Photonic Generation of Frequency 16-Tupling Millimeter-Wave Signal without Optical Filter

A generalized optical filterless approach to achieve photonic generation of frequency 16-tupling millimeter-wave (mm-wave) signal based on two cascaded dual-parallel Mach-Zehnder modulators (DPMZMs) is presented. A theoretical analysis leading to the operating conditions to achieve frequency 16-tupling is developed. Different modulation indices (MIs) can be implemented to achieve the frequency multiplication by adjusting the delay of tunable optical delay line (TODL). It is confirmed by simulation that the proposed scheme is effective, and the radio frequency spurious suppression ratio (RFSSR) of the generated frequency 16-tupling signal can be as high as 40 dB when the sub-MZMs have extinction ratios of 30 dB. Influencing factors such as extinction ratio, DC bias drift, phase shift deviation and RF voltage deviation on the performance of optical sideband suppression ratio (OSSR) and RFSSR are also investigated.


Introduction
Microwave generation by photonic techniques has been intensively investigated for the advantages of low phase noise, high frequency and wide frequency tunability [1] [2]. Many approaches for photonic generation of microwave have been demonstrated in the few past years. Among them, external modulation based on Mach-Zehnder modulator (MZM) for optical frequency multiplication has been considered as an attractive solution due to the system simplicity, operation stability, large frequency tunability and high spectral purity of the generated mi-Journal of Applied Mathematics and Physics crowave signal [1] [2] [3].
For the external modulation approaches, frequency quadrupling [2]- [8], sextupling [1] [9] and octupling [1] [10] [11] [12] signals have been achieved. To generate higher frequency signal or further reduce the need for the response bandwidth of the modulator, a higher multiplication factor is needed. A frequency 12-tupling scheme was proposed by using a DPMZM, a semiconductor optical amplifier and an optical inter-leaver (IL) [13], the OSSR was 30 dB for the generated optical signal after the IL, however, the system was complicated, and the IL worked as an OF which limited the utilization for wavelength-division-multiplexing (WDM) systems. A frequency 16-tupling signal can be generated by using two parallel DPMZMs with RFSSR as high as 55 dB [12], but the MI as 5.520 or 8.654 was too high to realize for a commercial DPMZM. An optical filterless scheme based on three parallel MZMs was proposed to achieve multiplication factors as high as 12 and 18 with RFSSRs as 50 dB and 32 dB respectively [14], however, the scheme was hard to practically utilize for the same reason that the MIs should be 5.520 and 9.761 respectively. The two cascaded DPMZMs scheme can be used to generate a frequency 16-tupling signal [15], but no generalized investigation has been reported.
In this paper, a generalized approach to generate 16-tupling mm-wave signal using two cascaded DPMZMs is presented. The significance of the configuration is that different MIs can be implemented to achieve the frequency 16-tupling while the MIs are smaller than 4, which is more practical for utilization. In addition, since no OF is required, the proposal can be used in WDM systems. Optical mm-wave signals with frequencies up to 640 GHz can be achieved by the proposed scheme if two commercially available 40 GHz DPMZMs and a wide enough bandwidth PD are employed.

Principle
The proposed scheme using two cascaded DPMZMs to achieve frequency 16-tupling mm-wave signal is shown in Figure 1. The system consists of a laser diode (LD), two DPMZMs, a tunable optical delay line (TODL), a photodiode (PD), a local oscillator (LO), an electrical phase shifter (PS), and three electrical power dividers. A low-frequency microwave signal from the LO is divided into four paths by three power dividers, and applied to the two DPMZMs. The PS is used after the first power divider to introduce a phase difference between two sub-MZMs of each of the DPMZMs. The TODL can be replaced by two electrical PSs [15]. The function of TODL is to introduce a phase difference between different optical sidebands. Erbium-doped fiber amplifier (EDFA) may be used to boost the optical power of the signals output from DPMZMs.
Assuming that the incident light wave is E 0 cos(ω c t), where E 0 is the amplitude of the optical field, and ω c is the angular frequency of incident light wave. Both the sub-MZMs of DPMZM1 are biased at the maximum transmission point (MATP) to suppress the odd-order sidebands, and the main MZM of DPMZM1 is set to let the signals from the two arms in phase. The phase difference introduced by PS is π/2, and then the optical field at the output of the DPMZM1 can be expressed as where ω is the angular frequency of the electrical driving signal, m is the MI of DPMZM1, J n is the nth-order Bessel function of the first kind. As can be seen, only the carrier and ±4th-order sidebands are obtained. When the light wave is traveling through the TODL, a phase difference φ between the two adjacent sidebands would be introduced and the optical field E TOD (t) at the output of the TODL can be written as [1] ( ) E TOD (t) is then sent into DPMZM2. The DPMZM2 is biased identical to the case of DPMZM1, and the MI of DPMZM2 is also m. The optical field at the output of DPMZM2 can be expressed as If the following conditions are satisfied where k is an integer, E 2 (t) can be simplified into As can be seen, only the ±8th-order sidebands are presented, the beating of the two sidebands at the PD would generate a frequency 16-tupling mm-wave signal. Journal of Applied Mathematics and Physics  In the electrical domain, the RFSSR is limited by the tenth-order harmonic component. The measured OSSR and RFSSR of the generated mm-wave signal are degraded to 9 dB and 18 dB respectively, as shown in Figure 3(a) and Figure   3 The generation of the mm-wave signal is achieved by adjusting the voltage of the oscillator, the phase difference between the driving signal, the time delay of the TODL, and the DC bias of the modulators. For the practical application, these parameters are not ideal, and they may degrade the performance of the proposed scheme. The influence of imperfect factors on the performance of OSSR and RFSSR for the generated mm-wave signal will be discussed in this part. Figure 7 shows the simulation results of the OSSR and RFSSR against the power split ratio of the sub-MZM. The range of the extinction ratio of sub-MZM is 20 -50 dB. The OSSR has a linear relationship with the extinction ratio as shown in Figure 7(a). The RFSSR increases along with the increase of extinction ratio firstly, because the undesired components are suppressed better when the extinction ratio is higher. Then the RFSSR retains unchanged when the extinction ratio is high enough, because the undesired components are lower than the noise power and the RFSSR is restricted by the noise. It also can be seen that, when the extinction ratio is given, a better performance can be obtained when a higher MI is provided.  If the phase deviation is smaller than ±1. 5    means that, when no EDFA is used, the optical power loss between the output of DPMZM2 and the output of LD, and they are estimated by the simulation results. The power compensation of optical amplifier means the gains needed in the simulation to guarantee the average receiving optical signal power of PD appropriates −4 dBm. It can be seen that when m = 3.999, the power of LO is 3 dB -5 dB higher than the other three cases, but the power penalty of optical system is 20 dB -30 dB lower.

Conclusion
A filterless frequency 16-tupling optical mm-wave signal generation approach is demonstrated. Compared with the reference [15], this paper gives a generalized investigation of the two cascaded DPMZMs scheme. Different MIs can be implemented to achieve the frequency 16-tupling signal by adjusting the delay of TODL. It is confirmed by simulation that the proposed scheme is effective. Influencing factors such as extinction ratio, DC bias drift, PS deviation and RF voltage deviation on the performance of OSSR and RFSSR are investigated. The simulation results show that the RFSSR of the generated frequency 16-tupling signal can be as high as 40 dB when the sub-MZMs have extinction ratios of 30 dB. Compared with the previous high-frequency multiplication factor schemes proposed in references [13] [15], the cascaded DPMZMs approach is more practical for application, because the value of MI is 2.405, 2.672 or 3.999, which is much lower than the previous schemes as 5.520, 8.654 or 9.761.