the taper device, to be below the other prominent unwanted RF signals in the whole spectrum like at the points C and D, leading towards a high RF suppression over 38 dB over the 20 GHz instantaneous bandwidth. The whole system is still arbitrarily tunable by simultaneously tuning the frequencies of the Brillouin pumps in both filtering stages. The MetroCor fiber can be substituted with other Brillouin devices with larger interaction strengths (better RF link gain), less mediated acoustic modes (less unwanted RF peaks in the final filter spectrum), higher acoustic frequencies (larger instantaneous bandwidth) and smaller footprints. Example 8: Tunable Brillouin-based Microwave Photonic Bandpass Filter with sub-MHz Bandwidth

[0076] This study demonstrates a continuously tunable, ultranarrow bandwidth photonic bandpass filter based on FIM-FAM in a few-mode fiber taper. Wideband frequency tunability is experimentally demonstrated by tuning the filter response over 10 GHz (7-19 GHz), limited only by current component constraints, with an out-of-band rejection ratio exceeding 25 dB. The filter bandwidth at the 3-dB point is demonstrated to be approximately 270 kHz at all measured frequencies, which, to the best of our knowledge represents an order of magnitude bandwidth improvement for Brillouin-based continuously tunable photonic bandpass filters.

[0077] The FIM-FAM based bandpass filter system is demonstrated through a technique based on selective phase modulation sideband modification (Fig.18). The RF data is first modulated onto the optical carrier with a phase modulator, with the generated higher (lower) frequency sideband in-phase (out-of-phase) with the carrier. The modulated carrier is then coupled into the fundamental mode of the FIM-FAM active few-mode fiber taper through a mode-selective coupler. A distinct Brillouin pump is coupled with the other port of the same coupler into a single higher-order mode, and spectrally positioned such that the higher frequency carrier sideband coincides with the FIM-FAM Stokes response relative to the pump (Fig.18, Panel a-b). The Brillouin pump then selectively amplifies the part of the sideband within the Lorentzian FIM-FAM linewidth, breaking the amplitude symmetry between the two out-of-phase carrier sidebands. Another mode selective coupler then removes the excess pump from the signal, and the two sidebands individually beat with the carrier with a relative π phase difference on the final detector. Non-perfect destructive interference only occurs for the RF signal corresponding to the FIM-FAM amplified optical sideband, creating a bandpass response with the passband positioned by the FIM-FAM process. To measure the filtering response, a tunable single-frequency RF source is applied to the phase modulator, and the RF power is measured from the detector output at the same frequencies. This frequency is continuously swept over a broadband to represent RF data (Fig.18, Panel c-d).

[0078] In prior narrowband FIM-FAM devices based on fiber tapers, the transmission of the higher-order optical mode was limited by the non-adiabaticity of the taper transition regions. Here, through an improved fabrication procedure to be described elsewhere, a fiber taper is developed with improved adiabaticity leading to an increase in the available pump power for FIM-FAM. The Brillouin pump in the TM01 higher-order mode is first positioned for a filter response centered at 13 GHz, yielding a measured 3-dB bandwidth of 275 kHz (Fig.19, Panel a). The out-of-band rejection is 29 dB over 500 MHz, with small residual sidebands from undesired high-order optical modes that have not yet been fully suppressed. The instantaneous bandwidth can be increased beyond 500 MHz through mitigation of mode cross-coupling leading to residual pump in the detected signal. The central filter frequency is varied over the bandwidth of the currently implemented modulators and detectors, yielding a measured filter response from 7 to 19 GHz, with the 3-dB bandwidth varying negligibly around 273 kHz (±3 kHz in Fig.19, Panel b), and the out-of-band rejection exceeding 25 dB over 500 MHz in all cases, without additional optimization. From the sub-MHz level demonstrated here, the filter bandwidth can be further reduced through improving the devicehomogeneity or through enhancing the stimulated interaction with increased pump powers or longer lengths of the FIM-FAM device.

[0079] In summary, a FIM-FAM based photonic bandpass filter platform is demonstrated using a few-mode fiber taper. Sub-MHz bandwidth (~270 kHz) is measured over a wide and continuously tunable range (7-19 GHz shown here) with large out-of-band rejection ratios (> 25 dB over 500 MHz in all cases measured). Photonic devices leveraging FIM-FAM are well suited for microwave and signal-processing applications requiring large frequency tailorability, wideband operation, and high spectral resolutions.

[0080] 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.

[0081] 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 any sequence which is effective to meet the objectives there intended, unless the context specifically indicates the contrary.

Claims

WHAT IS CLAIMED IS:

1. A method of filtering using inter-modal Brillouin scattering, comprising a stage of: generating by a first probe light source an optical field having a first optical signal in a first optical waveguide; phase modulating via a first phase modulator the first optical signal by broadband radiofrequency (RF) data containing a first carrier to produce a phase modulated first optical signal; producing an input higher frequency optical sideband and an input lower frequency optical sideband on either side of the phase modulated first optical signal; generating by a first Brillouin pump light source a second optical field having a second optical signal in a second optical waveguide; coupling through a mode combiner the phase modulated first optical signal to the second optical signal, so that the first optical signal and second optical signal become a first set of coupled optical signals within a multi-mode third optical waveguide, and the first optical signal and the second optical signal have different spatial optical modes; connecting via the multi-mode third optical waveguide the mode combiner to an inter- modal Brillouin device; receiving the first set of coupled optical signals in the inter-modal Brillouin device; driving an acoustic mode in the inter-modal Brillouin device, wherein gain and loss bands are created by the second optical signal on the phase modulated first optical signal through inter-modal Brillouin scattering; receiving through a mode splitter connected to the inter-modal Brillouin device the first set of coupled optical signals exiting the inter-modal Brillouin device, wherein the mode splitter removes the second optical signal, and the phase-modulated first optical signal with gain and loss sidebands remains as a first exit signal; receiving the first exit signal on a first photodetector, wherein the first exit signal is passed through the first photodetector; and outputting an RF signal from the first exit signal passed through the first photodetector.

2. The method of filtering of Claim 1, wherein the first optical signal is a fundamental optical mode.

3. The method of filtering of Claim 1, wherein the second optical mode is a higher- order optical mode.

4. The method of filtering of Claim 1, wherein the inter-modal Brillouin device is a FIM-FAM device that comprises a suspended waveguide that is axially homogeneous.

5. The method of filtering of Claim 4, wherein the inter-modal Brillouin device is a FIM-FAM device that comprises a suspended waveguide that is adiabatically tapered.

6. The method of filtering of any one of Claims 1-5, further comprising a second stage of: generating by a second probe light source an optical field having a third optical signal in a fourth optical waveguide; phase modulating via a second phase modulator the third optical signal by the RF signal of Claim 1 for a second filtering frequency band to form a phase modulated third optical signal, wherein said second carrier is different from the first carrier; producing a first pair of higher frequency optical sidebands, wherein the first pair comprises a first higher frequency optical passband and a second higher frequency optical passband, and a second pair of lower frequency optical sidebands, wherein the second pair comprises a first lower frequency optical passband and a second lower frequency optical passband, wherein said first pair and said second pair on either side of the phase modulated third optical signal; generating by a second pump light source an optical field having a fourth optical signal in a fifth optical waveguide, wherein the frequency of the fourth optical signal is selected so as to increase or decrease the power on any one of the optical passbands on either side of the phase modulated third optical signal; coupling through a mode combiner the phase modulated third optical signal to the fourth optical signal to become a second set of coupled optical modes within a shared waveguide, and the third optical signal and the fourth optical signal have different spatial optical modes; receiving through a frequency filter device the second set of coupled optical modes; receiving through a mode splitter connected to the frequency filter device the second set of coupled optical modes exiting the frequency filter device, wherein the mode splitter removes the fourth optical signal and the phase-modulated third optical signal remains as a second exit signal; receiving the second exit signal through a second photodetector, wherein the second exit signal is passed through the second photodetector; and outputting an RF signal from the second exit signal passed through the second photodetector.

7. The method of filtering of Claim 6, wherein the second pump light source is a Brillouin pump light source.

8. The method of filtering of Claim 6, further comprising amplifying at least one RF signal to create at least one amplified RF signal.

9. The method of filtering of Claim 6, wherein the frequency filter device is an inter- modal Brillouin device.

10. The method of filtering of Claim 6, wherein the inter-modal Brillouin device is a FIM-FAM device.

11. The method of filtering of Claim 10, wherein the FIM-FAM device comprises a suspended waveguide that is axially homogeneous.

12. The method of filtering of Claim 10, wherein the FIM-FAM device comprises a suspended waveguide that is adiabatically tapered.

13. The method of filtering of any one of Claims 1-12, wherein the link gain is 0 dB.

14. The method of filtering of any one of Claims 1-12, wherein the noise figure is less than 20 dB.

15. The method of filtering of any one of Claims 1-14, wherein at least one mode combiner or mode splitter is a spatial mode filter.

16. The method of filtering of any one of Claims 1-14, wherein at least one phase modulator is a single sideband modulator.

17. The method of filtering of any one of Claims 1-14, wherein at least one phase modulator is an electrooptic phase modulator.

18. The method of filtering of any one of Claims 6-17, wherein there is an increase of power of one selected from the group consisting of the first higher frequency optical passband, or the second higher frequency optical passband, or the first lower frequency optical passband, or the second lower frequency optical passband.

19. The method of filtering of any one of Claims 6-17, wherein there is a decrease of power of one selected from the group consisting of the first higher frequency optical passband, or the second higher frequency optical passband, or the first lower frequency optical passband, or the second lower frequency optical passband.

20. The method of filtering of any one of Claims 1-19, wherein the input higher frequency sideband and input lower frequency sideband are of unequal amplitudes and opposite in phase.

21. The method of filtering of any one of Claims 1-19, wherein said input higher frequency optical sideband and said input lower frequency optical sideband have same amplitude but are out-of-phase.

22. The method of filtering of any one of Claims 1-19, wherein said input higher frequency optical sideband and said input lower frequency optical sideband have different amplitudes and are out-of-phase.

23. The method of filtering of Claim 6, further comprising a third stage of: generating an fifth optical signal with a probe light source; passing the fifth optical signal through an optical delay line; modulating the fifth optical signal with an intensity modulator to get the third exit signal; receiving the third exist signal on the second photodetector, with a 180 degree phase difference compared to the received second exist signal in the RF domain; and outputting an RF signal from the mixed second and third exit signals passed through the second photodetector.

24. A system of filtering using inter-modal Brillouin scattering, comprising: a first probe light source that generates a probe optical field having a first optical signal in a first optical waveguide; a first phase modulator that modulates the first optical signal by broadband radiofrequency (RF) data containing a first carrier to produce a phase modulated first optical signal; a first Brillouin pump light source that generates a second optical field having a second optical signal in a second optical waveguide; a mode combiner that is input connected to the first optical waveguide and the second optical waveguide, and output connected to a multi-mode third optical waveguide; an inter-modal Brillouin device connected to the mode combiner via the multi-mode third optical waveguide at its input, and having a multi-mode fourth optical waveguide at its output; a mode splitter input connected to the inter-modal Brillouin device via the multi-mode fourth optical waveguide and is output connected to a fifth optical waveguide; and a first photodetector, wherein the photodetector is input connected by a fifth optical waveguide to the mode splitter.

25. The system of filtering of Claim 24, further comprising:a second probe light source that generates a third optical signal in a sixth optical waveguide; a phase modulator that modulates the third optical signal; a second Brillouin pump light source that generates a fourth optical field having a fourth optical signal in a seventh optical waveguide; a mode combiner; a filter frequency device; and a second photodetector.

26. The system of Claim 25, further comprising: at least one optical amplifier.

27. The system of Claim 25, further comprising: at least one acoustic amplifier.

28. The system of any one of Claims 25-27, wherein the filter frequency device is an inter-modal Brillouin device.

29. The system of Claim 28, wherein the inter-modal Brillouin device is a FIM-FAM device.

30. The system of Claim 29, wherein the FIM-FAM device comprises a suspended waveguide that is axially homogeneous.

31. The system of Claim 29, wherein the FIM-FAM device comprises a suspended waveguide that is adiabatically tapered.

32. The system of any one of Claims 25-31, further comprising: an optical delay line connected to a probe light source; and an intensity modulator connected to the optical delay line and to the second photodetector.

33. The system of any one of Claims 24-32, wherein at least one mode combiner or mode splitter is a spatial mode filter.

34. The system of any one of Claims 24-32, wherein at least one phase modulator is a single sideband modulator.

35. The system of any of Claims 24-32, wherein at least one phase modulator is an electrooptic phase modulator.

36. The system of any one of Claims 24-35, wherein at least one optical waveguide is an optical fiber.

37. A filter system for inter-modal Brillouin scattering, comprising: a phase modulator; a mode combiner, connected to the phase modulator by at least one optical waveguide;a frequency filtering device connected to the mode combiner by a multi-mode optical waveguide; a mode splitter connected to the frequency filtering device by a multi-mode optical waveguide; and a photodetector connected to the mode splitter by a single mode optical waveguide.

38. The filter system of Claim 37, further comprising: at least one amplifier, wherein said at least one amplifier is either an optical amplifier or an acoustic amplifier; and a second phase modulator.

39. The filter system of Claim 37, wherein the filter frequency device is an inter- modal Brillouin device.

40. The filter system of Claim 39, wherein the inter-modal Brillouin device is a FIM- FAM device.

41. The filter system of Claim 40, wherein the FIM-FAM device comprises a suspended waveguide that is axially homogeneous.

42. The filter system of Claim 40, wherein the FIM-FAM device comprises a suspended waveguide that is adiabatically tapered.

43. The method of any one of Claims 1-23, wherein the acoustic mode is a fundamental acoustic mode.

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