All-optical modulation-transparent wavelength multicasting in a highly nonlinear fiber Sagnac loop mirror

Dawei Wang; Tee-Hiang Cheng; Yong-Kee Yeo; Jianguo Liu; Zhaowen Xu; Yixin Wang; Gaoxi Xiao

doi:10.1364/OE.18.010343

1. Introduction

Optical wavelength multicasting, where an input channel can be simultaneously replicated onto multiple output wavelengths, is one of the key enabling techniques for implementing a multicast-capable optical network. By using this technique, the efficiency and throughput of wavelength-division-multiplexed (WDM) optical networks can be improved significantly in the presence of multicast traffic [1].

There are several approaches to realize all-optical wavelength multicasting, such as using self-phase modulation (SPM) in photonic crystal fiber (PCF) [2], cross-phase modulation (XPM) in highly nonlinear fiber (HNLF) [3], semiconductor optical amplifier based Mach-Zehnder interferometer (SOA-MZI) [4], cross-gain modulation (XGM) in SOA or in fiber optic parametric amplifier [5,6], cross-absorption modulation (XAM) in electro-absorption modulator [7,8], single-pump modulated parametric amplifier [9], and self-seeded parametric amplifier [10]. However, due to the operation principles [2–9] and phase noise generated by phase modulated high power pumps – which increases the threshold of the stimulated Brillouin scattering (SBS) effect [10,11], these schemes can only be applied to on-off keying (OOK) modulated signals. Since modern optical communications systems should have the flexibility to use different modulation formats [12–14], a multicasting technique that is transparent to the modulation format and bit rate is highly desirable. To achieve such transparency, several multicasting schemes based on multi-pump induced FWM have been proposed [15–18]. The main drawback of these schemes is that the number of achieved multicast channels strongly depends on the number of pumps used. When more number of pumps is used, more pump-pump generated idlers are produced. Some of the idlers may have the same wavelengths as the multicast channels and induce significant crosstalk. This complicates the design and operation as careful selection of pump wavelengths is critical to reduce the crosstalk [18].

In this paper, we make use of a HNLF Sagnac loop mirror [19–22] to realize optical multicasting based on the multi-pump FWM approach, which can overcome the problem of pump-pump generated idler overlapping with the multicast channels. Owing to the Sagnac loop mirror, the pumps, pump-pump generated idlers, and pump amplifier spontaneous emission (ASE) noise can be greatly suppressed at the output of the multicast channels. Consequently, clear eye diagrams can be observed even when the wavelength of a multicast channel has the same wavelength as the pump-pump generated idler. In addition, the proposed design does not need a filter to remove the pump amplified ASE noise. Note that a filter inevitably introduces some insertion loss to the pump power, which is not desirable.

The generation of six and ten 10-Gb/s OOK/differential phase-shift keying (DPSK) multicast channels has been demonstrated experimentally by using two- and three-pump lasers, respectively. The maximum power penalty of these multicast channels, including those overlapping with pump-pump idlers, is less than 3.5 dB. The eye diagrams of those overlapped multicast channels, however, are closed when we employ the non-loop configuration. Furthermore, our experimental results show that the Sagnac loop based configuration outperforms the simple non-loop one as there is up to 1.2 dB power penalty improvement for the multicast channels.

2. Operation principles

Figure 1(a) illustrates the operation principle of the proposed wavelength multicasting using Sagnac loop configuration. Beams from two pump lasers together with the pump amplifier ASE noise (E_P ₁, E_P2 and E_ASE) are coupled into the Sagnac loop via Input 1, while the signal (E_S) is injected into the loop via Input 2. With the FWM effect in HNLF, the clockwise and counterclockwise beams return to a 3 dB optical coupler (OC). By adjusting the polarization controller (PC) in the symmetric loop mirror, the pump beams and the ASE noise (E_P1, E_P2 and E_ASE) exit from Output 1, while the signal (E_S) leaves through Output 2. The FWM waves (E_f) leave through either Output 1 or 2, depending on their phase conjugation.

Fig. 1 Operation principle of the proposed wavelength multicasting technique using Sagnac loop configuration. HNLF: highly nonlinear fiber. PC: polarization controller. CIR: circulator.

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Using the FWM wave $ω_{P 1 P 1 S}$ as an example, the complex amplitudes of the FWM wave E_f3 and E_f4 at ports 3 and 4 after propagating through the loop can be expressed as [19]

E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{S}^{*} \exp [i (ω_{f} t + ϕ_{f})],

E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{S}^{*} \exp [i (ω_{f} t + ϕ_{f})],

where η denotes the conversion efficiency of the FWM process.

ω_{f}

and

ϕ_{f}

denote the frequency and phase of the FWM wave respectively.

When E_f3 and E_f4 interfere at ports 1 and 2, the FWM output powers P₁ (at Output 1) and P₂ (at Output 2) can be expressed as

P_{1} = \frac{| E_{f 3} - i E_{f 4} |^{2}}{2} = 0,

P_{2} = \frac{| - i E_{f 3} + E_{f 4} |^{2}}{2} = P_{F W M},

where

P_{F W M} = | E_{f 3} |^{2} + | E_{f 4} |^{2}

is the total power of the generated FWM waves. As a result, the FWM wave

ω_{P 1 P 1 S}

will leave through Output 2 and no light component will appear at Output 1.

Table 1 summarizes the phase relationship of all the FWM waves and the output ports through which they exit.

Table 1. Phase relationship of all the FWM waves and their corresponding output port.

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It is clearly shown in Table 1 that the FWM products ( $ω_{P 2 P 2 P 1}$ , $ω_{S S P 1}$ , $ω_{P 1 P 1 P 2}$ , and $ω_{S S P 2}$ ) will leave through Output 1 while the rest ( $ω_{P 2 P 2 S}$ , $ω_{P 1 P 2 S}$ , $ω_{P 2 S P 1}$ , $ω_{P 1 P 1 S}$ , and $ω_{P 1 S P 2}$ ) will leave through Output 2. Therefore, at the outputs of the multicast channels (Output 2), the pumps, pump-pump idlers, and pump amplifier ASE noise can be greatly suppressed.

In addition, as the phases of pump 1 ( $ϕ_{p 1}$ ) and pump 2 ( $ϕ_{p 2}$ ) are constant and do not carry data information, the differential phase information and the amplitude information of the input signal are preserved in the multicast channels.

3. Experimental results and discussions

Figure 2 shows the experimental setup. The signal (S) at wavelength of 1550.92 nm is first intensity modulated (IM)/phase modulated (PM) by a 10-Gb/s 2³¹-1 pseudo-random bit sequence (PRBS) data and then amplified by an erbium doped fiber amplifier (EDFA 1). After the ASE noise is filtered, the signal (around 14 dBm) is coupled into the HNLF Sagnac loop via circulator 1 (CIR 1).

Fig. 2 Experimental setup. FL: fixed wavelength laser. CIR: circulator. OSA: optical spectrum analyzer. IM: intensity modulator. PM: phase modulator. PC: polarization controller. HNLF: highly nonlinear fiber. OC: optical coupler. EDFA: erbium doped fiber amplifier. PRBS: pseudo-random bit sequence. TF: tunable filter. DI: delay interferometer. SMF: single mode fiber.

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Fixed wavelength laser (FL) 2 (at 1551.72 nm denoted as P₁), FL 3 (at 1554.12 nm denoted as P₂), and FL 4 (at 1557.32 nm denoted as P₃) are used as pumps. These three pumps are combined and then amplified by EDFA 3, which has a high saturated output power of around 32 dBm. Then, the pumps and the EDFA 3 introduced ASE noise are coupled into the HNLF loop via CIR 2.

Tunable filter (TF) 1 is used to select the desired multicast channel at port 3 of CIR 1. EDFA 2 is used to amplify the multicast channel and TF 2 is used to reject the ASE noise before the eye diagram and bit error rate (BER) are measured. In the case of DPSK, a 100-ps delay interferometer (DI) is employed to demodulate the 10-Gb/s DPSK multicast channels before the eye diagrams and BER are measured.

In our experimental setup, the nonlinear coefficient of HNLF is 11W⁻¹Km⁻¹ and the dispersion zero wavelength λ₀ is 1560 nm. The dispersion slope and the total fiber loss at λ₀ are 0.035 ps/km-nm² and 2.3 dB respectively. The coupler used has a coupling ratio of 49:51. Note that the performance degradation of Sagnac loop mirror due to coupling ratio perturbation has been well investigated [23,24].

In order to achieve the best conversion efficiency (CE) for all the multicast channels, PC 1, PC 2, PC 3, and PC 4 are adjusted to make the signal and the three pumps co-polarized with each other.

3.1 Optical wavelength multicasting with 2 pumps

At first, only FL 2 and FL 3 are turned on as pump lasers and the power of each pump after EDFA 3 is adjusted to 15.5 dBm.

The SBS threshold of the continuous wavelength (CW) laser in this 1km HNLF is around 10 dBm [25]. Taking into consideration the insertion loss at CIR 2 and 3-dB optical coupler, the effective optical power of the CW pump laser is around 11 dBm, which is just close to the threshold value. Therefore, the SBS effect on the CW pump is very small and can be neglected.

Figures 3(a) and 3(b) show the optical spectra at port 3 of CIR 1 and port 3 of CIR 2 when multicasting the OOK modulated signal. By adjusting PC 5 within the Sagnac loop mirror, the power of the two pumps as well as the P₁-P₂ generated idlers (I_P2P2P1 at 1556.52 nm and I_P1P1P2 at 1549.32 nm) can be suppressed by more than 30 dB at the output of the multicast channels [see Fig. 3(a)]. The background ASE noise is also suppressed by about 10 dB. At port 3 of CIR 2, the signal and multicast channels are suppressed significantly with a suppression ratio of about 30 dB [see Fig. 3(b)]. Due to the high level of background ASE noise, the suppressed multicast channels are not so obvious in Fig. 3(b). If a perfect 50:50 coupler is employed, a higher suppression ratio (around 40 dB) of the pumps and crosstalk is expected to be achieved [22]. Nevertheless, the suppression ratio of around 33 dB as obtained in our loop mirror is high enough to enable clear eye diagrams of the overlapped multicast channels to be observed. The ripples in Figs. 3(b) and 3(c) are due to the side modes of the distributed feedback (DFB) laser used.

Fig. 3 (a). Optical spectra at port 3 of CIR 1. (b). Optical spectra at port 3 of CIR 2. (c). Optical spectra of the non-loop configuration (at point B after passing through the HNLF).

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For the non-loop configuration, the spectra, which is measured at point B after the beams passing through HNLF (see Fig. 2), is illustrated in Fig. 3(c). It can be seen from Fig. 3(c) that the optical signal-to-noise ratio (OSNR) of the multicast channels is not as good as that of the Sagnac loop configuration [see Fig. 3(a)]. This is due to the ASE noise arising from pump amplifier and side modes from the DFB laser.

The BER performances of the OOK and DPSK multicast signals for the loop and noon-loop configurations are shown in Figs. 4(a) and 4(b). Figures 4(c) and 4(d) show their corresponding eye diagrams. Compared with the back to back (BTB) input data signal, the maximum power penalty of the six multicast signals in the Sagnac loop configuration is approximately 1.2 dB and 1.4 dB with respect to the OOK and DPSK signals. An extra power penalty of up to 1.1 dB is incurred by using the non-loop configuration compared to the loop configuration. This increased power penalty is due to the degradation of OSNR. In addition, it can be seen that the mark level of Ch3 and Ch6 is much noisier compared with other channels. The main reason is that the converted power of Ch3 and Ch6 is around 3 dB lower than that of the other channels and more noise is introduced due to the large noise figure (NF) of EDFA 2.

Fig. 4 BER curves of the BTB signal and the multicast channels and their corresponding eye diagrams. (a) and (c) for OOK signals. (b) and (d) for DPSK signals. L: Loop configuration. NL: Non-Loop configuration. Ch: channel.

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The detailed performance comparisons between the proposed Sagnac loop configuration and non-loop configuration are summarized in Table 2 . As the pumps and signal have a 3 dB coupling loss at the OC, the CE in the non-loop configuration is lower than that in the Sagnac loop configuration. There is approximately 10 dB OSNR improve in the loop configuration owing to the suppressed background ASE noise. Therefore, no filters are required to reject the pump amplifier ASE noise in the loop configuration.

Table 2. Performance comparison between the loop (L) and non-loop (NL) structures (2 Pump)

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3.2 Optical wavelength multicasting with 3 pumps

As there is a possibility that the intended multicast channel may be located at the same wavelength as the pump-pump generated idler, we turn on FL 4 to verify that our Sagnac loop configuration can indeed filter the overlapped channel. In this experiment, the power of each pump after the EDFA 3 is still maintained at 15.5 dBm.

Figures 5(a) and 5(b) show the optical spectra at port 3 of CIR 1 and port 3 of CIR 2. Figure 5(c) shows the measured spectra as the non-loop configuration. It can be seen from Fig. 5 that ten usable multicast channels have been generated by the FWM effect in the HNLF loop. Because the wavelength of the multicast channel, I_P2P2S at 1557.32 nm, is located at the same wavelength as FL 4 (P₃ at 1557.32 nm) and the power of the suppressed P₃ is still very high at the output of the multicast channels, we do not measure the BER performance and eye diagram of this channel. According to Fig. 5(c), five of the multicast channels (Ch1, Ch2, Ch6, Ch7, and Ch9) are located at the same wavelengths as the other FWM generated idlers (I_SSP2, I_P1P2P3, I_P1P3P2, I_P2P2P1, and I_P2P3P1). If we adopt the non-loop configuration, these multicast channels will not be filtered due to the in-band crosstalk. However, by using the Sagnac loop configuration, the other FWM generated idlers (I_SSP2, I_P1P2P3, I_P1P3P2, I_P2P2P1, and I_P2P3P1) will leave through port 3 of CIR 2 [see Fig. 5(b)], while the five overlapped multicast channels will leave through port 3 of CIR 1 [see Fig. 5(a)], which lead to wide openings in the eye diagrams of these overlapped channels.

Fig. 5 (a). Optical spectra at port 3 of CIR 1. (b). Optical spectra at port 3 of CIR 2. (c). Optical spectra of the non-loop configuration (at point B after passing through the HNLF).

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Figure 6 shows the BER performances and the corresponding eye diagrams of the OOK and DPSK multicast signals. It can be seen that Ch10 has the maximum power penalty due to its relatively small CE compared with the other channels. This is owing to the fact that as the frequency detuning of the signal from the pump increases, the phase mismatching parameter also increases and that leads to the poor CE [26]. If a HNLF with a smaller dispersion slope [26,27] is used, the CE of Ch10 will remain as large as that of the other channels. The power penalty of Ch10 is around 3.5 dB for OOK signal and 2.7 dB for DPSK signal in loop configuration and it increases to about 4.7 dB for OOK signal and 3.7 dB for DPSK signal in non-loop configuration. Due to the smaller CE, the overlapped Channel Ch1 has a large power penalty of about 3.4 dB for OOK signals and 2.2 dB for DPSK signals.

Fig. 6 BER curves of the BTB signal and the multicast channels and their corresponding eye diagrams. (a) and (c) for OOK signals. (b) and (d) for DPSK signals. L: Loop configuration. NL: Non-Loop configuration. Ch: channel. OL: overlapped.

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Table 3 gives the detailed performance comparisons between the loop and non-loop configuration. The reason why Ch3 has 23 dB OSNR in non-loop configuration is that the P2-P3 generated idler I_P2P2P3 is located at the same wavelength as Ch3 and introduces in-band crosstalk to Ch3. Owing to the high input signal power, the power penalty of Ch3 is approximately 0.8 dB for both OOK and DPSK signals. Moreover, it can be seen that a power penalty improvement of up to 1.2 dB can be achieved by using the loop configuration.

Table 3. Performance comparison between the loop (L) and non-loop (NL) structures with overlapped channels existing (3 pumps)

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4. Conclusion

In conclusion, we have experimentally demonstrated an all-optical modulation-transparent wavelength multicasting technique using the FWM effect in a HNLF Sagnac loop. Our proposed design overcomes the undesirable effect of pump-pump generated idlers overlapping with the multicast channels. The experimental results show that the pumps and the pump-pump idlers can be greatly suppressed by more than 30 dB at the output of the multicasting channels. The background ASE noise arising from the pump amplifier has a suppression ratio of around 10 dB. Six and ten 10-Gb/s OOK/DPSK multicast channels complying with the ITU grid have been generated by using two- and three-pump lasers. The power penalty of these multicast channels is found to be less than 3.5 dB. If we employ the non-loop configuration, the eye diagrams of the overlapped multicast channels are closed due to the in-band crosstalk arising from the pump-pump idlers. Comparing the proposed Sagnac loop configuration with the non-loop configuration, we observed that the former can achieve up to 1.2 dB improvement in power penalty. Another advantage of the proposed technique is that the pump amplifier ASE noise can be suppressed at the output of the multicast channels without the need of having an extra filter, which has the effect of not incurring the insertion loss due to the filter.

Acknowledgments

This work is supported by Singapore’s Agency for Science, Technology, and Research (A*STAR) under SERC project Grant No. 0721010019.

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FWM wave	Frequency ( $ω_{f}$ )	Phase ( $ϕ_{f}$ )	Differential Phase	E_f3 and E_f4	P_out1	P_out2
$ω_{P 2 P 2 S}$	$2 ω_{P 2} - ω_{S}$	$2 ϕ_{P 2} - ϕ_{S}$	$- ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{P 2 P 2 P 1}$	$2 ω_{P 2} - ω_{P 1}$	$2 ϕ_{P 2} - ϕ_{P 1}$	0	$E_{f 3} = - i {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0
$ω_{P 1 P 2 S}$	$\begin{array}{l} ω_{P 1} + ω_{P 2} \\ - ω_{S} \end{array}$	$\begin{array}{l} ϕ_{P 1} + ϕ_{P 2} \\ - ϕ_{S} \end{array}$	$- ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 1} E_{P 2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 1} E_{P 2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{P 2 S P 1}$	$\begin{array}{l} ω_{P 2} + ω_{S} \\ - ω_{P 1} \end{array}$	$\begin{array}{l} ϕ_{P 2} + ϕ_{S} \\ - ϕ_{P 1} \end{array}$	$ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 2} E_{S} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 2} E_{S} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{P 1 P 1 S}$	$2 ω_{P 1} - ω_{S}$	$2 ϕ_{P 1} - ϕ_{S}$	$- ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{S S P 1}$	$2 ω_{S} - ω_{P 1}$	$2 ϕ_{S} - ϕ_{P 1}$	0	$E_{f 3} = i {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = - {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0
$ω_{P 1 P 1 P 2}$	$2 ω_{P 1} - ω_{P 2}$	$2 ϕ_{P 1} - ϕ_{P 2}$	0	$E_{f 3} = - i {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0
$ω_{P 1 S P 2}$	$\begin{array}{l} ω_{P 1} + ω_{S} \\ - ω_{P 2} \end{array}$	$\begin{array}{l} ϕ_{P 1} + ϕ_{S} \\ - ϕ_{P 2} \end{array}$	$ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 1} E_{S} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 1} E_{S} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{S S P 2}$	$2 ω_{S} - ω_{P 2}$	$2 ϕ_{S} - ϕ_{P 2}$	0	$E_{f 3} = i {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = - {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0

Channels	Wavelength (nm)	L/NL	Conversion Efficiency (dB)	OSNR (dB)	Power penalty (dB)
Channels	Wavelength (nm)	L/NL	Conversion Efficiency (dB)	OSNR (dB)	OOK	DPSK
Ch 1	1548.52	L	−17	45	1	1.3
Ch 1	1548.52	NL	−21	34	1.4	1.8
Ch 2	1550.92	L		61	0.2	0.3
Ch 2	1550.92	NL		50	0.2	0.4
Ch 3	1552.52	L	−20	40	1.2	1.4
Ch 3	1552.52	NL	−23	28	2.3	1.9
Ch 4	1553.32	L	−17	43	0.7	0.9
Ch 4	1553.32	NL	−21	33	1.2	1.4
Ch 5	1554.92	L	−17	43	0.6	1.2
Ch 5	1554.92	NL	−20	33	1.3	1.8
Ch 6	1557.32	L	−20	38	1.1	1.4
Ch 6	1557.32	NL	−24	27	2.1	1.9

Channels	Wavelength (nm)	L/NL	Conversion Efficiency (dB)	OSNR (dB)	Power penalty (dB)
Channels	Wavelength (nm)	L/NL	Conversion Efficiency (dB)	OSNR (dB)	OOK	DPSK
Ch 1	1547.72	L	−25	37	3.4	2.2
Ch 1	1547.72	NL
Ch 2	1548.52	L	−18	42	1.7	1.3
Ch 2	1548.52	NL
Ch 3	1550.92	L		54	0.2	0.3
Ch 3	1550.92	NL		23	0.8	0.8
Ch 4	1552.52	L	−21	40	1.3	1.4
Ch 4	1552.52	NL	−25	27	2.4	1.8
Ch 5	1553.32	L	−18	41	0.7	1.1
Ch 5	1553.32	NL	−21	29	1.3	1.6
Ch 6	1554.92	L	−18	41	1.5	1.6
Ch 6	1554.92	NL
Ch 7	1556.52	L	−21	38	1	1.2
Ch 7	1556.52	NL
Ch 8	1558.12	L	−21	36	0.7	1.3
Ch 8	1558.12	NL	−24	25	1.4	1.9
Ch 9	1560.52	L	−21	36	1.7	1.9
Ch 9	1560.52	NL
Ch 10	1563.72	L	−28	29	3.5	2.7
Ch 10	1563.72	NL	−31	17	4.7	3.7

FWM wave	Frequency ( $ω_{f}$ )	Phase ( $ϕ_{f}$ )	Differential Phase	E_f3 and E_f4	P_out1	P_out2
$ω_{P 2 P 2 S}$	$2 ω_{P 2} - ω_{S}$	$2 ϕ_{P 2} - ϕ_{S}$	$- ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{P 2 P 2 P 1}$	$2 ω_{P 2} - ω_{P 1}$	$2 ϕ_{P 2} - ϕ_{P 1}$	0	$E_{f 3} = - i {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = {(η / 8)}^{1 / 2} E_{P 2}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0
$ω_{P 1 P 2 S}$	$\begin{array}{l} ω_{P 1} + ω_{P 2} \\ - ω_{S} \end{array}$	$\begin{array}{l} ϕ_{P 1} + ϕ_{P 2} \\ - ϕ_{S} \end{array}$	$- ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 1} E_{P 2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 1} E_{P 2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{P 2 S P 1}$	$\begin{array}{l} ω_{P 2} + ω_{S} \\ - ω_{P 1} \end{array}$	$\begin{array}{l} ϕ_{P 2} + ϕ_{S} \\ - ϕ_{P 1} \end{array}$	$ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 2} E_{S} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 2} E_{S} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{P 1 P 1 S}$	$2 ω_{P 1} - ω_{S}$	$2 ϕ_{P 1} - ϕ_{S}$	$- ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{S}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{S S P 1}$	$2 ω_{S} - ω_{P 1}$	$2 ϕ_{S} - ϕ_{P 1}$	0	$E_{f 3} = i {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = - {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 1}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0
$ω_{P 1 P 1 P 2}$	$2 ω_{P 1} - ω_{P 2}$	$2 ϕ_{P 1} - ϕ_{P 2}$	0	$E_{f 3} = - i {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = {(η / 8)}^{1 / 2} E_{P 1}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0
$ω_{P 1 S P 2}$	$\begin{array}{l} ω_{P 1} + ω_{S} \\ - ω_{P 2} \end{array}$	$\begin{array}{l} ϕ_{P 1} + ϕ_{S} \\ - ϕ_{P 2} \end{array}$	$ϕ_{S}$	$E_{f 3} = - {(η / 8)}^{1 / 2} E_{P 1} E_{S} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = i {(η / 8)}^{1 / 2} E_{P 1} E_{S} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$	0	Yes
$ω_{S S P 2}$	$2 ω_{S} - ω_{P 2}$	$2 ϕ_{S} - ϕ_{P 2}$	0	$E_{f 3} = i {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$ $E_{f 4} = - {(η / 8)}^{1 / 2} E_{S}^{2} E_{P 2}^{} \exp [i (ω_{f} t + ϕ_{f})]$	Yes	0

Channels	Wavelength (nm)	L/NL	Conversion Efficiency (dB)	OSNR (dB)	Power penalty (dB)
Channels	Wavelength (nm)	L/NL	Conversion Efficiency (dB)	OSNR (dB)	OOK	DPSK
Ch 1	1548.52	L	−17	45	1	1.3
Ch 1	1548.52	NL	−21	34	1.4	1.8
Ch 2	1550.92	L		61	0.2	0.3
Ch 2	1550.92	NL		50	0.2	0.4
Ch 3	1552.52	L	−20	40	1.2	1.4
Ch 3	1552.52	NL	−23	28	2.3	1.9
Ch 4	1553.32	L	−17	43	0.7	0.9
Ch 4	1553.32	NL	−21	33	1.2	1.4
Ch 5	1554.92	L	−17	43	0.6	1.2
Ch 5	1554.92	NL	−20	33	1.3	1.8
Ch 6	1557.32	L	−20	38	1.1	1.4
Ch 6	1557.32	NL	−24	27	2.1	1.9

All-optical modulation-transparent wavelength multicasting in a highly nonlinear fiber Sagnac loop mirror

Abstract

1. Introduction

2. Operation principles

3. Experimental results and discussions

3.1 Optical wavelength multicasting with 2 pumps

3.2 Optical wavelength multicasting with 3 pumps

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Tables (3)

Equations (4)

Optics Express