Impact of pump-phase noise in PPLN-based optical parametric amplifier and wavelength converter for digital coherent transmission

Shimpei Shimizu; Akira Kawai; Takayuki Kobayashi; Masanori Nakamura; Takushi Kazama; Takushi Kazama; Masashi Abe; Koji Enbutsu; Takeshi Umeki; Takeshi Umeki; Yutaka Miyamoto

doi:10.1364/OE.521216

1. Introduction

Spectral efficiency improvement in fiber-optic transmission using digital coherent technology is approaching the theoretical limit with the maturity of digital signal processing (DSP). Therefore, wideband wavelength-division multiplexing (WDM) transmission technologies are important to drastically improve fiber throughput. In current long-haul optical fiber networks, the transmission bandwidth over 4–5 THz within the C- or L-band, which has lowest propagation loss in optical fibers and is supported using erbium-doped fiber amplifiers (EDFAs), can be used. To broaden the optical transmission bandwidth, the combined use of C- and L-bands has been well studied and partially practical [1–3]. Meanwhile, the low-loss bandwidth of optical fibers spans tens of THz. For the other bands, however, transceivers, optical amplification technologies, optical node configurations, and so on are still in the research phase. The use of the S-band has also been actively investigated with a thulium-doped fiber amplifier (TDFA), semiconductor amplifier, and Raman amplifier [4–8]. Using the triple bands of S-, C-, and L-bands, > 100-Tbps fiber throughput was demonstrated.

For broadening the transmission bandwidth in optical networks, an optical parametric amplifier (OPA) based on nonlinear optical effects has been attracting research attention. There are two types of OPAs: one based on four-wave mixing (FWM) in χ⁽³⁾-nonlinear media such as a highly nonlinear fiber (HNLF) [9,10] and the other based on the differential frequency generation (DFG) process in χ⁽²⁾-nonlinear media such as the periodically poled LiNbO₃ (PPLN) waveguide [11]. Figure 1 shows application examples of OPAs on multiband transmission systems. An OPA has attractive features for constructing multiband WDM systems. One is its wide-gain bandwidth; the potential for amplification bandwidth approaching 20 THz has been demonstrated using an HNLF-based OPA [9]. PPLN-based OPAs are superior in terms of power tolerance because of fewer unwanted nonlinear optical effects such as interactions between wavelength channels and nonlinear light scattering. Therefore, they can be applied as wideband inline amplifiers, and inline amplified WDM transmission over an 80-km-span single-mode fiber (SMF) link with a bandwidth of >14 THz over the S-, C-, and L-bands has been demonstrated using an inline OPA with PPLN ridge waveguides [12]. Since idler light is generated with signal amplification, a configuration that splits the input signal in two has been utilized to fully use the gain bandwidth of the OPA (Fig. 1(a)).

Fig. 1. Applications of OPA. (a) Wideband inline amplification. (b) Multiband transceiver using wavelength conversion. (c) Multiband optical node using wavelength conversion.

Download Full Size | PDF

OPAs can be used not only as simple amplifiers but also for various applications due to their optical-signal-processing functions. One type of optical signal processing with OPAs utilizes the idler light simultaneously generated with the signal amplification. The idler light is allocated at a band symmetric to the signal light with respect to the center frequency of the gain band (degenerate frequency) and is a phase-conjugated copy of the signal light. The expansion of transmission bandwidth, i.e., multiband transmission with the beyond C + L-band, originally required the development of optical components adapted to the additional transmission bands. Inter-band wavelength conversion using the idler light enables conventional optical components to be used for additional bands such as the S-band and U-band, and its applications to multiband transceivers, optical cross-connect, and inline amplifiers have been investigated [13–18]. In such applications, wavelength converters (WCs) are used in pairs. In multiband-transceiver applications (Fig. 1(b)), for example, a C-band WDM signal generated using conventional transponders can be converted to new bands using a WC on the transmitter side, and vice versa on the receiver side [13]. This expands the transmission bandwidth without the need of developing transponders for such additional bands. In optical-node applications (Fig. 1(c)), a configuration in which an amplifier, gain equalizer, and/or wavelength-selective switch (WSS) are sandwiched by WCs is used. The WDM signal in the additional band is converted once to the C-band (or L-band) with a pre-WC, undergoes processing such as inline amplification, equalization, and/or channel add/drop of WDM channels by a subsystem for a conventional band, then reconverted to the original band with a post-WC [14–16]. It also contributes to additional functions of optical nodes [15]. The above applications involve the conversion and reconversion of a WDM signal between conventional and additional bands with a pair of WCs. Signal light can also be transmitted while converting it to the phase conjugated light at each transmission span at the optical node to mitigate nonlinear distortions caused by fiber nonlinearities [19].

One of the challenges of an OPA is the transfer of pump noise, which can degrade signal quality. The transferred pump noise is classified as amplitude noise and phase noise (frequency modulation noise). High-gain optical parametric amplification requires watt-level pump light. Therefore, the pump light is amplified using the high-power optical amplifier before input to the nonlinear medium. (Other means of obtaining a strong pump could include the use of high-power fiber lasers.) In accordance with the input power of the pump light to the amplifier, the optical signal-to-noise ratio (OSNR) of the pump light is varied due to amplified spontaneous emission (ASE) noise from the amplifier. The noisy pump causes the transfer of the excess amplitude noise to the amplified signal and idler lights [20]. Nevertheless, the OSNR of the pump can be easily made high enough so that this effect is almost negligible in typical cases. Meanwhile, the phase-noise transfer can lead to significant penalty to wavelength-converted idler light [21,22]. In high-gain operation of the HNLF-based OPA, the pump-phase dithering is necessary for suppressing the stimulated Brillouin scattering for obtaining the high-power pump, and thus, the transfer of the phase dither is an important issue. Methods have been attempted to cancel out the phase noise in the optical domain with correlated dual-pumping FWM process [23,24] or mitigate the effect of pump dithering by DSP [25]. In an PPLN-based OPA with χ⁽²⁾-nonlinearity, pump-phase dithering is not required because the stimulated Brillouin scattering is typically negligible. However, the transfer of the original phase noise of the pump laser is present even without pump dithering. Although a configuration of an χ⁽²⁾-based OPA that cancels out transferred phase noise via cascaded multiple nonlinear optical processes has also been proposed [26,27], it inherently limits the signal bandwidth and is not suitable wideband applications.

In this paper, we investigate the transfer characteristics of the phase noise of pump lasers in optical parametric amplification and wavelength conversion using PPLN waveguides and its impact on signal quality in digital coherent fiber-optic transmission. Using coherent signals up to 96 Gbaud, we analytically and experimentally show that the phase noise transferred to the idler light can have a similar impact on signal quality as equalization-enhanced phase noise (EEPN) due to the combination of a local oscillator (LO) and chromatic dispersion (CD) compensation in a digital coherent receiver. The EEPN effect due to the combination of pump-phase noise and digital CD compensation had not been studied in detail, but it is important for applying an OPA to actual fiber-optic transmission systems. We experimentally evaluate these effects with several pump lasers with different linewidths. In addition, we propose a method of using correlated pump lights between a WC pair to suppress the transfer of phase noise while maintaining the basic configuration consisting of second-harmonic generation (SHG) and DFG that is capable of simultaneous wideband wavelength conversion. The remainder of this paper is organized as follows. In Section 2, we theoretically explain the phase-noise transfer from a pump laser to signal light via an SHG-DFG process and derive the analytical EEPN penalty induced by the transferred pump-phase noise in digital coherent transmission. We also describe the proposed correlated pumping scheme sharing the pump laser between a WC pair. In Section 3, we experimentally show the phase-noise-transfer characteristics in PPLN-based optical parametric amplification and wavelength conversion by directly measuring the phase noise of the amplified signal and wavelength-converted idler components. In Section 4, we discuss our evaluation of the effect of the transferred pump-phase noise on signal quality over recirculating digital coherent transmission. The penalty due to the pump-phase noise is compared with the analytical EEPN penalty. The comparisons are conducted with 32-, 64-, and 96-Gbaud signals and over different dispersive transmission links. In Section 5, we present our experimental demonstration the proposed correlated pumping scheme and investigate the effect of optical path-length difference between WC pairs on the performance of correlated pumping schemes.

2. Analysis of effect of phase-noise transfer from pump laser on signal and idler components

This section analytically discusses the transfer of phase noise in a pump laser to the amplified signal and wavelength-converted idler lights and its effect on signal quality in the optical parametric amplification process. We assumed the PPLN-based optical parametric amplification process with χ⁽²⁾-nonlinearity.

2.1 Transfer of phase noise from pump laser

Figure 2 shows the frequency allocation in χ⁽²⁾-based optical parametric amplification and an analytical system model. For simplicity, Fig. 2(b) shows only a signal that undergoes amplification or wavelength conversion with the OPA. In actual operation, however, it is assumed that other band signals will coexist and will be multiplexed and demultiplexed via WDM couplers before and after the OPA. In the output of the OPA, either the amplified signal or wavelength-converted idler is extracted. In a χ⁽²⁾-based OPA, to obtain a watt-level second-harmonic (SH) pump at 2ω_p, a configuration is used in which CW pump laser at ω_p (fundamental pump) in the telecommunication band is amplified using an optical amplifier (e.g., EDFA) then converted to the SH pump by SHG. The coupled-wave equation for the SHG process in a nonlinear medium is given as [28]

(1)$$\left\{ {\begin{array}{{c}} {\frac{{d{E_{\textrm{SH}}}(z )}}{{dz}} = j\kappa {E_\textrm{p}}^2(z ){e^{ - j\Delta \beta z}}}\\ {\frac{{d{E_\textrm{p}}(z )}}{{dz}} = j\kappa {E_\textrm{p}}^\ast (z ){E_{\textrm{SH}}}(z ){e^{j\Delta \beta z}}} \end{array}} \right., $$

where E_SH and E_p are the complex amplitude of the SH pump and fundamental pump, respectively, κ is the coefficient of the efficiency of the nonlinear process, and Δβ is the phase mismatch. Assuming E_SH(0) = 0, from Eq. (1), the initial phase of the SH pump at the input end is given as

(2)$${\phi _{\textrm{SH}}} = 2({{\phi_\textrm{p}} + \Delta {\phi_\textrm{p}}(t )} )+ \frac{\mathrm{\pi}}{2}, $$

where ϕ_p is the initial phase of the fundamental pump and Δϕ_p(t) is the phase noise of the pump laser, which is stochastic for time. We can see that the SHG process doubles the phase noise in the pump laser. In the following description of the optical parametric amplification process, we ignore the static phase offset and assume the complex amplitude of the SH pump as

(3)$${E_{\textrm{SH}}}(t )= \sqrt {{P_{\textrm{SH}}}} {e^{j2\Delta {\phi _\textrm{p}}(t )}}, $$

where P_SH is the optical power of the SH pump.

Fig. 2. System model. (a) Frequency allocation in optical parametric amplification process. (b) System configuration using PPLN-based OPA and wavelength converter.

Download Full Size | PDF

In the optical parametric amplification process with the input lights as the SH pump at 2ω_p and signal at ω_s, the output signal and idler components are given as [28]

(4)$${E_\textrm{s}}^\prime (t )= {E_\textrm{s}}(t )\cosh ({gL} ), $$

(5)$${E_\textrm{i}}^\prime (t )= j\frac{\kappa }{g}{E_{\textrm{SH}}}(t ){E_\textrm{s}}^\ast (t )\sinh ({gL} )= j{E_\textrm{s}}^\ast (t )\sinh ({gL} ){e^{j2\Delta {\phi _\textrm{p}}(t )}}, $$

where E_s(t) is the input complex amplitude of the signal, L is the length of the nonlinear medium, g is the gain coefficient as a function of κ, Δβ, and P_SH (≡ {κ²P_SH − (Δβ/2)²}^1/2), and * denotes the phase conjugation. The idler angular frequency ω_i is determined by 2ω_p − ω_s. Note that, Eqs. (4) and (5) assume no pump depletion, no optical absorption, and the perfect phase matching (Δβ = 0) in the medium. We also ignore the frequency dependence of κ. Since the complex amplitude of the SH pump is multiplied to the idler component, double the phase noise of the original pump laser at ω_p is transferred to the wavelength-converted idler. The Lorentzian linewidth is given as a linear function of the white-noise floor of the power spectral density (PSD) spectrum of the phase noise. The PSD spectrum (with a unit of Hz²/Hz) is given as the square of the Fourier spectrum of the instantaneous frequency depending on the phase noise. The PSD spectrum of the phase noise of the fundamental pump laser is expressed as [29]

(6)$${S_{\textrm{PSD,p}}}(f )= \left\langle {{{\left|{{\textrm{FT}} \left[ {\frac{1}{{2\mathrm{\pi}}}\frac{{d\Delta {\phi_\textrm{p}}(t )}}{{dt}}} \right]} \right|}^2}} \right\rangle,$$

where FT[x] indicates the Fourier transform, and $<x>$ indicates the expectation value. That of the transferred phase noise in the idler is given as

(7)$${S_{\textrm{PSD,i}}}(f )= \left\langle {{{\left|{\textrm{FT} \left[ {\frac{1}{{2\mathrm{\pi}}}\frac{{d2\Delta {\phi_\textrm{p}}(t )}}{{dt}}} \right]} \right|}^2}} \right\rangle = 4\left\langle {{{\left|{\textrm{FT} \left[ {\frac{1}{{2\mathrm{\pi}}}\frac{{d\Delta {\phi_\textrm{p}}(t )}}{{dt}}} \right]} \right|}^2}} \right\rangle = 4{S_{\textrm{PSD,p}}}(f ). $$

Thus, the linewidth transferred from the pump laser to the idler broadens quadruply. In the same manner, considering wavelength-conversion and re-conversion using different pump lasers with the phase noises Δϕ_p1(t) and Δϕ_p2(t), the idler light reconverted to the original signal frequency is expressed as

(8)$${E_\textrm{i}}^{\prime \prime }(t )\propto {E_\textrm{s}}(t ){e^{j({ - 2\Delta {\phi_{\textrm{p}1}}(t )+ 2\Delta {\phi_{\textrm{p2}}}(t )} )}}. $$

Therefore, the phase noise of a signal transmitted with repeated wavelength conversion is a summation of the phase noise of all SH pumps. In contrast, the amplified signal light E_s´ is not affected by the pump phase (see Eq. (4)). The reason for this would be the femtosecond-order ultra-fast response of a nonlinear optical process and the mechanism of the optical parametric amplification process. In the optical parametric amplification process, the interaction between the signal and pump produces an idler. The interaction between the idler and pump then reconverts the idler to the signal frequency. Thus, the signal is amplified by being coherently superposed with the reconverted idler. In this conversion and reconversion between the signal and idler, perfectly correlated pump-phase noises are transferred due to the fast response of nonlinear optical effects. Since this noise is canceled out due to their phase-conjugation relationship, the amplified signal has no additional phase noise induced by the pump laser. From this discussion, it is expected that the acceptable linewidth and phase noise characteristics of the pump laser can be loose when an OPA is used only as a signal amplifier. For the amplified signal component, the impact of the pump-phase noise will be determined from gain modulation effects rather than from the phase-noise transfer. Instantaneous pump-frequency modulation caused by the pump-phase noise causes phase-matching fluctuation [30,31]. Because the signal gain depends on the amount of phase-mismatch, the phase-matching fluctuation can be converted to the gain modulation. In the χ⁽²⁾-based OPA process, therefore, the phase-matching bandwidth of SHG (typically, in GHz scale [32,33]) will determine the phase noise (frequency stability) requirement of the pump laser.

2.2 Conversion of transferred pump-phase noise to EEPN-induced timing jitter

In wavelength conversion applications, the phase noise in a pump laser has a similar effect on signal quality as LO-phase noise in a coherent receiver. The LO-phase noise can be compensated for by carrier phase recovery (CPR) in receiver DSP. In terms of phase continuity, the compensation capability of the phase noise is higher for higher symbol-rate signals. Meanwhile, in actual digital coherent fiber-optic transmission, the excessive signal degradation caused by the combination of the LO-phase noise and digital CD compensation is known as EEPN and has been widely studied both experimentally and analytically [34–36]. EEPN is a phenomenon in which the LO-phase noise is converted to group delay fluctuation, i.e., timing jitter in the receiver, via digital CD compensation. Unlike phase noise, the EEPN-induced timing jitter is greater for higher-symbol-rate signals and cannot be compensated by the CPR. The phase noise transferred from the pump laser in wavelength conversion will also lead to an EEPN-like effect on signal quality after digital CD compensation, but this effect has not been studied in detail.

We first assume the use of wavelength-band conversion in the transmitter and receiver in the multiband-transmission system with the beyond C + L-band [13]. Figure 3(a) shows the path of the WDM signal in the additional band, e.g., the S-band and U-band. Such a WDM signal in the additional band is generated and received via WCs, as shown in Fig. 1(b). The output from the WC in the receiver side is expressed as

(9)$$r(t )\propto {[{\{{{E_\textrm{s}}^\ast (t )\cdot {E_{\textrm{SH,Tx}}}(t )} \}\otimes h(t )} ]^\ast } \cdot {E_{\textrm{SH,Rx}}}(t ), $$

where h(t) is the time-domain impulse response of the transmission line representing CD, ⊗ denotes the convolution, and E_SH,Tx and E_SH,Rx are the complex amplitude of the pump lights in the WCs at the transmitter and the receiver sides, respectively. After the coherent detection with the receiver LO, the received signal is expressed as

(10)$${r_{\textrm{Rx}}}(t )\propto {[{\{{{E_\textrm{s}}^\ast (t )\cdot {E_{\textrm{SH,Tx}}}(t )} \}\otimes h(t )} ]^\ast } \cdot {E_{\textrm{SH,Rx}}}(t )\cdot {E_{\textrm{LO}}}(t ), $$

where E_LO(t) is the complex amplitude of the LO. The additional phase-noise component generated on the transmit side due to E_SH,Tx is subjected to the same linear transfer function as the transmitted signal. Thus, it will not enhance EEPN. However, the additional phase noise generated on the receiver side due to E_SH,Rx is mixed with the LO-phase noise, as in Eq. (10). Therefore, it will enhance the impact of EEPN on signal quality as though the signal is received by the LO with a wider linewidth, which corresponds to the sum of the phase noise of the E_SH,Rx and E_LO.

Fig. 3. Analytical model for pump-induced EEPN effect. Tx: optical transmitter, Rx: coherent optical receiver, and WC: wavelength converter. (a) Application to Tx/Rx. (b) Application to optical node.

Download Full Size | PDF

We next discuss when a pair of WCs is applied within an optical node as shown in Fig. 3(b). It is assumed in this case that WCs are used to apply subsystems for conventional bands to additional bands [14–16]. Any component, such as an optical amplifier and WSS, can be included between a WC pair, as shown in Fig. 1(c). The signal light output from the 1^st WC pair is expressed as

(11)$${r_1}(t )\propto [{{E_\textrm{s}}(t )\otimes {h_1}(t )} ]\cdot {E_{\textrm{SH,pre}}}^\ast (t )\cdot {E_{\textrm{SH,post}}}(t )\propto [{{E_\textrm{s}}(t )\otimes {h_1}(t )} ]\cdot {x_1}(t ), $$

where E_SH,pre and E_SH,post are the complex amplitude of the SH pump in the pre- and post-WC, respectively. Here, x₁(t) is the transferred phase component in the 1^st optical node and given by

(12)$${x_1}(t )= {e^{j\Delta {\phi _1}(t )}}, $$

where Δϕ₁(t) is the sum of the phase noise of the SH pumps in pre- and post-WCs. The signal that passes through the next span and is subjected to the same processing at the 2^nd optical node and received with the coherent receiver is expressed as

(13)$${r_{\textrm{Rx}}}(t )\propto [{\{{[{{E_\textrm{s}}(t )\otimes {h_1}(t )} ]\cdot {x_1}(t )} \}\otimes {h_2}(t )} ]\cdot {x_2}(t )\cdot {E_{\textrm{LO}}}(t ). $$

Here, x₂(t) is the transferred phase component in the 2^nd optical node, i.e., it is the sum of the phase noise of the SH pumps in the pre- and post-WCs in the 2^nd optical node, Δϕ₂(t), as in Eq. (11), that is,

(14)$${x_2}(t )= {e^{j\Delta {\phi _2}(t )}}. $$

If this signal is received by the coherent receiver and subjected to digital CD compensation, x₂(t) transferred to the signal at the 2^nd node will enhance the EEPN effect, similar to widening the LO linewidth as in Eq. (10). The transmitted signal has a CD of only one span at the 1^st node. Therefore, x₁(t) does not enhance the EEPN effect as much as x₂(t). That is, the pump lasers of the WCs closer to the receiver have a greater impact on the signal. The pump phase component added by the WCs closer to the transmitter exhibits a CD close to that given to the transmitted signal component so does not lead much timing jitter. Therefore, the effect of timing jitter due to EEPN in the application of the WCs to optical nodes cannot be regarded as a simple increase in the receiver-LO linewidth by summing the phase noise of each pump laser. Timing jitter due to the receiver-LO linewidth scales due to the accumulated CD, i.e., a transmission distance, so the effect of transferred phase noise at each WC on timing jitter will also scale due to the transmission distance to it.

According to previous studies [34–36], the noise variance (the noise power normalized by signal power in the signal bandwidth) caused by receiver-LO-induced EEPN can be analytically given as

(15)$$\sigma _{\textrm{EEPN,LO}}^2 = \frac{{\mathrm{\pi} \cdot c \cdot {D_{\textrm{total}}} \cdot B}}{{2{f_\textrm{r}}^2}}\Delta {\nu _{\textrm{LO}}}, $$

where c is the speed of light, D_total is the accumulated total CD over the fiber transmission, B is the symbol rate, Δν_LO is the Lorentzian linewidth of the LO, and f_r is the center frequency of the received signal. It is possible to estimate signal quality with a trend similar to the experimental results by considering the EEPN effect as equivalent to additive white Gaussian noise (AWGN) corresponding to Eq. (15) [34–36]. By modifying Eq. (15), we introduce the analytical noise variance for the EEPN effect induced by pump-phase noise transferred at WCs. Taking into account the transmission distance to each WC, the total noise variance caused by EEPN in the received signal passing through the WC pairs M times is expressed as

(16)$$\sigma _{\textrm{EEPN,}M}^2 = \sum\limits_m^M {\frac{{\mathrm{\pi} \cdot c \cdot {D_m} \cdot B}}{{2{f_\textrm{r}}^2}}({4\Delta {\nu_{\textrm{pre},m}} + 4\Delta {\nu_{\textrm{post},m}}} )} + \sigma _{\textrm{EEPN,LO}}^2, $$

where D_m is the accumulated CD over the transmission to the mth WC pair and Δν_pre,m and Δν_post,m are the Lorentzian linewidths of the pump lasers respectively used in the pre- and post-WCs at the mth optical node section. Note that, the factor of “4” multiplied to pump linewidths comes from transferring double the phase noise of the original pump laser to the idler light via the SHG-DFG process (see Eqs. (5)–(7)). Here, we assumed that conversion and reconversion take place within a single node, as shown in Fig. 3(b). For wavelength conversion at the transmitter and receiver, as shown in Fig. 3(a), four times the receiver-side pump linewidth should be just added to the receiver-LO linewidth in Eq. (15). As mentioned above, for fiber optical networks using optical parametric wavelength conversion, the increase in the effect of EEPN-induced timing jitter as well as the simple phase noise of the pump lasers will be taken into account when designing the OSNR margin and specifying the pump laser.

2.3 Phase noise cancellation using a pair of wavelength converters with correlated pumping scheme

We propose a configuration of applying WCs to an optical node with correlated pumping for suppressing the transfer of pump-phase noise. When a wavelength conversion and reconversion are executed using a pair of WCs with the same pump frequency in a single node section, the WCs can share the pump laser. In this case, the phase noises in two WCs are correlated in accordance with the delay difference between two paths of pump components. Figure 4 shows the system diagram with the proposed correlated pumping scheme. The reconverted light can be expressed as

(17)$${E_\textrm{i}}^{\prime \prime }({t + {\tau_1}} )\propto {E_\textrm{s}}({t + {\tau_1}} )\cdot {e^{j({ - 2\Delta {\phi_\textrm{p}}({t + {\tau_1}} )+ 2\Delta {\phi_\textrm{p}}({t + {\tau_2}} )} )}}, $$

where Δϕ_p(t) is the phase noise of the pump laser at ω_p, τ₁ is the delay time between the WC pair in the signal path, and τ₂ is the delay time differences between the pump paths for each WC. By adjusting the delay length of the pump path to the second WC so that τ₁ = τ₂, the phase noise can be cancelled out. When τ₁ ≠ τ₂, the interference between transferred phase noise in accordance with the phase difference of each frequency component occurs. The phase difference is a function of the optical delay length d corresponding to the delay time difference of |τ₁ − τ₂| and expressed as

(18)$${\theta _\textrm{d}}(f )= \frac{{2\mathrm{\pi} \cdot n \cdot d}}{c}f, $$

where n is the refractive index of the fiber. As a result of this interference, the normalized PSD of the sum of the transferred phase noise from two pump lasers with θ_d is defined as the ratio of the phase noise transferred in a pair of WCs and that transferred in a single WC and is expressed as follows:

(19)$${S_{\textrm{PSD,sum}}}(f )= 2({1 - \cos [{{\theta_\textrm{d}}(f )} ]} ). $$

S_PSD,sum = 1 (with θ_d = π/3) is equivalent to the phase noise transferred from a single WC, and S_PSD,sum = 2 (with θ_d = π/2) is equivalent to the phase noise transferred from a WC pair with uncorrelated pumping. The frequency components of the transferred phase noise with θ_d = π lead to constructive interference, resulting in S_PSD,sum = 4, which is double the PSD of phase noise in the uncorrelated pumping scheme. Figure 5 shows the normalized PSD spectrum of the transferred phase noise in the correlated pumping scheme as a function of d (n = 1.45). Interference fringes of phase noise can be observed in the frequency direction. This configuration would be an effective solution for reducing the effect of the transferred phase noise without compromising the bandwidth of the OPA, though it is limited to cases in which a WC pair is operated at the same point and the same degenerate frequency. To use correlated pump light between a distant WC pair, one possible method is to co-transmit the pump light with the signal light and use it as the pump light in the subsequent WC. In this case, OSNR regeneration of the pump light using optical injection locking may be effective in suppressing the transfer of amplitude noise from the pump to the signal due to the OSNR degradation associated with transmission.

Fig. 4. System diagram of wavelength conversion with proposed correlated pumping.

Download Full Size | PDF

Fig. 5. Normalized PSD of transferred phase noise in correlated pumping scheme as function of d. S_PSD,sum = 1 means that phase noise transferred from WC pair is equivalent to that from single WC.

Download Full Size | PDF

3. Phase-noise measurement with CW probe light in optical parametric amplification and wavelength conversion

We measured the phase noise in the signal and idler components output from the PPLN-based OPA using continuous wave (CW) light as probe light. The measurements were conducted in the following three cases: (i) a single signal amplification and wavelength conversion, (ii) two wavelength conversions with different (uncorrelated) pump lasers, and (iii) two wavelength conversions with shared (correlated) pump laser.

3.1 Signal amplification and wavelength conversion with different pump lasers

Figure 6 shows the experimental setup for the phase-noise measurement. We used the 2-stage OPA configuration in which the first stage has a different medium for SHG than that of the second one for DFG [37]. For DFG, we used a 4-port PPLN module, in which dichroic filters (DFs) for pump (de-)combining and a PPLN ridge waveguide are integrated [38]. We measured the PSD spectrum of the phase noise of light wave by using a delayed self-heterodyne interferometer (DSHI) [39] and DSP [29]. The CW probe from an external cavity laser (ECL) at 193.0 THz was input to the 4-port PPLN module. The degenerate frequency of the PPLN waveguide was 194.0 THz. The pump light at 194.0 THz was amplified by an EDFA and converted to the SH pump with the PPLN waveguide for SHG. The SH pump was then combined and de-combined with the probe light via the DFs in the 4-port module. The output from the PPLN waveguide for DFG had an amplified signal component at 193.0 THz and wavelength-converted idler component at 195.0 THz. For the measurement of case (i), either the amplified signal component or the wavelength-converted idler component was extracted using a bandpass filter (BPF), and the extracted component input the DSHI. For the measurement of case (ii), the extracted idler component was input to another OPA, reconverted to 193.0 THz, extracted using a BPF, and input to the DSHI. For the wavelength reconversion, the different pump laser with the same phase noise characteristic of that for the 1^st wavelength conversion was used. The amplification/conversion gain of the OPA was ∼10 dB with the SH pump at ∼1 W. The input signal power to the 4-port PPLN modules was −10 dB.

Fig. 6. Experimental setup for phase-noise measurement of amplified signal component, wavelength-converted idler component, and reconverted component.

Download Full Size | PDF

Figure 7(a) shows the PSD spectrum of the phase noise of the probe, pump, amplified signal (case (i)), wavelength-converted idler (case (i)), and reconverted light (case (ii)). The Lorentzian linewidth of the laser is defined by πQ_FM, where Q_FM is a white-noise floor of the PSD spectrum of the phase noise (with a unit of Hz²/Hz). The Lorentzian linewidths of the probe and pump lasers were ∼0.7 and ∼47 kHz, respectively. The phase noise of the amplified signal component almost corresponded to that of the probe laser with no effect of the pump laser, as suggested by Eq. (4). In contrast, the phase noise of the idler component was affected by the pump laser. For case (ii), the phase noise of the reconverted component was increased from the idler component in case (i). Figure 7(b) shows the white-noise floor of the PSD spectrum of the phase noise with 400-sample (∼0.33-MHz bandwidth) moving average in dB to examine the phase noise transfer characteristics to the idler component in detail. The PSD spectrum in the idler component (case (i)) was ∼6 dB (four times) larger than the original phase noise of the pump laser. This is because the phase noise of the pump laser was enhanced by SHG, as suggested by Eqs. (5)–(7). After the reconversion of the idler component to 193.0 THz, the PSD of the phase noise increased by ∼3 dB (two times). This indicated that the transfer of the phase noise from multiple independent pump lasers can be considered by their summation, corresponding to Eq. (8).

Fig. 7. Measurement results. (a) PSD spectrum of phase noise of probe, pump, amplified signal, wavelength-converted idler, and reconverted light. (b) White-noise floor comparison with 400-sample (∼0.33-MHz bandwidth) moving average in dB notation.

Download Full Size | PDF

3.2 Two wavelength conversions with corelated pumping

Figure 8 shows the experimental setup for the measurement in case (iii). The pump laser was shared in the 1^st and 2^nd wavelength conversion. The optical delay line between two wavelength conversions changed the correlation of the phase noise transferred from the pump laser in them. Figure 9 shows the measurement results. For a 0-m delay, which corresponded to the case of τ₁ = τ₂ in Eq. (17), the PSD spectrum of the phase noise of the reconverted idler component agreed with that of the probe laser because the transferred phase noise in two WCs canceled each other. As the delay increased, interference of the phase noise was observed on the PSD spectrum due to a misalignment in the phase correlation of the two transferred phase noise. The first peak point and first bottom out point from the lower frequency in the PSD spectrum correspond to phase shifts of π and 2π, respectively. The positions of those characteristic frequency points observed in the experiment corresponded well with the analytical results shown in Fig. 5. Therefore, we have confirmed the possibility that sharing pump lasers (using correlated pump lasers) in a WC pair can significantly improve the tolerance to the linewidth of the pump lasers.

Fig. 8. Experimental setup for phase noise measurement of reconverted idler component using shared pump laser (correlated pumping scheme).

Download Full Size | PDF

Fig. 9. PSD spectrum of phase-noise of reconverted idler light with certain optical delay amounts.

Download Full Size | PDF

4. Effect on signal quality in digital coherent transmission

This section describes the effect of the phase noise transferred from the pump lasers on signal quality with a dual-polarization (DP-) PCS-64QAM signal. We used a recirculating loop system to investigate its accumulative characteristics. Various pump laser sources with different Lorentzian linewidths were evaluated. Using the results, we validated the analytical EEPN penalty due to pump-phase noise shown in Eq. (16). We also examined the CD dependence of the penalty using a standard single-mode fiber (SSMF) and non-zero dispersion-shifted fiber (NZ-DSF). Finally, the symbol-rate dependence of the effect of the pump-phase noise was evaluated using 32-, 64-, and 96-Gbaud DP-PCS-64QAM signals.

4.1 Experimental setup

To amplify or wavelength-convert a DP signal, we used a polarization-diverse OPA in which two 4-port PPLN modules are sandwiched by a polarization-beam splitter (PBS) and a polarization-beam combiner (PBC) [11]. Figure 10(a) shows the configuration of this polarization-diverse PPLN-based OPA. Pump light for amplifying each polarization component was provided from a single pump laser source. Various lasers with different Lorentzian linewidths were used as a pump laser. To suppress polarization-mode dispersion (PMD), the difference in the optical-path length between two polarization-diverse arms was compensated for with a variable delay line to <0.1 mm corresponding to a ∼0.5-ps PMD.

Fig. 10. Experimental setup. (a) Configuration of polarization-diverse PPLN-based OPA. (b) Recirculating transmission setup and input/output (I/O) optical spectra of 1^st OPA with 96-Gbaud signal. (c) OSNR-SNR characteristics in back-to-back configuration. LUT: laser under test, PBS/PBC: polarization-beam splitter/combiner, ECL: external cavity laser, IQM: I/Q modulator, PDME: polarization-division-multiplexing emulator, BPF: band-pass filter, VOA: variable optical attenuator, SW: optical switch, and LSPS: loop-synchronous polarization scrambler.

Download Full Size | PDF

Figure 10(b) shows the recirculating transmission setup. On the transmitter side (Tx), a 32-, 64-, or 96-Gbaud Nyquist-pulse-shaped DP-PCS-64QAM optical signal with a roll-off factor of 0.03 was generated using an I/Q modulator and polarization-division-multiplexing emulator (PDME) with a 15-m delay line between the orthogonal polarization components. The entropy of the DP-PCS-64QAM signal was 10.57 bits per 4D symbol. The ECL in the transmitter was the same as the probe laser in the previous section. The signal was amplified using an EDFA and input to the recirculating loop. We mainly used the 96-Gbaud signal, except when evaluating symbol rate dependence.

The recirculating loop consisted of a transmission fiber, two PPLN-based polarization-diverse OPAs, a loop-synchronous polarization scrambler (LSPS), EDFA, optical switch (SW), and variable optical attenuators (VOAs). The transmission fiber was basically a 30-km SSMF, but a 20-km NZ-DSF was also used for validating the EEPN effect described in Section 4.3. For evaluating the amplified signal component, the BPFs after the 1^st and 2^nd OPAs extracted the signal component at 193.0 THz. For evaluating the wavelength-converted idler component, the BPF after the 1^st OPA extracted the idler component at 195.0 THz, and that after the 2^nd OPA extracted the idler component at 193.0 THz. The amplification gain of the polarization-diverse OPAs was ∼15 dB with an SH pump power of 1.5 W per polarization. The output power ratio of the signal and idler components depends on the operation gain: the idler output power is smaller than signal output power at small gain. The experimental condition of 15-dB gain was sufficiently large to output almost the same power for both components (see the spectrum in Fig. 9(b)). Therefore, the linear noise difference between the signal and idler components was negligible. The input power to the 30-km SMF and 1^st OPA were −3.0 and −9.0 dBm, respectively. The CD accumulated with the 30-km SSMF transmission was ∼502 ps/nm. The VOA between the two OPAs attenuated the amplification gain so that the input power to each OPA was the same. The EDFA provided the gain needed for recirculation. The input power to the EDFA repeater was also adjusted to −9 dBm. The noise figures (NFs) of the OPAs and the EDFA repeater were ∼5.5 and ∼4.5 dB, respectively.

On the receiver side (Rx), the signal was amplified using an EDFA and received using a coherent receiver, the laser of which for coherent detection had the same characteristics as that of Tx. The received signal was demodulated with offline DSP. First, the CD compensation with a frequency-domain equalizer was conducted. Polarization demultiplexing and symbol recovery were then executed with an 8 × 2 adaptive equalizer (AEQ) [40] and CPR. The AEQ and CPR were performed using a data-aided algorithm. When using the blind-phase search algorithm for the CPR, the averaging length must be optimized for the EEPN penalty [36]. Therefore, for simplicity, we used a data-aided algorithm that does not require such optimization. To evaluate the signal quality, an effective SNR was calculated on the basis of the variance of recovered symbols. Figure 10(c) shows the dependence of the effective SNR on the OSNR in the back-to-back configuration directly connecting Tx and Rx for each symbol-rate signal. The noise bandwidth in calculation of the OSNR was 0.1 nm. We converted the measured effective SNR to OSNR using these dependencies to evaluate the OSNR penalty with the wavelength conversion.

4.2 Pump linewidth tolerance

We first evaluated the dependence of the penalty on the Lorentzian linewidth of the pump lasers with a 96-Gbaud signal. Figure 11 shows the PSD spectrum of the phase noise (frequency modulation noise) of each laser under test (LUT). LUT A was a measurement-instrument laser, LUTs B and C were commercially available tunable lasers, and LUT D was a distributed feedback laser (DFBL). LUT A had the same characteristic as Tx and Rx lasers. The Lorentzian linewidths of LUTs A, B, C, and D estimated from a white-noise floor Q_FM of the PSD spectrum were ∼0.7 kHz, ∼15 kHz, ∼47 kHz, and ∼2.1 MHz, respectively. Here, Q_FM of each LUT were estimated by averaging PSDs within 20–30 MHz. Different laser sources with the same phase noise characteristics were used for two OPAs. The launch power to the 30-km SSMF was −3.0 dBm, which did not cause significant fiber nonlinearity. The input power to each OPA was −9.0 dBm, which did not lead gain saturation caused by pump depletion.

Fig. 11. Phase noise characteristics of lasers under test (LUTs). Estimated Lorentzian linewidths of LUTs A, B, C, and D were ∼0.7 kHz (Q_FM = 225 Hz²/Hz), ∼15 kHz (Q_FM = 4.8 × 10³ Hz²/Hz), ∼47 kHz (Q_FM = 1.5 × 10⁴ Hz²/Hz), and ∼2.1 MHz (Q_FM = 6.8 × 10⁵ Hz²/Hz), respectively.

Download Full Size | PDF

Figure 12(a) shows the experimental results for the amplified-signal and wavelength-converted-idler components using each LUT. For the amplified-signal component (OPA application), there was little difference within 0.4 dB in signal quality between different pump lasers. Even if a DFBL with a linewidth of 2.1 MHz (LUT D) was used for the pump laser, the nearly the same signal quality was observed as when a narrow linewidth laser (LUT A) was used. These results are in agreement with the suggestion from Eq. (4) and the phase-noise measurement results in Fig. 7. For the idler component (wavelength conversion application), however, a clear difference in signal quality between different pump lasers was confirmed. The wider the linewidth pump lasers, the greater the penalty. For LUT A, the SNR degradation was less than 1 dB from the amplified signal component. For LUT D, an SNR degradation of ∼3 dB was observed even with only two conversions (1^st lap). In the constellation diagrams shown in Fig. 12(b), the idler with LUT D was subjected to phase noise as the symbol spread in the azimuthal direction. The constellation diagram of the idler with LUT C at the 6^th lap clearly differed from that with LUT D at 1^st lap, even though their SNR was nearly the same. It is considered that the quality of the idler with LUT C degraded due to the EEPN-induced timing jitter, rather than simple phase noise. Figure 13(a) shows the OSNR penalty, which is the amount of difference between the OSNR of idler components and that of signal components. The OSNR was calculated with the OSNR-SNR characteristics shown in Fig. 10(c). For LUTs A, B, and C, the OSNR penalties at the 1^st lap were 0.4, 0.4, and 0.6 dB, respectively. Likewise, those at the 14^th lap were 0.7, 1.3, and 3.5 dB, respectively. For LUTs C and D, there was a significant accumulative increase in the phase-noise effect of the pump laser. Figure 13(b) plots the dependence of OSNR penalty on linewidth. We observed that the penalty difference due to linewidth was enhanced as the number of laps increased. This is because the total phase noise transferred from the pump lasers was larger for many passes of wavelength conversion. In the EEPN effect, the increase in CD associated with the transmission of the 30-km SSMF in each lap would also contribute to enhancing the penalty difference.

Fig. 12. Experimental results for comparing effects of pump laser on signal quality (symbol rate: 96 Gbaud, transmission line: 30-km SSMF). (a) Effective SNR as function of lap. (b) Constellation diagrams of signal and idler components with LUT D at 1^st lap and idler component with LUT C at 6^th lap.

Download Full Size | PDF

Fig. 13. Results of OSNR penalty. (a) OSNR penalty as function of laps. (b) OSNR penalty as function of pump laser linewidth at 1^st, 7^th, and 14^th laps.

Download Full Size | PDF

4.3 Validation of EEPN-effect quantification

To verify the quantification of the EEPN effect from pump lasers, we compared the experimental results of wavelength-converted idlers with analytical noise variance given as Eq. (16). The additional noise variance in the experimental results for the idlers at the Mth lap was calculated using the SNRs of the signal (SNR_sig,M) and those of the idler (SNR_idl,M) as

(20)$$\Delta \sigma _{\textrm{Ex,}M}^2 = \left( {\frac{1}{{{\textrm{I}_{\textrm{SNR - OSNR}}}[{SN{R_{\textrm{idl,}M}}} ]}} - \frac{1}{{{\textrm{I}_{\textrm{SNR - OSNR}}}[{SN{R_{\textrm{sig,}M}}} ]}}} \right) \cdot \frac{{{W_\textrm{s}}}}{{{W_{\textrm{0}\textrm{.1 nm}}}}}, $$

where I_SNR-OSNR[x] indicates interpolation using the SNR-OSNR relation shown in Fig. 10(c) to convert the measured SNR to OSNR, W_s is the signal bandwidth (= symbol rate), and W_0.1nm is the 0.1-nm frequency bandwidth around the signal frequency (the noise bandwidth in OSNR calculation). We also estimated the effective SNR of the idler components at each lap using the analytical noise variance σ²_EEPN,M as

(21)$$SN{R_{\textrm{est,}M}} = {\textrm{I}_{\textrm{OSNR - SNR}}}\left[ {{{\left( {\frac{1}{{OSN{R_{\textrm{est,}M}}}} + \sigma_{\textrm{EEPN,}M}^2 \cdot \frac{{{W_{\textrm{0}\textrm{.1 nm}}}}}{{{W_\textrm{s}}}}} \right)}^{ - 1}}} \right], $$

where I_OSNR-SNR[x] indicates interpolation using the OSNR-SNR relation shown in Fig. 10(c) to convert the OSNR to SNR, and OSNR_est,M is the OSNR estimated by the NFs of the OPAs and the EDFA repeater and optical signal power at each point. The estimated SNR of the signal component is given by replacing σ²_EEPN,M with σ²_LO,M.

Figure 14(a) shows the comparison of the analytical noise variance caused by the EEPN effect with the experimental results for each LUT. The analytical noise variances clearly showed the trends in the experimental results for each LUT, and Eq. (16) describes the impact of the phase noise of the pump laser on signal quality in digital coherent transmission applying wavelength conversion by a SHG-DFG process with a χ⁽²⁾-platform. In previous studies [36,41], the analytical LO-induced EEPN penalty shown in Eq. (15) was reported to be overestimated under the application of CPR. It has also been shown that this overestimation is small in regions where the penalty is relatively small. In this experimental setup, the CD was not so large, so the EEPN penalty induced by pump lasers was also not so large for LUTs A, B, and C with relatively narrow linewidths. Therefore, in these LUTs, the experimental results agree well with the analytical noise variance shown in Eq. (16). For LUT D, however, the penalty was large due to its wide linewidth on the MHz scale; as a result, the analytical penalty seemed to be overestimated. Thus, these experimental results are analogous to the description of the EEPN penalty caused by LO-phase noise reported in previous studies [36,41]. Figure 14(b) shows the comparison of analytically estimated SNRs and experimentally measured SNRs. The estimated result of the signal component was in good agreement with the experimental result with LUT A, indicating that the effect of fiber nonlinearities was negligible under this experimental condition. For LUTs A, B, and C, the effective SNR of the wavelength-converted idler could be accurately estimated with an error of <0.6 dB using the analytical noise variance. These results indicate that Eq. (16) can be used to estimate signal quality including the actual EEPN penalty. For LUT D with the overestimation of the noise variance induced by the EEPN effect, the SNR was underestimated with an error of 1.4 dB at 3^rd lap.

Fig. 14. Comparison of experimental and analytical results for each LUT (symbol rate: 96 Gbaud, transmission line: 30-km SSMF). (a) Additional noise variance between experimentally measured signal and idler components and analytical noise variance induced by EEPN effect (calculated with Eq. (16)). (b) Experimentally measured SNRs and estimated SNRs with analytical noise variance.

Download Full Size | PDF

4.4 Chromatic dispersion dependence

We next compared the impact of the pump-phase noise on signal quality on the SSMF and NZ-DSF links. If a transferred phase noise affects signal quality as EEPN-induced timing jitter, its effect should be smaller in the NZ-DSF link than in the SSMF link due to a small CD. We conducted a similar experiment using LUT C (linewidth of ∼47 kHz), replacing the 30-km SSMF in the setup shown in Fig. 10(b) with the 20-km NZ-DSF. The CD accumulation over the 20-km NZ-DSF transmission was ∼60 ps/nm, which was one-eighth that over the 30-km SSMF transmission. The fiber-launch power was set to −3.8 dBm to account for the difference in attenuation in the fiber so that the input power to the OPAs and EDFA repeater would be the same so as not to change the linear ASE noise those in the SSMF-transmission case. Figure 15(a) shows the experimental results. The SNRs of the signal components were well matched by tuning the fiber-launch power, indicating that distortion due to fiber nonlinearities was almost negligible. Although the total amount of the transferred phase noise was equivalent, the impact of that on the SNR was much smaller for the NZ-DSF link than for the SMF link as expected. The results clearly indicated the presence of the EEPN effect, which depends on the amount of CD in the transmission link, in the application of WCs to digital coherent transmission. Figure 15(b) shows the comparison of experimentally measured additional noise variance in the idler and analytical EEPN-induced noise variance calculated with Eq. (16). The analytical noise variances were a good representation of the experimental trends, showing the validity of Eq. (16) even for different accumulative CD of the transmission lines.

Fig. 15. Comparison of 30-km-span SSMF link and 20-km-span NZ-DSF link with LUT C (symbol rate: 96 Gbaud). (a) Experimental results of effective SNR. (b) Experimental results of additional noise variance between signal and idler components and analytical noise variance induced by EEPN effect.

Download Full Size | PDF

4.5 Symbol-rate dependence

The impact of the EEPN-induced timing jitter on signal quality cannot be compensated for by the CPR block in the receiver DSP and is greater for signals with higher symbol rates due to shorter symbol duration as shown in Eq. (15). Therefore, we next evaluated the dependence of the penalty on the symbol rate.

Figure 16 shows the experimental results for 32-, 64-, and 96-Gbaud DP-PCS-64QAM signals over the 30-km-span SSMF link. As in the previous sub-section, we compared the case of amplified signal components and idler components with uncorrelated pumping. The pump laser was LUT C. As expected from Eq. (16), it was observed that the lower the symbol rate of the signal, the smaller the SNR penalty. Figure 16(b) shows the OSNR penalty. The OSNR penalty increased as the number of laps increased. The slope of this increase was clearer for the higher symbol-rate signals. Since the EEPN effect depends on the symbol rate, this trend is a good indication of the presence of this effect. Figure 17 shows the comparison of noise variance difference between signal and idler components and analytical noise variance induced by the EEPN effect. The experimental penalty on the wavelength-converted idler and analytical EEPN penalty agreed well for each symbol rate. The validity of Eq. (16) was demonstrated for any symbol rate: 32, 64, or 96 Gbaud.

Fig. 16. Experimental results of symbol-rate dependence for 32-, 64-, and 96-Gbaud signals with LUT C (transmission line: 30-km SSMF). (a) Effective SNR. (b) OSNR penalty.

Download Full Size | PDF

Fig. 17. Comparison of noise variance difference between signal and idler components and analytical EEPN-induced noise variance for 32-, 64-, and 96-Gbaud signals (transmission line: 30-km SSMF).

Download Full Size | PDF

5. Evaluation of correlated pumping scheme

This section experimentally evaluates the proposed correlated pumping scheme to suppress the impact of the transferred pump-phase noise on the wavelength-converted idler. This configuration assumes a case in which wavelength conversion and reconversion are executed within a single optical node by a PPLN-WC pair with the same degenerate frequency. In addition to showing the effect of correlated pumping in improving signal quality, the penalties caused by delay misalignment are discussed.

5.1 Delay adjustment for correlated pumping

We used the setup shown in Fig. 10 to evaluate the penalty of wavelength-converted idler with the proposed correlated pumping scheme. The pump laser source was shared between the two OPAs, and the correlation between the phase noise transferred from each OPA was controlled using the scheme as shown in Fig. 8. The results in Fig. 9 were obtained in a single polarization system. However, delay adjustment was required in all four possible paths to achieve correlated pumping in a polarization-diversity OPA. Therefore, we first carried out path-length adjustment between two OPAs. Figure 18(a) shows the setup for adjusting the path length of the signal and pump lights. The pump-laser source was LUT C with ∼47-kHz linewidth and shared between two OPAs. The probe light at 193.0 THz was input to the 1^st OPA with a polarization controller (PC) selecting the polarization state of either TM or TE. The probe light output from the 1^st OPA passed through the BPF extracting the idler components, and input to the 2^nd OPA while its polarization state was selected with a PC again. Thus, we could measure and adjust the phase noise of the idler component that passed through each of the four polarization diverse paths (i.e., TM-TM, TM-TE, TE-TM, and TE-TE paths). The adjustment used three delay lines allocated at one pump path in the 1^st OPA, the pump path between the 1^st and 2^nd OPAs, and one pump path in the 2^nd OPA. Figure 18(b) shows the phase noise of the idler component generated in each path resulting from the delay adjustment. We adjusted the length of each path using polarization-maintaining fiber patch cords in 10-cm increments. Slight delay misalignment might cause the transfer of high-frequency components of the phase noise, but components of <50 MHz, the measurement limit of our DSHI setup, could be suppressed. Assuming this condition to be a 0-m delay, we inserted an additional delay line in the signal path between the two OPAs and measured the signal quality in the case with delay misalignment.

Fig. 18. Delay adjustment in polarization-diverse configuration. (a) Setup for adjustment in each polarization-diverse path of WC pair. PC: polarization controller. (b) Measurement results of phase noise of idler component for each polarization path with LUT C (d = 0).

Download Full Size | PDF

5.2 Results and discussion

Figure 19 shows the experimental results. For comparison, the signal component and idler component with uncorrelated pumping (the use of different pump sources for two OPAs) are also plotted. For the 0-m delay, the signal quality was significantly increased from that of the uncorrelated pumping and comparable to that using LUT A with ∼0.7-kHz linewidth. The reason for the difference with the signal component is thought to be a slight delay misalignment, which can be clearly seen in the TM-TE path component. The slight delay misalignment would cause the transfer of higher frequency components in the pump phase noise than >50 MHz. As the delay was increased, the signal quality approached that of uncorrelated pumping; for delays greater than 0.3 m, the signal quality nearly coincided with that of the uncorrelated pumping. With a 0.1-m misalignment, a penalty of ∼1-dB compared with the 0-m case was observed at the 14^th lap, indicating that a delay adjustment on the order of centimeters is important.

Fig. 19. Effective SNR of wavelength-converted idler with correlated pumping scheme using LUT C with additional delay d of 0, 0.04, 0.1, 0.3, and 2 m. SNRs of amplified signal component (denoted as “Signal”) and wavelength-converted idler component with uncorrelated pumping (denoted as “Uncorr. pump”) are also plotted for comparison (symbol rate: 96 Gbaud, transmission line: 30-km SSMF).

Download Full Size | PDF

Figure 20 shows the results of the OSNR penalty of the correlated pumping scheme with LUTs A, B, C, and D (d = 0 m). The results for LUTs A, B, and C were in good agreement around 1 dB and almost independent of the lap numbers. Because the EEPN effect should increase with accumulating CD, this may be a result of the EEPN effect becoming negligible due to the suppression of the transferred phase noise of at least <50 MHz by correlated pumping. However, the OSNR penalty for LUT D with a linewidth of 2.1 MHz was less than that with uncorrelated pumping, but still remained significant. Thus, we found that if the linewidth of the pump laser is too wide, high-frequency components of the phase noise can cause a large penalty. In such a case, more precise delay adjustment will be required for suppressing the penalty.

Fig. 20. OSNR penalty of wavelength-converted idler with correlated pumping scheme (d = 0 m) for LUTs A, B, C, and D (symbol rate: 96 Gbaud, transmission line: 30-km SSMF).

Download Full Size | PDF

We also examined the symbol-rate dependence in the correlated pumping scheme with LUT C (d = 0 m). Figure 21 shows the OSNR penalty for 32-, 64-, and 96-Gbaud signals. Similar to the LUT dependence, the OSNR penalty for each symbol rate was nearly identical, indicating that the EEPN effect had been suppressed. The above experimental results indicate that for a pump laser of up to ∼50 kHz, centimeter-order delay adjustment is sufficient to suppress the EEPN effect. Note that the optical path length can drift over time. If the path length fluctuates on the centimeter scale, it may need to be adaptively controlled.

Fig. 21. OSNR penalty with correlated pumping scheme using LUT C for 32-, 64-, and 96-Gbaud signals (transmission line: 30-km SSMF).

Download Full Size | PDF

6. Conclusion

We comprehensively investigated the transfer of the phase noise of the pump laser in optical parametric amplification and wavelength conversion with a PPLN-based OPA. In particular, we assumed that an OPA would be applied to the optical node section and discussed the impact of the pump-phase noise on signal quality in digital coherent fiber transmission.

We showed that the phase noise of the pump laser transfers only to the idler component and has no effect on the amplified signal component from direct measurement of the phase noise and evaluation of the signal quality. In signal-amplification applications, high tolerance for a pump linewidth was observed. Even when a DFBL with a MHz-scale linewidth was used as the pump laser, the signal quality of the amplified signal was nearly the same as that with a 0.7-kHz-linewidth laser. In contrast, it was found that the phase noise corresponding to four times the PSD spectrum of the original pump laser was transferred to the idler in the SHG-DFG cascaded configuration. The penalty on signal quality due to transmitted pump-phase noise depended on the linewidth of the pump laser. In addition, experimental results comparing the NZ-DSF link with the SSMF link clearly indicated the presence of the EEPN effect via dispersive fiber transmission and digital CD compensation in receiver DSP. The penalty due to the phase noise was large for higher symbol-rate signals, which also suggested the presence of the EEPN effect. Moreover, we attempted to quantify the effect of the pump-phase-noise-induced EEPN-effect. A theoretical analysis of the transmission systems with WCs, combined with the well-known impact of a receiver-LO linewidth, explained the experimental results well.

We next proposed and evaluated the correlated pumping scheme. We found that when pump light is shared between WCs, interference occurs in transferred phase noise depending on the delay difference between the pump components, and that it is possible to compensate for the phase noise by adjusting the delay. The delay adjustment between a pair of WCs on centimeter scale effectively suppressed the phase noise components of at least <50 MHz and significantly improved pump linewidth tolerance.

PPLN-based optical parametric amplification and optical signal processing such as wavelength conversion are expected to be key technologies for constructing future ultra-wideband optical networks. The content discussed in this paper will be important for applying OPAs to optical fiber transmission systems.

Funding

National Institute of Information and Communications Technology (JPJ012368C04501).

Acknowledgments

Part of this work used the results from a research project commissioned by National Institute of Information and Communications Technology (NICT) of Japan (JPJ012368C04501).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. H. Masuda, A. Sano, T. Kobayashi, et al., “20.4-Tb/s (204 × 111 Gb/s) Transmission over 240 km using Bandwidth-Maximized Hybrid Raman/EDFAs,” in Opt. Fiber Commun. Conf. (2007), paper PDP20.

2. A. Ghazisaeidi, I. F. de Jauregui Ruiz, R. Rios-Muller, et al., “Advanced C + L-Band Transoceanic Transmission Systems Based on Probabilistically Shaped PDM-64QAM,” J. Lightwave Technol. 35(7), 1291–1299 (2017). [CrossRef]

3. M. Ionescu, D. Lavery, A. Edwards, et al., “74.38 Tb/s Transmission Over 6300 km Single Mode Fiber with Hybrid EDFA/Raman Amplifiers,” in Opt. Fiber Commun. Conf. (2019), paper Tu3F.3.

4. F. Hamaoka, M. Nakamura, M. Takahashi, et al., “173.7-Tb/s Triple-Band WDM Transmission Using 124-Channel 144-GBaud Signals With SE of 9.33 b/s/Hz,” in Opt. Fiber Commun. Conf. (2023), paper Th3F.2.

5. J. Renaudier, A. Meseguer, A. Ghazisaeidi, et al., “First 100-nm Continuous-Band WDM Transmission System with 115Tb/s Transport over 100 km Using Novel Ultra-Wideband Semiconductor Optical Amplifiers,” in Eur. Conf. Opt. Commun. (2017), paper Th.PDP.A.2.

6. B. J. Puttnam, R. S. Luís, G. Rademacher, et al., “S-, C- and L-band transmission over a 157 nm bandwidth using doped fiber and distributed Raman amplification,” Opt. Express 30(6), 10011–10018 (2022). [CrossRef]

7. M. A. Iqbal, L. Krzczanowicz, I. Phillips, et al., “150 nm SCL-Band Transmission through 70 km SMF using Ultra-wideband Dual-stage Discrete Raman Amplifier,” in Opt. Fiber Commun. Conf. (2020), paper W3E.4.

8. X. Zhao, S. Escobar-Landero, D. Le Gac, et al., “200.5 Tb/s Transmission with S + C+L Amplification Covering 150 nm Bandwidth over 2×100 km PSCF Spans,” in Eur. Conf. Opt. Commun. (2022), paper Th3C.4.

9. R. Malik, A. Kumpera, M. Karlsson, et al., “Demonstration of Ultra Wideband Phase-Sensitive Fiber Optical Parametric Amplifier,” IEEE Photon. Technol. Lett. 28(2), 175–177 (2016). [CrossRef]

10. V. Gordienko, F. M. Ferreira, C. B. Gaur, et al., “Looped Polarization-Insensitive Fiber Optical Parametric Amplifiers for Broadband High Gain Applications,” J. Lightwave Technol. 39(19), 6045–6053 (2021). [CrossRef]

11. S. Shimizu, T. Kobayashi, T. Kazama, et al., “PPLN-Based Optical Parametric Amplification for Wideband WDM Transmission,” J. Lightwave Technol. 40(11), 3374–3384 (2022). [CrossRef]

12. T. Kobayashi, S. Shimizu, M. Nakamura, et al., “103-ch. 132-Gbaud PS-QAM Signal Inline-Amplified Transmission With 14.1-THz Bandwidth Lumped PPLN-Based OPAs Over 400-km G.652.D SMF,” in Opt. Fiber Commun. Conf. (2023), paper Th4B.6.

13. T. Kato, S. Watanabe, T. Yamauchi, et al., “Real-time transmission of 240×200-Gb/s signal in S + C+L triple-band WDM without S- or L-band transceivers,” in Eur. Conf. Opt. Commun. (2019), paper PD.1.7.

14. C. Guo, A. Shamsshooli, Y. Akasaka, et al., “Investigation of hybrid S-band amplifier performance with 8-channel × 10 GBaud 16-QAM signals,” in Eur. Conf. Opt. Commun. (2021), paper Tu2A.3.

15. H. Minami, K. Hirose, T. Fukatani, et al., “Low-Penalty Band-Switchable Multi-Band Optical Cross-Connect Using PPLN-Based Inter-Band Wavelength Converters,” J. Lightwave Technol. 42(4), 1242–1249 (2024). [CrossRef]

16. S. Shimizu, T. Kobayashi, A. Kawai, et al., “L- and U-Band WDM Transmission Over 6 THz Using PPLN-Based Optical Parametric Amplification and Wavelength-Band Conversion,” J. Lightwave Technol. 42(5), 1347–1355 (2024). [CrossRef]

17. D. Soma, T. Kato, S. Beppu, et al., “25-THz O + S+C + L+U-Band Digital Coherent DWDM Transmission Using a Deployed Fibre-Optic Cable,” in Eur. Conf. Opt. Commun. (2023), paper Th.C.2.2.

18. M. Abe, T. Kazama, S. Shimizu, et al., “Expansion of Transmission Bandwidth Over 16 THz in S + C+L + U Bands by Combining Cband Transceiver with PPLN-Based Wavelength Converters,” in Front. Opt. Laser Sci. Conf. (2023), paper FM5D.2.

19. T. Umeki, T. Kazama, A. Sano, et al., “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]

20. P. Kylemark, M. Karlsson, T. Torounidis, et al., “Noise Statistics in Fiber Optical Parametric Amplifiers,” J. Lightwave Technol. 25(2), 612–620 (2007). [CrossRef]

21. S. T. Naimi, SPÓ Dúill, and L. P. Barry, “Detailed investigation of the pump phase noise tolerance for wavelength conversion of 16-QAM signals using FWM,” J. Opt. Commun. Netw. 6(9), 793–800 (2014). [CrossRef]

22. S. Moro, A. Peric, N. Alic, et al., “Phase noise in fiber-optic parametric amplifiers and converters and its impact on sensing and communication systems,” Opt. Express 18(20), 21449–21460 (2010). [CrossRef]

23. M. Ho, M. E. Marhic, K. Y. K. Wong, et al., “Narrow-linewidth idler generation in fiber four-wave mixing and parametric amplification by dithering two pumps in opposition of phase,” J. Lightwave Technol. 20(3), 469–476 (2002). [CrossRef]

24. C. Li, M. Luo, Z. He, et al., “Phase Noise Canceled Polarization-Insensitive All-Optical Wavelength Conversion of 557-Gb/s PDM-OFDM Signal Using Coherent Dual-Pump,” J. Lightwave Technol. 33(13), 2848–2854 (2015). [CrossRef]

25. T. T. Nguyen, S. Boscolo, A. A. I. Ali, et al., “Digital Compensation of Residual Pump Dithering in Optical Phase Conjugation of High-Order QAM,” in Opt. Fiber Commun. Conf. (2021), paper M3I.4.

26. G. W. Lu, A. Albuquerque, B. J. Puttnam, et al., “Pump-linewidth-tolerant optical wavelength conversion for high-order QAM signals using coherent pumps,” Opt. Express 22(5), 5067–5075 (2014). [CrossRef]

27. G. W. Lu, A. Albuquerque, B. J. Puttnam, et al., “Pump-phase-noise-free optical wavelength data exchange between QAM signals with 50-GHz channel-spacing using coherent DFB pump,” Opt. Express 24(4), 3702–3713 (2016). [CrossRef]

28. R. W. Boyd, Nonlinear Optics, 4th ed. (Academic Press, 2020).

29. K. Kikuchi, “Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers,” Opt. Express 20(5), 5291–5302 (2012). [CrossRef]

30. A. Vedadi, A. Mussot, E. Lantz, et al., “Theoretical study of gain distortions in dual-pump fiber optical parametric amplifiers,” Opt. Commun. 267(1), 244–252 (2006). [CrossRef]

31. M. Bastamova, V. Gordienko, and A. Ellis, “Impact of Pump Phase Modulation on Fibre Optical Parametric Amplifier Performance for 16-QAM Signal Amplification,” in Eur. Conf. Opt. Commun. (2022), paper Tu5.6.

32. T. Kazama, T. Umeki, M. Abe, et al., “Low-Parametric-Crosstalk Phase-Sensitive Amplifier for Guard-Band-Less DWDM Signal Using PPLN Waveguides,” J. Lightwave Technol. 35(4), 755–761 (2017). [CrossRef]

33. L. G. Carpenter, S. A. Berry, A. C. Gray, et al., “CW demonstration of SHG spectral narrowing in a PPLN waveguide generating 2.5 W at 780 nm,” Opt. Express 28(15), 21382–21390 (2020). [CrossRef]

34. W. Shieh and K. Ho, “Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef]

35. A. Kakkar, J. R. Navarro, R. Schatz, et al., “Comprehensive Study of Equalization-Enhanced Phase Noise in Coherent Optical Systems,” J. Lightwave Technol. 33(23), 4834–4841 (2015). [CrossRef]

36. A. Arnould and A. Ghazisaeidi, “Equalization Enhanced Phase Noise in Coherent Receivers: DSP-Aware Analysis and Shaped Constellations,” J. Lightwave Technol. 37(20), 5282–5290 (2019). [CrossRef]

37. M. Asobe, T. Umeki, O. Tadanaga, et al., “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO₃ waveguide module,” Electron. Lett. 45(10), 519–521 (2009). [CrossRef]

38. T. Kazama, T. Umeki, S. Shimizu, et al., “Over-30-dB Gain and 1-dB Noise Figure Phase-Sensitive Amplification Using Pump-Combiner-Integrated Fiber I/O PPLN Module,” Opt. Express 29(18), 28824–28834 (2021). [CrossRef]

39. Z. Zhao, Z. Bai, D. Jin, et al., “Narrow laser-linewidth measurement using short delay self-heterodyne interferometry,” Opt. Express 30(17), 30600–30610 (2022). [CrossRef]

40. T. Kobayashi, M. Nakamura, F. Hamaoka, et al., “35-Tb/s C-band transmission over 800 km employing 1-Tb/s PS-64QAM signals enhanced by complex 8×2 MIMO equalizer,” in Proc. Opt. Fiber Commun. Conf. (2019), paper Th4B.2.

41. H. Wang, X. Yi, J. Zhang, et al., “Extended Study on Equalization-Enhanced Phase Noise for High-Order Modulation Formats,” J. Lightwave Technol. 40(24), 7808–7813 (2022). [CrossRef]

Impact of pump-phase noise in PPLN-based optical parametric amplifier and wavelength converter for digital coherent transmission

Abstract

1. Introduction

2. Analysis of effect of phase-noise transfer from pump laser on signal and idler components

2.1 Transfer of phase noise from pump laser

2.2 Conversion of transferred pump-phase noise to EEPN-induced timing jitter

2.3 Phase noise cancellation using a pair of wavelength converters with correlated pumping scheme

3. Phase-noise measurement with CW probe light in optical parametric amplification and wavelength conversion

3.1 Signal amplification and wavelength conversion with different pump lasers

3.2 Two wavelength conversions with corelated pumping

4. Effect on signal quality in digital coherent transmission

4.1 Experimental setup

4.2 Pump linewidth tolerance

4.3 Validation of EEPN-effect quantification

4.4 Chromatic dispersion dependence

4.5 Symbol-rate dependence

5. Evaluation of correlated pumping scheme

5.1 Delay adjustment for correlated pumping

5.2 Results and discussion

6. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (21)

Equations (21)

Optics Express