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Abstract
A receiver for weak frequency-coded microwave signal reception based on microring resonators array is proposed. This setup uses the nonlinear interaction of a microwave signal and an optical pump to generate an up-conversion signal to achieve the wideband signal reception. The minimum detectable power of this method reaches -93.2 dBm, which is suitable for the detection of weak signals. The results demonstrate a huge power conversion efficiency with η = 4.37×104, a wide conversion bandwidth of 2π×200 MHz, and a large 1-dB compressed dynamic range of 70.2 dB. The receiver can directly use the microwave signal received by the antenna that greatly reduces the volume and power consumption of the detection system. It is highly competitive in microwave photonics radar fields.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microwave radar signals are exploring higher frequency bands with the scarcity of microwave frequency resources and the requirement of higher signal bandwidth. High frequency microwave radars and millimeter-wave radars have become important fields in radar research, because of its ability to work in complex environments [1–5]. However, the complicated electromagnetic interference leads to a plight that few continuously available bands are suitable for signal propagation. The frequency-coded signal is widely used to overcome this predicament and has achieved a better ranging resolution [6,7].
Microwave photonics mainly studies the reception and processing of high-frequency microwave signals in the optical domain. It is a technology that enables various functionalities which are complex or even not directly possible in the microwave domain [8]. The electro-optical modulator is a key component in microwave signal reception and optical conversion [9]. It requires a high signal-to-noise ratio (SNR) and large driving power for the modulated signal. The minimum detectable power required is a few milliwatts that cannot meet the requirement of the weak signal reception [10–12]. Whereas, the high-frequency microwave signal is prone to attenuation during atmospheric transmission, especially in a humid environment, which greatly reducing the effective range of the radar [13,14]. It is indispensable to use high-power radar and additional electrical amplification equipment to enhance the echo signal, which undoubtedly increases energy loss and is not suitable for complex environments.
Extensive studies have been carried out on the reception of the weak signal in microwave and terahertz frequencies [15–17]. Whispering gallery mode (WGM) resonators have been introduced to realize the conversion of microwave to an optical frequency and to achieve the reception of weak microwave signals at room temperature [18–21]. Nonetheless, the inherent bandwidth of the WGM resonator limits the bandwidth of the received signal, which is particularly prominent in the field of high-frequency radar. Since the high-frequency radars usually need to transmit large time-bandwidth product signals to improve range resolution. A micro-ring resonators (MRRs) array will be suitable for receiving the frequency-coded signal, which meets the requirement of receiving large-time bandwidth radar signal in complex environments.
This paper proposes a receiver for frequency-coded microwave signal reception based on the electro-optic up-conversion effect. The nonlinear interaction between microwave and pump light in the microring resonator is used to convert the microwave signal to the optical domain, which greatly improves the weak microwave signal receiving capability. We have designed a radius-coded MRRs array that matches the frequency-coded signal that pulse sequences with different carrier frequencies are received by disparate MRRs, thus realize the reception of wideband weak signals. Different from the traditional microwave photonic radar signal receiving method, the receiver can directly use the microwave signal received by the antenna to complete the process of electro-optical conversion and adaptive filtering that greatly reduces the volume and power consumption of the detection system. It solves the dilemma of the weak signal reception and the large time-bandwidth product signal processing in microwave photonic radar.
2. Method and principle
The frequency-coded signal usually presents as the stepped-frequency pulse signal, as shown in Fig. 1(a). The stepped-frequency pulse signal is a set of pulse sequences with carrier angular frequencies of ωn = ω0+(n-1)Δω (n = 0, 1…, N) [6,7]. The pulse duration is T, the stepped angular frequency is Δω, and the pulse period is Tr. The transmitted signal can be expressed as:
Fig. 1. (a) The stepped-frequency pulse signal with the pulse duration of T, the stepped frequency of Δω, and the pulse period of Tr. (b) The schematic of the MRRs array for receiving frequency-coded pulse signal.
The MRRs are made out of z-cut lithium niobate coupled via a waveguide by evanescent-field coupling. The microwave resonator is an open microstrip. The resonator is overlapped with the optical cavity to maximize the mode overlap and thus the electro-optic coupling [15]. The received signals from the antenna are fed into the microwave resonators on the optical cavities through the series microstrip lines, then interact with the pump light to realize the up-conversion of the microwave signal to an optical one. The pulse signals of different frequencies will be received by different up-conversion units, thus the energy received can be fully exploited, of course, the energy conservation and phase matching of the up-conversion need to be satisfied. The length difference ΔL of the output waveguides should satisfy ΔL = 2πk (k = 0, 2, 3…) to eliminate the potential crosstalk between the different MRRs, and maintain the phase consistency of the signals. The structure details are shown in Fig. 2(a).
Fig. 2. (a) The details of the up-conversion cavity. The t1, t2 are the transmission coefficients of the add-port and drop-port, respectively, and κ is the coupling coefficient of the MRR. (b) The spectra of the optical input, the microwave signal and the output optical signal with multiple sidebands ωc − ωm and ωc + ωm generated by the cavity.
The laser pump with angular frequency ωc and the microwave signal with angular frequency ωm interact in the cavity to generate a sum frequency signal and difference frequency signal. Figure 2(b) shows the process of generating the sum frequency signal and difference frequency signal in the resonator. Multi-order sidebands will be generated during the interaction. Since the energy of the higher-order sidebands is extremely weak, only the first-order Stokes and anti-Stokes sidebands with frequencies of ωc-ωm and ωc+ωm, respectively, are considered.
In the up-conversion process, the relationship between the up-converted optical signal power Ps, input microwave power Pm and pump light power Pc can be expressed as [18,19]:
When the received microwave signal power Pm is less than the saturation power of the receiver, Pm< Pmax = ħωm2ωc2/32g2QmQ2, the small-signal approximation condition is satisfied. The relationship between the output up-converted optical signal and the input microwave signal power can be approximately linear, Ps = ηPcPm [19]. Therefore, the power conversion efficiency can be expressed as:
3. Simulation and analysis
To achieve a stable output of the up-converted optical signal, it is indispensable to satisfy that the frequency of the input microwave signal is equal to the free spectral range (FSR) of the optical cavity. At this condition, the up-converted sum frequency signal produces resonance in the cavity, and the signal conversion efficiency reaches the maximum. The FSR of the cavity is:
where R is the radius of the cavity, ne is the effective refractive index of the cavity, and c is the speed of light in a vacuum.The selected parameters in the simulation are: the input laser wavelength is λ = 1550 nm; the microwave signal angular frequency is 2π×30 GHz; to meet the up-conversion conditions, the microwave signal angular frequency will be ωm = 2πc/mλne, (m = 1, 2, 3, … is the number of resonance stages); the pulse sequence of the stepped-frequency pulse signal N = 10; pulse width T = 50 ns, thus the single pulse bandwidth B = 2π×20 MHz; in radar signal transmission, the stepped frequency Δω is generally equal to the single pulse bandwidth; the pulse period is Tr = 100 μs.
The lithium niobate crystal exhibits low dispersion in the 1550 nm wavelength range [22]. Considering the low dispersion, the refractive index of the pump light and the up-converted optical signal can be regarded as equal, nc = 2.21. Similarly, the dispersion of the microwave signal in the lithium niobate crystal can also be ignored, and almost no loss, the refractive index is nm = 5.1 [23]. The radius of the MRR is calculated to be R = 3596.35 μm with a width of 1000 μm at the resonance stage of m = 5. The frequency-coded pulse signal contains a series of sub-pulses with multiple carrier frequencies. By coding the radius of the MRRs in the array, the real-time reception of multiple carrier frequencies can be realized.
The FSR of the optical cavity decreases as the radius of the MRR increases, the relationship between the increment of the FSR and the radius of the MRR is shown in Fig. 3(a). The radius codes of different MRR are represented by dots in Fig. 3(a), according to the stepped frequency Δω = -ΔR (c /R2ne).
Fig. 3. (a) The increment of FSR versus the radius of the cavity, (b) The conversion bandwidth of the receiver versus the coupling coefficient of MRR in different radius offset.
When the single pulse bandwidth B matches the signal conversion bandwidth of the MRR, the received noise can be suppressed and the maximum output SNR can be achieved. The signal conversion bandwidth of the receiver depends on the coupling coefficient of MRR,
Usually, the add-drop ring resonators with a symmetrical structure will have t1 = t2; κ is the coupling coefficient of the MRR, κ2+t2 = 1 [24]; a is the loss coefficient of MRR. Here we ignore the loss, the relationship between the conversion bandwidth of the receiver, and the transmission coefficient of the MRR is shown in Fig. 3(b). The change of the bandwidth is 0.13 MHz with a radius offset of 20 μm. Therefore, we can ignore the influence of the small offset of the cavity radius on the up-conversion bandwidth.
The conversion process requires that the input pump light and microwave signal meet the phase-matching condition. By changing the thickness of the optical cavity, the mode distribution of the optical field and microwave field can be adjusted to achieve phase matching. As shown in Fig. 4, the maximum conversion efficiency can be achieved while the thickness of the optical cavity is h = 1441 μm. Similarly, the potential crosstalk between the different MRRs will be eliminated by setting the output waveguide to the same length.
Fig. 4. The effective refractive index of the microwave field and optical field in the cavity versus the thickness of the cavity.
The strength of the nonlinear interaction g in the electro-optical up-conversion resonator can be expressed as [18–21]:
In this case, the strength of the interaction g will be enhanced by increasing the superposition integral of the electric fields. The electric field distribution and the superposition integral of the input microwave field and optical field are calculated by the finite element method. In the simulation, we choose the TE mode with the polarization along the y-axis which is perpendicular to the direction of light propagation. The anisotropic medium tensor element of lithium niobite r33 is 31 m/V, χ(2) = r33ne4/4. To get a bandwidth of 2π×20 MHz, we assume that the coupling coefficient of the MRR is κ = 0.102, thus the quality factors of the resonators will be Q ≈ 107 and Qm = 150, such high quality factor resonators have been reported [25–27].
The interaction strength of the resonator g is calculated to be g = 2π×79.92 Hz in the simulation. According to Eq. (2), the relationship between the up-converted optical power spectral density and the input microwave power spectral density is shown in Fig. 5. The black curve shows that the up-converted optical power increases with the input microwave power linearly. The red line is the linear approximation (Ps = ηPm). The power conversion efficiency is approximated to be 4.37×104 (pump optical power Pc = 10 dBm). In small-signal approximation, the output power of the up-converted optical signal is a quasi-linear function that increases with input microwave power Pm. As the input microwave power spectral density increases to -96.0 dBm/Hz, and the microwave power is Pm = -23.0 dBm with designed single pulse bandwidth of 2π×20 MHz, the up-converted optical signal is compressed by 1-dB. Therefore, the received microwave signal power spectral density should be considered below Pm = -96.0 dBm/Hz.
Fig. 5. The up-converted optical power spectral density versus the input microwave power spectral density.
We recall the Eq. (3) and introduce the gain coefficient of the receiver:
4. Results and discussion
The optical output from the MRR array then enters the optical link that contains the pump light and the up-converted optical signal. An optical band-pass filter will filter out the pump light, and the optical heterodyne technology can be used to complete the signal detection. The schematic of detection processing is shown in Fig. 6. The signal is received by an antenna. Then it is up-converted into an optical one by the MRRs array. After being filtered, it enters the optical mixer. The local oscillator signal branch goes to a modulator and is converted into an optical one, then enters the optical mixer. The two signals meet at the optical mixer and the frequencies beat. Finally, intermediate frequency signals are output by the photodetector (PD).
Fig. 6. The schematic of weak microwave signal reception. OBPF, optical band-pass filter; MRRs array, microring resonators array; DFB, distributed feedback laser; LO, local oscillator; PD, photodetector.
The total conversion bandwidth of the receiver corresponds to the response function of the MRRs array, which is G(ω) = N·B. The receiver is equivalent to a matched filter, which can filter the input noise to the maximum and improve the output SNR. The minimum detectable power of the system mainly depends on the noise in the optical link. After electro-optical up-conversion and amplification, shot noise N1, thermal noise N2, and relative intensity noise N3 in the optical link are introduced, the corresponding noise can be expressed as,
The relationship between the output SNR of the receiver and the input microwave power spectral density is shown in Fig. 7. When the output signal power reaches the minimum detectable value where SNR = 1, the minimum detectable power spectral density is -166.2 dBm/Hz, and the minimum detectable power is Pmin = -93.2 dBm (4.79 ×10−10 mW) with single pulse bandwidth of 2π×20 MHz. This result shows a large improvement in detectable power compared to a traditional electro-optic modulator, whose drive voltage is about 1×102 mV [9,12]. Besides, this setup demonstrates a huge power conversion efficiency of η = 4.37×104 with an extended conversion bandwidth of 2π×200 MHz, and the large 1-dB compressed dynamic range is 70.2 dB.
The photon conversion efficiency of the resonant cavity is ηe = ωmη/ωc ∼ 6.78×10−2, which is greatly enlarged due to the enhanced modal overlap of the MRRs. The photon conversion efficiency improved more than 10 times compared with the state-of-the-art scheme. That enables the receiver to work in a weak signal environment. Our theoretical results are consistent with the results of the reported verification experiment [18,19].
It is worth noting that the large-bandwidth array-based weak signal receiver we proposed does not limit in a unique signal. It can adapt to any frequency-coded pulse signal, the stepped frequency of the signal can be adjusted by coding the radiuses of MRRs. Moreover, the thermo-optical effect can be exploited to realize the adjustment of the carrier frequency to meet the utilization in complex environments.
5. Conclusion
In summary, we propose a large-bandwidth array-based frequency-coded pulse signal receiver. This setup demonstrates a huge power conversion efficiency with extended conversion bandwidth and a large 1-dB compressed dynamic range. The receiving signal will not be limited, which can adapt to any frequency-coded pulse signal, since the stepped frequency of the signal can be adjusted by coding the radiuses of MRRs. Different from the traditional modulators, the receiver can directly use the microwave signal received by the antenna to complete the process of electro-optical conversion and adaptive filtering. It is suitable for weak signal reception with a large time-bandwidth product signal in microwave photonic radar.
Disclosures
The authors declare no conflicts of interest.
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