Waveband-shift-free optical phase conjugator based on difference-frequency generation

Yasuhiro Okamura; Atsushi Takada

doi:10.1364/OE.387590

1. Introduction

Fiber nonlinearity compensation techniques have been drawing intense research interest because the nonlinear impairments resulting from the Kerr effect in transmission fibers are major bottlenecks for future high-speed optical communication systems [1,2]. Two main approaches, i.e., digital signal processing (DSP) and optical signal processing (OSP), have been studied to overcome the issue. In the DSP approach, linear and nonlinear impairments can be compensated by receiver-side DSP algorithms such as the digital backpropagation methods [3,4], Volterra equalizers [5], perturbation based digital nonlinear compensation methods [6–8], and neural network algorithms [9,10], without additional devices. However, nonlinear signal-noise interaction (NSNI) occurring in transmission fibers are concerning because it limits the compensation performance [11,12] in proportion as the transmission distance because of NSNI accumulation. Furthermore, latency due to calculations in the receiver-side DSP will increase and is a significant problem for real-time applications. Therefore, reducing the complexity of DSP algorithms is also an important research topic as well as mitigation of the nonlinear impairments [13]. In the meantime, the OSP techniques such as phase-sensitive optical amplification (PSA) [14–16] and optical phase conjugation (OPC) [17] mitigate waveform distortion resulting from NSNI because nonlinear impairments are compensated in the process of optical fiber transmission.

In PSA, a frequency non-degenerate PSA can be used for amplifier repeaters that compensate nonlinear phase noise in each transmission span. However, phase-conjugated twin wave transmission, in which a signal wave and its phase-conjugated wave are wavelength-division multiplexed and simultaneously transmitted, is necessary for PSA and this leads to spectral efficiency (SE) degradation. In OPC, an optical phase conjugator is located in the middle of a transmission link, and distorted signals due to linear and nonlinear impairments in the first half of the link are inputs to the OPC. Subsequently, phase-conjugated (PC) waves are generated and launched into the second half of the link. After the transmission, the linear and nonlinear impairments from the first half of the link are canceled because of the PC wave transmission. Nevertheless, the OPC scheme also involves SE degradation because bandwidth reservation is a basic requirement for wavelength shift when the PC wave is generated. Meanwhile, a wavelength-shift-free OPC based on four-wave mixing (FWM-OPC) has been proposed and experimentally demonstrated [18,19]. The FWM-OPC, which is composed of a Sagnac loop interferometer (SLI) with a DE and χ⁽³⁾ optical nonlinear medium, generates PC waves through a degenerate FWM process with two pumps. The generated PC waves have the same wavelength as input signal waves and are output from the FWM-OPC. However, the FWM-OPC requires a relatively long DE that will severely narrow the free spectral range (FSR) of the SLI in the FWM-OPC. This will lead to a limitation of the operation bandwidth of the FWM-OPC. On the other hand, recently waveband-shift-free OPCs [20–23] have been experimentally demonstrated. In these OPCs, the waveband was not shifted between before and after the OPCs and the SE degradation has been mitigated, even though the spectrum layout of incoming wavelength-division multiplexed (WDM) signals was inverted at the center wavelength of the WDM signals. However, in the case of the waveband-shift-free OPCs with FWM [20–22], guard bands between pump waves and the WDM signals are required to avoid nonlinear channel crosstalk through the PC wave generation, and this leads to the SE degradation. Additionally, broadband operation is challenging because of the phase-matching between the pump waves and WDM signals. In the case of waveband-shift-free OPCs with difference-frequency generation (DFG), the guard bandwidth for a pump wave is reduced and broadband operation is achievable. In the OPC demonstration of [22], PC wave generation of 2.3-THz bandwidth signal was achieved and guard band for a pump wave was 25 GHz. Nevertheless, the OPC still included wavelength selective switches (WSSs) and its configuration was relatively complex. This could be a problem when integrating OPC circuits.

In this paper, a novel waveband-shift-free OPC based on DFG (DFG-OPC) is proposed and theoretically analyzed. The DFG-OPC is demonstrated analytically to achieve broadband operation. This paper is organized as follows. In Section 2, the principle of the DFG-OPC is analytically derived. In Section 3, the dependence of the output PC wave power on DE length difference is analytically investigated. In Section 4, the wavelength characteristics of the DFG-OPC are demonstrated through numerical calculations and they reveal that the DFG-OPC can achieve broadband operation.

2. Waveband-shift-free OPC with DFG

The proposed DFG-OPC is composed of an SLI with a χ⁽²⁾ optical nonlinear material and two DEs and enables a PC wave output with the same waveband as an input signal wave by using a feature of the SLI. The main difference between the DFG-OPC and FWM-OPC in the setup configuration is the optical nonlinear material. In addition, the DFG-OPC can achieve broadband operation owing to relatively short DE length difference as will be shown in Section 4 even though the estimated bandwidth of the FWM-OPC is approximately 4 nm under the condition of [18]. The schematic of the DFG-OPC is shown in Fig. 1.

Fig. 1. Schematic of the DFG-OPC composed of an SLI with two DEs and a χ⁽²⁾ optical nonlinear material. The insets show optical spectra at each point of the clockwise direction in the SLI.

Download Full Size | PDF

Signal and pump waves with optical angular frequencies ω_s and ω_p(=2ω_s) are launched into port 1 of the 50:50 optical coupler (CPL). Here, the pump wave with 2ω_s is generated through the second-harmonic generation process. When electric field amplitudes of the signal and pump waves are E_s and E_p, the CPL outputs from ports 3 and 4 can be described as follows.

(1)$$\left\{ {\begin{array}{c} {{E_{s3,p3}} = \sqrt r {E_{s,p}}}\\ {{E_{s4,p4}} ={-} j\sqrt {1 - r} {E_{s,p}}} \end{array}} \right.. $$

Here, r is the splitting ratio of the CPL and is ideally 0.5 for 3-dB splitting. First, we consider the PC wave generation through the clockwise path of the SLI. The signal and pump waves propagate through DE₁ with a phase constant β₁ and length L₁. Subsequently, the phase delayed signals $E_{cw}^s$ and pump $E_{cw}^p$ can be written as follows.

(2)$$\left\{ {\begin{array}{c} {E_{cw}^s = \sqrt r \exp ({ - j{\beta_1}({{\omega_s}} ){L_1}} ){E_s}}\\ {E_{cw}^p = \sqrt r \exp ({ - j{\beta_1}({{\omega_p}} ){L_1}} ){E_p}} \end{array}} \right.. $$

Here, a point to note is that |β₁(ω_p)–β₁(ω_s)| is relatively large because of its optical frequency difference. The phase delayed signal and pump waves are guided into a χ⁽²⁾ optical nonlinear material such as a periodically poled lithium niobate (PPLN) waveguide. Subsequently, PC waves are generated through the DFG process as the following analytical solution of the mode-couple equations under the assumption that pump depletion and χ⁽²⁾ waveguide loss are negligible [24].

(3)$$\left\{ {\begin{array}{c} {{E_s}(z ){e^{j\Delta kz/2}} = {E_s}(0 )\left[ {\cosh ({sz} )+ \frac{{j\Delta k}}{{2s}}\sinh ({sz} )} \right] - j\frac{g}{{2s}}E_{pc}^\ast (0 )\sinh ({sz} )}\\ {E_{pc}^\ast (z ){e^{ - j\Delta kz/2}} = E_{pc}^\ast (0 )\left[ {\cosh ({sz} )- \frac{{j\Delta k}}{{2s}}\sinh ({sz} )} \right] + j\frac{{{g^\ast }}}{{2s}}{E_s}(0 )\sinh ({sz} )} \end{array}} \right.. $$

In Eq. (3), the gain coefficient g = κE_p(0) where κ is the coupling coefficient. Δk is the phase mismatching among the signal, pump, and PC waves defined as Δk = |k_p – k_s – k_pc| –2π/Λ. Here, k_p, k_s, and k_pc are the phase constants of the pump, signal, and PC waves, respectively. Λ is the polarization inverted period for quasi-phase matching. Furthermore, $s = \sqrt {{{|{g/2} |}^2} - {{({\Delta k/2} )}^2}} $. Because E_pc(0) = 0, Eq. (3) can be simplified as follows.

(4)$${E_{pc}}\left( z \right) = - \frac{{j\kappa }}{{2s}}{E_p}\left( 0 \right)E_s^*\left( 0 \right)\sinh \left( {sz} \right){e^{ - j{\Delta }kz/2}}.$$

Substituting Eq. (2) into Eq. (4), we obtain

(5)$$\begin{aligned}{E_{pc}}(z )&={-} \frac{{j\kappa }}{{2s}}E_{cw}^pE{_{cw}^{s\ast} }\sinh ({sz} ){e^{ - j\Delta kz/2}}\\ &={-} \frac{{j\kappa r}}{{2s}}{E_p}E_s^\ast \sinh ({sz} )\exp \left[ { - j\left\{ {({{\beta_1}({{\omega_p}} )- {\beta_1}({{\omega_s}} )} ){L_1} + \frac{{\Delta k}}{2}z} \right\}} \right] \end{aligned}. $$

Subsequently, the generated PC signal E_pc is passed through DE₂ with the phase constant β₂ and length L₂, and is phase-shifted.

(6)$$\begin{aligned}E_{cw}^{pc}(z )&= {E_{pc}}(z )\exp ({ - j{\beta_2}({{\omega_{pc}}} ){L_2}} )\\ &={-} \frac{{j\kappa r}}{{2s}}{E_p}E_s^\ast \sinh ({sz} )\exp \left[ { - j\left\{ {({{\beta_1}({{\omega_p}} )- {\beta_1}({{\omega_s}} )} ){L_1} + {\beta_2}({{\omega_{pc}}} ){L_2} + \frac{{\Delta k}}{2}z} \right\}} \right] \end{aligned}. $$

From DE₂, the PC wave is input to port 4 of the CPL. In the same manner, the PC wave generated from the counter-clockwise path of the SLI is input to port 3 of the CPL and can be described as follows.

(7)$$E_{ccw}^{pc}(z )={-} \frac{{j\kappa (1 - r)}}{{2s}}{E_p}E_s^\ast \sinh ({sz} )\exp \left[ { - j\left\{ {({{\beta_2}({{\omega_p}} )- {\beta_2}({{\omega_s}} )} ){L_2} + {\beta_1}({{\omega_{pc}}} ){L_1} + \frac{{\Delta k}}{2}z} \right\}} \right]. $$

The PC waves $E_{cw}^{pc},E_{ccw}^{pc}$ from the clockwise and counter-clockwise directions of the SLI are coupled by the CPL. For simplicity, r = 0.5 and ω_s = ω_pc. Subsequently, the output power of PC waves from ports 1 and 2 can be described as follows.

(8)$$\begin{aligned}{P_{pc1}} &\propto {\left|{\frac{{E_{ccw}^{pc}}}{{\sqrt 2 }} - \frac{{jE_{cw}^{pc}}}{{\sqrt 2 }}} \right|^2}\\ &= {P_{pc}} + {P_{pc}}\sin [{\{{{\beta_2}({{\omega_p}} )- 2{\beta_2}({{\omega_s}} )} \}{L_2} - \{{{\beta_1}({{\omega_p}} )- 2{\beta_1}({{\omega_s}} )} \}{L_1}} ]\end{aligned}. $$

(9)$$\begin{aligned}{P_{pc2}} &\propto {\left|{\frac{{E_{cw}^{pc}}}{{\sqrt 2 }} - \frac{{jE_{ccw}^{pc}}}{{\sqrt 2 }}} \right|^2}\\ &= {P_{pc}} - {P_{pc}}\sin [{\{{{\beta_2}({{\omega_p}} )- 2{\beta_2}({{\omega_s}} )} \}{L_2} - \{{{\beta_1}({{\omega_p}} )- 2{\beta_1}({{\omega_s}} )} \}{L_1}} ]\end{aligned}. $$

Here, ${P_{pc}} = {\kappa ^2}{|{{E_s}{E_p}} |^2}{\sinh ^2}({sz} )/16{s^2}$. From Eqs. (8) and (9), the output PC wave power depends on the phase shift due to the DEs, and the maximum output power of the PC wave at port 2 can be obtained when the sine term equals –1. In this condition, the PC and signal waves are completely decomposed and only the PC wave is output from port 2 as the input signal and pump waves, circled around the SLI, are output from port 1 due to the SLI property. As described above, the proposed scheme accomplishes a waveband-shift-free OPC.

3. Dependence of difference in dispersive element lengths on PC wave power

According to Eqs. (8) and (9), the output PC wave power depends on the DE length and its adjustment plays an important role to obtain the maximum output power of the PC waves. In this section, the relationship between the output PC wave power and DE length is analytically clarified using Eqs. (8) and (9).

Normalized PC wave power P_pc_1,2/2P_pc as a function of the length difference between DEs is calculated using the following parameters and conditions. First, supposing that β₁ = β₂, Eqs. (8) and (9) can be simplified as the following formulas.

(10)$${P_{pc1}} \propto {P_{pc}} + {P_{pc}}\sin [{\{{2{\beta_1}({{\omega_s}} )- {\beta_1}({{\omega_p}} )} \}\Delta L} ]. $$

(11)$${P_{pc2}} \propto {P_{pc}} - {P_{pc}}\sin [{\{{2{\beta_1}({{\omega_s}} )- {\beta_1}({{\omega_p}} )} \}\Delta L} ]. $$

Here, ΔL is the length difference between DE₁ and DE₂ and is defined as ΔL = L₁–L₂. In this calculation, ΔL ranges from 0 to 200 μm. The phase constant β(ω) is determined by β(ω) = n(ω)ω/c where c is the speed of light in a vacuum and n(ω) is the refractive index. The refractive index n(ω) has frequency (wavelength) dependence and can be written as the following experimental formula for fused silica [24].

(12)$$n(\lambda )= {c_0} + {c_1}{\lambda ^2} + {c_2}{\lambda ^4} + \frac{{{c_3}}}{{({{\lambda^2} - a} )}} + \frac{{{c_4}}}{{{{({{\lambda^2} - a} )}^2}}} + \frac{{{c_5}}}{{{{({{\lambda^2} - a} )}^3}}}. $$

where c₀ = 1.4508554, c₁ = –0.0031268, c₂ = –0.0000381, c₃ = 0.0030270, c₄ = –0.0000779, c₅ = 0.0000018, a = 0.035, and the unit of λ is μm. In this calculation, the wavelengths of the pump and PC (signal) waves are assumed to be 775 and 1550 nm, respectively; therefore, β₁(ω_p) = 1.4541 and β₁(ω_s_(pc)) = 1.4444.

Figure 2 shows normalized PC wave power P_pc_1,2/2P_pc as a function of the DE length difference ΔL. The dashed and solid lines indicate output PC wave power from ports 1 and 2, respectively. As Fig. 2 shows, both lines sinusoidally vary with an 80-μm period and are mutually inverted waveforms. The PC wave power distributed to the CPL output ports 1 and 2 is observed to be determined by the phase shift resulting from the DEs, and the shortest ΔL is 20 μm for the maximum PC wave power at the desired output port 2. Figure 2 is also understood as the tolerance of the DE length difference ΔL on the PC wave generation, and indicates relatively precise adjustment of ΔL is required to obtain the maximum output PC wave power.

Fig. 2. Normalized output PC wave power as a function of the DE length difference, ΔL. Dashed and solid lines show PC wave output power from ports 1 and 2 of the CPL. The maximum output PC wave power can be obtained from the desired output port 2 of the CPL when ΔL = 20.0, 99.9, and 180.0 μm.

Download Full Size | PDF

4. Bandwidth characteristics of the DFG-OPC

As described in Section 3, the DFG-OPC requires a 20-μm DE length difference even though approximately 20-m optical fiber was used as a DE in FWM-OPC. The DFG-OPC is expected to be capable of broadband operation. In this section, we calculate the bandwidth characteristics of DFG-OPC.

The numerical model is identified with Fig. 1. Regarding the DEs, L₂ = 20 m to compare the FWM-OPC demonstration of the paper [18] in which a 20-m polarization-maintaining fiber was used as a DE, and L₁ = ΔL + L₂. Actually the length of DE₂ is not important because the operation bandwidth of the DFG-OPC depends on the DE length difference ΔL. Phase constants β₁(ω) and β₂(ω) are calculated using the index profile n(ω) in Eq. (12). Incidentally, the index profile n(ω) corresponds to a 21.5-ps/nm/km dispersion and 0.064-ps/nm²/km dispersion-slope at 1.55 μm. Concerning χ⁽²⁾ nonlinear optical material, a PPLN waveguide is assumed. The analytical solutions given by Eq. (3) and the following parameters are used for the PPLN waveguide analysis. The PPLN waveguide length is 5 cm and the coupling coefficient κ is 63 W^−1/2m⁻¹. The polarization inverted period for quasi-phase matching Λ is 23.9 μm for Δk = 0 when λ_p = 775 nm and λ_s = 1550 nm. The Sellmeier dispersion formula is employed to take into account dispersion effects in the PPLN waveguide [25].

(13)$$\left\{ {\begin{array}{{l}} {{n_o} = \sqrt {4.9048 + \frac{{0.117680}}{{{\lambda^2} - 0.047500}} - 0.027169{\lambda^2}} }\\ {{n_e} = \sqrt {4.5820 + \frac{{0.099169}}{{{\lambda^2} - 0.044432}} - 0.021950{\lambda^2}} } \end{array}} \right.. $$

Here, n_o is the refractive index of an ordinary beam for the signal and PC waves and n_e is the refractive index of an extraordinary beam for a pump wave. The splitting ratio of the CPL r is 0.5. The pump and signal powers are set to 350 mW and 1μW. The pump wavelength is fixed at 775 nm and the signal wavelength ranges from 1450 to 1650 nm. Subsequently, we can obtain the wavelength characteristics of the DFG-OPC.

According to Fig. 2, the output PC wave power is periodically maximized with the DE length difference ΔL which is expressed as ΔL = NΔL_int + 20.0 µm where N is an integer number. ΔL_int is the interval between adjacent peaks in Fig. 2 and approximately equal to 80 µm. Therefore, we calculated wavelength characteristics of DFG-OPC in the scenarios of N = 0, 126, 1278, 3808, and 12507 which take the maximum values of output PC wave power. Additionally, 3-dB bandwidth of DFG-OPCs BW_3dB values are evaluated for each ΔL and are 54.49, 54.39, 48.19, 33.67, and 19.15 nm, respectively. The wavelength characteristic of the DFG process itself is also depicted in Fig. 3. Figure 3 indicates the bandwidth of the DFG process itself is the limiting factor for the DFG-OPC, and its 3-dB bandwidth is 54.49 nm which is as same as the DFG-OPC bandwidth with ΔL = 20.0 µm. Then, the 3-dB bandwidths of the DFG-OPCs BW_3dB narrows as the DE length difference ΔL increases because the bandwidth of the SLI is limited as ΔL increases.

Fig. 3. Wavelength characteristics of DFG-OPC. The vertical axis is the output PC power P_pc2 normalized by P_pc. The scenarios of N = 0, 126, 1278, 3808, and 12507 are depicted. The top spectrum is the wavelength characteristic of the DFG process itself for comparison.

Download Full Size | PDF

Subsequently, a dependence of DFG-OPC bandwidth on DE length difference ΔL is calculated. Figure 4 shows a 3-dB bandwidth of DFG-OPC as a function of the DE length difference, ΔL. For ΔL <0.01 m, the DFG-OPC bandwidth BW_3dB is approximately 54.5 nm. When ΔL >0.01 m, the DFG-OPC bandwidth BW_3dB exponentially decreases. However, the DFG-OPC bandwidth BW_3dB is approximately 19.2 nm even though ΔL = 0.9998778 m (N = 12507); these results reveal that DFG-OPCs enable relatively wide-band operations.

Fig. 4. Dependence of DFG-OPC bandwidth BW_3dB on DE length difference, ΔL.

Download Full Size | PDF

5. Influence of crosstalk due to the incompleteness of the coupler splitting ratio

The splitting ratio of the CPL plays an important role in a DFG-OPC. When an ideal 3-dB CPL with r = 0.5 is employed, signal and pump waves are not output from port 2 of the CPL in Fig. 1 because destructive interference occurs between the clockwise and counter-clockwise propagating waves with the same electric field amplitude at port 2, and the interfered waves cancel out each other. However, when r $\ne $ 0.5, a part of the signal and pump waves are output from port 2 because interfered waves at the port do not have the same electric field amplitude due to the CPL splitting ratio and do not perfectly cancel out. As a result, the signal wave outputting from port 2 interferes with the desired PC wave, and crosstalk occurs whereas the pump wave outputting from port 2 can be removed by an optical bandpass filter. In this section, we numerically investigate the influence of the CPL splitting ratio on the output PC wave in the DFG-OPC.

The calculation conditions are identical to the previous section except for the CPL splitting ratio r. Additionally, not only PC and signal waves but also a pump wave pass through the CPL with the splitting ratio r in this calculations. First, the dependence of the DE length difference ΔL on the output PC and signal wave power from port 2 of the CPL is determined when the CPL splitting ratio r ranges from 0.465 to 0.535 and depicted in Fig. 5.

Fig. 5. Output PC/signal wave power as a function of DE length difference, ΔL. The solid and dashed lines show the power of the PC and signal waves. The PC wave power P_pc₂ and signal wave power P_s₂ are normalized by 2P_pc. The CPL splitting ratio r is changed and the scenarios of r = 0.465, 0.475, 0.485, 0.495, 0.505, 0.515, 0.525, and 0.535 are depicted.

Download Full Size | PDF

In the vertical axis, the output PC and signal wave power P_pc₂, P_s₂ are normalized by 2P_pc. The solid and dashed lines indicate the PC and signal wave powers. The peak values in the PC wave curves are approximately the same whether the CPL splitting ratio r is 0.5 or not. In the meantime, the signal wave power increases as the CPL splitting ratio shift Δr = |r–0.5| increases because of the imperfection of the balancing out between the clockwise and counter-clockwise propagating signal waves.

Subsequently, the PC wave power to signal wave power ratio (PXR) as a function of the DE length difference is calculated and shown in Fig. 6.

Fig. 6. PC wave-to-crosstalk power ratio (PXR) as a function of DE length difference, ΔL. The left and right Figs. indicate the scenarios of r = 0.505∼0.535 and r = 0.465∼0.495.

Download Full Size | PDF

In Fig. 6(a), the PXR has peaks at ΔL = 20.0, 99.9, and 180.0 μm. When r = 0.505, 0.515, 0.525, and 0.535, the PXR values at ΔL = 20.0 μm are 35.5, 25.9, 21.5, and 18.6 dB, respectively. Figure 6(b) is the same as Fig. 6(a). When r = 0.495, 0.485, 0.475, and 0.465, the PXR values at ΔL = 20.0 μm are 35.5, 25.9, 21.5, and 18.6 dB, respectively. From these results, the PXR decreases as the CPL splitting ratio r departs from r = 0.5.

Finally, the PXR value when ΔL = 20.0 μm as a function of the CPL splitting ratio shift Δr is calculated. Here, the CPL splitting ratio shift is defined as Δr = |r–0.5|. As shown in Fig. 7, PXR decreases as the CPL splitting ratio shift Δr increases because of the signal wave power rising as discussed above. Here, we hypothesize that at least a 20-dB PXR is required for the implementation of DFG-OPCs. When the CPL splitting ratio shift Δr is less than 0.03, a PXR of over 20 dB can be obtained. This result indicates that the tolerance of the CPL splitting ratio r is ${\pm} $6% to eliminate crosstalk for high-quality PC wave generation with DFG-OPCs.

Fig. 7. PXR at ΔL = 20.0 μm as a function of the CPL splitting ratio shift Δr with the solid line. The dashed line indicates the required PXR (20 dB).

Download Full Size | PDF

6. Summary

In this paper, we proposed and theoretically investigated a DFG-OPC enabling a waveband-shift-free PC wave generation. The DFG-OPC has advantages over the recent studies [20–23] in that it enables broadband operation and relatively narrow guard band for a pump wave with a simple configuration. In Section 2, the working principle of DFG-OPC was described. The DFG-OPC was mathematically proven to generate a PC wave without waveband shift. In Section 3, the optimum DE length difference, ΔL, for the PC wave generation was theoretically investigated, and the minimal DE length difference ΔL was 20.0 µm. In Section 4, the wavelength characteristics of the DFG-OPC were obtained through numerically simulations. A 3-dB bandwidth of the DFG-OPC of 54.5 nm was accomplished when the DE length difference ΔL <0.01 m, and this indicated that the DFG-OPC enabled a broadband operation. In Section 5, crosstalk due to the splitting ratio of the CPL in the DFG-OPC was numerically studied. The results indicated that the CPL splitting ratio r was necessary to be from 0.47 to 0.53 to avoid crosstalk. From these results, the DFG-OPC opens up new possibilities for the fiber nonlinearity compensation mitigating SE degradation. Further studies of the influence of DE parameters such as the dispersion and dispersion slope on the PC wave generation by the DFG-OPC, performance of optical fiber transmission systems with DFG-OPCs, limitation of the number of WDM channels on the systems, and proof of principle experiment should be conducted. In the experimental demonstration, the adjustment of the DE length difference would be a challenge. Moreover, it would be of interest to study the DFG-OPC integration.

Disclosures

The authors declare no conflicts of interest.

References

1. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef]

2. R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101(16), 163901 (2008). [CrossRef]

3. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

4. E. Ip, “Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]

5. K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997). [CrossRef]

6. W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in ECOC 2011, (Optical Society of America, 2011), paper Tu.3.A.2.

7. Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-Free Intrachannel Nonlinearity Compensating Algorithm Operating at Symbol Rate,” J. Lightwave Technol. 29(17), 2570–2576 (2011). [CrossRef]

8. T. Oyama, H. Nakashima, S. Oda, T. Yamauchi, Z. Tao, T. Hoshida, and J. C. Rasmussen, “Robust and Efficient Receiver-side Compensation Method for Intrachannel Nonlinear Effects,” in OFC 2014 (Optical Society of America, 2014), paper Tu3A.3.

9. E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. 40(21), 5113–5116 (2015). [CrossRef]

10. C. Hager and H. D. Pfister, “Nonlinear interference mitigation via deep neural networks,” in OFC 2018 (Optical Society of America, 2018), paper W3A.4.

11. P. Serena, “Nonlinear Signal – Noise Interaction in Optical Links with Nonlinear Equalization,” J. Lightwave Technol. 34(6), 1476–1483 (2016). [CrossRef]

12. A. Ghazisaeidi, “A Theory of Nonlinear Interactions between Signal and Amplified Spontaneous Emission Noise in Coherent Wavelength Division Multiplexed Systems,” J. Lightwave Technol. 35(23), 5150–5175 (2017). [CrossRef]

13. E. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express 16(20), 16124–16137 (2008). [CrossRef]

14. M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13(19), 7563–7571 (2005). [CrossRef]

15. S. L. I. Olsson, H. Eliasson, E. Astra, and P. A. Andrekson, “Long-haul optical transmission link using low-noise phase-sensitive amplifiers,” Nat. Commun. 9(1), 1–7 (2018). [CrossRef]

16. T. Umeki, O. Tadanaga, M. Asobe, Y. Miyamoto, and H. Takenouchi, “First demonstration of high-order QAM signal amplification in PPLN-based phase sensitive amplifier,” Opt. Express 22(3), 2473–2482 (2014). [CrossRef]

17. A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4(2), 52–54 (1979). [CrossRef]

18. K. Mori, T. Morioka, and M. Saruwatari, “Wavelength-shift-free spectral inversion with an optical parametric loop mirror,” Opt. Lett. 21(2), 110–112 (1996). [CrossRef]

19. K. Mori, H. Takara, and M. Saruwatari, “Wavelength-shift-free FWM.based dispersion compensation in non-DSF transmission utilizing optical parametric loop mirror,” in CLEO ‘97., (Optical Society of America, 1997), paper CThU6.

20. I. Sackey, C. Schmidt-Langhorst, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, and T. Hoshida, “Waveband-Shift-Free Optical Phase Conjugator for Spectrally Efficient Fiber Nonlinearity Mitigation,” J. Lightwave Technol. 36(6), 1309–1317 (2018). [CrossRef]

21. S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of Nonlinear Effects on WDM QAM Signals Enabled by Optical Phase Conjugation With Efficient Bandwidth Utilization,” J. Lightwave Technol. 35(4), 971–978 (2017). [CrossRef]

22. A. D. Ellis, M. Tan, M. Asif Iqbal, M. A. Z. Al-Khateeb, V. Gordienko, G. S. Mondaca, S. Fabbri, M. F. C. Stephens, M. E. McCarthy, A. Perentos, I. D. Phillips, D. Lavery, G. Liga, R. Maher, P. Harper, N. Doran, S. K. Turitsyn, S. Sygletos, and P. Bayvec, “4 Tb/s Transmission Reach Enhancement Using 10 × 400 Gb/s Super-Channels and Polarization Insensitive Dual Band Optical Phase Conjugation,” J. Lightwave Technol. 34(8), 1717–1723 (2016). [CrossRef]

23. T. Umeki, T. Kazama, A. Sano, K. Shibahara, K. Suzuki, M. Abe, H. Takenouchi, and Y. Miyamoto, “Simultaneous nonlinearity mitigation in 92 × 180-Gbit/s PDM-16QAM transmission over 3840 km using PPLN-based guard-band-less optical phase conjugation,” Opt. Express 24(15), 16945–16951 (2016). [CrossRef]

24. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications Sixth Edition (Oxford, 2007).

25. D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17(3), 332–335 (1976). [CrossRef]

Waveband-shift-free optical phase conjugator based on difference-frequency generation

Abstract

1. Introduction

2. Waveband-shift-free OPC with DFG

3. Dependence of difference in dispersive element lengths on PC wave power

4. Bandwidth characteristics of the DFG-OPC

5. Influence of crosstalk due to the incompleteness of the coupler splitting ratio

6. Summary

Disclosures

References

Cited By

Figures (7)

Equations (13)

Optics Express