1. Introduction

Microwave signal has been extensively exploited in broadband wireless access networks, sensor networks, radar, radio-over-fiber, and so on [1]. Over the past three decades, many schemes have been adopted to generate microwave signal. Among these methods, the pure electronic methods such as gyrotron, electronic oscillator and crystal oscillator face the following issues: high power loss, low operating frequency, high electromagnetic sensibility [2]. In comparison, the photonic-assisted microwave generation methods (e.g., optical heterodyning, external modulation and optoelectronic oscillator) could mitigate these problems [1]. Specially, an optoelectronic oscillator (OEO) can generate a stable microwave signal and its phase noise is independent of frequency [3]. Unfortunately, electro-optic modulation and photoelectric conversion are unavoidable in an OEO and the electronic bottleneck from electronic devices limits the frequency and operation bandwidth of the generated microwave signal. Microwave signal generation using pure optical technology provides new access to solve the electronic bottleneck problem in traditional pure electrical or photoelectric hybrid microwave generation technology.

An AOMO based on a passively mode-locked quantum dash laser was demonstrated in Ref. [4], which could generate a photonic microwave signal with the frequency dependent on the length of the laser cavity. However, a very short cavity length was required to generate a photonic microwave signal with high frequency, and the tunability was almost lost due to the fixed length of the device. In our previous work, we proposed a new AOMO to improve its tunability [5]. The oscillation frequency was selected by the Brillouin selective sideband amplification effect in fiber, and the functions of microwave envelope detection and feedback modulation were implemented by a semiconductor optical amplifier (SOA). By using this AOMO, a microwave signal with a frequency of 10.87 GHz was generated, which was corresponding to the Stokes frequency shift of the stimulated Brillouin scattering (SBS) in the single-mode fiber (SMF). Unfortunately, the tuning range of the AOMO was only 284 MHz. In addition, several similar schemes were proposed to simplify the system [6] or improve the tunability [7,8] and the side-mode suppression ratio (SMSR) [9] of the generated microwave signal. In these systems, although the long fiber that is used to produce SBS can increase the Q value of an AOMO, it makes the system bulky. With the development of research, some AOMOs based on P1 oscillation in DFB-LD were developed by different research groups [10–13]. These systems were more compact, cheaper, and easier to integrate since they do not contain long fibers and the main component is only the DFB-LD. Meanwhile, the tunability of the generated microwave signal is improved. However, the quality of the generated microwave signal is not so good [14]. In these existing schemes, the P1 oscillation is realized by external light injection or self-delayed optical feedback. For an all-optical microwave generator based on the external light injection, the stability of the generated microwave signal is mainly limited by the line-width of the slave laser. In general, the slave laser is a DFB-LD and its line-width is ∼MHz. It means that the generated microwave signal is still not stable. Recently, different research groups proposed some method to improve the line-width of the generated microwave signal, e.g., dual feedback loop [10], single feedback loop [11] and filtered optical feedback loop [12]. However, the experimental results show that the optimum 3 dB line-width of the generated microwave signal is about 8.2 MHz. For one AOMO based on the self-delayed optical feedback injection [13], although the 3 dB line-width of the generated microwave signal is less than 50 kHz, there are multiple side modes near the center frequency, and the SMSR is only 23.9 dB. To improve the SMSR of the P1 signal, some additional feedback loops such as the SOA feedback loop and the Sagnac loop are used. In summary, the feedback loop is necessary to improve stability of the generated microwave signal. But the filter in the additional feedback loops limits the operating bandwidth of generated microwave signal. More importantly, the length matching between the main loop and the additional feedback loops causes the system to be more complex.

In this paper, we report an AOMO based on mutual-injection coupling between two DFB-LDs. This system contains only a mutual injection loop consisting of two DFB-LDs and a few passive components. In this AOMO, the microwave seed signal originates from the P1 oscillation in one of the DFB-LDs. The functions of microwave envelope detection and feedback modulation are implemented by another DFB-LD. Then through the coupling between the P1 signal and a resonant mode of the mutual injection loop, the stability of the P1 signal is improved and a high-quality microwave signal is generated. Different from the previous schemes, the stability of the P1 signal was improved by the coupling between two DFB-LDs and a mutual injection loop while other additional feedback loops are unnecessary. Compared with an all-optical microwave generator based on external light injection [10–12], the line-width of the generated microwave signal is dramatically narrowed by mutual light injection. Meanwhile, since the P1 oscillation is sensitive to injected light, the frequency of the P1 signal can be easily adjusted, which makes the AOMO easy to be tuned. These advantages make the AOMO have great potential for application.

2. Principle

The schematic diagram of the AOMO is shown in Fig. 1(a). Two similar thermally-tuned DFB-LDs (DFB-LD1 and DFB-LD2) are important components of this AOMO. The light from DFB-LD1 is injected into DFB-LD2 after passing through a circulator (Cir1), an optical coupler (OC1), an attenuator (ATT1), a polarization controller (PC1), and Cir2 in turn. Similarly, the light from DFB-LD2 is also injected into DFB-LD1 in the same way. These two optical paths are completely equivalent, which form the so-called mutual injection loop. The dynamic states of the two DFB-LDs are controlled by a set of parameters including the power and polarization of the injected light, their temperature, and bias current.

 

Fig. 1. (a) Schematic diagram of an AOMO based on mutual-injection coupling between DFB-LDs. (b) The schematic diagram of optical spectra of DFB-LDs in different stages: (I) the free-running DFB-LD2, (II) the output of the DFB-LD2 is injected to DFB-LD1 and the P1 oscillation is presented, (III) the P1 signal is fed back to the DFB-LD2 and the mode regeneration and the optical-optical modulation are presented, (IV) the regenerated mode and the modulated optical signal is fed back to the DFB-LD1, the P1 signal is enhanced and the optical-optical modulation is also presented. DFB-LD: distributed feedback laser diode, Cir: circulator, OC: optical coupler, ATT: attenuator, PC: polarization controller, PD: photodetector, OSA: optical spectrum analyzer, ESA: electrical spectrum analyzer; λ₀₁: the wavelength of free-running DFB-LD1 output; λ₀₂: the wavelength of free-running DFB-LD2 output; λ₁: the wavelength of DFB-LD1 output after red-shift; Δλ: The wavelength difference between the nearest neighbor two modes of the P1 signal.

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For convenient analysis, it is assumed that the DFB-LD1 is driven into P1 oscillation, and the mode regeneration [15] and optical-optical modulation [6] occur in DFB-LD2. Firstly, the bias current and temperature of the two DFB-LDs are properly set so that their wavelength and power are almost equal under free-running. By appropriately changing the power and polarization of the light from DFB-LD2 through ATT2 and PC2, the DFB-LD1 is driven into P1 oscillation which is the seed signal. Through the mutual injection loop, the P1 signal is injected into DFB-LD2. The optical carrier of the P1 signal is regenerated in DFB-LD2 through stimulated radiation. Because the wavelength of the optical carrier is close to that of the DFB-LD2 (after red-shift), the optical injection locking [16] may be presented in DFB-LD2 and the mode of DFB-LD2 will be locked by the optical carrier. In summary, both the optical injection locking and the mode regeneration can be presented in the DFB-LD2 cavity. At the same time, the envelope of the P1 signal is also modulated to the optical carrier through cross-gain modulation (XGM) and cross-phase modulation (XPM) [17], in other words, the XGM and the XPM play as optical-optical modulation. As a result, the P1 signal is modulated to the optical carrier and the phase of the center frequency of the two DFB-LDs are highly correlated due to the optical injection locking. When the optical carrier is high phase correlated and the P1 signal is fed back to the DFB-LD1, the P1 signal will be enhanced. The schematic diagram of optical spectra of DFB-LDs in different stages is shown in Fig. 1(b). Although the above operation could improve the stability of the P1 signal, it is still a multimode microwave signal. Furthermore, we should notice that there is a set of oscillation modes with some stationary free spectrum range (FSR) in the mutual injection feedback oscillation loop. The gain region of the loop determines the number of oscillation modes that is mainly determined by the gain curve of the two DFB-LDs. Because the line-width of the two DFB-LDs narrows under the low optical power injection [18,19] the effective gain curve of the mutual injection loop narrows accordingly, which means that the number of oscillation modes is reduced. Similar to the vernier caliper effect [20], if one mode of the P1 signal is aligned with one of the oscillation modes with the stationary FSR, the system will form stable oscillation and generate a single-mode microwave signal. In addition, the microwave seed signal originates from the P1 oscillation of the DFB-LD1. In fact, the P1 oscillation comes from the relaxation oscillation while the essence of the relaxation oscillation is the fluctuation of the carrier in DFB-LD1. The relaxation time of the relaxation oscillation in DFB-LD1 can be changed by changing the operating parameters of two DFB-LDs (e.g., the bias current and the operating temperature) or the injected light (e.g., the optical power and the polarization). Therefore, the frequency of generated microwave signal can be easily changed.

3. Experiment and results

To verify the feasibility of the proposed scheme, an experiment is carried out based on the setup shown in Fig. 1. Two commercial thermally-tuned DFB-LDs without internal isolator are employed to implement mutual optical injection and they have similar characteristics. Their optical power is controlled by the bias current and the optical wavelength is mainly affected by temperature. The threshold current (I_th) of the two DFB-LDs is 8.5 mA. The DFB-LD1 is biased at 16.7 mA (2I_th), and the temperature is maintained at 23.0 °C by a thermo-electric cooler. These parameters of DFB-LD2 are 20.0 mA (2.4I_th) and 26.7 °C respectively. Under the free-running condition, the DFB-LD1 outputs a single-mode wave with a wavelength of 1548.806 nm and optical power of 2.32 dBm, and these parameters of DFB-LD2 are 1548.810 nm and 2.32 dBm respectively. An optical spectrum analyzer (YOKOGAWA AQ6370C) and an electrical spectrum analyzer (Agilent N9010A) were used to measure the optical spectrum and corresponding electrical spectrum, respectively.

Firstly, we discuss the stability of the P1 signal under the unidirectional injection. Under the condition of which port 1 of the Cir2 is disconnected, the output of the DFB-LD2 is injected into the DFB-LD1 then it can be driven into P1 oscillation by adjusting the ATT2 and PC2. From port A of the OC1, we measure the optical and electrical spectra of the output from DFB-LD1. Similarly, under the condition of which port 1 of the Cir1 is disconnected, the output of the DFB-LD1 is injected into the DFB-LD2 and it can also be driven into P1 oscillation. The optical and electrical spectra of the output from DFB-LD2 can be measured from port B of the OC2. The measured optical and electrical spectra are all shown in Fig. 2. From the optical spectra we can see that both DFB-LDs are driven into P1 oscillation under unidirectional injection, but the frequencies of the two P1 oscillations are different. Furthermore, the electric spectrum results show that the stability of the P1 signal from the two DFB-LDs is poor. Their 3dB line-width is about 3 MHz. It means that there are a lot of random modes in the generated P1 signal.

 

Fig. 2. The measured spectra of DFB-LD1 and DFB-LD2 under unidirectional injection. (a) Optical spectrum of DFB-LD1; (b) Optical spectrum of DFB-LD2; (c) Electrical spectrum of DFB-LD1; (d) Electrical spectrum of DFB-LD2.

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To improve the stability of the P1 signal, the mutual injection loop as shown in Fig. 1 is used. Although the dynamic states of two DFB-LDs are diverse, in this AOMO, the mode regeneration, optical injection locking, and optical-optical modulation in DFB-LD are important for improving the stability of the P1 signal and they are investigated. The different dynamic states can be presented by changing the wavelength of the DFB-LDs, the power, and the polarization of the injection light. The output spectra of DFB-LD1 and DFB-LD2 in different dynamic states can be recorded from observation ports A and B, respectively. When the wavelength difference of the free-running DFB-LDs is large, the DFB-LDs cannot lock each other because the wavelength of the injection light is far away from the injection lock region. However, the mode regeneration is obvious as shown in Fig. 3. From Fig. 3(a), we can see that both the outputs of the DFB-LDs under mutual injection have two modes when the conditions of P1 oscillation in the DFB-LDs are all not satisfied. One is their optical cavity mode after redshift, the other is the regenerated mode. When the condition of P1 oscillation is satisfied in DFB-LD1 but not in DFB-LD2, the DFB-LD1 will be driven into P1 oscillation. From Fig. 3(b), we can see that the red-shift mode of DFB-LD2 is modulated by the P1 signal from DFB-LD1 due to the optical-optical modulation, and the mode regeneration is still obvious.

 

Fig. 3. The measured optical spectra of DFB-LD1 and DFB-LD2 with large wavelength difference under mutual injection. (a) The condition of P1 oscillation in the DFB-LDs is both not satisfied; (b) The condition of P1 oscillation in DFB-LD1 is satisfied but it is not satisfied in DFB-LD2.

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When the wavelengths of the two free-running DFB-LDs are almost equal, the DFB-LDs could lock each other because the wavelength of the injection light is in the injection locking region. However, the optical injection locking effect on improving the stability of the P1 signal depends on the condition of P1 oscillation in the DFB-LDs. Firstly, we discuss the case in which the P1 oscillation of one DFB-LD is satisfied but that of the other DFB-LD is barely not satisfied. In the experiment, we firstly adjust the power and the polarization of injection light to make the P1 oscillation in one DFB-LD strong and that in the other DFB-LD very weak at the unidirectional injection. The measured optical spectra are shown in Fig. 4(a-b). Based on this, the mutual injection loop is then enclosed and the values of the parameters are the same as the unidirectional injection. The measured optical spectra are shown in Fig. 4(d-e). From the results, we can see that the strong P1 oscillation is enhanced and the weak P1 oscillation is suppressed. Secondly, we discuss the case in which the P1 oscillation of the two DFB-LDs is both satisfied. The measured optical spectra at the unidirectional injection are shown in Fig. 4(c), and the corresponding results when the injection loop is enclosed are shown in Fig. 4(f). These results show that the P1 oscillation is destroyed and there is a wider spectrum because the two unstable P1 signal and their feedback aggravate the instability of the optical spectrum which cannot help to improve the stability of the generated signal.

We should notice that these P1 signals may be both enhanced when the frequency of one P1 signal is twice as that of the other P1 signal. The measured optical spectra under the unidirectional injection are shown in Fig. 5(a). Then the mutual injection loop is enclosed and the values of the parameters are the same as the unidirectional injection. The measured optical spectra are shown in Fig. 5(b). The corresponding electric spectrum is shown in Fig. 5(c). The frequencies of the period-two (P2) signal in DFB-LD1 are 8.54 GHz and 17.07 GHz at mutual injection. The results show that the DFB-LDs are driven into P2 oscillation at mutual injection. In general, there is no correlation between the two P1 oscillations as shown in Fig. 5(a). When the mutual injection loop is enclosed, one of the two P1 oscillations will suppress the other and dominate the oscillation of the coupling system. However, in the special case where the frequency of one P1 oscillation is twice as that of the other P1 oscillation, the result is very different. In DFB-LD1, the double frequency signal of the P1 oscillation of DFB-LD2 can strengthen the P1 oscillation of DFB-LD1 because they have the same frequency. In DFB-LD2, the beat signal between the two first-order side-bands can also strengthen the P1 oscillation of the DFB-LD2 because they have the same frequency. Therefore, these two P1 signals are both enhanced.

From the above discussion, the mode regeneration, optical injection locking, and optical-optical modulation in DFB-LDs could improve the stability of the P1 signal when the wavelength of the DFB-LDs is almost equal. However, the improved P1 signal is still not in single mode. The mutual injection loop is essentially an all-optical oscillation loop that provides a set of oscillation modes. The vernier caliper effect between the oscillation modes of the mutual injection loop and the improved P1 signal is also important for mode selection. We measure the electric spectrum when the P1 signal is enhanced (The corresponding optical spectrum is shown in Fig. 4(d)). The result is shown in Fig. 6. One set of oscillation modes with a stationary FSR of 7.1 MHz is provided by the mutual injection loop. Besides, the optical injection can reduce the line-width of one DFB-LD [18]. It means that the effective gain curve of the mutual injection loop has been narrowed and just a few modes of the P1 signal have sufficient gain to reach the start-oscillation condition. Via the vernier caliper effect between the oscillation modes of the mutual injection loop and the improved P1 signal, one single-mode microwave signal with high stability could be generated. The electrical spectra and the SSB phase noise of the generated microwave signal shown in Fig. 7 and Fig. 8 indicate this AOMO can generate one microwave signal with a frequency of 16.69 GHz and a SSB phase noise of −90.7 dBc/Hz@10 kHz. In the experiment, the frequency drift range of the generated microwave signal is less than 100 kHz within 1-hour under a frequency span of 500 kHz. Since the device characteristic, the stability of the generated microwave signal is affected by these factors, including mechanical stability, external vibration, temperature, etc. In fact, it can be improved by using waveguides or an integrated system. For this AOMO, the system is easy to integrate because the main component is the DFB-LD.

 

Fig. 4. The measured optical spectra of DFB-LD1 and DFB-LD2 under unidirectional injection (a-c) and mutual injection (d-f).

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Fig. 5. The measured spectra of P2 oscillation. (a) Optical spectra of DFB-LD1 and DFB-LD2 under unidirectional injection; (b) Optical spectra of DFB-LD1 and DFB-LD2 under mutual injection; (c) Electrical spectrum of DFB-LD1 under mutual injection.

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Fig. 6. The FSR of the mutual injection loop.

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Fig. 7. The measured RF spectra of different spans. (a) 26.5 GHz; (b) 2 GHz; (c) 20 MHz; and (d) 500 kHz.

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Fig. 8. SSB phase noise of the generated 16.69 GHz microwave signal.

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Finally, the tunability of the AOMO should be mentioned. The frequency of the generated microwave signal is determined by the frequency of the P1 signal and the FSR of the mutual injection loop. Therefore, the operating frequency can be simply tuned by varying the power and polarization of the injection light as well as the bias current and operating temperature of DFB-LDs. Figure. 9 shows a tuning range of the AOMO from 14.48 GHz to 21.45 GHz. The AOMO is possible to obtain a larger tuning range but the electrical spectrum cannot be measured due to bandwidth restrictions of the ESA.

 

Fig. 9. Tunability of the proposed AOMO with a tuning range from 14.48 to 21.45 GHz.

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4. Summary

In conclusion, a novel AOMO using mutual-injection coupling between DFB-LDs has been proposed and experimentally demonstrated. In this AOMO, the seed signal is generated based on the P1 oscillation in DFB-LD. Through the mode regeneration and the optical injection locking, the optical-optical modulation functions of microwave envelope detection and feedback modulation are achieved. Then, with the help of the feedback injection of the mutual injection loop, the phase correlation of two DFB-LDs is improved and the P1 signal is enhanced. Finally, a high-quality single-mode photonic microwave signal is generated based on the vernier caliper effect between the improved P1 signal and the FSR of the mutual injection loop. The experimental results have proved that the AOMO can generate a microwave signal with a frequency of 16.69 GHz and the SSB phase noise of −90.7 dBc/Hz@10 kHz. Meanwhile, the tuning range from 14.48 GHz to 21.45 GHz is verified. The primary advantage of this AOMO is that there is no electro-optic modulation and photoelectric conversion in the system. Additionally, the stability of the P1 signal in DFB-LD is greatly improved with just one mutual injection loop. The prominent significance of this AOMO is that only one mutual injection loop, which greatly reduces the cost and provides a powerful foundation for on-chip photonic systems design and application.