Photonic generation of flexible ultra-wide linearly-chirped microwave waveforms

Rui Zhu; Rui Zhu; Rui Zhu; Rui Zhu; Mei Xu; Mei Xu; Mei Xu; Mei Xu; Quanhua Liu; Quanhua Liu; Quanhua Liu; Quanhua Liu; Bin Wang; Bin Wang; Bin Wang; Bin Wang; Weifeng Zhang; Weifeng Zhang; Weifeng Zhang; Weifeng Zhang

doi:10.1364/OE.446788

1. Introduction

Pulse compression, as an important signal processing technique, has been extensively used in modern radar systems to increase the range resolution [1]. To have a large pulse compression ratio, a linearly chirped microwave waveform (LCMW) is one of the popular radar waveforms, because of its large time-bandwidth product (TBWP) [2]. Usually, the LCMWs are generated electronically using a voltage controlled electronic oscillator [3] or a digital frequency synthesizer [4]. Due to the relatively low speed of electronic devices, electronically generated LCMWs are limited in the center frequency and bandwidth. However, in the advanced radar systems for high-resolution detections of unmanned aerial vehicles, pilotless automobiles and smart navigators, an LCMW with a center frequency up to tens of gigahertz and a bandwidth as broad as several gigahertz are often required [5–8].

To overcome the problem of wideband LCMWs generation, photonics is a potential solution, which holds the key advantages in terms of high frequency and broad bandwidth [9–12]. In the past few years, numerous photonic approaches have been reported for LCMWs generation. Among the different photonic approaches, a straightforward approach is to use photonics-based frequency multiplication to generate wideband LCMWs. An electronically generated LCMW is modulated on an optical carrier, and by choosing the sidebands, frequency doubled or quadrupled LCMW signals can be realized with the bandwidth doubled or quadrupled [13–15]. For example, a frequency-quadrupled LCMW with a bandwidth up to 12 GHz has been experimentally demonstrated [15]. The main disadvantage is that a high-performance electronic LCMW source is required, which inevitably increases the system cost. To save the electronic LCMW source, optical spectral shaping and wavelength-to-time mapping (SS-WTT) is a solution, in which the spectral shaper is specifically designed to have a spectral response with a shape that is a scaled version of an LCMW. The generation of an LCMW with a bandwidth up to tens of gigahertz has been reported. However, the temporal duration of the generated LCMW is limited to a few nanoseconds, which leads to a small TBWP of ∼50 [16–18]. To largely improve the TBWP, LCMWs can also be generated with the use of optical heterodyne detection, where two lightwave signals from a frequency-swept laser source and a continuous wave (CW) laser source are combined by an optical coupler and detected by a high-speed photodetector (PD). This method can generate an ultra-wide LCMW with a bandwidth as broad as 50 GHz, but the generated signal suffers from a high phase noise since the two laser sources are not phase correlated [19–21]. To reduce the phase noise of the generated LCMWs, recently, a Fourier-domain mode-locked optoelectronic oscillator (FDML-OEO) was proposed. Different from the conventional OEO, in the FDML-OEO loop, a frequency-sweeping filter is used, whose frequency sweeping period is synchronized to the round-trip time of the OEO loop. The key advantage of the FDML-OEO includes the RF-source free, low phase noise and broad bandwidth of the generated LCMWs. Various implementations of the FDML-OEO have been proposed and experimentally demonstrated [22–27], and an ultralow phase noise of −134.5 dBc/Hz at a 10-kHz offset frequency has been achieved [22]. To date, an LCMW having a maximum bandwidth of 8 GHz was reported [28]. For higher resolution and multi-function operation of the radar system, the bandwidth needs to be further increased [29–33].

To overcome the challenge of small unmanned aerial vehicles detection and tracking, the higher resolution requirement drives the radar systems to have a multi-band operation since the resolution can be highly enhanced by the combination of different frequency bands [34–35]. In addition, in the distributed radar system, a multi-band microwave waveform source features the phase coherence between the different frequency signals, which would be of great benefit to the phase synchronized distribution between the remote antennas to save image refresh time [36]. Recently, a polarization-manipulated FDML-OEO incorporating a polarization modulator (PolM) was reported for the generation of wideband LCMWs and dual-band LCMWs [37]. However, the bandwidth of the generated LCMWs is still limited (∼6 GHz) even though a frequency-doubled operation was implemented, and the configurations used for the generation of single-band LCMWs and dual-band LCMWs are different, which highly reduces the system flexibility.

In this paper, we propose and experimentally demonstrate an approach to generating flexible ultra-wide LCMWs based on an FDML-OEO incorporating a dual-polarization quadrature phase-shift keying (DP-QPSK) modulator. In the DP-QPSK modulator, two dual-parallel Mach-Zehnder modulators (DP-MZMs) are integrated, and at the output of the DP-QPSK modulator, the modulated lightwave signals from the two DP-MZMs are polarization orthogonal, which can be separated using a polarization beam splitter. With the use of the upper DP-MZM that serves as a phase modulator, an FDML-OEO system is produced to generate a wideband LCMW with a flexible tuning in the center frequency and instantaneous bandwidth; with the injection of the generated LCMW into the lower DP-MZM, an ultra-wideband LCMW is generated via microwave frequency multiplication, and multi-band waveform generation is also enabled by controlling the bias condition of the lower DP-MZM. An experiment is performed and an LCMW with an ultra-wide bandwidth as broad as 10.8 GHz, a temporal duration of 24.7 µs is generated, corresponding to a TBWP of 2.6×10⁵. By adjusting the driving signal applied to the FDML-OEO, the generated LCMW can be tuned in the center frequency from 16.2 to 23.2 GHz and the bandwidth from 3.6 to 10.8 GHz, and by controlling the bias point of the lower DP-MZM, a dual-band LCMW is also experimentally demonstrated. Thanks to the ultra-wide bandwidth and strong flexibility of the generated LCMWs in terms of tunable center frequency, instantaneous bandwidth, and multiband operation, the proposed approach offers a promising LCMW generator in the next-generation high-resolution radar systems.

2. Principle

The schematic of the proposed ultra-wide LCMW generation system is shown in Fig. 1(a). A continuous-wave (CW) lightwave signal from a distributed feedback laser diode (DFB-LD) is injected into a DP-QPSK modulator, which consists of two DP-MZMs (DP-MZM₁ and DP-MZM₂). At the output of the DP-QPSK modulator, the modulated lightwave signals from the two DP-MZMs are polarization orthogonal, which can be separated using a polarization beam splitter (PBS). With the use of the DP-MZM₁, an FDML-OEO system is produced to generate a wideband LCMW with a tuning in the center frequency and instantaneous bandwidth. By sending the generated LCMW into the DP-MZM₂, an ultra-wideband LCMW is generated via microwave frequency multiplication, and multi-band waveform generation operation is also enabled by controlling the bias condition of the lower DP-MZM₂.

Fig. 1. Schematic of the proposed ultra-wide LCMW generation system. DFB-LD: distributed feedback laser diode; PC: polarization controller; DP-QPSK modulator: dual-polarization quadrature phase-shift keying modulator; DP-MZM: dual-parallel Mach-Zehnder modulator; PR: polarization rotator; PBS: polarization beam splitter; EDFA: erbium-doped fiber amplifier; OC: optical circulator; PS-FBG: phase-shifted fiber Bragg grating; PD: photodetector; EA: electrical amplifier; LPF: low-pass filter; EC: electrical coupler; OSC: oscilloscope; ESA: electrical spectrum analyzer.

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2.1 Wideband LCMW generation

In the implementation of the FDML-OEO, a CW lightwave signal from the DFB-LD is injected into the DP-QPSK modulator via a polarization controller (PC₁), and by controlling the bias point, the DP-MZM₁ can function as a phase modulator, where the sub-MZMs (MZM₁₁ and MZM₁₂) and the main-MZM of the DP-MZM₁ are biased at the minimum transmission point, the maximum transmission point, and the quadrature transmission point, respectively. When two identical microwave signals are injected into the DP-MZM₁, mathematically, the optical field at the output of the DP-MZM₁ can be written as:

(1)$$\begin{aligned} {E_{DP - MZM1}}(t )&= {E_{in}}(t )\cos \left[ {\frac{{\pi {V_s}\cos ({{\omega_s}t} )}}{{2{V_\pi }}}} \right]\\ &+ {E_{in}}(t )\cos \left\{ {\frac{{\pi [{{V_s}\cos ({{\omega_s}t} )- {V_\pi }} ]}}{{2{V_\pi }}}} \right\}\exp \left( {j\frac{\pi }{2}} \right)\\ &= {E_{in}}(t )\exp \left[ {j\frac{m}{2}\cos ({{\omega_s}t} )} \right] \end{aligned}$$

where E_in(t) is the optical field of the input lightwave signal, V_s and ω_s are the amplitude and angular frequency of the microwave signal, V_π is the half-wave voltage of the DP-QPSK modulator, and m=πV_s/V_π.

At the output of the DP-QPSK modulator, the modulated lightwave signals from the two DP-MZMs are polarization orthogonal. With the use of a PBS, by controlling the PC₂ to align the polarization directions of the optical signals to the main axis of the PBS, the two modulated optical signals can be separated with a high extinction ratio. The separated phase-modulated optical signal from the DP-MZM₁ is amplified by an EDFA₁, and then passes through a PS-FBG. If the phase-modulated optical signal is directly applied to a photodetector (PD₁), no microwave signal will be recovered due to the out of phase nature between the two first-order sidebands of a phase-modulated optical signal. If one of the two sidebands of the phase-modulated optical signal is filtered out by locating it in the notch of the reflection band of the PS-FBG, the phase-modulated signal is converted to an intensity-modulated single-sideband signal, and thus a microwave signal would be generated when applied to the PD₁. The entire operation corresponds to a bandpass microwave photonic filter (MPF), of which the spectral response is directly translated from the spectral response of the PS-FBG. Thanks to the ultra-narrow notch of the PS-FBG, the MPF has a narrow passband and its center frequency is tunable by controlling the driving signal applied to the DFB-LD. By feeding the microwave signal at the output of the MPF to its input and providing a sufficiently large gain using an electrical power amplifier, the OEO loop is produced. By tuning the optical carrier wavelength, the center frequency of the MPF filter is tuned, and thus the frequency of the generated microwave signal is tuned.

To achieve Fourier-domain mode locking for wideband LCMW generation, the repetition time (T_LD-drive) of the driving signal applied to the DFB-LD needs to match the round-trip time (T_round-trip) of the OEO loop, which can be given by

(2)$${T_{LD - drive}} = \frac{{{T_{round - trip}}}}{n}$$

where n is a positive integer. Thus, Fourier-domain mode locking is achieved and a broadband frequency-chirped microwave pulse is generated. By controlling the offset voltage and amplitude of the driving signal applied to the DFB-LD, the center frequency and bandwidth of the generated frequency-quadrupled LCMW can be tuned.

2.2 Frequency-quadrupled ultrawide LCMW generation

In a regular FDML-OEO system, the bandwidth of the generated LCMW is still difficult to meet the bandwidth requirements for the high-resolution imaging. To further elevate the bandwidth of the LCWM, the generated LCMW from the FDML-OEO is injected to the DP-MZM₂ (MZM₂₁ and MZM₂₂) for frequency quadrupling. As shown in Fig. 1(a), part of the generated LCMW from the FDML-OEO is injected into one sub-MZM (MZM₂₂) of the DP-MZM₂, which is working at the maximum transmission to suppress odd-order sidebands. The other sub-MZM (MZM₂₁) of the DP-MZM₂ has no microwave input. The main-MZM is biased at the minimum transmission point to introduce a π phase shift. At the output, the optical field can be expressed as

(3)$$\begin{aligned} {E_{DP - MZM2}}(t )&= \frac{1}{4}{E_{in}}(t )\left\{ {\exp [{ \pm jm\cos ({{\omega_s}t + \pi k{t^2}} )} ]\exp ({j{\phi_M}} )+ \cos \left( {\frac{\beta }{2}} \right)} \right\}\\ &= \frac{1}{4}{E_{in}}(t )\left\{ {\exp ({j\pi } )\sum\limits_{n ={-} \infty }^{n = \infty } {[{1 + {{({ - 1} )}^n}} ]{j^n}{J_n}(m )} \exp [{jn({{\omega_s}t + \pi k{t^2}} )} ]+ \cos \left( {\frac{\beta }{2}} \right)} \right\} \end{aligned}$$

where ω_s and k are the start angular frequency and chirp rate of the LCMW generated by the FDML-OEO, ϕ_M is the phase shift induced by the main-MZM, β=πV_a/V_π, V_a is the DC bias voltage of the MZM₂₁, and J_i is the Bessel function of the first kind (i = 0, 2, 4, …).

To generate frequency-quadrupled LCMWs, the optical carrier is suppressed by properly controlling the DC biases of the DP-MZM₂, where the condition of ${\textrm{J}_0}(m )= \frac{{\cos \left( {{\textstyle{\beta \over 2}}} \right)}}{2}$ is satisfied. Under the small-signal modulation condition, Eq. (3) can be simplified as

(4)$${E_{DP - MZM2}}(t )\approx \frac{1}{2}{E_{in}}(t ){J_2}(m )\exp [{ \pm j2({{\omega_s}t + k{t^2}} )} ]$$

According to Eq. (4), only the ±2nd-order sidebands are generated while other sidebands are suppressed. As illustrated in Fig. 1(b), thanks to the polarization orthogonality between the optical signals from the upper DP-MZM and the lower one in the DP-QPSK modulator, the modulated optical signal generated by the DP-MZM₂ is separated and detected by another high-speed PD (PD₂), and at the output the generated microwave signal can be given by

(5)$$\begin{aligned} {i_{DP - MZM2}}(t )&= \Re {E_{DP - MZM2}}(t )E_{DP - MZM2}^\ast (t )\\ &= \Re \frac{1}{4}E_{in}^2{\{{{J_2}(\beta )\exp [{j2({{\omega_s}t + k{t^2}} )} ]+ {J_2}(\beta )\exp [{ - j2({{\omega_s}t + k{t^2}} )} ]} \}^2}\\ &= \Re \frac{1}{2}E_{in}^2{J_2}^2(\beta )\exp [{j4({{\omega_s}t + k{t^2}} )} ]\end{aligned}$$

where $\Re$ is the responsivity of the PD₂. According to Eq. (5), a frequency-quadrupled LCMW is generated. Compared with the originally generated LCMW from the FDML-OEO, the central frequency, the bandwidth, and the TBWP of the frequency-quadrupled LCMW are significantly increased by four times. By tuning the offset voltage and amplitude of the driving signal applied to the DFB-LD, the center frequency and bandwidth of the generated frequency-quadrupled LCMW can be flexibly tuned. The key advantage is that the bandwidth of the generated LCMW is highly increased without the use of external microwave source and tunable optical bandpass filter (OBPF).

2.3 Dual-band LCMW generation

With the same configuration, when the DC bias condition of the DP-MZM₂ is changed, multi-band LCMW generation can be enabled, which is of great benefit to the multi-band radar system. As shown in Fig. 1(c), by adjusting the DC bias of the MZM₂₁, the optical power of the optical carrier and the ±2nd-order optical sidebands can be accurately controlled. Under the small signal modulation condition, the optical field at the output of the DP-MZM₂ can be expressed as

(6)$$\begin{aligned} E{^{\prime}_{DP - MZM2}}(t )&= \frac{1}{4}{E_{in}}(t )\left\{ {\exp [{ \pm jm\cos ({{\omega_s}t + k{t^2}} )} ]\exp ({j{\phi_M}} )+ \cos \left( {\frac{{\beta^{\prime}}}{2}} \right)} \right\}\\ &= \frac{1}{4}{E_{in}}(t )\left\{ {\cos \left( {\frac{{\beta^{\prime}}}{2}} \right) + \exp ({j\pi } )\sum\limits_{n ={-} \infty }^{n = \infty } {[{1 + {{({ - 1} )}^n}} ]{j^n}{J_n}(m )} \exp [{jn({{\omega_s}t + k{t^2}} )} ]} \right\}\\ &\approx \frac{1}{2}{E_{in}}(t )\left\{ { - {J_0}(m )+ \frac{1}{2}\cos \left( {\frac{{\beta^{\prime}}}{2}} \right) + {J_2}(m )\exp [{ \pm j2({{\omega_s}t + k{t^2}} )} ]} \right\} \end{aligned}$$

where β’ =πV_a’/V_π, V_a’ is the bias voltage of the MZM₂₁, whose value is different from V_a. The modulated optical signal from the DP-MZM₂ is detected by the high-speed PD₂, and the generated electrical signal can be rewritten as

(7)$$\begin{aligned} i{^{\prime}_{DP - MZM2}}(t )&= \Re E{^{\prime}_{DP - MZM2}}(t ){E^{\prime\ast}_{DP - MZM2}} (t )\\ &= \Re \frac{1}{4}E_{in}^2{\left\{ { - {J_0}(m )+ \frac{1}{2}\cos \left( {\frac{{\beta^{\prime}}}{2}} \right) + {J_2}(m )\exp [{ \pm j2({{\omega_s}t + k{t^2}} )} ]} \right\}^2}\\ &= \Re \frac{1}{4}E_{in}^2\left\{ \begin{array}{l} {J_0}^2(m )+ 2{J_2}^2(m )+ \frac{1}{4}{\cos^2}\left( {\frac{{\beta^{\prime}}}{2}} \right) - \cos \left( {\frac{{\beta^{\prime}}}{2}} \right){J_0}(m )\\ + {J_2}(m )\left[ {\cos \left( {\frac{{\beta^{\prime}}}{2}} \right) - 2{J_0}(m )} \right]\exp [{ \pm j2({{\omega_s}t + k{t^2}} )} ]\\ + {J_2}^2(m )\exp [{ \pm j4({{\omega_s}t + k{t^2}} )} ]\end{array} \right\} \end{aligned}$$

Ignoring the DC component, a dual-band LCMW is generated including the frequency-doubled LCMW and the frequency-quadrupled LCMW. Their power can be controlled to be equal when

(8)$$\cos \left( {\frac{{\beta^{\prime}}}{2}} \right) - 2{J_0}(m )= J_2^{}(m )$$

By controlling the DC biases of the DP-MZM₂, the proposed LCMW generation system can be switched to have a single-band LCMW generation with an ultra-wide bandwidth or have a dual-band LCMW generation. The switching time between the modes can be as short as a few tens of µs, which is determined by the modulation bandwidth of the DC input port of DP-MZM₂, which is as high as a few tens of kHz. The center frequency and bandwidth are tunable by controlling the driving signal applied to the DFB-LD. The proposed approach offers a flexible LCMW generator in the next-generation high-resolution multi-band radar systems.

3. Experiment and discussion

A proof-of-concept experiment is performed. An input optical signal from the DFB-LD (NEL Photonics, NLK1C5GAAA) with an output power of 14 dBm is sent to the DP-QPSK modulator (Fujitsu, FTM7977HQA) that has a half-wave voltage of ∼3.5 V (at 32 Gbps) and a 3-dB bandwidth of 23 GHz. The modulated optical signals from the DP-QPSK modulator are sent to a PBS via PC₂. By properly tuning PC₂, the orthogonally polarized optical signals from the DP-QPSK modulator are aligned to the two principal axis of the PBS and thus be separated. An optical spectrum analyzer (OSA, Yokogawa, AQ6370D-12) is used to real-time monitor the optical spectrum at the lower port of the PBS and to ensure that the orthogonally polarized optical signals from the DP-QPSK modulator are separated by the PBS with a high extinction ratio. The separated phase-modulated optical signal from the DP-MZM₁ is amplified by the EDFA₁ (Amonics, AEDFA-PA-35) and applied to a PS-FBG to implement PM-IM conversion. The PS-FBG has an ultra-narrow notch with a 3-dB bandwidth of 110 MHz and a center wavelength of 1550.14 nm. By passing through a non-zero dispersion-shifted fiber (NZDSF) with a length of 5 km and a dispersion coefficient of 4 ps/km$\cdot$nm, the PM-IM converted optical signal is send to a photodetector (PD₁, CONQUER, KG-PT-10G-A-SM-FC) with a 3-dB bandwidth of 10 GHz, where the signal is down-converted from the optical domain to the electrical domain. The electrical signal at the output of the PD₁ is amplified by an electrical amplifier EA (Multilink, MTC5515) with a bandwidth of 10 GHz and send back to the modulator to close the OEO loop. To remove the harmonics, a low-pass filter (LPF) with a cut-off frequency of 6.5 GHz is incorporated, which could be removed when a highly-linear EA is used.

3.1 Wideband LCMW generation

To realize the Fourier-domain mode locking, a sawtooth-wave driving signal generated by a narrowband arbitrary waveform generator (AWG) is applied to the DFB laser and its repetition time is determined by the round-trip time of the OEO loop. In our experimental set-up, the OEO loop round-trip time is 24.7 µs, and thus the driving signal is chosen to have a frequency of 40.47 kHz. The generated LCMWs by the FDML-OEO are captured by a real-time oscilloscope (OSC) and analyzed with the use of a wideband electrical spectrum analyzer (ESA).

Figure 2(a) shows the spectra of the generated LCMWs when a driving signal with an identical offset voltage of −1 mV and different amplitudes is applied. When the driving signal has the amplitude of 21 mV, the generated LCMW has a center frequency of 4.35 GHz and a bandwidth of 0.9 GHz, as shown in the blue line. When the driving signal has the amplitude of 41 mV, the generated LCMW has a center frequency of 4.50 GHz and a bandwidth of 1.8 GHz, as shown in the red line. When the driving signal has the amplitude of 61 mV, the generated LCMW has a center frequency of 4.65 GHz and a bandwidth of 2.7 GHz, as shown in the yellow line. As can be seen, the center frequency and bandwidth of the generated LCMWs can be tuned by controlling the driving signal applied to the DFB-LD. The slight difference between the center frequencies of the generate LCMWs is caused by the nonlinearity of the driving DFB-laser. Figure 2(b-(i)), 2(c-(i)) and 2(d-(i)) show the temporal profile of the generated LCMWs captured by the real-time OSC with a sampling rate of 100 GSa/s. The generated LCMWs are periodical and have a time duration of 24.7 µs, which is determined by the round-trip time of the OEO loop. The TBWPs of the three generated LCMWs are calculated to be 22,230, 44,460 and 66,690, which increase linearly with the bandwidth of the generated LCMWs. Figure 2(b-ii), 2(c-ii) and 2(d-ii) show the spectrograms of the generated LCMWs calculated using a short-time Fourier transform (STFT) algorithm, and the chirp rates are calculated to be 36 MHz/µs, 72 MHz/µs and 108 MHz/µs in the linear region, which are determined by the slope of the driving signal applied to the DFB-LD. To evaluate the linearity of the LCMW generated by the FDML-OEO, an ideal LCMW is produced for comparison with the generated LCMW within the linear region. The R-square values are calculated to be 0.9679, 0.9667, 0.9658 for the generated LCMWs with a bandwidth of 0.9, 1.8 and 2.7 GHz, respectively. To evaluate the quality of the generated LCMWs, an auto-correlation operation is implemented. Figure 2(b-iii), 2(c-iii) and 2(d-iii) show the compressed pulses, whose temporal widths are 1.3 ns, 0.68 ns and 0.44 ns, corresponding to compression ratios of 19,000, 36,323 and 56,136, respectively. Due to the nonlinearity of the DFB-LD, a slight nonlinear frequency-modulation of the generated LCMWs can be observed in Fig. 2(b-ii) to 2(d-ii), which leads to a deteriorated compression ratio compared with the TBWP.

Fig. 2. (a) Spectra of the generated LCMWs with a bandwidth of 0.9 (blue curve), 1.8 (red curve) and 2.7 GHz (yellow curve). (b-i), (c-i) and (d-i) temporal profile, (b-ii), (c-ii) and (d-ii) calculated spectrograms, and (b-iii), (c-iii) and (d-iii) compressed pulses of the generated LCMWs with a bandwidth of 0.9, 1.8 and 2.7 GHz.

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3.2 Frequency-quadrupled LCMW generation

To realize ultra-wide LCMWs generation, microwave frequency quadrupling is performed in the optical domain. The LCMW generated by the FDML-OEO is injected into the MZM₂₂, which is biased at the maximum transmission point to suppress the odd-order sidebands, while the MZM₂₁ has no microwave input. The main-MZM is biased at the minimum transmission point to introduce a π phase shift. By properly adjusting the DC bias of the main MZM, the optical carrier of the modulated optical signal from the MZM₂₂ and the optical carrier from the MZM₂₁ are out of phase. Thus, at the output of the DP-MZM₂, the optical carrier is suppressed and only the even-order sidebands are remained. Figure 3 shows the optical spectrum with the use of an optical spectrum analyzer. It is clear to see that only the ±2nd-order optical sidebands are observed while the optical carrier and other sidebands are heavily suppressed. The suppression ratio of the optical carrier and other unwanted sidebands is as high as 20 dB, which is mainly determined by the extinction ratio of the DP-QPSK modulator.

Fig. 3. Optical spectrum at the lower port of the PBS for frequency-quadrupled LCMW generation.

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With a high-speed photodetector (PD₂, Finisar, MPRV1331A) having a 3-dB bandwidth of 30 GHz, frequency-quadrupled LCMWs are generated. As shown in Fig. 4(a), when the bandwidth of the LCMWs generated by the FDML-OEO is tuned from 0.9 GHz to 2.7 GHz with a step of 0.9 GHz by changing the amplitude of the driving signal applied to the DFB-LD from 21 mV to 61 mV with a step of 20 mV, the bandwidth of the generated frequency-quadrupled LCMWs is also tuned from 3.6 GHz to 10.8 GHz with a frequency step of 3.6 GHz. The spectra of the generated frequency-quadrupled LCMWs with a bandwidth of 3.6 GHz, 7.2 GHz and 10.8 GHz are given by the blue, red and yellow lines in Fig. 4(a), respectively. Figures 4(b-(i)), 4(c-(i)) and 4(d-(i)) show the temporal profile of the generated frequency-quadrupled LCMWs, which are also periodical and have a time duration of 24.7 µs. The TBWPs of the three generated LCMWs can be calculated to be are 88,920, 177,840 and 266,760. The spectrograms of the generated frequency-quadrupled LCMWs calculated using the STFT algorithm are shown in Figs. 4(b-ii), 4(c-ii) and 4(d-ii), where the chirp rates of the frequency-quadrupled LCMWs are 146 MHz/µs, 292 MHz/µs and 437 MHz/µs in the linear region, which are increased by ∼4 times compared with the LCMWs generated directly by the FDML-OEO. To evaluate the quality of the generated LCWMs, an auto-correlation operation is implemented, and Figs. 4(b-iii), 4(c-iii) and 4(d-iii) show the compressed pulses, whose temporal widths are 0.3 ns, 0.15 ns and 0.11 ns, corresponding to compression ratios of 82,333, 164,666 and 224,545, respectively. The experimental results show that the bandwidth of the generated frequency-quadrupled LCMWs can be flexibly tuned by simply changing the amplitude of the driving signal applied to the DFB-LD.

Fig. 4. (a) Spectra of the frequency-quadrupled LCMWs with a bandwidth of 3.6 GHz (blue curve), 7.2 GHz (red curve) and 10.8 GHz (yellow curve). (b-i), (c-i) and (d-i) temporal profile, (b-ii), (c-ii) and (d-ii) corresponding spectrograms, and (b-iii), (c-iii) and (d-iii) compressed pulses of the generated frequency-quadrupled LCMWs with a bandwidth of 3.6 GHz, 7.2 GHz and 10.8 GHz.

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Flexible tuning in the center frequency of the generated frequency-quadrupled LCMWs is also performed by tuning the offset voltage of the driving signal applied to the DFB-LD. An LCMW with a center frequency of 4.075 GHz and a bandwidth of 0.55 GHz generated by the FDML-OEO is injected into the MZM₂₂. Figure 5(a) shows the spectra of the generated frequency-quadrupled LCMWs, which have a bandwidth of 2.2 GHz, corresponding to a TBWP of 54,340. By changing the offset voltage of the driving signal from −3 to 7 mV, the center frequency of the generated frequency-quadrupled LCMWs is tuned from 16.2 to 23.2 GHz with a frequency step of 3.5 GHz, and the spectra of the three generated LCMWs are given by the blue, red and yellow lines in Fig. 5(a). Figures 5(b-(i)), 5(c-(i)) and 5(d-(i)) show the temporal profile of the generated LCMWs, which are also periodical and have a time duration of 24.7 µs. Figures 5(b-ii), 5(c-ii) and 5(d-ii) show the spectrograms of the generated frequency-quadrupled LCMWs calculated using the STFT algorithm, and the chirp rates are calculated to be 89 MHz/µs in the linear region, which remains unchanged during the tuning of the center frequency since the slope of the driving signal remains. Figures 5(b-iii), 5(c-iii) and 5(d-iii) show the compressed pulses, whose temporal width is identical as long as 0.54 ns, corresponding to a compression ratio of 45,740. The experimental results show that the center frequency of the generated frequency-quadrupled LCMWs can be flexibly tuned by changing the offset voltage of the driving signal applied to the DFB-LD.

Fig. 5. (a) Spectra of the frequency-quadrupled LCMWs with a center frequency of 16.2 GHz (blue curve), 19.7 GHz (red curve) and 23.2 GHz (yellow curve). (b-i), (c-i) and (d-i) temporal profile, (b-ii), (c-ii) and (d-ii) corresponding spectrograms, and (b-iii), (c-iii) and (d-iii) compressed pulses of the generated frequency-quadrupled LCMWs with a center frequency of 16.2 GHz, 19.7 GHz and 23.2 GHz.

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3.3 Dual-band LCMW generation

Then, the generation of a dual-band LCMW is also experimentally demonstrated using the same configuration. The main difference is that the DC bias of the MZM₂₁ incorporated in the DP-MZM₂ is properly adjusted to generate a residual optical carrier, which is apparently different from the situation in the single-band frequency-quadrupled LCMW generation set-up where the optical carrier is heavily suppressed. Figure 6 shows the optical signal spectrum before the injection into the PD. As can be seen, the optical carrier and the ±2nd-order sidebands are generated. The power difference between the optical carrier and the ±2nd-order sidebands is controlled to be 7.1 dB to ensure that the generated frequency-doubled band and the frequency-quadrupled band have an identical power. The suppression ratio of the ±1st-order sidebands is 20 dB, which can be further improved using a DP-QPSK modulator with a higher extinction ratio.

Fig. 6. Optical spectrum for dual-band LCMW generation

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After the photodetection at the PD₂, dual-band LCWMs are generated, where the frequency-doubled band is generated by the beating between the optical carrier and the ±2nd-order sideband, and the frequency-quadrupled band is generated by the beating between the ±2nd-order sidebands. Firstly, when the driving signal has an offset voltage of −2 mV and an amplitude of 12 mV, a LCWM with a center frequency of 4.15 GHz and a bandwidth of 0.5 GHz is generated by the FDML-OEO and injected into the DP-MZM₂. By controlling the bias condition of the DP-MZM₂, a dual-band LCMW is generated and its electrical spectrum is shown in Fig. 7(a) in the blue line. Since the limited extinction ratio of the DP-QPSK modulator, other residual harmonics exist, which have a suppression ratio of 16 dB compared to the frequency-quadrupled band. Figures 7(b-(i)) and 7(c-(i)) show the temporal profile of the frequency-doubled band and frequency-quadrupled band, which are periodical with a time duration of 24.7 µs. Figures 7(b-ii) and 7(c-ii) show the spectrograms using the STFT algorithm. As can be seen, the frequency range of the generated dual-band LCMWs locates in the X- and Ku- band. The frequency-doubled band has a center frequency of 8.3 GHz and a bandwidth of range of 1 GHz, and the frequency-quadrupled band has a center frequency of 16.6 GHz and a bandwidth of range of 2 GHz. The chirp rates of the two frequency bands are calculated to be 40 MHz/µs and 81 MHz/µs in the linear region, which are two- and four- times of that of the LCMW generated by the FDML-OEO. Figures 7(b-iii) and 7(c-iii) show the compressed pulses after the autocorrelation. The temporal widths of the compressed pulses are 1.2 ns and 0.6 ns, of which the compression ratios are 20,583 and 41,166.

Fig. 7. (a) Spectra of the generated dual-band LCMWs; (b-i) and (c-i) temporal profile, (b-ii) and (c-ii) corresponding spectrograms, and (b-iii) and (c-iii) compressed pulses of the generated dual-band LCMWs with a frequency range of 7.8-8.8 GHz, and 15.6-17.6 GHz; (d-i) and (e-i) temporal profile, (d-ii) and (e-ii) corresponding spectrograms, and (d-iii) and (e-iii) compressed pulses of the generated dual-band LCMW with a frequency range of 10-12.2 GHz and 20-24.4 GHz.

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Furthermore, by changing the offset voltage of the driving signal applied to the DFB-LD, the center frequency of the generated dual-band LCMWs can be tuned. The red line in Fig. 7(a) shows the electrical spectrum of the generated dual-band LCMW when a driving signal with an offset voltage of 5 mV and an amplitude of 26 mV is applied to the DFB-LD. Compared to the blue line, the center frequency is apparently tuned. Figures 7(d-(i)) and 7(e-(i)) show the temporal profile of the frequency-doubled band and frequency-quadrupled band, and the corresponding spectrograms are shown in Figs. 7(d-ii) and 7(e-ii). The frequency range of the generated dual-band LCMWs locates in the X- and K- band. The frequency-doubled band has a center frequency of 11.1 GHz and a bandwidth of range of 2.2 GHz, and the frequency-quadrupled band has a center frequency of 22.2 GHz and a bandwidth of range of 4.4 GHz. The chirp rates are calculated to be 89 MHz/µs and 178 MHz/µs. Figures 7(d-iii) and 7(e-iii) show the compressed pulses after autocorrelation, where the temporal widths of the compressed pulses are 0.54 ns and 0.3 ns, of which the compression ratio are 45,740 and 82,333.

With the proposed system, ultra-wideband LCMWs with a flexible tuning in the center frequency, instantaneous bandwidth, and multi-band operation is generated by controlling the offset voltage and the amplitude of the driving signal applied to the DFB-LD and the bias condition of the DP-MZM₂. In the experiment, an LCMW with a maximum bandwidth of 10.8 GHz is produced, which can be further enhanced by using the wideband optoelectronic component including the EA and PD in the system. In addition, as can be seen in the spectrogram calculated from the generated LCMW, although a sawtooth-wave driving signal is applied to the DFB-LD, a nonlinearity of the frequency modulation can be observed, which is caused by the limited modulation bandwidth of the DFB-LD. To improve the linearity of the generated LCMWs, a pre-distortion operation on the drive signal is an effective solution [38]. In the proposed LCMW generation method based on FDML-OEO, no external RF source is required, which makes it suitable for practical applications thanks to its reduced cost and complexity.

4. Conclusion

An approach to generating flexible ultra-wide LCMWs based on an FDML-OEO incorporating a DP-QPSK modulator has been proposed and experimentally demonstrated. In the DP-QPSK modulator, two DP-MZM modulators are integrated. With the use of the upper DP-MZM, which that serves as a phase modulator, an FDML-OEO system was produced to generate a wideband LCMW with a flexible tuning in the center frequency and instantaneous bandwidth; with the injection of the generated LCMW into the lower DP-MZM, an ultra-wideband LCMW was generated via microwave frequency multiplication, and multi-band waveform generation operation was also enabled by controlling the bias condition of the lower DP-MZM. An experiment was performed and an LCMW with an ultra-wide bandwidth as broad as 10.8 GHz, a temporal duration of 24.7 µs, corresponding to a TBWP of 2.6×10⁵, was generated. By adjusting the driving signal applied to the FDML-OEO, the generated LCMW was tuned in the center frequency from 16.2 to 23.2 GHz and the bandwidth from 3.6 to 10.8 GHz. By controlling the bias point of the lower DP-MZM, a dual-band LCMW was experimentally demonstrated. Thanks to the ultra-wide bandwidth and strong flexibility of the generated LCMWs in terms of tunable center frequency, instantaneous bandwidth and multiband operation, the proposed approach offers a promising LCMW generator in the next-generation high-resolution radar systems.

Funding

2020 International Postdoctoral Exchange Fellowship Program; National Key Research and Development Program of China (2018YFE0201800); National Natural Science Foundation of China (62005018, 62071042).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Photonic generation of flexible ultra-wide linearly-chirped microwave waveforms

Abstract

1. Introduction

2. Principle

2.1 Wideband LCMW generation

2.2 Frequency-quadrupled ultrawide LCMW generation

2.3 Dual-band LCMW generation

3. Experiment and discussion

3.1 Wideband LCMW generation

3.2 Frequency-quadrupled LCMW generation

3.3 Dual-band LCMW generation

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Equations (8)

Optics Express