1. Introduction

Opto-electronic oscillators are sources of microwave-frequency tones that may reach very low noise levels [1,2]. In a typical arrangement, a radio-frequency electrical signal modulates an optical carrier wave at the input of an optical medium. Following optical propagation, the waveform is retrieved in the electrical domain through photo-detection at the far end. The detected signal is electrically amplified and fed back to modulate the optical input. Given sufficient gain, the opto-electronic loop may be driven into oscillations [1,2]. The phase noise levels of opto-electronic oscillators can be as low as -163 dBc × Hz^-1 [3]. The delay of the waveform typically relies on long optical fiber paths [1–3]. In many implementations, in-line radio-frequency filters are required to select a single frequency of operation from many closely spaced longitudinal modes of long feedback loops.

Much effort is dedicated to the realization of opto-electronic oscillators based on photonic integrated circuits. In one landmark example, Maleki demonstrated a microwave frequency source based on a whispering gallery mode resonator in lithium niobate [4]. The device relied on the electro-optic effect in the resonator material [4]. In another successful demonstration, Merklein and coworkers employed frequency-selective Brillouin amplification of a modulation sideband in a chalcogenide glass planar waveguide to reach oscillations [5]. Tang et al. realized an entire oscillator comprised of a modulated laser source, delay waveguide, detector, and associated electronics in a single indium-phosphide based device [6]. Other examples involved silicon photonic circuits: Zhang and Yao integrated the modulator element, a micro-disk resonator filter, and a detector in a silicon module [7]. Do et al. employed a narrowband silicon-photonic resonator filter as part of an opto-electronic oscillator [8]. However, the optical delay that can be accumulated over photonic-integrated waveguides is limited.

Radio-frequency oscillators are also commonly realized based on electro-mechanics in piezoelectric substrates [9,10]. An electrical waveform is applied to a pattern of inter-digital electrodes and launches surface acoustic waves (SAWs): solutions to the elastic wave equation which propagate along the surface discontinuity of a solid and anchored to it. Following an acoustic propagation delay, the signal is recovered in the electrical domain using a second array of electrodes, amplified, and applied back to the input end. The frequency of oscillations can be highly sensitive to mass loading of the surface [9,10]. The principle forms the basis for quartz micro-balance thickness monitors, which are parts of most deposition equipment. Piezoelectric microwave oscillators are widely used in precision sensing of chemical and biological species [11–13]. SAWs propagation can provide long delays within small footprint. On the downside, the frequencies of operation of most devices are restricted to hundreds of MHz or lower, and their electrical interfaces might not be suitable for certain environments.

The integration of SAW devices alongside and within photonic circuits is considered part of their roadmap [14]. The effect of SAWs on the electronic and optical properties of semiconductor materials has been investigated and used in the modulation of guided light [15]. A first silicon-photonic modulator driven by SAWs was reported by Gorecki et al. in 1997 [16]. SAW modulation has been demonstrated in resonator waveguides in aluminum nitride [17] and in photonic crystals within integrated circuits in gallium arsenide [18]. Recently, piezoelectric transduction has been integrated within a silicon photonic circuit to obtain traveling SAWs phase and amplitude modulation [19]. These developments and others highlight the increasing role of SAW technology as part of integrated photonics.

Over the last four years, our group has proposed and demonstrated SAW-photonic devices in the standard silicon-on-insulator material platform, using optical rather than electrical interfaces [20–23]. The devices serve as microwave-frequency filters [21,23]. An incoming radio-frequency waveform modulates an optical pump wave. The pump is absorbed in a grating of thin metallic stripes. Thermo-elastic actuation leads to the launch of SAWs away from the grating region [24–26]. The SAWs magnitude is proportional to that of the incident waveform. The slow velocity of the acoustic waves allows for the accumulation of long delays with small footprint: Delays as long as 175 ns have been demonstrated on-chip [21]. Information is converted back to optics through photoelastic modulation of an optical probe wave in a standard racetrack resonator waveguide. Both the thermo-elastic actuation and the photoelastic modulation are radio-frequency selective [20–23].

The output probe is detected to obtain a filtered electrical signal. Integrated microwave-photonic filters with a single passband that is only 7 MHz wide have been realized using the SAW-photonic silicon platform [23]. A microwave passband frequency as high as 8.8 GHz was achieved [20]. The passbands of the SAW-photonic devices are much narrower than those of integrated microwave-photonic filters based on all-optical paths [27–30], which are limited by the extent of attainable delay. Integrated filters based on stimulated Brillouin scattering reach sub-MHz bandwidths, support large dynamic ranges, and provide low losses [31–34]. However, Brillouin-active devices require the suspension of membranes or non-standard materials and processes [31–34]. By contrast, the SAW-photonic devices are implemented in the standard silicon-on-insulator layer stack. The main drawback of the SAW-photonic filters are large radio-frequency electrical power losses, presently on the order of 60-70 dB [21], due to the relative inefficiency of the thermo-elastic actuation mechanism. Frequency-selective, acoustic relay of microwave signals between pump and probe was previously used as the basis of oscillators over standard and multi-core fibers [35]. However, the principle has yet to be realized at the device level.

In this work, we report a thermo-elastic, electro-opto-mechanical oscillator based on the SAW-photonic silicon platform. The detected waveform at the output of the SAW-photonic filter is electrically amplified with sufficient gain to overcome the transmission losses of the SAW-photonic filter and driven back to modulate the input pump wave. The closed loop exhibits oscillations at 2.213 GHz frequency. The oscillator does not involve piezoelectricity or Brillouin-active materials, and its frequency of operation is higher than those of most quartz micro-balance devices. Acoustic propagation provides opportunities for the realization of long loop delays on-chip. Present performance in terms of linewidth and side-mode suppression is modest. However, the limitations are not fundamental, and metrics can be improved in future studies. The oscillators can be useful for microwave-frequency signal processing within silicon photonics [36,37], and for the precision analysis of thin layers and surfaces [11–13,22]. Results were briefly reported in a recent conference [38].

2. Principle of operation

A thermo-elastic, electro-opto-mechanical, microwave-frequency oscillator based on a SAW-photonic device is illustrated in Fig. 1. We analyze the hybrid cavity under steady-state oscillations at microwave frequency ${\Omega}$. A voltage of magnitude $V(\mathrm{\Omega } )$ is applied to an electro-optic Mach-Zehnder intensity modulator. The voltage required to switch the modulator output power between minimum and maximum values is denoted by ${V_\pi }$. The modulator is biased at the quadrature point. An optical pump wave from a first laser diode passes through the modulator. The pump wave at the modulator output is amplified to an average optical power ${\bar{P}_p}$ by an erbium-doped fiber amplifier. The magnitude [W] of instantaneous power modulation of the amplified pump wave at frequency $\mathrm{\Omega }$ is given by $\delta {P_p}(\mathrm{\Omega } )= {J_1}[{\pi V(\mathrm{\Omega } )/{V_\pi }} ]{\bar{P}_p}$. Here, ${J_1}$ is the first-order Bessel function of the first kind.

 

Fig. 1. Schematic illustration of a thermo-elastic, electro-opto-mechanical oscillator setup based on a surface acoustic wave-photonic device in silicon-on-insulator [38]. EDFA: erbium-doped fiber amplifier; PC: polarization controller; EOM: electro-optic Mach-Zehnder intensity modulator; Amp.: Radio-frequency electrical amplifier; LD: laser diode; PD: photodiode; BPF: tunable bandpass filter.

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The pump wave illuminates a grating of thin metallic stripes of length l and spatial period $\mathrm{\Lambda }$ (Fig. 1). Absorption of the modulated waveform leads to alternate heating and cooling of the grating elements. The thin metals thermalize within several picoseconds, and their temperature may follow intensity variations at tens of GHz rates [24–26]. Temperature variations are accompanied by thermo-elastic expansion and contraction of the grating structure. The resulting strain pattern, which is periodic in both space and time with respective periods $\mathrm{\Lambda }$ and $2\pi /\mathrm{\Omega }$, is transferred to the underlying silicon-on-insulator layer stack. The periodic strain may represent the boundary condition necessary for the generation of SAWs [24–26]. Actuation of the surface waves is the most efficient when $\mathrm{\Lambda \Omega }/({2\pi } )= {v_{ph}}$, where ${v_{ph}}$ is the phase velocity of a surface acoustic mode [24–26]. For a grating period $\mathrm{\Lambda }$ of 1.49 µm and a standard silicon-on-insulator substrate, that condition is met for an acoustic frequency $\mathrm{\Omega }/({2\pi } )$ near 2.2 GHz [23]. The bandwidth of thermo-elastic actuation is inversely proportional to the number of grating periods [23]. In the devices used in this work, that bandwidth is on the order of 100 MHz [23].

A racetrack resonator waveguide is patterned in the silicon device layer, in proximity to the metallic grating. The straight sections of the racetrack layout run parallel with the metallic grating stripes. The travelling SAWs front passes across the straight sections. The strain associated with the SAWs induces photoelastic perturbations $\mathrm{\Delta }n(\mathrm{\Omega } )\; $ to the effective refractive index of the optical mode in the resonator waveguide. The magnitude of index perturbations is proportional to the modulation of the optical pump waves: $\mathrm{\Delta }n(\mathrm{\Omega } )= {C_{TE}}(\mathrm{\Omega } )\cdot \delta {P_p}(\mathrm{\Omega } )$ [21]. The relation ${C_{TE}}(\mathrm{\Omega } )$, in refractive index units (RIU) per Watt, depends on thermo-elastic properties of the grating, photoelastic parameters of silicon and silica, the transverse profile of the guided optical mode, and the modulation frequency [21]. It is maximal when $\mathrm{\Lambda \Omega }/({2\pi } )= {v_{ph}}$. We have previously estimated $\textrm{max}\{{{C_{TE}}(\mathrm{\Omega } )} \}$ in our devices as 10⁻⁶ RIU × W^-1 [21]. This value is comparatively low, representing the relative inefficiency of thermo-elastic actuation when compared, for example, with piezoelectricity. The effect is nevertheless useful for integrated microwave photonic filtering [21,23], and in thin layers analysis [22].

A continuous optical probe wave from a second laser diode is coupled into the racetrack resonator waveguide. The SAWs induce photoelastic phase modulation of the probe wave along the straight waveguide section of the resonator, nearest the metallic grating. The magnitude $\Delta \varphi (\mathrm{\Omega } )$ of the phase modulation equals ${k_0}{\Delta }n\left( {\Omega } \right)l$, where ${k_0}$ is the vacuum wavenumber of the probe wave. Additional photoelastic phase modulation takes place at the second straight waveguide section, further away from the metallic grating, following an acoustic propagation delay $\tau $. We neglect the small acoustic propagation losses between the two waveguide sections. The combined magnitude of the two photoelastic phase modulation contributions equals $\Delta \varphi (\mathrm{\Omega } )[{1 + \textrm{exp}({j\mathrm{\Omega }\tau } )} ]$)]. It reaches a maximum value of $2\cdot \varphi (\mathrm{\Omega } )$ when $\mathrm{\Omega }\tau $ equals an integer multiple of $2\pi $. In the following, we define the photoelastic modulation frequency response as ${H_{PE}}(\mathrm{\Omega } )= [{1 + \textrm{exp}({j\mathrm{\Omega }\tau } )} ]$. ${H_{PE}}(\mathrm{\Omega } )$ is periodic with a free spectral range of $1/\tau $. Due to the slow acoustic velocity, comparatively long propagation delays can be accumulated in compact devices. SAWs at 2 GHz frequency may acquire hundreds of nanoseconds delays over sub-millimeter effective lengths, prior to their decay [21]. To achieve comparable delays over optical waveguides would require tens of meters.

The phasor addition ${H_{PE}}(\mathrm{\Omega } )$ of photoelastic modulation terms provides additional frequency selectivity to the device response, on top of that of the thermo-elastic actuation. Selectivity can be enhanced further using resonator layouts containing $N > 2$ straight waveguide sections, separated by equal propagation delays $\tau $ [21,23]. Devices based on the delay and sum of as many as 32 photoelastic modulation terms have been demonstrated [23]. The transfer function of these devices contains a single radio-frequency passband with a full width at half maximum of only 7 MHz [23].

Prior to the detection of the probe wave at the output of the device, its photoelastic phase modulation must be first converted to an intensity reading. Phase-to-intensity conversion is the most efficient when the wavelength of the probe wave is carefully aligned with a maximum spectral slope of the transfer function of optical power through the resonator. The modulation of the probe phase offsets its instantaneous frequency with respect to the resonator transfer function slope. The magnitude [W] of the output power modulation is approximately given by [21]:

In Eq. (1), ${\bar{P}_s}$ denotes the average optical power of the probe wave at the racetrack resonator output, Q represents the quality factor of the resonator transfer function, L is the racetrack resonator circumference, and ${n_g}$ is the group refractive index of the optical mode in the resonator waveguide.

The output probe wave is detected by a photo-receiver of responsivity R [V × W^-1]. The obtained signal $\delta V(\mathrm{\Omega } )= R\delta {P_s}(\mathrm{\Omega } )$ is amplified by an electrical radio-frequency amplifier of voltage gain G (electrical power gain of ${|G |^2}$). The gain must be large enough to compensate for the losses of electrical radio-frequency power between the modulation of the input pump wave and that of the detected output probe wave. The amplified voltage is fed back to modulate the input pump wave. Steady-state oscillations of the loop signal at frequency $\mathrm{\Omega }$ are obtained when $G\cdot \delta V(\mathrm{\Omega } )= V(\mathrm{\Omega } )$ [35], namely:

In Eq. (2), we disregard possible saturation of the electronic amplifier, so that saturation is dominated by the modulator response. This assumption is justified by the parameters of the experimental setup used (see Section 3.3). A threshold condition for small signal oscillations can be obtained with the approximation: ${J_1}[{\pi V(\mathrm{\Omega } )/{V_\pi }} ]\approx \pi V(\mathrm{\Omega } )/({2{V_\pi }} )$ [35]:

Oscillations would take place at the radio frequency $\mathrm{\Omega }$ for which the product ${C_{TE}}(\mathrm{\Omega } ){H_{PE}}(\mathrm{\Omega } )$ is the largest. That frequency would closely satisfy $\mathrm{\Lambda \Omega }/({2\pi } )= {v_{ph}}$, as well as $\mathrm{\Omega }\tau = 2\pi M$ where M is an integer.

3. Results

3.1. Device fabrication

Silicon-photonic racetrack resonator waveguides were fabricated in silicon-on-insulator 8” wafers at Tower Semiconductors foundry in Migdal Ha’Emek, Israel. The thickness of the silicon device layer was 220 nm, and that of the buried oxide layer was 2 µm. Ridge waveguides were defined through stepper UV photolithography and inductively coupled plasma reactive ion etching. The width of the ridge waveguide cores was 700 nm, and their partial etching depth was 70 nm. The circumference L of the racetrack resonators was 480 µm. Vertical grating couplers were patterned at the edges of the bus waveguides leading to and from the racetrack resonators. Metallic gratings were fabricated at Bar-Ilan University cleanroom facilities using photolithography, sputtering, and lift-off processes [20–23]. The grating stripes comprised of a 5 nm thick adhesion layer of chromium, followed by 20 nm of gold. Alignment markers were used to define the locations of the gratings with respect to the racetrack resonators. The gratings consisted of 43 stripes, each of length $l$ = 60 µm, with a spatial period $\mathrm{\Lambda }$ of 1.49 µm. A top-view optical microscope image of a SAW-photonic device is shown in Fig. 2.

 

Fig. 2. Top-view optical microscope image of a surface acoustic wave-photonic device used in an electro-opto-mechanical oscillator. Scale bar represents 50 µm.

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3.2 Open-loop characterization

Figure 3(a) shows an optical vector analyzer measurement of the normalized optical power transfer through a racetrack resonator device, as a function of wavelength. The spectral resolution of the analyzer is 3 pm. Periodic transmission notches with a free spectral range of 1.4 nm are observed. The group refractive index of the optical mode in the resonator waveguide ${n_g}$ equals approximately 3.5 RIU. The quality factor Q of the resonator is estimated as 150,000 (Fig. 3(b)). The extinction ratio of the transmission resonances is 7 dB. The end-to-end losses of optical power through the device at off-resonance wavelength are 29 dB. The losses are dominated by coupling losses at the vertical gratings, on the order of 10 dB per facet.

 

Fig. 3. (a): Measured normalized transfer function of optical power through a racetrack resonator device as a function of wavelength. (b): Magnified view of a single transmission notch at the wavelength of the probe waves used in this work (see below).

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The transfer of radio-frequency electrical power between the modulation of the input pump wave and that of the detected output probe wave was measured using the setup shown in Fig. 4(a). The modulation of the optical pump wave was driven by the output port of a vector network analyzer, and the detected output probe was monitored by the instrument’s input port. The average power of the amplified optical pump wave ${\bar{P}_p}$ was 600 mW. The voltage ${V_\pi }$ of the electro-optic intensity modulator equaled 3.5 V, and its input electrical impedance was 50 Ohm. The electrical power required for modulation with magnitude ${V_\pi }$ was therefore 24 dBm. The responsivity R of the photodetector was 27 V × W^-1. The probe wavelength was set to 1544.4 nm, on a maximum spectral slope of the racetrack resonator transfer function (see Fig. 3(b)). The average output power of the probe wave ${\bar{P}_s}$ was 1.5 dBm. A tunable optical bandpass filter was used to suppress the amplified spontaneous emission of erbium-doped fiber amplifiers at the probe output prior to photo-detection.

 

Fig. 4. (a): Schematic illustration of the setup for open-loop characterization of electrical power transmission through a surface acoustic wave-photonic device [38]. EOM: electro-optic Mach-Zehnder intensity modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller. LD: laser diode; PD: photodetector; BPF: bandpass filter. (b): Measured open-loop transfer function of radio-frequency electrical power between the modulation of the input pump wave and that of the detected output probe wave. (c): Impulse response corresponding to the transfer function of panel (b). A first pair of impulses represents photoelastic modulation in the two straight sections of the racetrack resonator. Additional pairs of events correspond to modulation by delayed reflection of dilatational and shear acoustic waves from the bottom surface of the silicon handle layer (see text).

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Figure 4(b) shows the measured transfer function of electrical radio-frequency power. The corresponding impulse response is shown in panel (c). Transmission is maximal at a radio frequency $\mathrm{\Omega }/({2\pi } )$ = 2.213 GHz, for which $\mathrm{\Lambda \Omega }/({2\pi } )= {v_{ph}}$ [20–23]. The losses of radio-frequency electrical power between the pump modulation input and the probe modulation output were 70 dB. These losses agree with expectations and with previous experiments [21], and they are primarily due to the comparative inefficiency of thermo-elastic actuation. The spectral envelope of about 100 MHz width corresponds to the frequency response ${C_{TE}}(\mathrm{\Omega } )$ of thermo-elastic actuation [23]. Periodic transmission bands with a free spectral range of 35 MHz are observed within the thermo-elastic response envelope. The passbands represent the superposition of two primary photoelastic modulation events in the two straight sections of the racetrack resonator waveguide, as discussed in Section 2 and seen in Fig. 4(c). The two modulation events are separated in time by an acoustic propagation delay $\tau $ of 28 ns.

Two additional pairs of events are seen in the impulse response of panel (c). These are delayed by 172 ns and 248 ns with respect to the first, strongest pair. The delays match the two-way times-of-flight of bulk dilatational and shear waves through the 725 µm-thick silicon handle layer of the silicon-on-insulator substrate. The separations between the two events in each of the delayed pairs of impulses remains 28 ns. We therefore assume that thermo-elastic actuation launches dilatational and shear acoustic waves downward into the layers stack, in addition to SAWs. Following two-way propagation through the substrate, the echoes of these waves are partially coupled to SAWs at the upper surface of the device and contribute delayed photoelastic response. The additional pairs of impulses manifest in a 6 MHz periodicity in the transfer function of Fig. 4(b), which is overlaid on top of the primary 35 MHz-wide passbands.

Figure 5(a) illustrates the cascaded chain of electrical radio-frequency amplifiers and bandpass filters used to amplify the detected output probe signal and compensate for transmission losses through the SAW-photonic device. The series consists of four amplifiers. The saturation output power of the final amplifier in the series is specified as 28 dBm. The saturation of the amplifiers chain was therefore higher than that of the electro-optic intensity modulator used, and saturation of the entire loop was therefore dominated by that of the modulator. Tunable radio-frequency bandpass filters were placed at the output of the photodetector and at the outputs of the first, third, and fourth amplifiers in the cascaded chain. The bandwidths of all filters were 20 MHz. The central transmission frequencies of the four filters were offset by several MHz above or below the peak SAW frequency of 2.213 GHz. The small offsets of each filter reduced the transmission bandwidth of the cascaded amplifiers-filters series below 20 MHz, to further suppress additive noise and sidelobes due to competing longitudinal modes of a closed loop (see Section 3.3).

 

Fig. 5. (a): Illustration of the series of radio-frequency amplifiers and bandpass filters used to amplify the output signal of a surface acoustic wave-photonic device. (b): Dashed blue trace - Measured normalized transfer function of radio-frequency electrical power between the input and output of the amplifiers series of panel (a). Maximum gain of 96 dB is obtained at 2.215 GHz frequency. The gain bandwidth is 9.5 MHz. Solid black trace - Measured open-loop normalized transfer function of radio-frequency electrical power between the modulation of the input pump wave and that of the detected output probe wave, following electrical amplification. A single transmission band is observed, with a peak frequency of 2.213 GHz and 2.8 MHz bandwidth. The amplifiers series compensates for the electrical power losses through the surface acoustic wave-photonic device for a net gain of 16 dB.

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Figure 5(b), dashed blue trace, shows a vector network analyzer measurement of the normalized transfer function of electrical power through the cascaded amplifiers and filters. The electrical signal at the amplifiers input was provided by the network analyzer, with a power level of -67 dBm. The frequency of peak amplification is 2.215 GHz, the gain bandwidth is 9.5 MHz, and the maximum gain is 96 dB ($G$ = 60,000). The gain is sufficiently large to compensate for the SAW-photonic device losses. The solid black trace in Fig. 5(b) presents the measured normalized transfer function of electrical radio-frequency power through the SAW-photonic device and the amplifiers chain combined. The signal from the network analyzer output port was used to modulate the optical pump wave. The electrical power of the modulating waveform was 0 dBm. The detected output probe wave was electrically amplified and monitored by the input port of the network analyzer. A single passband is observed in the combined transfer function, with a peak transmission frequency of 2.213 GHz and 2.8 MHz bandwidth. The transfer of electrical power at the peak frequency through the SAW-photonic device and the cascaded amplifiers combined resulted in a gain of 16 dB. The net gain suggests the possibility of radio-frequency voltage oscillations once the loop is closed.

3.3 Thermo-elastic surface acoustic wave-photonic oscillations

Following the open loop characterization of the amplified SAW-photonic device output (Fig. 5(b)), the electro-opto-mechanical feedback loop was closed: the amplified signal of the detected output probe wave was connected to drive the input pump wave modulator. Figure 6(a) presents radio-frequency power spectral densities of the closed loop signal, measured at an electrical tap (see Fig. 1). The measurement resolution bandwidth was 1 kHz. Traces were recorded for different optical power levels of the probe wave at the SAW-photonic device input (see legend). For low probe power levels, broadband noise spectra are observed which follow the shape of the open-loop transfer function (Fig. 5(b)). When the probe power is increased, periodic peaks emerge with a free spectral range of 1.2 MHz. The peaks represent longitudinal modes of the hybrid electro-opto-mechanical cavity. The free spectral range corresponds to a feedback loop delay of 830 ns, which consists of both optical and electrical paths, SAW propagation on chip, and group delays within radio-frequency amplifiers and filters.

 

Fig. 6. (a): Measured power spectral density of the loop output signal, for several optical power levels of the probe wave at the input of the photonic circuit (see legend). Oscillations at 2.213 GHz frequency are reached at a threshold power of -4 dBm. (b): Same as panel (a), for a broader frequencies range and for a probe power level of 9.1 dBm. Spurious signals are weaker than the primary oscillations peak by at least 45 dB. Relative harmonic distortion is below -67 dB.

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When the input probe power is increased above -4 dBm, the loop voltage reaches an oscillations threshold. At the highest input power tested of 9.1 dBm, the loop signal spectrum is dominated by a primary peak at 2.213 GHz frequency. The oscillations frequency matches the maximum transmission peak of the SAW-photonic device (Fig. 5(b)). Sidebands due to competing longitudinal modes are suppressed by at least 12 dB. The peak power spectral density is 32 dB above the background level of broadband noise between the longitudinal modes’ frequencies. The full width at half maximum of the primary peak spectrum is 35 kHz. The oscillations linewidth is 80 times narrower than that of the open loop transfer function (Fig. 5). The total power of the loop output signal was 19 dBm, below saturation of the electrical amplifiers, and 75% of that power fell within the primary peak. Harmonic distortion terms are strongly suppressed by the thermo-elastic actuation response and the in-line radio-frequency bandpass filters, and they are weaker than the primary oscillations peak by at least 67 dB (Fig. 6(b)). Spurious signals are weaker than the main peak of oscillations by at least 45 dB.

The loop signal at the electrical tap output was also sampled by real-time digitizing oscilloscope at 32 giga-samples per second rate and stored for further offline processing. The recorded trace was 1 ms long. The optical power of the input probe wave was 10.4 dBm. Figure 7 presents the magnitude squared of the short-time Fourier transform of the detected waveform. The length of the temporal window used in the transform calculation was 18.75 µs. Dominant oscillations at 2.213 GHz frequencies are again observed, alongside weaker terms at the frequencies of adjacent longitudinal modes of the hybrid feedback loop. The results suggest occasional modes competition: At 740 µs time, for example, the loop signal switched to the sidemode frequency of 2.2143 GHz for a duration of 30 µs, before returning to the primary peak frequency. Two shorter switching events can be observed within the first 100 µs of the recorded trace. Mode competition may be suppressed through the reduction of radio-frequency power losses through the SAW-photonic device (see Discussion section 4 below).

 

Fig. 7. Normalized magnitude of the short-time Fourier transform of the loop output signal. The temporal window of the Fourier transform calculation was 18.75 µs. The transform is dominated by the primary oscillations peak at 2.213 GHz frequency. Mode competition, however, does take place: 740 µs following the beginning of the trace, the oscillations switched to the sidemode frequency of 2.2143 GHz for a duration of 30 µs. Two shorter switching events were observed during the first 100 µs of the recording.

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The loop output strongly depends on the exact choice of probe wavelength: photoelastic modulation of the output probe intensity is the most efficient when its wavelength is aligned with a maximum slope of the racetrack resonator transfer function (see Section 2). Figure 8 presents measurements of the output power spectral density for several probe wavelengths, adjusted through precise thermal tuning of the laser diode source. The optical power of the probe wave at the SAW-photonic device input was 9.8 dBm. When the probe wavelength is outside the transmission resonance (1544.393 nm wavelength, see Fig. 3(b)), the radio-frequency spectrum is that of broadband noise, similar to the traces of Fig. 6(a) taken below threshold. Oscillations emerge and become stronger as the probe wavelength is gradually brought into the spectral slope of the resonator transfer function and reach a maximum for a wavelength of 1543.405 nm.

 

Fig. 8. Measured power spectral density of the loop output signal, for different wavelengths of the input probe wave (see legend). The input power of the probe wave was 9.8 dBm. Oscillations emerge and increase as the wavelengths is gradually scanned from outside a transmission resonance towards the maximum spectral slope of the racetrack resonator response (see Fig. 3(b)).

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4. Summary and discussion

In this work, we have proposed and demonstrated a microwave-frequency, thermo-elastic electro-opto-mechanical oscillator based on a standard silicon-photonic integrated device. Oscillations were obtained at a main frequency of 2.213 GHz, with 35 kHz linewidth. The oscillator includes the delay of slow-moving acoustic waves with small footprint, as a possible alternative for delay over long optical paths. The oscillator does not require piezoelectricity and can be realized on any substrate. The frequency of oscillations is higher than those of typical quartz micro-balance devices which make use of SAWs.

At this stage, the obtained linewidth and side-mode suppression are rather modest, and they fall short of previous demonstrations of electro-optic oscillators involving photonic integration [4–8]. Performance metrics were compromised by large losses in the thermo-elastic actuation of SAWs and in the coupling of probe waves between fibers and chip. The losses mandate the optical and radio-frequency amplification of signals within the oscillator loop, and the use of multiple radio-frequency bandpass filters to suppress the noise of cascaded electrical amplifiers. The efficiency of SAWs stimulation can be improved through optimization of the metallic grating elements and their embedding in the substrate [39,40]. In the present demonstration, noise due to amplified spontaneous emission of optical amplifiers at the probe wave path was 100 times stronger than all other noise contributions. Optical amplification of the output probe wave could be avoided with more efficient coupling between fibers and device, leading to potentially better noise characteristics. Laser diode sources, modulators, and detectors can be integrated on-chip, as well as part of the associated electronics [41–43].

The oscillator can be pre-designed for arbitrary microwave frequencies, through choice of the spatial period of the metallic gratings. We have previously demonstrated SAW-photonic devices operating up to 8.8 GHz frequency [20], and the thermo-elastic actuation of SAWs has reached tens of GHz [24–26]. Post-fabrication tuning of the frequency of operation is limited. The pump beam may be moved across multiple metallic gratings next to a common readout resonator, for the possible stimulation of SAWs with different frequencies.

The development of microwave-frequency oscillators based on SAW-photonic devices concurs with many efforts pursuing acousto-optic integrated technologies [14–19]. The proposed device might be suitable for integrated microwave-photonics signal processing applications [36,37], and for thin layers analysis on top of photonic circuits [11–13,22]. The linewidth of oscillations is 200 times narrower than the passbands of micro-wave photonic filters based on our previous SAW devices [23]. The oscillators demonstrated herein could therefore enhance the precision of recently proposed SAW-photonic thin layer analysis [22]. The high-frequency acoustic waves stimulated within the oscillator are tightly confined to the surface, and they probe the surface more directly than lower-frequency micro-balance devices. Future work will be dedicated to improving the oscillator performance and to its employment in the analysis of thin layers.