Flat Frequency Comb Generation Based on Efficiently Multiple Four-Wave Mixing Without Polarization Control

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2 86 Photonic Sensors be increased by using this scheme. 2. Theoretically analysis of the proposed scheme FWM effect in HNLF is a parametric process involving four different optical waves. For a typical FWM configuration, when two-pump waves at frequencies ω 1 and ω 2 (assume ω 1 <ω 2 ) are injected into HNLF [2], the signal (at ω 3 ) will be amplified, and the idle light (at ω 4 ) will be generated, as shown in Fig. 1. The relationship among four light frequencies can be described with equation ω1 + ω2 = ω3 + ω4. (1) The momentum conservation (namely phase matching) condition should also be satisfied in the FWM process. The phase matching condition is met when the net wave vector mismatch is κ=, where κ can be written as [11] κ = κ + κ NL (2) κnl = γ *( P1 + P2) (3) where Δκ and Δκ NL represent wave vectors mismatches related to dispersion and nonlinear effects, respectively. γ is the nonlinear coefficient of HNLF, and P 1 and P 2 are incident powers of ω 1 and ω 2, respectively. To obtain the phase matching condition, the pump wavelength should exceed the ZDW of HNLF (namely Δκ<), so that the net wave vector mismatch can be κ=. Fig. 1 Frequencies relationship of a typical FWM process. The proposed scheme is shown in Fig. 2. Two-pump waves pass through the phase modulator to suppress stimulated Brillouin scattering. An SMF is used to compensate the chirp induced by the phase modulator. The optimal length of the SMF is about 1 km [9], when the modulation speed is 2 GHz. Thus, a pulse train with very short pulse-width after the SMF can be achieved. The pulse trains are then amplified by an erbium-doped fiber amplifier (EDFA). An optical filter is used to suppress the spontaneous emission noise from the EDFA. Hence, pump waves with the higher peak power are obtained, which can enhance the multiple FWM effects in the HNLF2. In such a case, the SPM effect occurs in HNLF1 simultaneously due to the optical pulse injection. The SPM effect always leads to spectrum broadening. The feedback system containing two HNLFs aims at enhancing multiple FWM effects in HNLF2 and SPM effect in HNLF1 to generate OFC. Fig. 2 Proposed OFC generator (CW: continuous wave; RF: radio frequency; PM: phase modulation; SMF: single mode fiber; EDFA: erbium doped fiber amplifier; HNLF: high nonlinear fiber; OSA: optical spectrum analyzer). In the feedback structure, the output from Port d of the PBS is fed back to the input port of Coupler 2. The system and mechanism are similar to the optical parametric oscillator [12] (OPO), which is usually used for optical amplification with a single pump. Two couplers are used for optical feeding back. The feedback ratio can be changed by using optical couplers with different coupling ratios. For example, if the coupling ratios of Couplers 2 and 3 are both 9:1 (namely Port h stands for 1%, and Port e represents 9%), the feedback ratio will be 9%. If the coupling ratios of Couplers 2 and 3 are 7:3 (namely Port h stands for 3%, and Port e represents 9%) and 9:1, respectively, the feedback ratio is 27%. If two-pump waves are injected into the feedback system with the same frequency space and only the first-order sidebands induced by the FWM

3 Qimeng DONG et al.: Flat Frequency Comb Generation Based on Efficiently Multiple Four-Wave Mixing Without Polarization Control 87 processes are considered through HNLF every time, the total number of optical waves inside the fiber is 4 according to this recurrence formula [13] listed by (4). After the first round trip, the total number of optical waves inside the fiber will be 1. n= 3* N 2 (4) where N represents the number of pump lights launched into the feedback system, and n means the total number of optical waves inside the fiber. The PBS makes multiple FWM effects in HNLF efficient without a polarization controller (PC). 3. System simulation and results discussion Two continuous wave lasers fixed at 1553 nm and nm are coupled together with a 3-dB coupler. Pulse trains with very short pulse-width after the SMF are achieved in Fig. 3. The pulse trains are then amplified to 1 W by the EDFA. Then, the coupling ratios of Couplers 2 and 3 are 5:5 (namely Port h stands for 5%) and 9:1 (Port e represents 9%) to constitute a feedback system according to past works [14], and the feedback ratio is 45%. In the feedback system, two HNLFs with different ZDWs (the ZDW of HNLF1 is 16 nm, and the ZDW of HNLF2 is 155 nm) and a PBS are inserted. The length, nonlinear coefficient, and dispersion slope of the HNLFs are L = 3 m, γ = 26 W 1 km 1, and S =.3 ps/nm 2 /km. Here, we simulate with four different configurations. In the first configuration, we remove the SMF in the setup of Fig. 2. The output OFC is presented in Fig. 4, where about 15 coherent lines are obtained within 1-dB power deviation. In the second configuration, we remove HNLF1 in the setup of Fig. 2. The output OFC is shown in Fig. 5 where about 25 coherent lines are obtained within 1-dB power deviation. In the third configuration, we remove Coupler 2, Coupler 3, and PBS in the setup of Fig. 2. Pump lights after the SMF are injected into two HNLFs. The output OFC of two HNLFs is obtained as following in Fig. 6 where about 16 coherent lines are obtained within 8-dB power deviation. Finally, the output OFC for the proposed scheme (namely Fig. 2) is shown in Fig. 7, where the proposed scheme produces 128 coherent lines spaced to only 2 GHz within 6-dB power deviation. Compared with other schemes, the proposed scheme can not only increase the number of frequency lines, but also improve the flatness of it. power (dbm) Power (W) ps Time (ns) Fig. 3 Pulse shape of a pump after the SMF Fig. 4 Output OFC without the SMF Fig. 5 Output OFC without HNLF1.

4 88 Photonic Sensors Fig. 6 Output OFC without feedback. 5 6 db Fig. 7 Output OFC for the proposed scheme. Finally, we investigate the impact of the output pump power of EDFA and the length of two HNLFs on the available spectral lines by the following two graphs. In Fig. 8, the length of two HNLFs is 3 m. Other parameters are the same as the above simulation. The number of frequency lines with ΔP=1 db (below the max power of the multiple FWM products) increases when the output power of EDFA increases. When the pump power is fixed at.8 W, the number of frequency is 135. When the output power of EDFA increases further, the number of frequency decreases. When the output power of EDFA is 1.5 W, the number of frequency lines is 58, which is smaller than 135. The output power of EDFA has an optimal value. This is caused by the phase matching condition. From (3), we know that when the output power of EDFA increases, Δκ NL becomes larger while Δκ is invariable. It affects the net phase mismatching κ. When the output power of EDFA is.8 W, the phase matching is satisfied perfectly, which produces the largest number of frequency lines. Then, the output power of EDFA fixes at.8 W. Other parameters are the same as the above simulation. The number of frequency lines with ΔP =1 db related to the length of the fiber is shown in Fig. 9. Clearly, after a maximum is reached, the number of frequency with an acceptable ΔP decreases when the length of HNLFs increases. This makes clear that the use of very short fiber lengths enables highly efficient generation of the OFC. For this fiber, the optimal length is around L=3 m. Similarly, more frequency lines imply better phase matching. In order to ensure this phase matching, ΔβL < π [7] has to be satisfied where Δβ is the propagation constant mismatch. Number of frequency comb n with ΔP=1 db Output power after EDFA, P (W) Fig. 8 Relationship between the number of frequency lines and output power of EDFA Length of two HNLFs, l (m) Number of optical frequency comb n 13 Fig. 9 Relationship between the number of frequency lines and length of two HNLFs.

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