An All-Optical Microwave Frequency Divider with Tunable Division Factors Based on DP-DPMZM

Abstract

Based on a dual-polarization dual-parallel Mach–Zehnder modulator (DP-DPMZM), an all-optical frequency divider is proposed and experimentally demonstrated. Two radio frequency (RF) signals are modulated on an optical carrier to work as a dual-beam master laser (ML). The optical signals of the ML are injected into a distributed feedback (DFB) laser to initiate the period-two (P2) state oscillation. By beating the output of the slave laser (SL) via circulator in a photodetector, a frequency divider with tunable factors can be achieved. The innovation of the scheme lies in having a simple structure and only requires optical devices, which is operated in wide RF frequency range without any electrical amplifiers before the photodetector to increase the conversion gain. Experiment results also demonstrate that the frequency division factors can be adjusted.

1. Introduction

Frequency dividers are of great importance in radio astronomy, clock comparison and signal processing [1,2] because they can be widely used in generating millimeter waves or frequency synchronization. In radar systems, it is necessary to mix the received high-frequency echo signal with the local oscillator (LO) signal to realize frequency down conversion, so that low-speed electrical devices can be used for signal post-processing. In practical applications, instead of directly using an electrical signal generator to generate low-frequency signals, we need to process the received high-frequency signals to obtain low-frequency signals. Traditionally, frequency dividers include digital or analog types [3]. In contrast to several typical structures of the frequency dividers, they have a high operating band and low power consumption and serve as the first stage of high-frequency dividing. However, all these structures have limited bandwidth because of the bandwidth restrictions of electric filters. Previous designs have faced conflicts between achieving a high operating band and a wide locking range. Thanks to the advantages of microwave photonics, various photonic-based dividers are implemented using a regenerative technique or an injection-locking technique in an optoelectronic oscillator (OEO) loop. For a typical divider system, an OEO loop requires a number of optical and electrical components such as an electrical amplifier and electrical power splitter. For instance, by incorporating a frequency mixer and an optical filter, the frequency division factor can be tuned [4]. Furthermore, a Mach–Zehnder modulator (MZM) operated at the carrier suppression point was used to prevent OEO free-running oscillation [5]. The method in [6] employed an optical filter and a dual-parallel Mach–Zehnder modulator (DPMZM) to achieve tuning the frequency division factor by adjusting the delay of the OEO loop. Some other methods based on Fourier domain mode-locking [7] were proposed to achieve half-division of frequency.

All-optical microwave frequency dividers based on optical injection [8,9] were proposed to obtain different frequency-division factors, which can be implemented by harnessing the nonlinear dynamics of the semiconductor lasers. These reported techniques rely on direct modulation, which are limited by the low speed of carrier migration in the devices. To overcome this problem, a MZM operated by a radio frequency (RF) is used to generate dual beams which are injected into a distributed feedback (DFB) laser to realize a 1/2 frequency component [10]. However, none of these methods can realize a tunable frequency-division factor.

In this paper, we present a simple integrable and compact all-optical microwave divider with a tunable frequency-division factor. Theoretically, it can be designed with a high-operating frequency because it does not require any electrical amplifiers. By controlling the direct current (DC) bias voltage of the dual-polarization dual-parallel Mach–Zehnder modulator (DP-DPMZM) at a specific point to generate an RF-modulated optical signal for injection of a DFB laser to stimulate period-two (P2) oscillation, a frequency divider can be experimentally achieved. Two RF sources are used to realize a tunable frequency-division factor, and the power of the DFB is sensitive for the P2 station in our scheme. Owing to the frequency-tunable master laser, the dual-beam injection of P2 dynamics can be achieved.

2. Principle

The schematic diagram of the proposed all-optical frequency divider is shown in Figure 1. A continuous tunable laser with a carrier frequency f_c is fed into the DP-DPMZM, which is divided into two paths. The DP-DPMZM in the upper path consists of two orthogonally polarized dual-parallel Mach–Zehnder modulators (DPMZM). The x-DPMZM consists of sub-MZM1 and sub-MZM2, which are driven by RF₁ with the connect of a 90° hybrid. The y-DPMZM consists of sub-MZM3 and sub-MZM4, which are driven by RF₂ with the connect of another 90° hybrid. By biasing all four sub-MZMs at minimum transmission points, and we set the main DC biases of the DPMZMs at quadrature transmission points, and carrier-suppressed singe sideband (CS-SSB) modulated optical signals are generated. The DP-DPMZM can adjust the frequency division factor by changing RF₁ and RF₂ signals, respectively, to realize a carrier-suppressed single sideband. The optical field at the output of x-DPMZM is given by [11].

$$\begin{array}{c}{E}_x(t)\propto E_{MZM1}+E_{MZM2}{e}^{j{\varphi }_x}\\ \hspace{1em}\hspace{1em}\propto \frac{1}{8}{E}_0{e}^{j{\omega }_{0}t}\left[e^{j{\beta }_{RF1}\sin {\omega }_{RF}{}_{1}t}+e^{-j{\beta }_{RF1}\sin {\omega }_{RF}{}_{1}t+j\pi }+\left(e^{j{\beta }_{RF1}\cos {\omega }_{RF}{}_{1}t}+e^{-j{\beta }_{RF1}\cos {\omega }_{RF}{}_{1}t+j\pi }\right)e^{j{\varphi }_x}\right]\\ \hspace{1em}\hspace{1em}\propto \frac{1}{4}{E}_0{e}^{j{\omega }_{0}t}\left\{\begin{array}{l}{J}_1({\beta }_{RF1})e^{j{\omega }_{RF}{}_{1}t}-J_1({\beta }_{RF1})e^{-j{\omega }_{{{}_{RF}}_1}t}+\\ \left[J_1({\beta }_{RF1})e^{j{\omega }_{{{}_{RF}}_1}t+\frac{\pi }{2}}+J_1({\beta }_{RF1})e^{-j{\omega }_{{{}_{RF}}_1}t+\frac{\pi }{2}}\right]e^{j{\varphi }_x}\end{array}\right\}\hfill \end{array}$$

(1)

where ω₀ and E₀ are the angular frequency and amplitude of the optical carrier. ω_RF1 is the angular frequency of the RF₁ signal, β_RF1 = πV_RF1/V_π is the modulation index corresponding to RF₂ loaded on the sub-MZMs, V_π is the half-wave voltage of the sub-MZMs, J₀ and J₁ are the zeroth- and first-order Bessel functions of the first kind, ϕ_x is the phase shift introduced by main DC bias of the x-DPMZM.

Similarly, sub-MZM3 and sub-MZM4 are driven by the RF₂ signal in the CS-SSB station, the optical field at the output of y-DPMZM is given by [11].

$$\begin{array}{c}{E}_y(t)\propto E_{MZM3}+E_{MZM4}{e}^{j{\varphi }_y}\\ \hspace{1em}\hspace{1em}\propto \frac{1}{8}{E}_0{e}^{j{\omega }_{0}t}\left[e^{j{\beta }_{RF2}\sin {\omega }_{RF2}t}+e^{-j{\beta }_{RF2}\sin {\omega }_{RF2}t+j\pi }+\left(e^{j{\beta }_{RF2}\cos {\omega }_{RF2}t}+e^{-j{\beta }_{RF2}\cos {\omega }_{RF}{}_{2}t+j\pi }\right)e^{j{\varphi }_y}\right]\\ \hspace{1em}\hspace{1em}\propto \frac{1}{4}{E}_0{e}^{j{\omega }_{0}t}\left\{\begin{array}{l}{J}_1({\beta }_{RF2})e^{j{\omega }_{RF}{}_{2}t}-J_1({\beta }_{RF2})e^{-j{\omega }_{{}_{RF2}}t}+\\ \left[J_1({\beta }_{RF2})e^{j{\omega }_{{}_{RF2}}t+\frac{\pi }{2}}+J_1({\beta }_{RF2})e^{-j{\omega }_{{}_{RF2}}t+\frac{\pi }{2}}\right]e^{j{\varphi }_y}\end{array}\right\}\end{array}$$

(2)

where ω₀ and E₀ are the angular frequency and amplitude of the optical carrier, ω_RF2 is the angular frequency of the RF₂ signal, β_RF2 = πV_RF2/V_π is the modulation index corresponding to RF₂ loaded on the sub-MZMs, ϕ_y is the phase shift introduced by main DC bias of the y-DPMZM.

Afterwards, two orthogonally polarized signals are combined by a polarization beam combiner (PBC) and amplified by an erbium-doped fiber amplifier (EDFA). By tuning the state of the polarization controller (PC), the optical field of the DP-DPMZM is expressed as

$$\begin{array}{l}E(t)\propto \cos \left(\alpha \right)E_x\left(t\right)+\sin \left(\alpha \right)E_y\left(t\right)e^{j{\phi }_{PC}}\\ \hspace{1em}\hspace{1em}\propto \frac{1}{2}{E}_0\left[J_1({\beta }_{RF1})e^{\left(j{\omega }_{0}t+j{\omega }_{RF1}t\right)}+J_1({\beta }_{RF2})e^{\left(j{\omega }_{0}t+j{\omega }_{RF}{}_{2}t\right)}\right]\end{array}$$

(3)

where α is the angle between the axial direction of the polarizer and the principal axis of the PBC, and φ_PC is the PC-introduced phase shift between the two orthogonal polarization states. The RF₁ and RF₂ modulated optical signal are referred to as an injection light wave from a master laser (ML). The dual-beam is injected into the DFB slave laser (SL) by an optical circulator. The SL has a free running frequency f_s, which is between the dual-beam of the ML as shown in Figure 2.

For dual-beam optical injection locking of a semiconductor, the competitions of dynamics have been studied and analyzed [12]. Three general scenarios are shown during injecting a dual-beam from the ML into the SL, including stable locking, periodic oscillation, and chaos. There are two factors affecting nonlinear dynamic states in semiconductors, which is the injection strength ξ and the detuning frequency f_i. The ξ means the amplitude ratio between the ML and the SL. The f_i means the two injections beams frequencies offset from the ML. The SL is interacted with the dual-beam of the ML. Due to the modulation of the DP-DPMZM, the dual-beam frequencies of the ML can be adjusted by changing the RF₁ and RF₂ signals. This process will cause various nonlinear dynamic states, depending on the control of ξ and f_i. When the period-two (P2) dynamics are achieved, the output frequency spectrum of the SL consists of f_M1 − nΔf/2, f_M1 + Δf/2 and f_M2 + nΔf/2, where n is non-negative integer, f_M1 and f_M2 are frequency components of the two ML beams, then the frequency separation Δf = f_RF1 − f_RF2 is the subtraction of the RF₁ and RF₂ signals, and the SL frequency f_s is suppressed.

The dual-beam frequency of the ML is f_c + f_RF1 and f_c + f_RF2, as shown in Figure 2a. We define the f_c + f_RF1 as f − Δf and f_c + f_RF2 as f. The frequency division factor can be defined as the basic signal frequency divided by the obtained signal frequency. Therefore, in the P2 station, as shown in Figure 2b, the frequencies of SL output spectrum are including components at f ± nΔf/2. When the RF₁ has been determined, making the DFB oscillating at P2 state, we can obtain any frequency division factor by adjusting RF₂. The output electrical filed of the SL under P2 state can be expressed as

$$E_{SL}\left(t\right)\propto \frac{1}{2}{E}_0\left(t\right)e^{j{\omega }_{0}t}\cdot {\displaystyle \sum _{n=0}^{\infty }{A}_{\pm \frac{n}{2}}{e}^{\pm j\left(\frac{n}{2}{\omega }_{\Delta f}t\pm {\theta }_{\pm \frac{n}{2}}\right)}}$$

(4)

where A_±n/2 and θ_±n/2 are the amplitude and phase of the optical frequency at f ± nΔf/2. The output of the SL is detected by a photodetector via circulator. In the proposed system, we can change the injection strength to realize P2 state for microwave dividers, other than OEO loop, it does not need any electrical component or optical amplifiers to compensate the loss.

3. Experiment Results

A proof-of-concept experiment was carried out based on the schematic indicated in Figure 1. An optical carrier generated a continuous-wave (CW) from a tunable laser (Yenista Optics TUNIC-T100S-HP). It is coupled with a polarization controller (PC), which was adjusted to keep the polarization axis matching the DP-DPMZM (Fujistu FTM7977HQA). Two RF signals were generated by microwave signal generators. By setting the DC biases, the RF modulated optical signal, which is also regarded as the injection light from the ML, passed through a PC and PBC. After amplified by an EDFA, the optical signal was routed from Port 1 to Port 2 through an optical circulator. The DFB laser connected to Port 2 and the photodetector connected to Port 3 of the circulator.

The wavelength of the free running DFB laser is 1545.35 nm. The frequency components in Figure 3 are the original ML carrier and sidebands and P2 station. The P2 station frequency components are in the middle of the RF modulation sidebands and have different amplitudes. The frequency components close to the DFB laser frequency have higher amplitudes than those away from the DFB laser frequency. In the P2 state of the DFB laser, there are multiple frequency components, which are caused by the resonator in the laser and will not affect the system performance. The ML is modulated by RF signals, and its sidebands are adjustable to make SL wavelength in the middle. The spectrum of the optical signal was measured by the optical spectrum analyzer (OSA, Yokogawa AQ6730D). The resolution of the OSA is 0.02 nm, in which it is difficult to distinguish the RF and LO signals in optical spectra. When the ML is injected into the SL, the resonant state in the DFB cavity will change, with the upper and lower RF modulation sidebands. The frequency divider output spectrum is shown in Figure 3. The optical signal-to-noise ratio (OSNR) is related to the P2 state of optical injection and the input optical power. The optical frequency components contain the ML carrier and sidebands. By adjusting them in the middle of the RF modulation sidebands, they have different amplitudes. The optical signal near the SL frequency has higher optical power and better OSNR. The P2 station of the laser will also affect the OSNR, this is reflected in the influence of laser cavity length on P2 resonance. The DFB laser is operated at 25 °C and its output power is 0.35 dBm.

The electrical spectrum of microwave frequency divider is shown in Figure 4, which is measured with an electrical signal analyzer (ESA). The RF₁ and RF₂ signals are 5 GHz and 11 GHz, respectively. The beams emitted from the SL are captured by the photodetector (PD). The Δf/2 is 3 GHz, then the 8 GHz frequency component is obtained. This proves that the function of the frequency divider can be realized through an all-optical method. Because the RF signals peak frequency emitted by the two electrical signal generators are different between 5 GHz and 11 GHz, this causes the target signal peak frequency not to be 8 GHz. The power of the 8 GHz frequency component is −38.2 dBm, with the RF signal is 0 dBm, the system has a conversion gain of −38.2 dBm. The full width at half maximum (FWHM) depends on elements of device system, such as the RF signals generated from the electrical signal generators. There are no optical amplifiers before the photodetector, and there are no electrical amplifiers to increase the conversion gain.

Microwave frequency division for different input RF signals was investigated. By changing the RF₁ and RF₂ signals to obtain different Δf/2, we can obtain tunable frequency-division factors.

Table 1. The RF signal data in experiment.

RF1 (GHz)	RF2 (GHz)	Δf/2 (GHz)	ftarget (GHz)
5	11	3	8
7	11	2	9
5	15	5	10
6	14	4	10
7	13	3	10
7	15	4	11
7	17	5	12

shows the RF signals data in the experiment, f_target is the target frequency that we need to obtain. By changing the RF signals, the proposed all-optical frequency divider can realize any division factors, as shown in Figure 5. The frequency divider output electrical spectrum measured on ESA connected to PD. First, we adjust the RF₂ signal to 11 GHz. By changing the RF₁ signal to 5 GHz and 7 GHz, respectively, we can generate 8 GHz and 9 GHz f_target signals. Then the RF₁ signals are set to 5 GHz, 6 GHz and 7 GHz, respectively, and the corresponding RF₂ signals are set to 15 GHz, 14 GHz and 13 GHz, respectively, and the f_target values are all 10 GHz. At last, we adjusted RF₁ signal to 7 GHz and RF₂ signal to 15 GHz,17 GHz, so that f_target can generate 11 GHz and 12 GHz signals. The frequency component at 8 GHz to 12 GHz can be seen, this verifies the adjustable division factor frequency divider operation.

As shown in Figure 6, with the change in RF₁ and RF₂ signals, we keep the f_target as 10 GHz. The RF₁ signal is 5 GHz, 6 GHz, 7 GHz, respectively. The RF₂ signal is 15 GHz, 14 GHz, 13 GHz, respectively. The frequency divider corresponding to the change of different RF₁ and RF₂ signals has different frequency division factors, and the final target frequency signal is 10 GHz. The corresponding power of the state noise and frequency peak value under different frequency division factors is different. By controlling the RF signals, the proposed all-optical microwave frequency divider can achieve different frequency division factors. The systems parameters such as optical power and SL frequency can be optimized to extend the signal noise rate (SNR). In Figure 6, the State1 (RF₁ = 5 GHz, RF₂ = 15 GHz) has the SNR over 22 dBm, and the State 2 (RF₁ = 6 GHz, RF₂ = 14 GHz) and the State 3 (RF₁ = 7 GHz, RF₂ = 13 GHz) have the SNR about 18 dBm and 12 dBm, respectively. This is caused by the different RF signals value. For the influence of optical power for oscillation state, the ML power was changed accordingly as the input RF signal frequency value to ensure the SL was in P2 state.

4. Conclusions

A tunable division factors all-optical microwave divider is proposed, and experiment demonstrated. Based on the dual-beam injection effect, the DFB laser is oscillating in a P2 state. With the help of DP-DPMZM, two CS-SSB sidebands are generated to inject in the DFB by driving two RF signals in two orthogonal DPMZM branches. Then the optical frequency component is produced. There is no electrical component and optical or electrical amplifier in the proposed scheme. The power of the 8 GHz frequency component is −38.2 dBm, with the RF signal is 0 dBm, the system has a conversion gain of −38.2 dBm. Experimental results demonstrate that the frequency division factors can be adjusted.