## Abstract

A novel approach to photonically generate binary digital modulation radio frequency (RF) signals is proposed. In the proposed system, the short optical pulses are converted into high frequency RF signals based on optical pulse shaping followed by dispersion induced frequency-to-time mapping technique. And the generated signals are coded using a fast electro-optical switch based on polarization modulation. By properly configuring the system, binary digital modulation signals, including amplitude-shift keying (ASK), frequency-shift keying (FSK) and phase-shift keying (PSK) with required bit pattern are generated in the optical domain. A model describing the signal generation system is derived, which is verified via both simulations and a proof-of-concept experiment.

©2013 Optical Society of America

## 1. Introduction

Amplitude-shift keying (ASK), frequency-shift keying (FSK) and phase-shift keying (PSK) are fundamental digital modulation schemes in wireless communications, which convey data by modulating the amplitude, frequency or phase of a sinusoidal carrier wave. Traditionally, these digital modulation RF signals are generated in the electrical domain by using digital electronic circuits [1]. The major difficulty associated with traditional techniques, however, is that the frequency of the generated signals is limited to a few GHz due to the electronic bottleneck. With the increasing demand for higher communication capacity, high frequency RF signals in millimeter-wave regime are required for the emerging applications, such as millimeter-wave video transmission, indoor wireless systems and deep-space communications [2,3]. An effective alternative to generate high frequency RF signals is to generate RF signals in the optical domain, which has attracted intensive research interests in the last few years due to the advantages such as wide bandwidth, low loss, and immunity to electromagnetic interference offered by modern optics [4]. Among the existing techniques for the photonic generation of RF signals, optical pulse shaping followed by frequency-to-time mapping (FTTM) has been demonstrated to be a promising technique, in which a temporal RF pulse with a shape identical to the shaped optical pulse spectrum can be generated [5]. Recently, photonic generation of binary PSK RF signals based on optical pulse shaping and FTTM using a spatial light modulator (SLM) was demonstrated in [6]. The key advantage of using an SLM in RF signal generation is its flexibility because an SLM can be updated in real time. The major challenge associated with the SLM-based technique is that the pulse shaping is usually implemented in free space, making the system bulky, costly and complicated. On the other hand, the photonic generation of PSK signals can also be implemented using pure fiber-optic components [7–9], which offers the advantages such as lower loss, better stability and higher potential for integration. The generation of ASK RF signals has also drawn some attention recently [10]. However few efforts have been dedicated to the photonic generation of FSK RF signals.

In this paper, a novel approach to generate binary digital modulation RF signals in the optical domain is proposed. The proposed system is an all-optical technique, which can generate high frequency binary digital modulation RF signals, including ASK, FSK and PSK signals with required bit pattern. In addition, with proper configuration, the system can offer some flexibility in the generation of aforementioned RF signals, such as the tuning of the center frequency and duty cycle of the generated signals. A theoretical model describing the proposed system is derived, which is verified by simulations and a proof-of-concept experiment.

## 2. Principle and theoretical analysis

Figure 1 shows the schematic diagram of the proposed system. The optical pulses from a short pulse laser source (SPLS) are sent to a polarization modulator (PolM) that is connected to a polarization beam splitter (PBS). The PolM is driven by a binary digital data signal. When a linearly polarized incident light is oriented with an angle of 45° to one principal axis of the PolM, the polarization state of the output lightwave will change between two orthogonal linear polarization states in accordance with the applied data signal. The PBS is connected to the output of the PolM with one of its principal axes oriented at an angel of 45° to that of the PolM. Therefore, when a linearly polarized optical pulse train is sent to the PolM with an angle of 45° to one principal axis of the PolM, the optical pulse train will be split into two branches at the two outputs of the PBS under the control of the binary data signal applied to the PolM.

In each branch of the system, the optical pulses are spectrally shaped by two Mach-Zehnder fiber interferometers (MZI) respectively, and then combined by an optical coupler (OC). Then after filtered by a tunable optical filter (TOF), the spectrum-shaped optical signals are sent to a dispersive device, namely a length of single mode fiber (SMF), to perform linear FTTM. Finally the optical signals are converted into RF signals at the output of a high-speed photodetector (PD).

Theoretically, an MZI can be modeled as a two-tap delay-line filter with an impulse response given by

where the parameter$\tau $is the time delay difference between its two arms. Its intensity response can be obtained using the Fourier transform, which can be written asThe free spectral range (FSR) of the response, defined as the frequency separation between two adjacent fringes, can be expressed as$FS{R}_{f}=1/\tau $ .

The TOF can be modeled as a Gaussian filter, with a full-width at half-maxim (FWHM) bandwidth of${B}_{W}$, and its intensity response can be expressed as:

Therefore, for each branch of the system, the intensity transfer function of an MZI incorporated with a TOF can be expressed as:

An optical pulse from the SPLS can be modeled as a transform-limited Gaussian pulse, which can be expressed as

where${t}_{0}$is the half pulsewidth at$1/e$maximum. After passing through the pulse shaper consisting of an MZI incorporated with a TOF, the output pulse$y(t)$is given by calculating the convolution$y(t)=x(t)\ast h(t)$, where$\ast $denotes convolution operation and$h(t)$is the inverse Fourier transform of$H(f)$in Eq. (4). And in the frequency domain, the output optical pulse can be expressed as$Y(f)=X(f)\cdot H(f)$, where$X(f)$is the Fourier transform of $x(t)$in Eq. (5). Then the spectrum-shaped optical pulse is sent to a length of SMF with a dispersion value of${\Phi}_{\nu}$(ps^{2}) to perform linear FTTM, and the output signal can be expressed as [4]:

As can be seen from Eq. (6), after the FTTM in SMF, the envelope of the output signal is proportional to the spectrum of the spectrum-shaped optical pulse output from the TOF. Note that Eq. (6) is obtained if the duration of the input short pulse$\Delta t$and the dispersion ${\Phi}_{\nu}$satisfy$\left|\Delta {t}^{2}/{\Phi}_{\nu}\right|<<1$, which means that the pulse duration before the SMF is much smaller than that after experiencing the dispersion. This assumption is always true for picosecond optical pulses propagating in a few kilometers of SMF [10]. Therefore, after pulse shaping and FTTM, the input optical short pulse is converted into time-domain RF pulse after PD detection, which can be expressed as

The period of the RF signal carrier is calculated by

Additionally, based on the mapping relationship of the FTTM, the time-domain duration$\Delta T$of each RF pulse can be calculated by

By properly configuring the system, binary PSK, FSK and ASK can be obtained as follows: If the MZIs in two branches of the system have the same parameter$\tau $, and the time delay${T}_{D}$between two consecutive RF pulses is adjusted as$T/2$by tuning the TODL in the system, a$\pi $phase shift can be introduced to the generated RF signals due to the time-delay-induced phase shift [11]. As a result, binary PSK RF signals can be obtained. If the two MZIs with different parameter${\tau}_{1}$and${\tau}_{2}$are used, then RF signals with a pair of discrete frequencies${f}_{1}$and${f}_{2}$can be generated according to Eq. (8). As a result, binary FSK RF signals can be obtained with${f}_{1}$and${f}_{2}$representing the mark and space frequency respectively. In these two scenarios the optical switch in the system is set as on-state. If the optical switch is set as off-state, then the output signals from the upper branch of the system will be blocked, which can lead to the generation of binary ASK RF signals.

## 3. Simulation and experiment results

Figure 2 presents the simulation model of the proposed system using a commercial software package Virtual Photonic Incorporation (VPI) Transmission maker. The simulation model is set up based on Fig. 1, except that the optical switch is replaced by a variable optical attenuator (VOA). Besides switching off the upper branch of the system, the VOA can also be used to balance the amplitudes of the output signals from the two branches. The SPLS generates transform-limited Gaussian optical pulses with a FWHM pulsewidth of 1ps, a central wavelength of 1550nm, and a repetition rate of 10 GHz. The center wavelength of the TOF is adjusted to 1550nm, and the bandwidth is set as 250GHz. The bit rate of the digital data applied to the PolM is set as 10Gbps, which is synchronized with the optical pulse train from the SPLS. The SMF has a standard dispersion coefficient of 17ps/nm/km, and its length is set as 3km. Two erbium doped fiber amplifiers (EDFA) are used in both branches of the system to boost the intensity of the input optical pulses. Simulations are implemented to verify the generation of binary PSK, FSK and ASK RF signals respectively.

In the first scenario, the generation of binary PSK signals is verified with a 7-bits M-sequence, namely, code = {1,1,1,0,1,0,0}. The parameters of MZI1 and MZI2 are both taken as$\tau $ = 25ps. According to Eq. (9), the period of the generated RF carrier is calculated as $T$ = 15.4ps. Therefore the time delay${T}_{D}$should be set as $T/2$ = 7.7ps in order to acquire a$\pi $phase shift. The generated binary PSK signals are shown in Fig. 3 . For comparison, signals without coding (namely no phase shift) are also shown in Fig. 3 with dashed line.

As can be seen from Fig. 3, the binary PSK signals with required code pattern are successfully generated. The phase coding is realized due to the time-delay-induced phase shift.

In the second scenario, the generation of binary FSK signals is verified by the simulation. In order to generate two discrete frequencies, the parameters of MZI1 and MZI2 are set as ${\tau}_{1}$ = 25ps and${\tau}_{2}$ = 16ps respectively. According to Eq. (8), the mark and space frequencies of the generated binary FSK signals can be calculated as${f}_{1}$ = 66GHz and${f}_{2}$ = 42GHz respectively. Figure 4(a) shows the waveform of the generated binary FSK signals with the same 7-bits M-sequence. Figure 4(b) shows its corresponding power spectrum.

As seen from Fig. 4(a), the binary FSK RF signals with required bit pattern are successfully generated. And as seen from Fig. 4(b), the mark and space frequency${f}_{1}$and${f}_{2}$are 66GHz and 42GHz respectively, which verifies the theoretical predictions based on Eq. (8). The spectrum spikes in Fig. 4(b) are separated by a frequency interval of 10GHz, indicating a bit rate of 10Gbps.

The modulation index of the generated binary FSK signals, which is defined as the difference between${f}_{1}$and${f}_{2}$divided by the signal bit rate, is calculated as$m$ = 2.4. According to Eq. (8), if the dispersion is fixed, the mark and space frequency of the generated binary FSK signals can be varied by changing${\tau}_{1}$and${\tau}_{2}$of the two MZIs. Therefore, binary FSK RF signals with different modulation index can be obtained by properly designing the MZIs in the system.

In the proposed system, each input optical pulse is converted into an RF pulse with a time-domain duration of$\Delta T$, which is determined by Eq. (10). If$\Delta T$is adjusted properly to match the bit period (namely the reciprocal of the bit rate), then the generated binary FSK signals have a duty cycle close to 100%, which is the case in the above simulation results. If $\Delta T$is smaller than the bit period, for example$\Delta T$is only half of the bit period, then binary FSK RF signals with a duty cycle of 50% can be generated. This can also be achieved by doubling the bit period of the generated FSK signals. Figure 5 shows the simulation results when the repetition rate of the SPLS is reduced by half, while keeping all the other system parameters unchanged.

As seen from Fig. 5(a), the generated binary FSK signals have a duty cycle of about 50%, which verifies our theoretical prediction. Figure 5(b) shows the power spectrum of the generated signals, which is similar with that shown in Fig. 4(b) except that the frequency intervals between spectrum spikes are reduced to 5GHz. This can be explained by the halved bit rate.

On the other hand, the duty cycle of the generated RF signals can also be reduced by tuning the bandwidth of the TOF while keeping the system bit rate unchanged. According to Eq. (10), if the dispersion is fixed, $\Delta T$can be reduced by decreasing the bandwidth of the TOF. For example if we halve the bandwidth${B}_{W}$, then$\Delta T$will be reduced by half. So that FSK signals with duty cycle of 50% can also be achieved without reducing the bit rate. However it is found in our simulations that the reduction of${B}_{W}$leads to the reduced amount of carrier cycles within the pulse envelope, which can be explained by the reduced optical spectral width in the pulse shaping process.

From Eq. (10), we can see that$\Delta T$can also be reduced by decreasing the dispersion used in the system instead of tuning the bandwidth${B}_{W}$. This can be realized by decreasing the length of the SMF used in the system. However, according to Eq. (8), this will also vary the mark and space frequency${f}_{1}$and${f}_{2}$. In this case, the dispersion and${B}_{W}$of the system should be jointly optimized for specific requirements. Additionally, the dispersion should always be kept large enough to meet the requirement of FTTM as described in Eq. (6).

In the third scenario, the generation of binary ASK RF signals are verified by the simulation. The attenuation of VOA in the upper branch of the system is set as $\infty $ to simulate the off-state of an optical switch, which means the input optical pulses switched to the upper branch of the system will be blocked. The parameter of the MZI2 in the lower branch of the system is set as$\tau $ = 25ps. Figure 6 shows the simulation results, where the same bit pattern of 7-bits M-sequence is adopted.

As seen from Fig. 6, binary ASK RF signals with required bit pattern are successfully generated, which have the same center frequency as${f}_{1}$in Fig. 4(b). According to Eq. (8), we can predict that if we reduce the parameter of MZI2 to$\tau $ = 16ps, then the ASK RF signal with a center frequency equivalent to${f}_{2}$can be generated. Similarly with the results in Fig. 5(a), if we vary the bit period of the generated signal, binary ASK RF signals with different duty cycle can be generated.

An experiment based on the simulation model is carried out to verify the concept of the proposed system. The SPLS used in the experiment is a U2T Company’s model-locked laser (MLL), and the PolM used is VersaWave Company’s electro-optic polarization modulator. The MLL generates short light pulses at the repetition rate of 10GHz, with the FWHM pulsewidth of 1.3ps, and its FWHM bandwidth is measured to be 1.6nm. The bandwidth of the TOF used in the experiment is measured to be 220GHz. The PolM is driven by 10Gbps digital signals from Anritsu Company’s pulse pattern generator (PPG). Each of the MZI in the system is welded by two 2 × 2 optical couplers where the parameter$\tau $is controlled by the length difference of their two arms. After careful design, three MZIs with their parameter measured to be${\tau}_{a}$ = 24.52ps, ${\tau}_{b}$ = 24.69ps and ${\tau}_{c}$ = 16.39ps are successfully fabricated. 3 km SMF is used as the dispersion device in the system. Two EDFAs are used in both arms of the system to boost the intensity of the input optical pulses. And the generated RF signals are measured by Agilent Company's sampling oscilloscope.

The experiments are implemented based on the three scenarios of the simulation analysis. Firstly the generation of the binary PSK signals is implemented, where the two MZIs with ${\tau}_{a}$and${\tau}_{b}$are used in the two arms of the system respectively. The experiment results are shown in Fig. 7(a) . Secondly, the generation of binary FSK signals is implemented, where the two MZIs with${\tau}_{b}$and${\tau}_{c}$are used in the two arms of the system respectively. The experiment results are shown in Fig. 7(b). Finally, for the generation of binary ASK signals, only one arm of the system is used, while the other arm is disconnected from the system. Two MZIs with ${\tau}_{b}$and${\tau}_{c}$are used to generate two versions of binary ASK signals respectively. The experiment results are shown in Figs. 7(c) and 7(d) respectively. In all the above cases, the same 7-bits M-sequence code pattern is adopted.

In Fig. 7(a), $\pi $-phase shifts are introduced to the generated PSK signals by carefully tuning the OTDL in the system. As seen from Fig. 7(a), the generated binary PSK signals agree well with the simulation results shown in Fig. 3. The slight inconsistency of the carrier cycles under the signal envelope are mainly due to the difference of system parameters used in experiments and theoretical analysis.

In Fig. 7(b), binary FSK RF signals are generated, where the VOA is tuned to balance the amplitude of the signals from two branches. As seen from Fig. 7(b), the generated binary FSK signals agree well with the simulation results in Fig. 4(a). The power spectrum of the generated signals is not measured due to the lack of high bandwidth RF spectrum analyser. However the center frequencies of the mark and space frequency of the generated FSK signal can be estimated by the reciprocal of the time period of pulse trace. The time period of the carrier under symbol “1” and “0” are measured as 16ps and 23ps respectively. Therefore the mark frequency${f}_{1}$and the space frequency${f}_{2}$of the generated binary FSK signals are estimated to be 63GHz and 43GHz respectively, which are very close to the simulation results. The difference is mainly due to measurement errors and the difference of system parameters used in experiments and theoretical analysis. In Fig. 7(c), the MZI of${\tau}_{b}$ = 24.69ps is used to generate binary ASK RF signals. As can be seen, the experiment results agree well with the simulation results shown in Fig. 6. The center frequency of the generated binary signals can be estimated to be equivalent to${f}_{1}$ = 63GHz because the same MZI with${\tau}_{b}$ = 24.69ps is used. Figure 7(d) shows the generated binary ASK signals of a second version, where the alternative MZI of${\tau}_{c}$ = 16.39ps is used. As can be estimated from Fig. 7(d), the center frequency of this binary ASK RF signals is around 43GHz, which is consistent with our theoretical predication. Comparing Fig. 7(c) with Fig. 7(d), it is noted that the number of carrier cycles under the signal envelopes in Fig. 7(d) is fewer than that in Fig. 7(c). This is because in Fig. 7(d), the MZI with a smaller parameter${\tau}_{c}$is used. According to Eq. (7), when the parameter of the MZI is smaller, fewer cycles will be generated within a fixed optical bandwidth${B}_{W}$.The experiment results indicate that if tunable MZI is used, then the center frequency of the generated FR signals can be tuned, which can add more flexibility to the proposed system. For this purpose, a tunable MZI structure should be used [12].

On the other hand, the duty cycle of the generated RF signals can also be tuned by changing the repetition rate of the SPLS. And if a pulsed laser with tunable repetition rate is used [13], then digital modulation signals with flexible bit rate can be achieved by the proposed system. Therefore the proposed system can offer some flexibility in the generation of RF binary digital modulation signals, which is very desirable for practical applications.

The main difficulty in our experiment lies in the design and fabrication of the MZI devices used in our experiment, which are sensitive to environmental variations. It is found that by packing it up in a box filled with plastic foam can relieve this problem. This problem can be ultimately solved by using sophisticated integrated devices. Besides, the PCs in the system need to be carefully adjusted to realize good extinction ratio of the electro-optic switch based on polarization modulation. And if the SMF in the proposed system can be replaced by a dispersion tunable device, the tunability of our proposed system can be enhanced. A further experimental study is needed to investigate the tunability of the proposed system, which will be the focus of our future work when the related devices and equipments are available to us.

## 4. Conclusion

A novel approach to photonically generate fundamental digital modulation RF signals, including PSK, FSK and ASK signals was proposed. And a theoretical model was derived, which was verified by simulations and experiments. The proposed approach is an all-optical solution which can easily generate high frequency RF signals in millimeter wave regime without the need of microwave reference sources. Therefore it can fully explore the advantages offered by modern optics such as small size, low loss, and immunity to magnetic interference. Furthermore, the proposed system is simple and can be implemented using all-fiber-optic components, which provides the potential for integration. Additionally, the proposed system can offer some flexibility in the generation of RF signals, which can find applications in future high speed wireless communications systems.

## Acknowledgments

This work was supported by National Nature Science Foundation of China (NSFC) under grant No. 61032005, National Key Basic Research Program of China under the grant No 2012CB315603, and China Postdoctoral Science Foundation under grant No. 2012M510442.

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