Time–frequency-varying multicarrier generation using dynamic recirculating frequency shifter

Abstract. A time–frequency-varying multicarrier generation scheme based on dynamic single-sideband recirculating frequency shifter is proposed and experimentally demonstrated. Through the use of two time-domain sinusoidal signals with stationary phase shift provided by a phase control module, multicarriers with flexible frequency intervals are obtained without carrier-to-noise ratio and flatness loss. We have experimentally attained multicarriers with 10-/12.5-/15-GHz carrier intervals in 3-nm bandwidth, and carriers with arbitrary intervals can be achieved when using the proposed scheme combined with a flexible wavelength selective switch.


Introduction
Frequency-locking optical multicarrier has unparalleled advantages in fiber communications and optical sensing applications, such as wavelength division multiplexing (WDM) transmission, optical orthogonal frequency division multiplexing signal generation, spectral measurement, and analysis. [1][2][3] For example, an optical multicarrier source with high quality and a large number of carriers is a good candidate to serve as a laser array at the transmitter or a local oscillator array at the receiver side for ultra-high speed and high-spectrum efficiency optical transmission systems. For such applications, highly coherent optical multicarrier sources with stable flatness and uniform power distribution are desirable. Many endeavors have been made on the generation of optical multicarriers, conventional multicarrier sources are mainly based on highly nonlinear fibers, 4 microring resonators, 5,6 cascaded modulators, 7 and recirculating frequency shifter (RFS). 8 RFS has attracted wide attention in recent years because of its simple structure, low driving voltage, and flat subcarrier. IQ modulator with three direct current (DC) bias controls is widely used to realize the continuous and recirculated single-sideband (SSB) modulation with special frequency spacing. At present, 50 or more stable frequency-locked carriers have been successfully generated, 9 and many improvement techniques have been proposed to achieve better performance, 10 such as using optical-FIR filter for amplified spontaneous emission noise suppression, 11 multifrequency and multichannel shifting method for increasing carrier numbers, 12 and modified modulators to enlarge the carrierto-carrier spacing; [13][14][15] while these methods increase the complexity of the RFS scheme, at the same time, the carrier interval of the proposed methods is fixed due to the stationary frequency of the RF source and the phase shifter. The generated multicarrier frequencies are not selective and therefore cannot be flexibly scheduled.
In this paper, we improved the recirculating frequency shifter and proposed a time-frequency-varying multicarrier generation method, by adjusting the delay of two sinusoidal signals in time domain to lock their phase difference, the flexible interval optical multicarriers in frequency domain can be obtained, multicarriers with different carrier spacing have been generated, and two subcarriers can be obtained at any interval. To meet the increasing demand for bandwidth in the future, the scheme is a good candidate for passiveoptical-network (PON) integrated with radio-over-fiber (ROF) and photon frequency hopping radar.

Principle of Flexible Interval Multicarrier
Generation The structure of the basic RFS is shown in Fig. 1, the RFS consists of a tunable light source that provides the seed carrier of frequency f 0 and a closed fiber loop, which comprises a 50:50 coupler, a radio frequency (RF) signal source, I/Q modulator, an optical bandpass filter (OBPF), which is used to control the number of carriers required, an erbiumdoped fiber amplifier (EDFA) to compensate the losses in the loop, and a polarization controller to stabilize the state of polarization.
The I/Q modulator consists of two parallel Mach-Zehnder modulators and a π∕2 phase shifter. In order to make the modulator work in the SSB state and implement carrier frequency shift, two RF signals, which are fed into the I/Q modulator, are supposed to have equal power but π∕2 phase shift. Conventionally, we use an RF signal source to generate a clock signal with the frequency f s and then split it into two branches, with a phase shifter in one branch to make it π∕2 phase-shifted. Ideally, the input optical field is E in ðtÞ ¼ A expðj2πf 0 tÞ, the two RF drive signals are f I ðtÞ ¼ V pp sin (2πf s t), f Q ðtÞ ¼ V pp sinð2πf s t þ θÞ, where f s represents the frequency of the RF signal and θ represents the phase difference between two RF signals determined by phase shifter. The electronic field of the I/Q modulator output is represented by Ref. 8 (1) using the Jacobi-Anger expansion, Eq. (1) can be expressed as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 6 3 ; 4 4 7 where δ m ¼ πV pp ∕2V π denotes the phase modulation depth, and J ð2k−1Þ ðδ m Þ is the odd-order Bessel function of the first kind. According to Euler's formula, E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 6 3 ; 2 3 9 according to the characteristics of Bessel function, the third-order harmonic plays a dominant role among all the harmonics, ignoring all the high-order harmonics beyond the third-order, the output of the RFS after the first round trip (RT) can be expressed as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 3 2 6 ; 6 9 7 If θ is equal to π∕2, the I/Q modulator works at ideal SSB condition: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 3 2 6 ; 5 8 0 which depends on drive voltage V pp of the I/Q modulator, we can apply appropriate driving voltage to make jcj ≪ 1 and the crosstalk of third-order harmonic could be neglected. When RF is set to 12.5 GHz and I/Q phase difference is π∕2, two RF time-domain signal is shown in Fig. 2(a), where θ ¼ 2πΔT∕T, the I/Q modulator works at perfect SSB condition, optical spectrum after the first RT is shown in Fig. 2(b), λ 0 is seed frequency and λ 1 is the shifted frequency, at this time, we can achieve flat and stable multicarrier when the loop is closed.
In order to achieve flexible interval optical carriers, we need to change the RF frequency fs while keeping two RF signals π∕2 phase-shifted, but in conventional RFS, the phase shifter is fixed or manual, if we only change the frequency without adjusting the frequency shifter, θ will deviate from π∕2, odd-order negative frequency component will introduce crosstalk and impact the performance of multicarrier. As shown in Fig. 3, when we change RF from 10 to 15 GHz, I/Q phase difference with fixed phase shifter is shown in Fig. 3(a), imperfectly matched RF time-domain signal at 10 and 15 GHz, is shown in Figs. 3(b) and 3(d), optical spectrum after the first RT is shown in Figs. 3(c) and 3(e), at this time, we cannot achieve flat and stable multicarriers when the loop is closed.
To address this problem and achieve multicarriers with high flatness and stability, the RF drive signals are supposed to be perfect balanced. We implement a phase control module, as shown in Fig. 4, which is composed of a digital phase shifter (DPS), an oscilloscope (OSC), a computer, and splitters. The sinusoidal frequency is generated by a RF source and divided into two branches, one branch passes through a DPS while the other is output directly; the OSC collects the time domain signal of the two branches with two power splitters and send it to a computer. We make the computer automatically calculate the phase difference between the two channels and feedback the control message to the DPS. The phase detector keeps working until 90-deg phase difference is detected, in this way, when we change the RF frequency; dynamic adjustments will be made by the phase control module, and two π∕2 phase-shifted RF signals that

Experimental Results
Experimental setup is shown in Fig. 6, the center wavelength of seed light source runs at 1549.5 nm, which is generated by an external cavity laser with the typical linewidth of 25 kHz. After injected in a 50:50 coupler, the seed lightwave is sent to an I/Q modulator with insertion loss less than 5 dB. RF signal generator with the frequency range from 10 MHz to 18 GHz is used to generate the sinusoidal signal, which is fed into a phase control module; the improved module works adaptively and outputs two RF driven signals with π∕2 phase shift automatically; the amplitudes of the driven signals are carefully adjusted by two tunable electrical amplifiers to ensure equal power. For the purpose of making the I/Q modulator locked in SSB state, the output of the modulator is sent to a 1:99 coupler, whose 1% output port is connected to a modulator bias controller (MBC), it can implement automatic bias control and two DC bias voltages are locked at null points. A flat-top shape OBPF with 3-dB bandwidth of 3 nm is launched in the loop to select the required frequency window, and the center wavelength of OBPF is set to 1548 nm. To compensate for the insertion loss of the I/Q modulator and the filter, an EDFA with low noise figure has been applied, which provides a saturation output power of 23 dBm. At first, RF tone frequency is set to 12.5 GHz, as shown in Fig. 7, we successfully generate 30 stable carriers, the result is observed using the optical spectrum analyzer YOKOGAWA AQ6370D with a resolution of 1 pm. With the help of MBC, the I/Q modulator works stably at SSB condition to induce a 12.5-GHz frequency shifting to the input optical signal; λ 0 ¼ 1549.5 nm represents the wavelength of seed laser and λ 29 is 1546.6 nm; the carrier number is restricted due to the limited bandwidth of OBPF; and the generated stable 30 carriers have superior performance with 1.3-dB flatness fluctuation and above 54.2 dB carrierto-noise ratio (CNR).
To verify the effectiveness of the proposed scheme, with the combination of the SSB-RFS and the improved module, we achieve variable interval optical carriers with dynamic RFS. When RF is changed from 12.5 to 10 GHz and anything else has not been adjusted, as shown in Fig. 8(a), 38 carriers in 3-nm bandwidth are obtained. The measured CNR value is about 53.9 dB with 1.5-dB flatness fluctuation;   By implementing a flexible wavelength selective switch (WSS) after the generation of flexible interval multicarriers, carriers with arbitrary intervals can be achieved. The flexible WSS is implemented by a programmable optical processor (WaveShaper 16000S). Experimental results are shown in Fig. 9, carriers with 40-/80-/120-GHz interval are obtained when RF is set to 10 GHz in dynamic RFS, carriers with 50-/75-/100-GHz interval are obtained when RF is set to 12.5 GHz, and when RF is set to 15 GHz, carriers with 60-/90-/120-GHz interval are obtained after WSS. Therefore, carriers with arbitrary intervals can be achieved with the proposed scheme, which is very suitable for WDM-PON integrated with radio-over-fiber (ROF) and photon frequency hopping radar.

Conclusion
In this paper, the principle of flexible interval multicarrier generation with SSB-RFS is analyzed and a timefrequency-varying multicarrier generation configuration with phase control module is proposed. Experimental demonstration is also carried out, flat and stable multicarriers with the variable interval from 10 to 15 GHz can be achieved, and results show that negligible CNR and flatness loss is induced by using the proposed scheme. With dynamic RFS and a flexible WSS, carriers with arbitrary intervals can be achieved. The outcomes will pave the way to support spectrum flexible optical transmission, WDM-PON, and photon frequency hopping technology.