Optical pump phase locking to a carrier wave extracted from phase-conjugated twin waves for phase-sensitive optical amplifier repeaters

Yasuhiro Okamura; Masashi Abe; Kotaro Kondo; Yuya Ohmichi; Takushi Kazama; Takeshi Umeki; Masafumi Koga; Atsushi Takada

doi:10.1364/OE.24.026300

1. Introduction

In fiber-optic communication systems, the nonlinear Shannon limit is one of the pressing issues that should be addressed to respond to ever-increasing capacity demands. Phase-conjugated twin waves (PCTWs) transmission has recently received broad attention because nonlinear phase noise is compensated by simple receiver-side digital signal processing [1]. PCTWs are also applicable to frequency nondegenerate optical parametric phase-sensitive amplifiers (ND-PSAs) [2–4], which enable nonlinear phase noise suppression and low-noise amplification. It is expected that multi-span transmission of PCTWs with ND-PSA repeaters in dispersion compensated/managed links will expand the transmission distance compared to the conventional erbium doped fiber amplifier links. For implementation of the ND-PSA, PCTWs and a pump wave are guided into an optical nonlinear medium such as a highly nonlinear fiber or a periodically poled lithium niobate (PPLN) waveguide, and must be phase-synchronized mutually. Optical phase-locking methods used in previous studies can be classified into either the optical injection locking method with a pilot carrier transmission [5] or the optical phase-locked loop (OPLL) method. In the former method, a guard band is mandatory among signal waves, phase-conjugated waves, and the pilot carrier to avoid crosstalk due to optical fiber nonlinearities in wavelength-division-multiplexing (WDM) transmission. This leads to spectral efficiency degradation in such WDM transmission systems. On the other hand, generally, the OPLL method is used for optical signal reception, and homodyne reception of 20-Gbit/s optical quadrature phase-shift keying (QPSK) signals by the OPLL method has been demonstrated [6]. In the case of ND-PSA links, the OPLL method can avoid pilot carrier transmission, and an OPLL circuit with Costas-loop configuration enables application of an individual pump source in ND-PSA repeaters [7]. However, the Costas OPLL requires high-speed balanced photodetectors (BPDs) and a wide bandwidth microwave mixer because detected signals have intermediate frequency which is at least half of optical frequency spacing between a signal wave and its phase-conjugated wave. This requirement can be mitigated by using a sideband modulated pump wave [8]; however, WDM-PCTWs cannot be phase-synchronized because of beat noise resulting from neighboring WDM channels.

We have proposed an OPLL assisted by sum-frequency generation and second-harmonic generation (SS-OPLL) for ND-PSA repeaters [9]. The SS-OPLL has three main features. The first one is a simple configuration based on a balanced OPLL. The reason is that carrier extraction of PCTWs is achieved for reference light generation in the SS-OPLL. The carrier extraction from WDM-PCTWs are also available and contributes to signal-to-noise ratio improvement because of simultaneous generation of SF waves from WDM-PCTWs. The second feature is that the SS-OPLL is applicable for every PCTWs generated by a two-stage second-harmonic generation (SHG)/optical parametric amplification (OPA)-based method [10], a four-wave mixing-based method [3], an intensity modulation with intermediate signal method [9], and an individual generation method [11]. The third feature is that the SS-OPLL can be integrated with PSAs based on a χ⁽²⁾ optical nonlinear medium, because the SS-OPLL also includes χ⁽²⁾ optical nonlinear media. Fundamental experiment has been conducted in [9]; however, an identical laser was used for signal and pump sources.

In this paper, optical phase locking between PCTWs and a pump wave generated from individual laser sources is experimentally demonstrated by the SS-OPLL for the first time. This paper is organized as follows. In Section 2, a basic configuration of the SS-OPLL is shown, and its analytically derived error signals are extracted by the SS-OPLL for the first time. In Section 3, an optical phase locking between a 20-Gbit/s QPSK-PCTWs and a pump wave is carried out by using the SS-OPLL circuit as a proof-of-principle experiment. In Section 4, a waveform and spectra of error signals between the PCTWs and the pump wave are shown as the experimental results.

2. Principle of OPLL assisted by SFG and SHG

For ND-PSA, when PCTWs consist of a signal wave with optical frequency ν₁ and its phase-conjugated wave with optical frequency ν₂, a pump wave needs to be located in ν_c = (ν₁ + ν₂)/2. Additionally, the pump wave must be phase-locked to the averaged phase of the PCTWs. The proposed SS-OPLL technique enables optical phase locking between a pump wave and PCTWs and has advantages over the Costas-OPLL in that an error detector and a carrier extractor can be composed of relatively simple devices, such as an optical 3-dB coupler, one BPD, and one χ⁽²⁾ optical nonlinear medium. The basic configuration of the SS-OPLL is shown in Fig. 1. Incoming PCTWs e_s(t) consisting of a signal wave with phase information θ_d₁ and its phase-conjugated wave with phase information θ_d₂ can be described as

\begin{matrix} e_{s} (t) = {[E_{s 1} \exp (j (θ_{d 1} + ε_{s 1})) \exp (j 2 π ν_{s 1} t) + E_{s 2} \exp (j (θ_{d 2} + ε_{s 2})) \exp (j 2 π ν_{s 2} t)] + c . c .} / 2 \\ = {[E_{s 1} \exp (j (θ_{d 1} + ε_{s 1})) \exp (j 2 π ν_{s 1} t) + E_{s 2} \exp (j (- θ_{d 1} + ε_{s 2})) \exp (j 2 π ν_{s 2} t)] + c . c .} / 2. \end{matrix}

Here, E_s₁ and E_s₂ indicate the electric field amplitude of the signal and its phase-conjugated waves, respectively. ε_s₁ and ε_s₂ are phase fluctuations of optical fields resulting from spontaneous emission of laser sources [12] for a signal and its phase-conjugated waves. c.c. means complex conjugate. Because of the PCTWs, the relationship between phase information of the signal and its phase-conjugated waves is θ_d₁ = −θ_d₂. Then, the PCTWs e_s(t) are input to the SS-OPLL circuit and χ⁽²⁾ optical nonlinear medium 1 for carrier extraction. Sum-frequency (SF) and second-harmonic (SH) waves e_ss(t) are generated by the χ⁽²⁾ optical nonlinear medium 1 with a conversion coefficient k₁ and can be described as

e_{s s} (t) = k_{1} {e_{s}^{2} (t)} = e_{S H 1} + e_{S H 2} + e_{S F} + e_{D F} + D C c o m p o n e n t s .

Here, the DC components and the difference frequency wave e_DF from the PCTWs can be neglected. Hence, e_ss(t) can be rewritten as

e_{s s 2} (t) = \frac{1}{2} {[\begin{matrix} \frac{k_{1} E_{s 1}^{2}}{2} \exp (j (4 π ν_{s 1} t + 2 θ_{d 1} + 2 ε_{s 1})) \\ + \frac{k_{1} E_{s 2}^{2}}{2} \exp (j (4 π ν_{s 2} t + 2 θ_{d 2} + 2 ε_{s 2})) \\ + k_{1} E_{s 1} E_{s 2} \exp (j (2 π (ν_{s 1} + ν_{s 2}) t + θ_{d 1} + θ_{d 2} + ε_{s 1} + ε_{s 2})) \end{matrix}] + c . c .} .

The first, second, and third terms denote an SH wave of the signal wave, an SH wave of the phase-conjugated wave, and an SF wave of the PCTWs, respectively. Here, we focus on the SF wave; it can be rewritten as

\begin{matrix} e_{S F} (t) = {k_{1} E_{s 1} E_{s 2} \exp (j (2 π (ν_{s 1} + ν_{s 2}) t + θ_{d 1} + θ_{d 2} + ε_{s 1} + ε_{s 2})) + c . c .} / 2 \\ = {k_{1} E_{s 1} E_{s 2} \exp (j (2 π (ν_{s 1} + ν_{s 2}) t + ε_{s 1} + ε_{s 2})) + c . c .} / 2. \end{matrix}

A point to notice here is that the phase information θ_d₁ and θ_d₂ are canceled because θ_d₁ = −θ_d₂. Therefore, the SF wave is an extracted carrier and can be used as a reference light for the SS-OPLL. On the other hand, a continuous wave (CW) output from an optical voltage-controlled oscillator (OVCO) used as a pump source can be written as

e_{L} (t) = {E_{L} \exp (j (2 π ν_{L} t + θ_{L} + ε_{L})) + c . c .} / 2.

E_L, θ_L, and ε_L are the constant electric field amplitude, control phase of the OVCO output, and phase fluctuations of the pump wave, respectively. As described previously, ν_L needs to be equal to (ν_s₁ + ν_s₂)/2 for the ND-PSA. However, there is actually an optical frequency difference Δf defined as Δf = ν_L − (ν_s₁ + ν_s₂)/2, because individual light sources are used for the PCTWs and pump wave. The OVCO output e_L(t) is launched into χ⁽²⁾ optical nonlinear medium 2 with a conversion coefficient with k₂, and an SH wave e_LSH(t) is generated:

\begin{array}{l} e_{L S H} (t) = k_{2} {e_{L}^{2} (t)} \\ = \frac{1}{2} {\frac{k_{2} E_{L}^{2}}{2} \exp [j (2 π (2 ν_{L}) t + 2 θ_{L} + 2 ε_{L})] + c . c .} \\ = \frac{1}{2} {\frac{k_{2} E_{L}^{2}}{2} \exp [j (2 π (ν_{s 1} + ν_{s 2} + 2 Δ f) t + 2 θ_{L} + 2 ε_{L})] + c . c .} . \end{array}

Here, the DC term is neglected. Then, the output waves e_SS₂(t) and e_LSH(t) from the two χ⁽²⁾ optical nonlinear media are interfered by an optical coupler. Outputs from the constructive and destructive ports of the coupler can be represented as

e_{C} (t) = \frac{1}{2} {[\begin{array}{l} \frac{k_{1} E_{s 1} E_{s 2}}{\sqrt{2}} \exp [j (2 π (ν_{s 1} + ν_{s 2}) t + ε_{s 1} + ε_{s 2})] \\ + \frac{k_{2} E_{L}^{2}}{\sqrt{2}} \exp [j (2 π (ν_{s 1} + ν_{s 2} + 2 Δ f) t + 2 θ_{L} + 2 ε_{L} - \frac{π}{2})] \end{array}] + c . c .}

e_{D} (t) = \frac{1}{2} {[\begin{array}{l} \frac{k_{1} E_{s 1} E_{s 2}}{\sqrt{2}} \exp [j (2 π (ν_{s 1} + ν_{s 2}) t + ε_{s 1} + ε_{s 2} - \frac{π}{2})] \\ + \frac{k_{2} E_{L}^{2}}{\sqrt{2}} \exp [j (2 π (ν_{s 1} + ν_{s 2} + 2 Δ f) t + 2 θ_{L} + 2 ε_{L})] \end{array}] + c . c .} .

The interference signals e_C(t) and e_D(t) are detected by photodetectors with responsivity R in a BPD, and the BPD output signals I_Err(t) are given by

I_{E r r} (t) = R α \bar{{e_{C}^{2} (t) - e_{D}^{2} (t)}} = \frac{R α k_{1} k_{2} E_{s 1} E_{s 2} E_{L}^{2}}{2} \sin {2 π (2 Δ f) t + 2 θ_{L} + 2 ε_{L} - (ε_{s 1} + ε_{s 2})} .

Here, the coefficient α denotes the ratio of the effective beam area to the impedance of the free space, and terms with optical frequency ν_s₁ + ν_s₂ are neglected because of the band limitation of the BPD. To simplify the analysis, it is assumed that Δf = 0 and 2θ_L + 2ε_L – (ε_s₁ + ε_s₂) << 1. Then, Eq. (9) can be rewritten as

I_{E r r} (t) = G_{P D} (θ_{L} + ε_{P N}) .

Here, G_PD = Rαk₁k₂E_s₁E_s₂E_L², and ε_PN = ε_L – 0.5(ε_s₁ + ε_s₂). As clearly seen in Eq. (10), total phase fluctuation, namely the phase error, ε_PN, is extracted. After that, the BPD output signals I_Err(t) as error signals are fed back to the OVCO through a loop filter. As a result, the OVCO phase θ_L is controlled to compensate the phase error ε_PN, and optical phase locking between the PCTWs and the OVCO output is accomplished by the SS-OPLL. Finally, the pump carrier from the OVCO is generated and can be used for ND-PSA based on a χ⁽²⁾/χ⁽³⁾ material. When an ND-PSA with the SS-OPLL is composed of fiber-pigtailed devices, an additional circuit such as a piezoelectric transducer (PZT) based phase stabilizer is required in an OPA stage because of relative phase drift in input fibers of the OPA module. In the case of a χ⁽²⁾ based ND-PSA, the OPA module and the SS-OPLL circuit can be integrated on the same platform, and in that case, the PZT phase stabilizer is not necessary. The SS-OPLL is applicable to not only M-PSK-PCTWs, but also M-QAM-PCTWs. Because a line spectrum can be extracted by the SFG process even though amplitude modulation component remains in a generated SF wave of M-QAM-PCTWs.

Fig. 1 Basic configuration of SS-OPLL.

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3. Proof-of-principle experiment

Optical phase locking between 20-Gbit/s QPSK-PCTWs and a pump wave by the SS-OPLL was demonstrated for a proof-of-principle experiment. In this experiment, individual lasers were used for signal generation and an OVCO, and PPLN waveguides were used as χ⁽²⁾ optical nonlinear media. Figure 2 shows the experimental setup, which is composed of a PCTWs generation section and the SS-OPLL circuit. In the PCTWs generation, a two-stage SHG/OPA process [10] was used. First, a continuous wave (CW) launched from a tunable laser diode (TLD) with a 100-kHz linewidth and 1553.34-nm center wavelength was modulated by 20-Gbit/s QPSK baseband signals. On the other hand, a CW from external cavity laser (ECL) 1 with a 9-kHz linewidth and 1552.5-nm center wavelength was amplified, and up-converted by a PPLN waveguide for SHG. After that, the SH wave with 776.25-nm wavelength and the generated optical QPSK signals were input to a PPLN waveguide for the DFG process; then, 20-Gbit/s QPSK-PCTWs were generated. The generated PCTWs depicted in the upper inset (curves in black) were input into the SS-OPLL circuit and guided into a PPLN waveguide for SFG. Meanwhile, in the SS-OPLL circuit, an OVCO was implemented mainly by ECL 2 with a 6.5-kHz linewidth and 1552.6-nm wavelength, and an optical intensity modulator (IM) driven by an approximately 10-GHz sinusoidal wave from an electric VCO. The OVCO output had some sidebands as depicted in the upper inset (curves in red), and the first shorter-wavelength sideband with approximately 1552.5-nm wavelength was used for optical phase locking. The sidebands and the PCTWs were launched into PPLN waveguides, respectively; then, as shown in the lower inset, an SH wave of the first-order sideband (curves in red) and an SF wave of the PCTWs (curves in black) were generated. The reason why the observed output spectrum of PPLN for SHG is more of a continuum than sharp peaks is that an SFG wave between fundamental and its sidebands is simultaneously generated in the same PPLN waveguide. The SF wave and the SH wave of the first shorter-wavelength sideband were coupled by an optical 3-dB coupler, and interference signals from a constructive and destructive ports of the coupler were detected by a BPD with 100-MHz bandwidth and 0.53-A/W responsivity. Here, beat signals between the SF wave of the PCTWs and the SH waves of the sidebands except the first shorter-wavelength sideband can be neglected because of the BPD bandwidth. The BPD output, i.e., error signals, was applied to the electric VCO through a loop filter. Then, the optical phase locking was carried out.

Fig. 2 Experimental setup of optical phase locking between 20-Gbit/s QPSK-PCTWs and a CW pump with SS-OPLL.

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4. Results and discussion

Error signals were observed at the output of the BPD and the electric VCO. Figure 3(a) shows the BPD output waveform observed by an oscilloscope (OSC). Before the SS-OPLL operation, the waveform is distorted because of phase errors between the PCTWs and the pump wave. Conversely, the error components were reduced by the SS-OPLL circuit operating in the time duration colored in orange. Figures 3(b) and 3(c) show the electric VCO output spectra. When the SS-OPLL is not operating, not only a fundamental peak with 10.69 GHz but also error components colored in orange can be observed as shown in Fig. 3(b). In contrast, when the SS-OPLL is working, the error components vanish, and the fundamental peak only remains at 10.77-GHz frequency. These results show we successfully demonstrated optical phase locking between the PCTWs and the pump by using the SS-OPLL circuit.

Fig. 3 Error signal waveform and spectra. Waveform (a) is observed at the BPD output. Spectra (b) and (c) observed at the electric VCO output are the OPLL off and on state, respectively.

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5. Summary

In this paper, optical phase locking between 20-Gbit/s QPSK-PCTWs and an individual pump source was experimentally demonstrated for the first time. In the SS-OPLL, carrier extraction from PCTWs and reference light generation were conducted by the SFG process, and the generated SF waves were used as reference light. When the SS-OPLL operated, the error signal amplitude observed at the BPD output was obviously reduced, and error components in the electric VCO output spectrum were also suppressed. The experimental results showed the SS-OPLL circuit enabled optical phase locking between PCTWs and a pump wave. An influence of signal-to-noise ratio of PCTWs on carrier extraction, theoretical noise figure of ND-PSA with the SS-OPLL, performance comparison between the SS-OPLL and the Costas-OPLL, and a transmission experiment with ND-PSA employing the SS-OPLL should be investigated further.

Acknowledgments

Part of this research uses results of the “R&D on Optical Signal Transmission and Amplification with Frequency/Phase Precisely Controlled Carrier” commissioned by the National Institute of Information and Communications Technology (NICT) of Japan.

References and links

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Optical pump phase locking to a carrier wave extracted from phase-conjugated twin waves for phase-sensitive optical amplifier repeaters

Abstract

1. Introduction

2. Principle of OPLL assisted by SFG and SHG

3. Proof-of-principle experiment

4. Results and discussion

5. Summary

Acknowledgments

References and links

Cited By

Figures (3)

Equations (10)

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