Theoretical investigation of photonic generation of frequency quadrupling linearly chirped waveform with large tunable range

Yulei Liu; Jun Liang; Xuan Li; Nan Xiao; Zhenghao Zhang; Xiaogang Yuan

doi:10.1364/OE.25.016196

1. Introduction

It is critical for modern radar systems with high resolutions to have the capability of generating chirped microwave or millimeter wave (mm-wave) pulse [1]. Chirped signals are conventionally obtained by using electronic circuits, but with limitations of small bandwidth and low central frequency. However, some radar systems have the requirement of the central frequency as much as tens or even hundreds of GHz [2]. In comparison with the methods based on electrical circuits, photonic methods have the advantage of large bandwidth, high frequency, wide tunability and low loss in chirped signal generation.

A variety of photonic methods of generating chirped signals have been reported. The direct space-to-time mapping on the basis of spatial light modulator [3] can generate the reconfigurable chirped pulse, but the system is bulky, lossy and complicated. Interfering of two dispersed optical pulses [4,5] can achieve a chirped pulse with tunable central frequency, but the systems are sensitive to environmental variations. A chirped pulse can be generated through optical spectral shaping followed by frequency-to-time mapping. However, for the all-fiber-based approaches [6,7], the generated pulses are usually fixed, while for the silicon chip-based approaches [8,9], tunable pulses can be achieved but with a simple signal profile. Recently, self-heterodyning is also proposed to generate a chirped pulse, the key components are the directly modulated laser diode (LD) and Mach-Zehnder interferometer [10]. However, both the central frequency as well as the bandwidth of the pulse generated cannot be controlled independently. A chirped pulse can also be generated by external phase modulating two phase-correlated wavelengths [11]. The key significance of this scheme is that the generated signal has both tunability and reconfigurability. To overcome the stability problem caused by separated optical paths, polarization modulator (PolM)-based approaches are intensively investigated [12–19]. This method also faces the challenge of the generation of two orthogonally polarized wavelengths, furthermore, frequency multiplication is needed to improve the signal frequency. For example, the adoption of a Mach-Zehnder modulator (MZM) followed by a differential group delay device [15] or a Mach-Zehnder interferometer followed by a polarization beam combiner (PBC) can achieve the frequency-doubled orthogonally polarized wavelengths [16], they also can be generated by using cascaded MZM and PolM combined with an optical filter (OF) [17], otherwise by using dual-parallel PolM [18]. For these approaches, however, the frequency multiplication factor (FMF) is only 2, a higher FMF is desired to support even higher frequency applications. Frequency-quadrupled orthogonally polarized wavelengths can be generated by using an MZM followed by an OF and a polarization-maintaining fiber Bragg grating (PM-FBG) [19], but the response of PM-FBG is wavelength-dependent, which makes the tunability of the generated signal limited.

This paper proposes an innovative photonic scheme for the generation of a linearly chirped pulse. Second-order optical sidebands in the proposed scheme are firstly produced as two orthogonally polarized phase-correlated wavelengths through the use of a dual-output dual-parallel Mach-Zehnder modulator (DPMZM) followed by a PBC and an OF. Then, a PolM driven by a parabolic signal is applied to the introduction of a parabolic phase deviation to both the two optical wavelengths. At last, balanced detection is applied to obtain the electrical linearly chirped pulse and suppress the distortion and background noise. As a result, the photonic waveform generator can be divided into three steps. Firstly, frequency quadrupling operation by using DPMZM and OF, then, reconfigurable waveform generation by using polarization modulation, and finally, background noise suppression by using balanced detection. The frequency multiplying operation leads to high frequency and large frequency tunable range for the generated signal, and the polarization modulation features good reconfigurability and high stability for the generated waveform. Considering the notch bandwidth of the OF and the operation frequency of the photodetector (PD), the scheme can provide a large and continuous frequency tunable range more than tens of GHz for the generated linearly chirped signal. The proposed method has potential applications in high frequency and frequency-agile radar systems.

2. Principle

Figure 1 shows how the proposed chirped mm-wave pulse is generated. A dual-output DPMZM, consisting of two sub-MZMs with identical performances placed in parallel and a directional coupler, receives the light sent by an LD. A sinusoidal microwave from the local oscillator (LO) is separated into two paths with a phase gap of 45° and applied to both of the two sub-MZMs (MZM1 and MZM2). Both the two MZMs are arranged to be biased at the maximum point for transmission so that the optical carrier and ± second-order sidebands can be obtained, while the higher sidebands which are even-order are omitted.

Fig. 1 Schematic of the proposed chirped mm-wave pulse generation. LO, local oscillator; LD, laser diode; DPMZM, dual-parallel Mach-Zehnder modulator; PBC, polarization beam combiner; OF, optical filter; PC, polarization controller; PolM, polarization modulator; OS, optical switch; PBS, polarization beam splitter; BPD, balanced photodetector.

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For the two ports of DPMZM, their optical fields can be written by

\begin{matrix} [\begin{matrix} E_{1} (t) \\ E_{2} (t) \end{matrix}] = [\begin{matrix} \sqrt{1 - μ} & j \sqrt{μ} \\ j \sqrt{μ} & \sqrt{1 - μ} \end{matrix}] [\begin{matrix} E_{M 1} (t) \\ E_{M 2} (t) \end{matrix}] \\ \propto E_{i n} (t) J_{0} (m) \exp (j \frac{π}{4}) [\begin{matrix} 1 \\ 1 \end{matrix}] + \\ \sqrt{2} E_{i n} (t) J_{2} (m) [\begin{matrix} \exp (- j 2 ω t) \\ \exp (j 2 ω t + j \frac{π}{2}) \end{matrix}] \end{matrix}

where μ = 1/2 is the coupling coefficient of directional coupler, E_M1(t) and E_M2(t) are the output signals of MZM1 and MZM2, respectively. E_in(t) is the incident light, m is the modulation index of MZM, ω refers to the frequency of the signals of the microwave, while J_n() is the first nth-order Bessel function. The output signals of the two MZMs have same sidebands (i.e. optical carrier and two second-order sidebands), but each of the sidebands has different phase due to the 45 degree phase difference introduced by the electrical phase shifter. At the output of the upper MZM, all the three components have a phase of 0 degree, while for the output of the bottom MZM, the −2nd-order sideband has a phase of −90 degree, the carrier has a phase of 0 degree and the 2nd-order sideband has a phase of 90 degree. Then, the two optical signals are sent into the directional coupler, which has a transmission matrix as expressed in Eq. (1), at the output of the upper port, the phase of the upper MZM will not change while the phase of the bottom MZM will change 90 degree. As a result, the two + 2nd-order sidebands from the two MZMs are out of phase and canceled each other. Only the carrier and −2nd-order sideband are reserved. Similarly, at the bottom port, the two −2nd-order sidebands are out of phase and cancelled each other. Only the carrier and + 2nd-order sideband are obtained.

All signals from port 1 and 2 are combined into one path with orthogonal polarization directions through a PBC. The optical carrier is then suppressed by an optical filter (OF), and orthogonally polarized ± second-order optical sidebands are obtained. The notch optical filter used in the scheme is a device to filter out the specific spectrum in the optical domain. The main parameters of an OF have the central frequency, the notch bandwidth and the notch depth. A polarization controller (PC1) is used to adjust the polarization directions of the two sidebands aligned with the principal axes of the PolM. The PolM equals to two parallel phase modulators (PMs) with complementary phase modulation indices connected by a polarization beam splitter (PBS) and a polarization beam combiner (PBC) [20]. The PBC selects the appropriate polarization component of each signal at the input ports and combined the selected polarization components, at the output of the PBC, two orthogonally-polarized optical signals are transmitted in same fiber [21]. The two optical sidebands are complementarily phase modulated through PolM by a driving signal V_ss(t), where V_s is the amplitude and s(t) is the normalized waveform. The optical signal at the output of the PolM is given by

\begin{matrix} {\overset{⇀}{E}}_{p} (t) \propto E_{i n} (t) J_{2} (m) \\ {\overset{⇀}{x} \exp [- j 2 ω t - j β s (t)] + \overset{⇀}{y} \exp [j 2 ω t + j \frac{π}{2} + j β s (t)]} \end{matrix}

where x- as well as y-directions represent two principal axes of PolM, β = πV_s/V_π represents the phase modulation index of PolM, V_π means the half-wave voltage of PolM.

A time domain optical switch (OS) is placed after the PolM to select the modulated optical signal. The balanced photo detection is applied to suppress the distortion and background noise in the detected signal [22]. By adjusting PC2 to let one principal axis of the polarization beam splitter (PBS) have an angle of 45° to one principal axis of the PolM, then the two output signals from the PBS are given as

\begin{matrix} \begin{array}{l} E_{o u t 1} \propto E_{i n} (t) J_{2} (m) {\exp [- j 2 ω t - j β s (t)] + \exp [j 2 ω t + j \frac{π}{2} + j β s (t)]} \\ E_{o u t 2} \propto E_{i n} (t) J_{2} (m) {\exp [- j 2 ω t - j β s (t)] - \exp [j 2 ω t + j \frac{π}{2} + j β s (t)]} \end{array} & T \leq t \leq T + τ \end{matrix}

where T represents the starting moment and τ is the time duration of the generated pulse, respectively.

The two output signals from the PBS are then sent to the balanced photodetector (BPD) for balanced detection. When s(t) represents a parabolic waveform, the generated pulse after BPD can be expressed as

\begin{matrix} i (t) \propto E_{i n}^{2} (t) J_{2}^{2} (m) \cos [4 ω t + \frac{π}{2} + 2 \frac{β}{τ^{2}} {(t - T)}^{2}] & T \leq t \leq T + τ \end{matrix}

As described in Eq. (4), in the upper PD, an electrical signal of ${| E_{o u t 1} |}^{2}$ is generated, while in the bottom PD, an electrical signal of ${| E_{o u t 2} |}^{2}$ is generated. As a result, at the two PDs, linearly chirped signals with carrier frequency of 40 GHz, DC components, distortion components with frequency of 20 GHz and 60 GHz are generated. The two linearly chirped signals are out of phase, on the other hand, the DC components are in phase and parts of the distortion components are in phase. Therefore, by subtraction, the linearly chirped signal will be enhanced by 3 dB, while the DC component will be efficiently cancelled, and the distortion components are partial suppressed. Thus, an mm-wave chirped pulse with a central frequency which four times of the LO frequency and a bandwidth of 2β/(πτ) is generated.

3. Simulation results and discussion

To verify our proposed scheme of chirped mm-wave pulse generation, a concept-proof system is built based on the OptiSystem platform as shown in Fig. 1. The laser works at a wavelength of 193.1 THz and a power of 16 dBm. Each of the MZMs in dual-output DPMZM has an insert loss of 5 dB and a modulation index of 1.88. The frequency of LO is 10 GHz. The central frequency and bandwidth of the notch OF reaches 193.1 THz and 10 GHz, respectively, and the depth of the notch stands at 50 dB. The filtered optical signal firstly amplified by an erbium doped fiber application amplifier (EDFA) with a gain of 20 dB and then combined by the PBC. The PolM has an insert loss of 5 dB and modulated by a parabolic pulse with a modulation index of 12.34 and time duration of 102 ns. The BPD has a responsivity of 0.85 A/W.

The output optical spectra from two ports of dual-output DPMZM are shown in Fig. 2, both of them are single-sideband signals, one consists of a carrier and -second-order sideband while the other consists also of both a carrier and + second-order sideband, which agree well with the theoretical derivation of Eq. (1). The forth-order sidebands, shown in Fig. 2, are also generated, with a power 37 dB lower than the second-order one.

Fig. 2 Optical spectra from (a) port 1 and (b) port 2 of dual-output DPMZM.

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The electrical power spectra for the signals generated by single-end and balanced detections are shown in Fig. 3. Figure 3(a) shows the single-end detection which obtained by sending the optical signal from output1 of PBS into PD1 of the BPD. The linearly chirped signal with a carrier frequency of 40 GHz is generated, as shown in the inset of the Fig. 3. Direct current component (background noise) and distortion components with a frequency of 20 GHz and 60 GHz are also generated because of the forth-order optical sidebands and the square-law detection. Through the balanced detection, both the noise and distortions are suppressed, a signal-to-noise and distortion-ratio of 24 dB is obtained, as shown in Fig. 3(b).

Fig. 3 Electrical spectra for the signals generated by (a) single-end and (b) balanced detection.

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The normalized waveform of generated mm-wave linearly chirped pulse is shown in Fig. 4. Figure 4(a) presents the waveform with a full-time duration, and Fig. 4(b) shows the zoom-in views of the waveform over the time span of 1 ns to 1.5 ns. As shown in the Fig. 4(b), the cosine profiles have a time spacing approximately 25 ps, which corresponding a frequency approximately 40 GHz.

Fig. 4 Generated pulse waveforms (a) full time duration (b) zoom-in with time span of 1 to 1.5 ns.

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The instantaneous frequency of the generated pulse can be obtained by using the Hilbert transform and numerical differentiation. The instantaneous frequency of the sent-out pulse is shown in Fig. 5. The chirp rate is maintained constant during the pulse duration, as expected for a linearly chirped pulse. As shown in the Fig. 5, the bandwidth of the waveform is 110 MHz, which agree well with the calculation result of 109 MHz. The time-bandwidth product (TBWP) is calculated to be 11 considering the time duration of 102 ns. The TBWP is relatively small, but it can be efficiently increased by recirculating phase modulation loop [23] or splitting the electrical parabolic signal [14].

Fig. 5 Instantaneous frequency of the generated pulse.

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The pulse-compression capability is also investigated. Figure 6 shows the auto-correlation function of the generated pulse. The peak-to-sidelobe ratio (PSR) is about 7.4 dB. The full width at half maximum (FWHM) of the compressed pulse is about 11 ns, corresponding to a pulse compression ratio (PCR) of 9.3. The PCR also can be improved by the approaches demonstrated in [14] and [23].

Fig. 6 Auto-correlation function of the generated pulse.

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In the proposed approach, the central frequency of the generated signal can be tuned by adjusting the frequency of LO, the minimum frequency is restricted by the notch bandwidth of the OF (about 10GHz), while the maximum frequency is limited by the bandwidth of BPD (more than 50GHz), thus it can provide a large and continuous frequency tunable range more than tens of GHz, which is much larger than the approach demonstrated in [19]. On the other hand, the FMF of the proposed approach is four, which can support high-frequency applications or ease the requirements of microwave drives as compared with approaches reported in [12]- [18]. Furthermore, the generated pulse has good reconfigurability as the form of the generated pulse can be altered by changing the driving signal waveform applied to PolM.

4. Conclusions

In summary, we proposed a novel approach that generates linear chirped mm-wave signal with large frequency tunable range and demonstrated the method by the simulations. The key point in the system is the orthogonally polarized optical sidebands generation, which realized by using a dual-output DPMZM, a PBS and an OF. The ± second-order optical sidebands with orthogonal polarization directions were generated and phase modulated by a parabolic waveform in the PolM. The balanced detection was applied to suppress the noise and distortion in the generated signal. A linearly chirped pulse with a central frequency which four times of the LO frequency was achieved. The TBWP, PCR of the generated pulse were 11 and 9.3, respectively and the PSR is 7.4 dB. The proposal has both good reconfigurability and tunability, it can be continuously frequency tuned from about 10 GHz to over 50 GHz in principle. The proposed method has potential applications in high frequency and frequency-agile radar systems.

Funding

National Natural Science Foundation of China (NSFC) (61571461).

Acknowledgments

We would like to express our gratitude to all those who gave kind encouragement and useful instructions all through the writing. A special acknowledgment should be extended to the library assistants who supplied with reference materials of great value. We would like to thank the anonymous reviewers for their very helpful comments and feedbacks to improve the manuscript.

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Theoretical investigation of photonic generation of frequency quadrupling linearly chirped waveform with large tunable range

Abstract

1. Introduction

2. Principle

3. Simulation results and discussion

4. Conclusions

Funding

Acknowledgments

References and links

Cited By

Figures (6)

Equations (4)

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