## Abstract

A novel scheme of microwave photonic generation of binary digitally modulated signals is proposed and experimentally demonstrated, which can simultaneously generate 2ASK, 2PSK and 2FSK. By dynamically manipulating an optical frequency comb, different modulation formats can be switched. Moreover, the bit rate and carrier frequency of the generated RF signals can be tuned.

© 2017 Optical Society of America

## 1. Introduction

Microwave binary digitally modulated signals, such as amplitude shift keying (ASK), phase shift keying (PSK), frequency shift keying (FSK) signals, have been widely applied in antenna remoting, radio over fiber system, wireless communication systems and microwave signal analysis etc. Traditionally, these signals generated by the electronic circuits have a low operation bandwidth, which is limited by the electronic bottleneck. Nowadays, the photonic generation of microwave binary digitally modulated signals has been considered as a promising alternation due to its broad bandwidth, low loss, large tunability and immunity to electromagnetic interference, etc [1-3]. Many photonic approaches of microwave modulated signals generation have been investigated. In general, they can be classified into two categories: the technique based on frequency-to-time mapping (FTTM) and optical heterodyne technique [4-23]. In the FTTM-based technique, ASK/PSK/FSK signals have been separately generated using spatial light modulator (SLM) in [4-7]. And these signals are successfully switchable generated by means of parallel Mach-Zehnder interferometer (MZI) in [8]. Compared with FTTM-based technique, the optical heterodyne technique is priority due to the advantages of simplicity, stability and low loss etc. For the ASK signal, the structures based on Mach-Zehnder modulator (MZM), combination of mode locked laser and I/Q modulator, etc., have been proposed [9,10]. For the PSK signal, the structures based on MZMs, cascaded polarization modulators (PolM), Sagnac interferometers (SI), etc., have been proposed [10–21]. For the FSK signal, it can be realized based on MZM or the combination of a PolM and a dual-polarization MZM [22,23]. However, all these schemes based on the heterodyne technique can only achieve one modulation format. In order to enhance the flexibility of system, it is highly desirable to generate different kinds of modulation formats in single scheme.

In this paper, we propose a novel scheme to simultaneously generate multiple microwave binary digitally modulated signals in single structure based on the heterodyne technique. By rapidly tuning the tones of an optical frequency comb, we can obtain the microwave binary modulated signals with different modulation formats (i.e. ASK, FSK and PSK). This performance of rapid tunability is realized by the MZI of optical phase-coding signal. Moreover, the bit-rate of the generated digitally modulated signals can also be tuned, and their carrier frequencies are defined by the spacing of frequency tones. In our experiment, we successfully generate the 2ASK, 2PSK, 2FSK signals at same scheme when the bit-rate of data is 12.8-Gb/s. To verify the tunability of the scheme, the 2ASK, 2PSK and 2FSK signals with different carrier frequencies are separately generated when the bit-rate of data is changed to be 10.7-Gb/s.

## 2. Principle

Figure 1 is the conceptual diagram of proposed microwave signal generator, which consists of a phase modulator (PM), an MZI, an optical tunable filter (OTF), and a photodetector (PD). In our scheme, an optical comb with four frequency tones (i.e. *f*_{k}, *k* = i-1, i, i + 1, and i + 2,) is sent to the PM for optical phase coding, where a binary signal *s*(*t*) with the bit rate of *B*-bit/s is applied. Here the frequency tone of input can be expressed as *E*_{k}(*t*) = *A*_{k}exp(*j*2π*f*_{k}*t*), where *A*_{k} is the amplitude of frequency tones correspondingly. At the output of PM, the optical field of each frequency can be expressed as:

*γ*= π

*V*

_{s}/

*V*

_{π},

*V*

_{s}is the amplitude of binary signal,

*V*

_{π}is the half-wave voltage of the PM. Then the optical phase-modulated signals are launched into the MZI with tunable free spectral range (FSR, Δ

*f*). Here, the FSR of MZI is equal to the bit rate of the binary signal (i.e. Δ

*f*=

*B*).

The transmission function of MZI can be expressed as

where*δ*(

*t*) is the impulse function, and

*τ*= 1

*/*Δ

*f*is the time delay can be tuned correspondingly. Then the frequency response of the MZI can be obtained using the Fourier transform, which can be written as

In Eq. (3), the amplitude of maximum, medium, minimum points of *H*_{MZI}(*f*) is 1, 1/2, 0, respectively. When the optical phase-coding signal goes through the MZI, it can be expressed as

*s*´(

*t*) =

*s*(

*t*)-

*s*(

*t*-

*τ*) is the differential signal of

*s*(

*t*). Here the input four optical frequency tones are properly placed at the minimum, medium or maximum points of the MZI transmission function respectively (see Fig. 1), i.e.

*H*

_{MZI}(

*f*

_{i + 1}) = 1(maximum),

*H*

_{MZI}(

*f*

_{i-1,i + 2}) = 0(minimum),

*H*

_{MZI}(

*f*

_{i}) = 1/2(medium). When the adjacent bits of

*s*(

*t*) are same (i.e.

*s*´(

*t*) = 0), the optical signals after the MZI based on Eqs. (3) and (4) can be simplified as

When the adjacent bits of *s*(*t*) are different (i.e. *s*´(*t*) = 1), the optical signals after the MZI can be simplified as

It can be seen from Eqs. (5) and (6), when the bit of *s*´(*t*) is “0” (“1”), the frequency tones at the minimum points disappear (appear) after the MZI, and the frequency tones at maximum points appear (disappear). While the frequency tones at medium points would appear all the way whatever *s*´(*t*) is 0 or 1. Therefore, the frequency tones of optical comb can be rapidly switched based on the pattern of optical phase coding signal, i.e. *s*(*t*). By further choosing the proper frequency tones via an OTF as following, the modulation format of microwave signals can be shifted. To simplify the following analysis, the amplitude of the frequency tones is set to unit 1.

#### A. 2ASK generation

By adjusting the central wavelength and bandwidth of the OTF, we can get two frequency tones at medium, maximum (or minimum) points of the MZI transmission function (e.g. *f _{i}* and

*f*

_{i}_{+1}) respectively, as shown in Fig. 1(C

_{1}). 2ASK microwave signals will be obtained, as shown in Fig. 1(D

_{1}), which can be expressed as

If we tune the OTF to let the *f*_{i-1} and *f*_{i} go through, 2ASK signals with complementary amplitudes can be also obtained. Moreover, when two frequency tones (e.g. *f*_{i-1} and *f*_{i + 2}) are both at maximum (or minimum) points, we can also get ASK modulated signals.

#### B. 2FSK generation

The OTF can be tuned to place the three frequency tones at medium, maximum and minimum points of MZI transmission function (such as *f _{i}*,

*f*

_{i}_{+1},

*f*

_{i + 2}) respectively, and make sure that the frequency spacing between the maximum and medium is not equal to the frequency spacing between the minimum and medium, i.e. |

*f*

_{i + 2}-

*f*

_{i}|≠|

*f*

_{i}-

*f*

_{i + 1}|, as shown in Fig. 1(C

_{2}). At the output of the PD, the frequency tones

*f*

_{i + 1}and

*f*

_{i + 2}beat with frequency

*f*

_{i}, 2FSK microwave signals can be obtained, as shown in Fig. 1(D

_{2}), which can be expressed as

Moreover, if we tune the OTF to get four frequency tones, two of them are at the maximum points of MZI transmission function, another two are at the minimum points of MZI transmission function, make sure the frequency spacing between the two maxima is not equal to the frequency spacing between the two minima. After the PD, another 2FSK signal will be obtained.

#### C. 2PSK generation

As the OTF is tuned to get three frequency tones as before (such as *f*_{i-1}, *f*_{i}, *f*_{i + 1}), if there is a phase difference of π between the maximum and minimum, and the frequency spacing between the maximum and medium is equal to the frequency spacing between the minimum and medium, i.e. |*f*_{i + 1}-*f*_{i}| = |*f*_{i}-*f*_{i-1}| = *f*_{p}, as shown in Fig. 1(C_{3}), at the output of the PD, the frequency tones *f*_{i-1} and *f*_{i + 1} beat with frequency *f*_{i} alternatively, a 2PSK microwave modulated signal is obtained, as shown in Fig. 1(D_{3}), which can be expressed as

Here, the simplest method of optical modulation is employed to generate the three frequency tones. An optical carrier with the frequency of *f*_{c} (*f*_{i} = *f*_{c}) is sent to an intensity modulator (IM). Then a radio frequency (RF1) signal with frequency of *f*_{RF1} is applied to the IM for Doubled side-band modulation (DSM). The normalized optical field at the output of the IM can be written as *E*(*t*) = exp(*j*2π*f*_{c}*t*)[1 + exp(*jβ*sin(2π*f*_{RF1}*t*))], where *β* = π*V*_{RF1}/*V*_{πI} is the modulation index of the RF1 signal, *V*_{RF1} is the amplitude of RF1 signal, *V*_{πI} is the half-wave voltage of the IM. An expansion of *E*(*t*) with Bessel functions is *E*(*t*) = exp(*j*2π*f*_{c}*t*)[1 + Σ*J _{n}*(

*β*)exp(

*j*2

*n*π

*f*

_{RF1}

*t*)], where

*J*is the

_{n}*n*

^{th}-order Bessel function. When the modulation index is small, high-order terms can be ignored. While the first-order sidebands are considered,

*E*(

*t*) can be further described by

In the Eq. (10), *J*_{-1}(*β*) = -*J*_{1}(*β*), it can be shown that the phase difference of two first-order sidebands is π. Namely, taking the lower sideband of *f*_{c}-*f*_{RF1} is *f*_{i-1} and taking the upper sideband of *f*_{c} + *f*_{RF1} is *f*_{i + 1}.

The frequency tone of *f*_{i + 2} can be generated using a RF2 signal which is also applied to the IM. To make these frequency tones at corresponding points of MZI transmission function, the conditions in Eqs. (11) and (12) should satisfy.

*ξ*can be taken of 0 or Δ

*f*/4, and Δ

*f*is the FSR of MZI. It can be seen from Eqs. (11) and (12), when Δ

*f*is fixed, the different values of

*f*

_{RF1}and

*f*

_{RF2}can be taken for different

*n*and

*m*, thus the carrier frequencies of microwave modulated signals will be digitally tuned.

## 3. Experimental setup and results

To confirm the proposed scheme above, an experiment is demonstrated. The experimental setup is shown in Fig. 2. A continuous light-wave with the central wavelength of 1549.992-nm and output power of 13-dBm is transmitted from a TLS. Then it is sent to an IM. Two RF signals with frequencies *f*_{RF1} and *f*_{RF2} are generated by two analog microwave signal generators (MG1 and MG2), and applied to the IM with DSM, i.e. *f*_{i-1} = *f*_{i}-*f*_{RF1}, *f*_{i} = *f*_{c}, *f*_{i + 1} = *f*_{c} + *f*_{RF1}, *f*_{i + 2} = *f*_{c} + *f*_{RF2}. To compensate for the power loss in previous link, an Er-droped optical fiber amplifier (EDFA) with a tunable gain is employed. The binary signal is generated by a pulse-pattern generator (PPG, *Anritsu*, MT181), and is applied to the PM. The MZI with a tunable FSR value is used, followed by a bandpass OTF (*Santec*, OTF-350) with tunable central wavelength (1530~1610-nm) and bandwidth (0.1~15-nm). Finally, the output signal of the OTF is detected by a high-speed PD (*u ^{2}t*, XPDV3120R). The total system loss is ~16dB mainly from the modulators (IM & PM), MZI and OTF, and the highest frequency of generated RF signal is limited by the bandwidth of the PD.

Firstly, the bit-rate of binary signal *s*(*t*) is set to be 12.8-Gb/s with a fixed pattern of ”00001111”, and then *s*´(*t*) has a fixed pattern of “10001000”. The frequency and the output power of RF1 signal are set to be 16-GHz (*ξ* = Δ*f*/4, *n* = 2 in Eq. (11)) and 7-dBm, respectively. The frequency and the output power of RF2 signal are set to be 35.2-GHz (*m* = 1 in Eq. (12)) and 15-dBm, respectively. By adjusting the bias voltage of the IM, the DSM is achieved. The optical spectrum of the output DSM signal before the MZI is shown as the red solid line in Fig. 3. We properly adjust the voltage of *s*(*t*) to make the optical phase modulation with a precise phase difference of π between “0”- and “1”-bit. By adjusting the bias voltage of MZI to make the frequency tones at proper points of the MZI transmission function, the frequency response of MZI is shown as green dotted line in Fig. 3, the optical spectrum of signal at the output of MZI is shown as the blue dotted line in Fig. 3 (when the PPG is turned off).

At the output of the PD, the detected signals of one frequency tones at the maximum and minimum points of MZI transmission curve are shown in Figs. 4(a) and 4(b). The amplitudes of them are complementary, and it means that the output signals at minimum and maximum points appear alternatively. The central wavelength and bandwidth of the OTF are tuned to make the optical carrier of *f*_{c} and one sideband of *f*_{c} + *f*_{RF1} go through, a 16-GHz 2ASK microwave modulated signal is obtained as shown in Fig. 4(c).Then the OTF is tuned to make the optical carrier of *f*_{c} and the sidebands of *f*_{c} + *f*_{RF1}, *f*_{c} + *f*_{RF2} go through, a 2FSK signal has obtained as shown in Fig. 4(d) with RF frequencies of 16-GHz and 35.2-GHz. While the MG1 is turned off, by tuning the OTF to make the optical carrier of *f*_{c} and the sidebands of *f*_{c}-*f*_{RF2}, *f*_{c} + *f*_{RF2} go through, a 35.2-GHz 2PSK signal is obtained as shown in Fig. 4(e). As shown in Fig. 4, 2ASK, 2FSK and 2PSK microwave modulated signals can be generated.

Moreover, the above experimental parameters are changed as 10.7-Gb/s, *f*_{RF1} = 24.075-GHz (*ξ* = Δ*f*/4, *n* = 4 in Eq. (11)). At the support of the OTF, the detected 24.075-GHz 2ASK signals are shown in Figs. 5(a) and 5(b), and the 24.075-GHz 2PSK signal is obtained as Fig. 5(c). The *f*_{RF1} is changed to be 29.425-GHz (*ξ* = Δ*f*/4, *n* = 5 in Eq. (11)). The detected 29.425-GHz 2ASK signals are shown in Figs. 6(a) and 6(b) and the 29.425-GHz 2PSK signal is obtained as Fig. 6(c). Based on Figs. 5 and 6, the carrier frequencies of generated 2ASK/2PSK signals are digitally tuned at different *n* values. In addition, compared with the Fig. 4, it denotes that the bit rate of the obtained microwave modulated signals is defined by the bit rate of the binary signal.

Furthermore, when the bit rate of binary signal *B* = 10.7-Gb/s, we set *f*_{RF1} = 5.35-GHz (*ξ* = 0, *n* = 1 in Eq. (11)) and *f*_{RF2} = 21.4-GHz (*m* = 1 in Eq. (12)), the distribution of these generated frequency tones on the MZI transmission function is different from the previous experiments. A pair of sidebands are placed at the maxima, and another pair of sidebands are placed at the minima. The measured optical spectra before and after the MZI are shown in Fig. 7. The pattern of binary signal is set to be “11110101”along with the s´(*t*) being “00001111”. By turning off the MG2, a 10.7-GHz OOK signal is obtained as shown in Fig. 8(a). By turning off the MG1, a 21.4-GHz OOK signal is obtained as shown in Fig. 8(b). if MG1 and MG2 are tuned on at the same time, a 2FSK signal with carrier frequencies of 10.7-GHz and 21.4-GHz is obtained as shown in Fig. 8(c). Compared with the results of Fig. 4, the 2FSK signal is also obtained when the frequency tones are placed at different points of the MZI transmission function. For *f*_{RF1} = 16.05-GHz (*ξ* = 0, *n* = 3 in Eq. (11)) and *f*_{RF2} = 21.4-GHz, the 2FSK signal with RF frequencies of 21.4-GHz and 32.1-GHz is obtained as shown in Fig. 8(d). According to Figs. 8(c) and 8(d), it can be observed that the frequency of generated microwave modulated signals can be adjusted digitally for a given bit rate of the binary signal.

In addition, the bit pattern of the binary signal is changed to “0101111101101011”, along with the s´(*t*) being “1111000011011110”. The experimental parameters are set as B = 10.7-Gb/s, *f*_{RF1} = 5.35-GHz and *f*_{RF2} = 21.4-GHz. The detected 2FSK signal with carrier frequencies of 10.7-GHz and 21.4-GHz is shown in Fig. 9. Clearly the performance of the detected signal is as good as that of Fig. 8(c).Therefore the performance of the proposed scheme is unrelated to the length of the bit sequence.

## 4. Conclusion

In conclusion, a simple scheme is proposed and demonstrated to simultaneously generate 2ASK, 2PSK and 2FSK microwave binary digitally modulated signals by using one single structure. The bit rate and the carrier frequency can be adjusted. It is quite possible to generate high-order modulation formats signals (such as 4ASK/4PSK/4FSK) if the proposed scheme is combined in parallel or cascaded configurations. Such scheme may be used in various applications for dynamic high-speed communication networks.

## Funding

“863” National High-Tech Program (2015AA016903); National Natural Science Foundation of China (NSFC) (No. 61335005, 61325023, 61405165).

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