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Dual-frequency optoelectronic oscillator incorporating a single cavity and multiband microwave photonic filter

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Abstract

Dual-frequency optoelectronic oscillators (OEOs) have potential applications in dual-band wireless networking and dual-parameter sensing systems. We propose a dual-frequency OEO incorporating a multiband microwave photonic filter (MPF). In particular, the two microwave signals are generated simultaneously in a single OEO cavity. By simply varying the parameters of optical spectral slicing and sampling (e.g., with a programmable optical filter) used to implement the MPF, we can readily achieve simultaneous tuning of the dual-frequency output, as well as alternate switching between single-frequency and dual-frequency output. The multi-passband nature of the MPF, enabled via optical spectral slicing, opens a path to multi-frequency OEO operation by scaling our scheme in the future. Such a structure provides a flexible way to generate simultaneously tunable and reconfigurable multi-frequency microwave signals.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Dual-frequency signal generators have attracted significant interest due to their wide applications in global positioning systems (GPSs) [1], broadband microwave measurement systems [2], wireless networking [3], and dual-parameter sensing systems [4,5]. However, dual-frequency signal generators implemented using conventional electronic approaches have limitations in terms of tunability or reconfigurability and are more prone to electromagnetic interference; these limitations, in turn, impact system performance [6].

With the rapid development of microwave photonic (MWP) technologies over the past decades, optoelectronic oscillators (OEOs) have been actively investigated as they provide promising solutions to overcome the inherent barriers associated with conventional electronic approaches [79]. In general, the key components used to filter the oscillation mode in the OEO system are bandpass microwave filters, e.g., electrical bandpass filters (EBPFs) and microwave photonic filters (MPFs), whose central frequencies determine the oscillation frequencies. Despite significant developments on bandpass microwave filters, most demonstrations to date involve single-frequency OEO operation only [810]. On the other hand, generating multi-frequency microwave signals simultaneously could enhance the flexibility of the OEO system and facilitate high performance multi-frequency electronic systems [15,11]. Recently, dual-frequency OEOs with two independent parallel EBPF branches were demonstrated [1214]. Indeed, the use of EBPFs is straightforward to some extent. Nevertheless, it contradicts the original intention of introducing MWP technologies and the inherent bottlenecks caused by conventional electronic approaches still exist. Besides, the dual-frequency oscillating signals are not generated in a single cavity simultaneously, which may increase the complexity of the dual-frequency OEO system. Multiband MPFs, as an alternative filtering approach, open a path towards the simultaneous generation of multi-frequency microwave signals [4,5,1519] in OEO systems. For example, dual-frequency OEOs incorporating dual-passband MPFs based on phase modulation to intensity modulation conversion were reported [4,5,1517]. Due to the use of the phase-shifted fiber Bragg grating (PSFBG), the generated microwave signals are sensitive to the environment, allowing their applications in multi-parameter sensing systems [4,5,16,17]. However, it requires high-stable laser sources for small frequency drift. The stimulated Brillouin scattering (SBS) effect can also be employed to achieve narrow bandwidth dual-passband MPFs for selecting two oscillation modes and thus achieve dual-frequency OEO operation [18,19]. However, an additional laser source [18] or an additional radio frequency source [19] is required for dual-frequency operation, thereby increasing the system complexity . It is worth noticing that the dual-passband nature of most dual-passband MPFs used in the above-mentioned OEO systems are simply achieved by incorporating two individual single-passband MPFs.

In this paper, we propose a dual-frequency OEO incorporating a multiband MPF. The multiband MPF is implemented based on optical spectral slicing by way of a programmable sampling function. By appropriately defining the sampling function parameters, the multi-passband nature of the incorporated multiband MPF is enabled and results in the dual-frequency OEO. Compared with the dual-frequency OEO using two independent EBPF branches [12,13] or SBS excited by two pumps [19], our scheme lowers the overall complexity of the system. We also demonstrate that the simultaneous generation of two microwave signals can be achieved in a single OEO cavity. Similar to the mechanism of the dual-wavelength laser [20], two oscillation modes are simultaneously excited and amplified in a single cavity in our scheme. The results show that a dual-frequency OEO can be implemented where the frequency separation can be discretely tuned over a range of 360 MHz and where the smallest frequency separation is 144 MHz. By appropriately manipulating the sampling function, the output of our OEO, i.e., the switching nature of our OEO scheme, can be readily switched between single-frequency and dual-frequency operation. These results promise the flexibility of our scheme and facilitate broadband microwave measurement systems; the multiband nature of the MPF opens a possibility for obtaining multi-frequency output. Our demonstrated dual-frequency OEO can be used for the simultaneous interrogation of multiple FBGs, which can enable high-speed and high-resolution interrogation.

2. Principle of operation

A schematic of our proposed dual-frequency OEO is illustrated in Fig. 1. A broadband optical source (BOS), an in-line polarizer (ILP), and a polarization maintaining fiber (PMF)-based Sagnac interferometer are employed to provide a sinusoidal BOS signal with a free spectral range (FSR) of $\mathrm{\Delta }{f_{\textrm{FSR}}}$. Then according to a programmable periodic sampling function, the optical spectral slicing is implemented via a programmable optical filter or waveshaper (WS). In this work, a representative periodic rectangular sampling function $S(\Omega ) = \sum\nolimits_{k\textrm{ = 1}}^{{N_{\textrm{ch}}}} {\textrm{rect}\left( {\frac{{{\Omega - }{\mathrm{\Omega }_k}}}{{B \cdot D}}} \right)}$ is used as an example and shown in Fig. 1, where ${N_{\textrm{ch}}}$ is the number of optical channels, ${\mathrm{\Omega }_k}$ is the central frequency of the k-th optical channel, B and D are the full bandwidth and duty cycle of each optical channel, respectively. The multiple MPF passbands are then implemented by manipulating the weight of the sinusoidal BOS signal via sampling. Note that the profile of the sampling function can be set to other sampling profiles (e.g., a periodic apodizing Gaussian profile) according to the demand of the dual-frequency OEO applications. After modulation with a phase modulator (PM) and transmission through a length of dispersion compensating fiber (DCF), the sinusoidal BOS signal is amplified by an erbium doped fiber amplifier (EDFA) and then sent to a photodetector (PD) for electrical-to-optical conversion. The output microwave signals from the PD are ultimately amplified by an electrical amplifier (EA) and fed back to the PM via a 3-dB power divider. Thus, a hybrid dual-frequency OEO loop is formed and closed.

 figure: Fig. 1.

Fig. 1. Schematic and experimental of the proposed dual-frequency OEO with optical path shown in black and electrical path shown in red (BOS: broadband optical source; ILP: in-line polarizer; PMF: polarization maintaining fiber; PC: polarization controller; WS: Waveshaper; PM: phase modulator; DCF: dispersion compensating fiber; EDFA: erbium doped fiber amplifier; PD: photodetector; EA: electrical amplifier; ESA: electrical spectrum analyzer).

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The operation of the proposed dual-frequency OEO is discussed as follows. As reported in our recent work, the open-loop response of the dual-frequency OEO is a reconfigurable and tunable multiband MPF, which can be expressed as [21]

$$\begin{aligned}{H_{RF}}(f )&\propto \frac{1}{{2\pi }}\mathop \int \nolimits_0^\infty N(\Omega )\textrm{exp}[{ - j2{\pi^2}{\beta_2}{L_2}{f^2} + j4{\pi^2}{\beta_2}{L_2}f({\Omega - {\Omega _0}} )+ j\pi /2} ]\cr &\quad \cdot \left\{ {S(\Omega )\left( {1 + \textrm{cos}\left( {\frac{{2\pi \Omega }}{{\Delta {f_{\textrm{FSR}}}}}} \right)} \right) - S({\Omega - f} )\left[ {1 + \textrm{cos}\left( {\frac{{2\pi ({\Omega - f} )}}{{\Delta {f_{\textrm{FSR}}}}}} \right)} \right]} \right\}d\Omega \end{aligned}$$
where $N(\mathrm{\Omega } )$ presents the power spectral density of the BOS, ${\beta _\textrm{2}}$ (ps2/km) and$\; {L_\textrm{2}}$ are the dispersion and length of the DCF, respectively, $\pi/\textrm{2}$ in the exponential function corresponds to the phase modulation in this work, $\mathrm{\Omega }$ is the frequency of the optical signal, ${\mathrm{\Omega }_\textrm{0}}$ is the central frequency of the sinusoidal BOS signal, $\mathrm{\Delta }{f_{\textrm{FSR}}}\textrm{ = }c/\mathrm{\Delta }n{L_\textrm{1}}$ where c is the speed of light in vacuum, $\Delta n$ is the effective index difference between the fast and slow axes of the PMF, ${L_\textrm{1}}$ is the length of the PMF. Note that the total dispersion slope of the DCF is neglected in Eq. (1), considering the total bandwidth of the sinusoidal BOS signal ${\Delta \Omega \; = \; }B \cdot {N_{\textrm{ch}}}$ is limited and fixed via the WS. This leads to the narrow-bandwidth of the multiband MPF and consequently benefits the mode selection of the proposed dual-frequency OEO.

Next, the closed-loop response of the proposed dual-frequency OEO is discussed. When the total gain exceeds the loss in the hybrid dual-frequency OEO loop, oscillation signals will raise from the noise and become stable. Then at any instant of time, the output of the PD can be expressed as the summation of all circulating fields in the OEO loop and written as [22]

$$V({f,t} )\propto {V_{in}}\textrm{exp}({j2\pi ft} )\mathop \sum \nolimits_{m = 1}^\infty {[{{H_{RF}}(f )\cdot G(f )} ]^m}\textrm{exp}({ - jm\tau \cdot 2\pi f} ),$$
where ${V_{\textrm{in}}}$ is the amplitude of the feedback electrical signal at the input of PM, m is an integer, $G\textrm{(}f\textrm{)}$ is the total gain in the electrical part of the dual-frequency OEO loop, $\tau $ is the round-trip time of the dual-frequency OEO cavity. In this work, G(f) is mainly determined by the fixed gain GEA of the EA and the differential conversion gain GPD of the PD. After the oscillation of the proposed dual-frequency OEO is established, the corresponding output power can be expressed as below with ${H_{\textrm{RF}}}\textrm{(}f\textrm{)} \cdot G\textrm{(}f\textrm{)}$ being a little less than unity:
$$P(f )\propto \frac{1}{{1 + {{[{{H_{RF}}(f )\cdot G(f )} ]}^2} - 2{H_{RF}}(f )\cdot G(f )\cdot \textrm{cos}({2\pi ft} )}}$$

In general, the closed-loop responses of the OEO are mainly determined by the responses of the incorporated microwave filters. In our work, the multi-passband nature of the incorporated multiband MPF responses and the resulting dual-frequency nature of the proposed dual-frequency OEO are introduced by the multiple samples of the sampling function. Moreover, similar to the tunability of the multiband MPF in [21], the tunability of the dual-frequency OEO can be realized by changing the total optical channel number ${N_{\textrm{ch}}}$.

3. Experimental results

The experimental setup of the proposed dual-frequency OEO is illustrated in Fig. 1. A broadband EDFA (Keopsys, CEFA-C-HG) with an output power of 11.9 dBm works as the BOS. The sinusoidal BOS signal with $\mathrm{\Delta }{f_{\textrm{FSR}}}$ of 13.125 GHz (∼0.105 nm) and a power of -5.2 dBm is generated via the Sagnac interferometer based on PMF (Thorlabs, PM1550-XP) with ${\Delta }n{\; = \; \textrm{4}}\textrm{.2} \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$ and ${L_\textrm{1}}\; \textrm{= }$ 54.4 m. The optical spectral slicing is then implemented by way of a programmable sampling function via the WS (Finisar, WaveShaper 1000S) with a bandwidth setting resolution of 1 GHz. Note that the total bandwidth of the sampled sinusoidal BOS signal at the output of the WS is fixed at 1 THz (∼8 nm). In this case, the total dispersion slope of the DCF can be neglected for the sake of the narrow-bandwidth of the multiband MPF and the stable oscillation of the dual-frequency OEO. The sampled sinusoidal BOS signal is then modulated using a PM (EOSPACE) with a 3-dB bandwidth of 10 GHz. The measured overall optical loss from BOS to the output of PM varies approximately from 30 dB up to 35 dB depending on the sampling functions programmed at WS. After transmission through the DCF with $\; {L_\textrm{2}}\; \textrm{= }$ 16.4 km and ${\beta _\textrm{2}}\textrm{ = }$ 133.6 ps2/km and amplification by an EDFA (PriTel, FA-30), the modulated signal with a power level of 0 dBm is sent to a PD (Thorlabs, RXM25AF) with a 3-dB bandwidth of 25 GHz and an adjustable differential conversion gain ${G_{\textrm{PD}}}$ up to 7200 V/W at 1550 nm for electrical-to-optical conversion. The generated microwave signals are amplified by an electrical amplifier (EA, JDS, H310-1110) with a 3-dB bandwidth of 10 GHz and a typical gain of 24 dB. To measure the open-loop response of the proposed dual-frequency OEO, i.e., multiband MPF response, a frequency-sweeping RF signal generated by an RF source (Anritsu, MG3692A) is used to drive the PM, and the output microwave signal of the PD is observed via an electrical spectrum analyzer (ESA, Anritsu MS2668C). To measure the closed-loop response of the proposed dual-frequency OEO, the output signal of PD is fed back to the PM via a 3-dB power divider, the oscillation signals are then observed by the ESA.

The open-loop responses (multiband MPFs) and the corresponding closed-loop responses (dual-frequency OEOs) are investigated when a periodic rectangular function with a varying optical channel number ${N_{\textrm{ch}}}$ from 2 to 7 and a varying duty cycle D of optical channel are programmed as the sampling function. The experimental results with the frequency range of interest are shown in Fig. 2 with the corresponding optical spectra at the output of WS measured by an optical spectrum analyzer (OSA, Ando AQ6317; resolution: 0.01 nm) and shown in the respective insets. There is a good ‘alignment’ between the frequencies in the multiband MPF responses (blue solid curve) and the dual-frequency OEO output (red solid curve). It is seen in Figs. 2(a) to 2(f) that the frequency spacing between the central passband ${f_{\textrm{MPF1}}}\textrm{ = 1}/\textrm{2}\pi{\beta _\textrm{2}}{L_\textrm{2}}\mathrm{\Delta }{f_{\textrm{FSR}}}$ and the left first passband ${f_{\textrm{MPF2}}}$ of the multiband MPF are 136 MHz, 208 MHz, 292 MHz, 352 MHz, 428 MHz, and 488 MHz, respectively, while the frequency spacing between the two oscillation signals ${f_\textrm{1}}$ = 5.52 GHz and ${f_\textrm{2}}$ of the dual-frequency OEO are 144 MHz, 228 MHz, 288 MHz, 360 MHz, 432 MHz, and 504 MHz, respectively. This corresponds to discrete tuning of the frequency spacing of the dual-frequency OEO up to 360 MHz. Figure 3 reveals these experimental observations; the frequency spacing between ${f_{\textrm{MPF1}}}$ and ${f_{\textrm{MPF2}}}$ of the multiband MPF are also simulated and plotted for comparison. It is obvious that good agreement regarding frequency spacing is found between the simulation and experimental MPF responses as well as between the experimental MPF responses and OEO outputs. Moreover, the frequency separation increases linearly as ${N_{\textrm{ch}}}$ increases, which is similar to what was found in our earlier work [21]. This ultimately contributes to the linear variation in frequency separation of the corresponding dual-frequency OEO responses (see the linear fitting line in Fig. 3). To extend the frequency tunable range, a sampling function with more optical channels ${N_{\textrm{ch}}}$ for a given $\mathrm{\Delta }{f_{\textrm{FSR}}}$ could be employed. However, ${N_{\textrm{ch}}}$ cannot be increased arbitrarily due to the fact that sufficient number of FSR within each optical channel should be provided to enable the narrow bandwidths of multiband MPF passbands. This places an upper limit on the tunable frequency range. In addition, as we discussed in our previous work [21], a sinusoidal BOS signal with a smaller FSR would also benefit the frequency tunable range further as well as higher central frequency of the dual-frequency OEO. Moreover, it is worth noting that the criterion for choosing the appropriate values of D is developed based on minimizing the peak power variation of the incorporated multiband MPF responses. Nevertheless, the value of D is not unique for the sampling function with the fixed ${N_{\textrm{ch}}}$, and the combinations of different D and fixed ${N_{\textrm{ch}}}$ would result in dual-frequency OEO with different peak power variations.

 figure: Fig. 2.

Fig. 2. Measured dual-frequency OEO outputs (red solid curve) and corresponding multiband MPF responses (blue solid curve) when (a) Nch = 2, D = 31%, (b) Nch = 3, D = 25%, (c) Nch = 4, D = 33%, (d) Nch = 5, D = 31%, (e) Nch = 6, D = 24%, and (f) Nch = 7, D = 28% within the frequency range of interest. The figure insets show the corresponding measured optical spectra at the output of the WS.

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 figure: Fig. 3.

Fig. 3. Simulation (blue square) and experimental (red circle) frequency spacings between ${f_{\textrm{MPF1}}}$ and ${f_{\textrm{MPF2}}}$ of the multiband MPF along with the resulting experimental (orange triangle) frequency spacings between two oscillation signals when ${N_{\textrm{ch}}}$ varies from 2 to 7. The dotted black line corresponds to a fit through the experimental OEO responses.

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Representative dual-frequency OEO oscillation regimes in terms of output frequencies vs. the differential conversion gain ${G_{\textrm{PD}}}$ of the PD are investigated and shown in Fig. 4 when the sampling function is fixed with ${N_{\textrm{ch}}}$ = 4 and D = 33%. Similar to the mechanism of a dual-wavelength laser [20], it is obvious that the single-frequency operation as well as the simultaneous dual-frequency operation can be achieved by adjusting ${G_{\textrm{PD}}}$, and four distinct dual-frequency OEO oscillation regimes are witnessed. When ${G_{\textrm{PD}}}$ is relatively low (e.g., case 1 as shown in the black curve when ${G_{\textrm{PD}}}$ = 370 V/W), no oscillation can be observed. This is due to the fact that the total gain in the closed dual-frequency OEO loop is too low to support self-oscillation. Next, we properly arrange ${G_{\textrm{PD}}}$ to exceed the threshold of self-oscillation (e.g., case 2 as shown in the blue curve when ${G_{\textrm{PD}}}$ = 1100 V/W), the total gain at ${f_\textrm{1}}$ = 5.52 GHz in the oscillation cavity overcomes the loss at ${f_\textrm{1}}$, thus the single-frequency oscillation at ${f_\textrm{1}}$ is obtained. At the same time, a relatively low peak ${f_\textrm{2}}$ = 5.25 GHz at the left side of ${f_\textrm{1}}$ is also observed, as the dual-frequency OEO operates in a gain-competition mode. If we further increase ${G_{\textrm{PD}}}$ to a certain range (e.g., case 3 as shown in the red curve when ${G_{\textrm{PD}}}$ = 3750 V/W), dual-frequency OEO oscillation at ${f_\textrm{1}}$ and ${f_\textrm{2}}$ occurs and it clearly shows the gain-competition mode is switched to a gain-clamped mode where two oscillating signals have almost identical peak powers (in this case). For sufficiently high values of ${G_{\textrm{PD}}}$ that support dual-frequency operation, further increases in ${G_{\textrm{PD}}}$ (e.g., case 4 as shown in the green curve when ${G_{\textrm{PD}}}$ = 6750 V/W) would ultimately lead to a gain-saturation mode where the powers of both ${f_\textrm{1}}$ and ${f_\textrm{2}}$ decrease while the noise floor increases. Although we cannot determine the total gain in the closed dual-frequency OEO loop for each case without knowing the absolute gain from PD, the difference between the total gain for each case can be estimated from the known differential conversion gain values ${G_{\textrm{PD}}}$. Thus, the total gain difference between cases 1 and 2, cases 2 and 3, and cases 3 and 4 are 9.46 dB, 10.65 dB, and 5.11 dB, respectively.

 figure: Fig. 4.

Fig. 4. Experimental dual-frequency OEO output power of both frequencies (${f_\textrm{1}}$ = 5.52 GHz and ${f_\textrm{2}}$ = 5.247 GHz) when ${N_{\textrm{ch}}}$ = 4 and D = 33% as differential conversion gain ${G_{\textrm{PD}}}$ increases from 370 V/W (bottom) to 6750 V/W (top).

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4. Discussion

The tunability of the proposed dual-frequency OEO is achieved by varying the parameters of optical spectral slicing and sampling. Note that one of the oscillation signals is fixed at 5.52 GHz, which corresponds to the central frequency of the multiband MPF, and it is not tunable due to the fixed lengths of the PMF and DCF used in our experiment. However, it will be possible to tune the central frequency of the OEO, e.g., by changing $\mathrm{\Delta }{f_{\textrm{FSR}}}$ when the DCF used in the experiment is fixed (i.e., β2 and L2 are fixed). With this in mind, a Sagnac interferometer with multi-segment of PMFs or a Mach-Zehnder interferometer incorporating a tunable optical delay line can be used to obtain a variable $\mathrm{\Delta }{f_{\textrm{FSR}}}$. In the former scheme, $\mathrm{\Delta }{f_{\textrm{FSR}}}$ can be tuned by adjusting the polarization controller in the Sagnac loop, while $\mathrm{\Delta }{f_{\textrm{FSR}}}$ can be tuned by adjusting the length of the tunable optical delay line in the latter scheme.

The reconfigurability of the proposed dual-frequency OEO can be implemented by way of varying D, for a given ${N_{\textrm{ch}}}$ and a sufficiently high ${G_{\textrm{PD}}}$ that support multi-frequency operation. It is experimentally verified that if a dual-frequency oscillation can be observed when D is set within a range of [D1, D2], single-frequency oscillations can then be achieved by tuning D either below D1 (resulting in an oscillation only at f2) or above D2 (resulting in an oscillation only at f1). In addition, attention should be paid to some scenarios (i.e., when ${N_{\textrm{ch}}}$ is set to be a large number) that there exists a possibility of a triple-frequency oscillation if D is appropriately tuned within [D1, D2]. Indeed, a small third oscillation around 6 GHz is witnessed, for instance, in Fig. 2(f). The amplitude of such an oscillation signal could reach -20.6 dBm when ${N_{\textrm{ch}}}$ is between 8 and 10, and each of three oscillation signals has greater power variations in any of those cases compared to the case of dual-frequency oscillation. Note that, in order to neglect the dispersion slope of the DCF and minimize the deterioration of the incorporated multiband MPF, the total bandwidth of the sampled sinusoidal BOS signal ${\Delta \Omega }$ is confined via the WS [21]. This would benefit the stability of dual-frequency OEO, however, it places an upper limit on the tunable frequency range and the number of possible oscillation modes, which is also due to the fact that D cannot be decreased arbitrarily within the range [D1, D2]. Thus, to make triple-frequency OEO operation possible, a sufficient number of FSR with an appropriate ${N_{\textrm{ch}}}$ should be guaranteed within ${\Delta \Omega }$ to ensure the narrow bandwidths of the MPF passbands and thus suppress the mode competition in the multitone OEO system.

Ideally, a multiband MPF with similar peak powers will lead to a multitone OEO (e.g., multi-frequency OEO), and the central frequencies of each resulting oscillation mode are determined by the central frequencies of the corresponding MPF passbands. In our work, the MPF responses shown in Fig. 2 have several passbands yet the resulting OEO operates generally with two tones only. This is mainly due to two facets. The first facet is the nonuniform multiband MPF responses (having unequal passband peak powers). This is mainly introduced by the dispersion-induced power fading; however, it can be improved to some extent by tuning D in this work or eliminated by employing single-sideband modulation [23] or the Mach-Zehnder interference structure embedded with an electro-optical modulator [24]. The second facet is the severe mode competition in the OEO cavity. In our OEO configuration, the average full-width-at-half-maximum (FWHM) of each electrical passband is around 70 MHz, while the FSR of the OEO is only 12.4 kHz, corresponding to the round-trip time of the OEO cavity. This implies there are more than 5,500 modes participating in the mode competition within each electrical MPF passband. In addition, the total electrical gain in the OEO cavity is shared between all potential oscillation modes from the different MPF passbands. Therefore, with the above-mentioned two facets in mind, our OEO is largely restricted to dual-frequency operation, and it may be challenging to scale our existing scheme to generate a larger number of output frequencies. However, the multi-passband nature of our multiband MPF still offers the possibility for multi-frequency OEO operation, although additional mechanism or strategies are required in the implementation and testing.

The mode competition also results in reduced stability, however, due to the equipment availability, i.e., lack of a signal source analyzer or an ESA with a phase noise measurement module, the phase noise performance of our dual-frequency OEO cannot be provided. Instead, we evaluate the phase noise performance and stability for single-frequency operation, i.e., when a single-passband rectangular function is used. To achieve the fine mode selection and improve the stability, a fiber ring resonator (FRR) [25] consisting of a 30/70 optical coupler and a 100-m single-mode optical fiber is used and connected between the EDFA and PD. The phase noise at 10 kHz offset of ${f_\textrm{1}}$ = 5.52 GHz for single-frequency OEO is then measured as -90.91 dBc/Hz, and the observed maximum frequency drift for ${f_\textrm{1}}$ is 13.8 kHz over a period of 30 minutes. Note that the insertion of such an FRR, to our notice, also improves the stability of the dual-frequency OEO, however, it still requires a further investigation on optimization of the fiber length in the FRR to improve the phase noise performance. In addition, a dual-loop FRR is also worth trying for the dual-frequency OEO.

From the evaluated phase noise performance of the single-frequency OEO achieved by our scheme, we can infer that the phase noise performance is not good enough and it would need to be improved if our dual-frequency OEO is proposed for communication system applications. However, thanks to the use of PMF and Sagnac interferometer, the frequency of our OEO would shift with temperature due to the thermal expansion of optical fiber and the thermo-optic effect. Thus, our dual-frequency OEO can be used towards the applications of OEO-based high-speed and high-resolution optical sensing, which has a relatively low requirement regarding the phase noise performance [26]. In addition, our dual-frequency OEO is measured to have an average signal-to-noise ratio (SNR) of 20 dB (as seen in Fig. 2), and this SNR figure, related to the SNR of the wavelength interrogation scheme [27], is comparable with the values obtained through traditional optical sensors [28,29] or wavelength–to-intensity conversion using an edge filter [30] for the applications of OEO-based high-speed and high-resolution optical sensing.

5. Summary

In summary, we have presented a dual-frequency OEO based on optical spectral slicing. Taking advantages of the flexible optical spectral slicing and the incorporated multiband MPF, simultaneous generation of dual-frequency microwave signals is achieved in a single OEO cavity. By simply varying the parameters of the sampling function for the optical spectral slicing, the tunability of the dual-frequency OEO as well as its switching nature (i.e., alternate switching between single-frequency and dual-frequency outputs) are verified in the proof-of-concept experiments. The discrete tunable frequency range of 360 MHz is experimentally demonstrated for a dual-frequency OEO with the smallest frequency separation being 144 MHz. The use of either a larger optical channel number ${N_{\textrm{ch}}}$ or a sinusoidal BOS signal with a smaller FSR would both make contributions to broaden the tunable frequency range and potentially promote scaling the number of OEO output frequencies, although they cannot be extended arbitrarily.

Different from the dual-frequency OEO based on two individual cavities, the dual-frequency OEO in our work has two frequency responses simultaneously in a single cavity, providing a simple way to support its applications such as simultaneous multi-parameter measurement systems. Moreover, compared with dual-frequency OEOs based on two individual single-passband MPFs, the tunability and switching ability of our work are enabled by simply varying the sampling parameters via a programmable WS without changing the experimental setup, which allows the flexibility of our method. Thanks to the multi-passband nature of the incorporated multiband MPF, our scheme has a great potential to be scaled or extended to multi-frequency OEO operation and thus would support OEO-based multi-parameter sensing applications. Considering that the multiple reflection peaks corresponding to the central wavelengths of multiple FBGs is similar to the sampling of the optical taps in our work, such scheme would also support the high-speed and high-resolution interrogation of multiple FBG-based sensing systems.

Funding

China Scholarship Council; Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada.

Acknowledgment

We would like to thank J. Azaña for providing a number of components used in the experiments.

Disclosures

The authors declare no conflicts of interest.

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Figures (4)

Fig. 1.
Fig. 1. Schematic and experimental of the proposed dual-frequency OEO with optical path shown in black and electrical path shown in red (BOS: broadband optical source; ILP: in-line polarizer; PMF: polarization maintaining fiber; PC: polarization controller; WS: Waveshaper; PM: phase modulator; DCF: dispersion compensating fiber; EDFA: erbium doped fiber amplifier; PD: photodetector; EA: electrical amplifier; ESA: electrical spectrum analyzer).
Fig. 2.
Fig. 2. Measured dual-frequency OEO outputs (red solid curve) and corresponding multiband MPF responses (blue solid curve) when (a) Nch = 2, D = 31%, (b) Nch = 3, D = 25%, (c) Nch = 4, D = 33%, (d) Nch = 5, D = 31%, (e) Nch = 6, D = 24%, and (f) Nch = 7, D = 28% within the frequency range of interest. The figure insets show the corresponding measured optical spectra at the output of the WS.
Fig. 3.
Fig. 3. Simulation (blue square) and experimental (red circle) frequency spacings between ${f_{\textrm{MPF1}}}$ and ${f_{\textrm{MPF2}}}$ of the multiband MPF along with the resulting experimental (orange triangle) frequency spacings between two oscillation signals when ${N_{\textrm{ch}}}$ varies from 2 to 7. The dotted black line corresponds to a fit through the experimental OEO responses.
Fig. 4.
Fig. 4. Experimental dual-frequency OEO output power of both frequencies ( ${f_\textrm{1}}$  = 5.52 GHz and ${f_\textrm{2}}$  = 5.247 GHz) when ${N_{\textrm{ch}}}$  = 4 and D = 33% as differential conversion gain ${G_{\textrm{PD}}}$ increases from 370 V/W (bottom) to 6750 V/W (top).

Equations (3)

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H R F ( f ) 1 2 π 0 N ( Ω ) exp [ j 2 π 2 β 2 L 2 f 2 + j 4 π 2 β 2 L 2 f ( Ω Ω 0 ) + j π / 2 ] { S ( Ω ) ( 1 + cos ( 2 π Ω Δ f FSR ) ) S ( Ω f ) [ 1 + cos ( 2 π ( Ω f ) Δ f FSR ) ] } d Ω
V ( f , t ) V i n exp ( j 2 π f t ) m = 1 [ H R F ( f ) G ( f ) ] m exp ( j m τ 2 π f ) ,
P ( f ) 1 1 + [ H R F ( f ) G ( f ) ] 2 2 H R F ( f ) G ( f ) cos ( 2 π f t )
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