Electro-opto-mechanical radio-frequency oscillator driven by guided acoustic waves in standard single-mode fiber

An opto-electronic radio-frequency oscillator that is based on forward scattering by the guided acoustic modes of a standard single-mode optical fiber is proposed and demonstrated. An optical pump wave is used to stimulate narrowband, resonant guided acoustic modes, which introduce phase modulation to a co-propagating optical probe wave. The phase modulation is converted to an intensity signal at the output of a Sagnac interferometer loop. The intensity waveform is detected, amplified and driven back to modulate the optical pump. Oscillations are achieved at a frequency of 319 MHz, which matches the resonance of the acoustic mode that provides the largest phase modulation of the probe wave. Oscillations at the frequencies of competing acoustic modes are suppressed by at least 40 dB. The linewidth of the acoustic resonance is sufficiently narrow to provide oscillations at a single longitudinal mode of the hybrid cavity. Competing longitudinal modes are suppressed by at least 38 dB as well. Unlike other opto-electronic oscillators, no radio-frequency filtering is required within the hybrid cavity. The frequency of oscillations is entirely determined by the fiber opto-mechanics.

2 along a section of fiber. The light wave is detected at the output of the fiber, and the recovered RF signal is fed back to modulate the optical input. When the feedback gain is sufficiently high, stable self-sustained RF oscillations may be achieved. OEOs can provide RF tones with extremely low phase noise [3], and they are pursued for applications in coherent communication, radars and precision metrology [4]. OEO cavities are typically long, and support a large number of longitudinal modes that are separated by a comparatively narrow free spectral range. The selection of the specific frequency of oscillations is often aided by a narrow inline RF filter.
Various photonic devices exhibit mechanical resonances at radio and microwave frequencies.
The interactions between guided light waves and these mechanical modes may give rise to microwaves generation. In one example, the coupling between whispering-gallery optical and mechanical modes in a silica micro-sphere led to oscillations at 11 GHz [5]. Backward stimulated Brillouin scattering (SBS) processes in wedge-shaped silica resonators [6,7], chalcogenide glass waveguides [8], and standard optical fibers [9,10] were also used in the generation of microwaves up to 40 GHz frequencies.
In this work we demonstrate stable RF oscillations that are driven by GAWBS in a standard single-mode fiber (SMF). An optical pump wave is used to stimulate acoustic vibrations.
These vibrations, in turn, induce phase modulation to a co-propagating optical probe wave of a different wavelength. The phase modulation spectrum consists of a series of narrowband resonances, each corresponding to a different acoustic mode. The magnitude of GAWBS in SMF is orders of magnitude weaker than in PCFs and in micro-structured fibers, and it is not sufficient to introduce self-oscillations. To work around this limitation, feedback is provided in the form of a hybrid electro-opto-mechanical cavity. A Sagnac loop configuration, which was initially proposed towards the characterization of GAWBS [14,18], is used to convert the probe phase modulation to an intensity signal. The detected waveform is then amplified and fed back to modulate the pump wave. With sufficient optical pump power and RF amplification, the cavity reaches stable oscillations. Unlike most OEO realizations, the frequency of operation is entirely determined by the fiber opto-mechanics. No electrical RF filter is used.
The principle is experimentally demonstrated using a 200 meters long section of SMF. Stable oscillations are obtained at 319 MHz, the frequency of the guided acoustic mode for which phase modulation of the probe wave is the most efficient. Scattering due to competing, weaker acoustic modes does not match the hybrid cavity losses, and oscillations at the corresponding frequencies are strongly suppressed. Furthermore, the linewidth of the acoustic resonance is narrow enough to support oscillations at a single longitudinal mode of the hybrid cavity. Oscillations at the frequencies of adjacent longitudinal modes are strongly suppressed as well. 4 Optical fibers support several classes of guided acoustic modes. Optical stimulation and scattering in SMF is the most efficient for radial modes, denoted herein as 0m R where m is an integer. Each mode is characterized by a cut-off frequency m  and a linewidth m  [12,13].
The material displacement in GAWBS by 0m R modes is purely radial, and the associated strain field is entirely transverse. The normalized displacement profile is given by [12,13]: Here a is the cladding radius, The phase modulation spectrum The instantaneous phase modulation of the probe wave At the acoustic resonance frequencies, we obtain [16]: Opto-mechanical phase modulation was measured experimentally in a 200 meters-long SMF section and in a 1 km-long commercial highly nonlinear fiber (HNLF). Both fibers were subsequently used in demonstrations of electro-opto-mechanical oscillations. (For details of the measurement setup and procedures, see [14,18,21]). Figure 1 µm) are shown in Fig. 1(b) and Fig. 1(c)   In conclusion, electro-opto-mechanical RF oscillations in SMF were proposed and demonstrated experimentally. Oscillations are reached due to forward, intra-modal scattering by guided acoustic modes of the fiber, which couple the optical pump and probe waves. The PSD of scattering by guided acoustic waves consists of a series of resonances, which are sufficiently narrow to restrict the operation of the OEO to a single frequency with no electrical RF filtering. The RF waveform propagates as an electrical signal along part of the hybrid cavity, takes up the form of a modulated optical carrier in another part, and also assumes the form of a mechanical vibration. The results can provide a link between the OEO community, who works in SMF and seldom considers guided acoustic waves, and the optomechanics community, who for the most part works in specialty fibers and does not focus on 10 OEOs. Both communities might consider the opto-mechanics of SMF too weak to be employed. The method presented herein works around that difficulty. This concept has several limitations. Tuning of the oscillations frequency is very limited, opto-mechanical interactions are much weaker than those observed in PCFs or in microstructured fibers, and the phase noise of the RF output is not as low as those of state-of-theart OEOs that have been developed over 20 years [2][3]24]. However, the use of GAWBS towards frequency discrimination in OEOs can be regarded as a complementary mechanism, rather than a competing one. Opto-mechanics may be incorporated alongside existing lowphase-noise techniques [24], such the use of dual fiber loops, in attempt to enhance performance even further. The phase noise performance of OEOs is known to improve with the cavity propagation delay [2,3]. Long cavities would be simpler to implement based on SMF, which is readily available to everyone, than in using micro-structured fibers or PCFs.
Future work would include a comprehensive noise analysis, and address the incorporation of GAWBS in advanced OEO setups [24].