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Proposal and simulation for all-optical format conversion between differential phase-shift keying signals based on cascaded second-order nonlinearities
Optics Communications 281 (2008) 5019–5024
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Proposal and simulation for all-optical format conversion between differential phase-shift keying signals based on cascaded second-order nonlinearities Jian Wang, Junqiang Sun *, Xinliang Zhang, Deming Liu, Dexiu Huang Wuhan National Laboratory for Optoelectronics, College of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, PR China
a r t i c l e
i n f o
Article history: Received 16 April 2008 Received in revised form 22 June 2008 Accepted 22 June 2008
PACS: 42.65.k 42.65.Wi Keywords: Nonlinear optics All-optical signal processing All-optical format conversion Cascaded second-harmonic generation and difference-frequency generation (cSHG/ DFG) Cascaded sum- and difference-frequency generation (cSFG/DFG) Periodically poled lithium niobate (PPLN) Differential phase-shift keying (DPSK)
a b s t r a c t We propose and simulate simple realizations of all-optical format conversion between differential phaseshift keying (DPSK) signals based on cascaded second-order nonlinearities in a periodically poled lithium niobate (PPLN) waveguide. Four kinds of 40 Gb/s all-optical format conversion from non-return-to-zero differential phase-shift keying (NRZ-DPSK) to return-to-zero differential phase-shift keying (RZ-DPSK) are investigated based on cascaded second-harmonic generation and difference-frequency generation (cSHG/DFG) or cascaded sum- and difference-frequency generation (cSFG/DFG). The optical spectra, temporal waveforms, eye diagrams, constellation diagrams, and time-related phase distribution are analyzed, which indicate successful implementation of NRZ-DPSK-to-RZ-DPSK format conversion. The obtained results also confirm the phase preservation characteristic of PPLN. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction In future optical networks, different modulation formats may be selectively employed depending on the network scales and applications. Compared to conventional cost-effective on–off keying (OOK) modulation formats such as non-return-to-zero (NRZ) and return-to-zero (RZ), differential phase-shift keying (DPSK) modulation formats including NRZ-DPSK and RZ-DPSK are robust against fiber nonlinear effects and capable of improving the receiver sensitivity by a factor of 3 dB. Moreover, DPSK has preferably exhibited better performance than OOK for long-haul transmission systems [1]. All-optical format conversion is considered to be an important technology in all-optical signal processing to enhance the flexibility of optical networks. So far, there have been various reports on format conversion between OOK signals, especially from NRZ to RZ using semiconductor optical amplifier (SOA)-based loop mirror [2] and Mach–Zehnder interferometer (MZI) [3]. However, all-optical format conversion from NRZ-DPSK to RZ-DPSK has not yet been reported before. * Corresponding author. Tel.: +86 27 8779 2242 804; fax: +86 27 8779 2225. E-mail address: [email protected] (J. Sun). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.06.068
Recently, a promising candidate called periodically poled lithium niobate (PPLN) waveguide has attracted an increased attention in all-optical signal processing for its distinct advantages of ultrafast response, negligible spontaneous emission noise, and complete transparency to bit rate and modulation format [4]. Up to now, various PPLN-based all-optical signal processing applications have been reported showing impressive operation performance, including all-optical wavelength conversions [5–16], all-optical logic gates [17–29], all-optical format conversions [30–35], etc. We have previously suggested and numerically verified PPLN-based all-optical NRZ-to-RZ format conversion [30,31]. In this Paper, we propose and investigate simple realizations of four kinds of alloptical NRZ-DPSK-to-RZ-DPSK format conversions by using the cascaded second-order nonlinearities in a PPLN. The phase preservation characteristic of PPLN is also verified.
2. Principle of operation Fig. 1 shows the schematic diagram and illustrates the operation principle of the proposed PPLN-based NRZ-DPSK-to-RZ-DPSK format conversion. It is expected that PPLN is capable of
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Remarkably, the normalized complex amplitude of the converted idler has a linear relationship with the input signal for all the above four kinds of cSHG/DFG or cSFG/DFG processes according to Eqs. (1)–(4). The linear relationship between the idler and signal indicates that the converted idler can preserve the phase information carried by the input signal. Moreover, the optical power of the idler depends both on the input signal and pump. As a result, it is interesting to find that NRZ-DPSK signal and synchronized pump optical clock will produce RZ-DPSK idler, which corresponds to the NRZ-DPSK-to-RZ-DPSK format conversion from the signal to the idler as shown in Fig. 1f. The above four kinds of operation regimes are, respectively, referred to as schemes 1–4 for description simplicity.
PPLN
(a) DFG Signal Pump SHG (b) Idler SH
Control SFG Signal (c) Pump
Control DFG SFG Idler Signal (d) SF
DFG Idler SF
DFG Signal SFGControl Idler (e) Pump SF
Pump
3. Theoretical model and simulation results
(f) NRZ-DPSK Signal Pump RZ-DPSK Idler
NRZ-DPSK-to-RZ-DPSK 0 1 1 0
0
0
Demodulation (FDI) 1 1 0 0
Fig. 1. Schematic diagram and operation principle of PPLN-based NRZ-DPSK-to-RZDPSK format conversion.
performing all-optical format conversion from NRZ-DPSK to RZDPSK as shown in Fig. 1a. According to either cascaded second-harmonic generation and difference-frequency generation (cSHG/ DFG) or cascaded sum- and difference-frequency generation (cSFG/DFG), there exist four kinds of operation regimes for the proposed NRZ-DPSK-to-RZ-DPSK format conversion. Note that NRZDPSK signal and synchronized pump optical clock are employed in the cSHG/DFG processes, and another continuous-wave (CW) control is needed in the cSFG/DFG processes. (1) cSHG/DFG: The pump optical clock is set at the SHG quasiphase matching (QPM) wavelength of PPLN. As shown in Fig. 1b, the pump taking part in SHG is converted into second-harmonic wave, which simultaneously interacts with the signal to yield a new idler wave via DFG. Under the non-depletion approximation, the normalized complex amplitude of the idler wave (Ai) can be derived by
Ai / A2P AS
ð1Þ
where AS and AP denote the normalized complex amplitudes of the input signal and pump, respectively. (2) cSFG/DFG with SFG occurring between the signal and pump: As shown in Fig. 1c, the signal and pump participate in SFG to generate a sum-frequency wave. At the same time, the sum-frequency wave mixes with the CW control to produce a new idler wave by the subsequent DFG. We can deduce a similar expression as
Ai / AS AP AC
ð2Þ
where AC represents the normalized complex amplitude of the CW control. (3) cSFG/DFG with SFG occurring between the signal and control: As shown in Fig. 1d, we can obtain following relationship written by
Ai / AS AC AP
oAP oAP i o 2 AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jSHG1 AP ASH expðiDkSHG1 zÞ 2 2 oz ot ot ð5aÞ oASH oASH i o2 ASH 1 þ aSH ASH þ b1SH þ b2SH 2 2 oz ot ot2 i ¼ xSH jSHG1 AP AP expðiDkSHG1 zÞ 2 þ ixSH jDFG1 AS Ai expðiDkDFG1 zÞ
ð4Þ
ð5bÞ
2
oAS oAS i o AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jDFG1 Ai ASH expðiDkDFG1 zÞ 2 2 oz ot ot ð5cÞ oAi oAi i o2 Ai 1 þ b1i þ b2i 2 þ ai Ai ¼ ixi jDFG1 AS ASH expðiDkDFG1 zÞ 2 oz ot 2 ot ð5dÞ Scheme 2:
oAS oAS i o 2 AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jSFG2 AP ASF expðiDkSFG2 zÞ 2 2 oz ot ot ð6aÞ 2
oAP oAP i o AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jSFG2 AS ASF expðiDkSFG2 zÞ 2 2 oz ot ot ð6bÞ 2
oASF oASF i o ASF 1 þ aSF ASF þ b1SF þ b2SF 2 2 oz ot ot2 ¼ ixSF jSFG2 AS AP expðiDkSFG2 zÞ þ ixSF jDFG2 AC Ai expðiDkDFG2 zÞ
ð6cÞ
2
oAC oAC i o AC 1 þ b1C þ b2C 2 þ aC AC ¼ ixC jDFG2 Ai ASF expðiDkDFG2 zÞ 2 2 oz ot ot ð6dÞ
ð3Þ
(4) cSFG/DFG with SFG occurring between the pump and control: As shown in Fig. 1e, similar formula can be obtained by
Ai / AP AC AS
For the proposed four approaches (schemes 1–4) of NRZ-DPSKto-RZ-DPSK format conversion, under the slowly varying envelope approximation, where the electric field amplitude changes slowly relative to the fast optical carrier frequency, we can derive the following coupled-mode equations for scheme 1 (Eq. (5)), scheme 2 (Eq. (6)), scheme 3 (Eq. (7)), and scheme 4 (Eq. (8)) describing the well-known cSHG/DFG and cSFG/DFG processes [30,31]. Scheme 1:
2
oAi oAi i o Ai 1 þ ai Ai ¼ ixi jDFG2 AC ASF expðiDkDFG2 zÞ þ b1i þ b oz ot 2 2i ot 2 2 ð6eÞ
J. Wang et al. / Optics Communications 281 (2008) 5019–5024
Scheme 3: 2
oAS oAS i o AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jSFG3 AC ASF expðiDkSFG3 zÞ oz ot 2 2 ot ð7aÞ oAC oAC i o2 AC 1 þ b1C þ b2C 2 þ aC AC ¼ ixC jSFG3 AS ASF expðiDkSFG3 zÞ 2 2 oz ot ot ð7bÞ oASF oASF i o2 ASF 1 þ aSF ASF þ b1SF þ b2SF 2 2 oz ot ot 2 ¼ ixSF jSFG3 AS AC expðiDkSFG3 zÞ þ ixSF jDFG3 AP Ai expðiDkDFG3 zÞ
ð7cÞ
oAP oAP i o2 AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jDFG3 Ai ASF expðiDkDFG3 zÞ 2 2 oz ot ot ð7dÞ oAi oAi i o 2 Ai 1 þ ai Ai ¼ ixi jDFG3 AP ASF expðiDkDFG3 zÞ þ b1i þ b oz ot 2 2i ot2 2 ð7eÞ Scheme 4:
oAP oAP i o2 AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jSFG4 AC ASF expðiDkSFG4 zÞ 2 2 oz ot ot ð8aÞ oAC oAC i o2 AC 1 þ b1C þ b2C 2 þ aC AC ¼ ixC jSFG4 AP ASF expðiDkSFG4 zÞ 2 2 oz ot ot ð8bÞ oASF oASF i o2 ASF 1 þ aSF ASF þ b1SF þ b2SF 2 2 oz ot ot 2 ¼ ixSF jSFG4 AP AC expðiDkSFG4 zÞ þ ixSF jDFG4 AS Ai expðiDkDFG4 zÞ
ð8cÞ
2
oAS oAS i o AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jDFG4 Ai ASF expðiDkDFG4 zÞ 2 2 oz ot ot ð8dÞ oAi oAi i o 2 Ai 1 þ b1i þ b2i 2 þ ai Ai ¼ ixi jDFG4 AS ASF expðiDkDFG4 zÞ 2 oz ot 2 ot ð8eÞ Where
! ok 1 dn ; j ¼ S; P; C; SH; SF; i nj kj b1j ¼ ¼ oxx¼xj c dk k¼kj k3j d2 n o2 k b2j ¼ ¼ ; j ¼ S; P; C; SH; SF; i 2 ox 2pc2 dk2 x¼xj k¼kj sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 jSHG1 ¼ deff ; jDFG1 ¼ deff cnS ni nSH Aeff cn2P nSH Aeff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 jSFG2 ¼ deff ; jDFG2 ¼ deff cnS nP nSF Aeff cnC ni nSF Aeff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 ; jDFG3 ¼ deff jSFG3 ¼ deff cnS nC nSF Aeff cnP ni nSF Aeff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 jSFG4 ¼ deff ; jDFG4 ¼ deff cnP nC nSF Aeff cnS ni nSF Aeff 2p nSH nP 1 DkSHG1 ¼ kSH 2kP ¼ 2p 2 K kSH kP K 2p nSH nS ni 1 DkDFG1 ¼ kSH kS ki ¼ 2p K kSH kS ki K 2p nSF nS nP 1 DkSFG2 ¼ kSF kS kP ¼ 2p K kSF kS kP K 2p nSF nC ni 1 DkDFG2 ¼ kSF kC ki ¼ 2p K kSF kC ki K
ð9Þ ð10Þ
ð11Þ ð12Þ ð13Þ ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ
2p nSF nS nC 1 DkSFG3 ¼ kSF kS kC ¼ 2p K kSF kS kC K 2p nSF nP ni 1 DkDFG3 ¼ kSF kP ki ¼ 2p K kSF kP ki K 2p nSF nP nC 1 DkSFG4 ¼ kSF kP kC ¼ 2p K kSF kP kC K 2p nSF nS ni 1 DkDFG4 ¼ kSF kS ki ¼ 2p K kSF kS ki K
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ð19Þ ð20Þ ð21Þ ð22Þ
In the above equations, AS, AP, AC, ASH, ASF and Ai, as functions of the position z and time t, denote the normalized complex amplitudes of the signal, pump, control, second-harmonic wave, sumfrequency wave, and converted idler wave, respectively. b1j and b2j are the first and second derivatives of the propagation constant kj with respect to the angular frequency x, evaluated at xj (j = S, P, C, SH, SF, i). aj is the waveguide propagation loss coefficient. jSHG1, jDFG1, DkSHG1, and DkDFG1, respectively refer to the SHG coupling coefficient, DFG coupling coefficient, SHG phase mismatching, and DFG phase mismatching for scheme 1. jSFG2, jDFG2, DkSFG2, and DkDFG2, respectively denote the SFG coupling coefficient, DFG coupling coefficient, SFG phase mismatching, and DFG phase mismatching for scheme 2, while those for scheme 3 are represented by jSFG3, jDFG3, DkSFG3, and DkDFG3, and those for scheme 4 are known as jSFG4, jDFG4, DkSFG4, and DkDFG4. Aeff is the effective nonlinear interaction area. nj (j = S, P, C, SH, SF, i) are the refractive indexes for different optical waves. The parameter l0 is the permeability and c is the light velocity in vacuum. deff = d33 2/p is the effective nonlinear coefficient. K is the microdomain period of the periodically poled structure in the PPLN waveguide. The above coupled-mode Eqs. (5)–(8) can be numerically solved using the finite difference beam propagation method [10,11]. In the following simulations, a 50 mm long PPLN is assumed. It has a microdomain period of 18.8 lm and a QPM wavelength of 1543.2 nm. The waveguide propagation losses of 0.35 dB/cm in the 1.5 lm band and 0.70 dB/cm in the 0.77 lm band are considered, i.e. aS = aP = aC = ai = 0.35 dB/cm and aSH = aSF = 0.70 dB/cm. The input signal is considered as a 40 Gb/s 27 1 pseudo-random binary sequence (PRBS) NRZ-DPSK. The synchronized 40 GHz pump optical clock has a hyperbolic-secant pulse type and a 5 ps pulse width. For scheme 1, the signal (kS) and pump (kP) wavelengths are set at 1550.0 and 1543.2 nm. The signal (PS) and pump (PP) peak powers are assumed to be 100 and 200 mW. For scheme 2, kS = 1550.0 and kP = 1536.5 nm are considered to satisfy the SFG QPM condition. The CW control (kC) is tuned at 1555.0 nm. PS = 100 and PP = 200 mW are assumed. The optical power of the CW control (PC) is assumed to be 100 mW. For scheme 3, kS = 1550.0, kC = 1536.5 and kP = 1555.0 nm as well as PS = 100, PC = 100 and PP = 200 mW are considered. For scheme 4, kP = 1550.0, kC = 1536.5 and kS = 1555.0 nm together with PP = 200, PC = 100 and PS = 100 mW are assumed. Fig. 2 clearly depicts the simulation results for four kinds of NRZDPSK-to-RZ-DPSK format conversion. Fig. 2(a1) and (a2) show the optical spectra of input 40 Gb/s NRZ-DPSK signal and synchronized 40 GHz pump optical clock. Note that the signal central wavelength is changed to1555.0 nm for scheme 4, while the pump central wavelength is changed to 1543.2 nm for scheme 1, 1555.0 nm for scheme 3, and 1550.0 nm for scheme 4. Fig. 2(a3)–(a6) plot the optical spectra of the converted idler corresponding to schemes 1–4, respectively. It can be seen that the converted idler spectra are similar to the referenced RZ-DPSK spectrum as shown in Fig. 2(a7). The referenced 40 Gb/s RZ-DPSK adopted has a duty cycle of 1/3, corresponding to a pulse width of 8.33 ps. Fig. 2(b1)–(b13) and (c1)–(c12) display the temporal waveforms and eye diagrams of NRZ-DPSK-to-RZ-DPSK format conversion. It should be noted
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that Fig. 2(b2)(b5)(b7)(b9)(b11)(b13)(c2)(c4)(c6)(c8)(c10)(c12) are, respectively, the constructive demodulation output of Fig. 2(b1) (b4)(b6)(b8)(b10)(b12)(c1)(c3)(c5)(c7)(c9)(c11) by using a fiber delay interferometer (FDI) with a relative time delay of 25 ps between two fiber arms. It is found that the temporal waveforms and eye diagrams of the converted idler for schemes 1–4 as shown in Fig. 2(b4)–(b11) and (c3)–(c10) are also agreement with those of the referenced RZ-DPSK as shown in Fig. 2(b12)(b13) and (c11)(c12). Fig. 2(d1)–(d7) illustrate the constellation diagrams of different optical waves, from which it can be concluded that the constellation diagrams of the converted idler for schemes 1–4 as shown in Fig. 2(d3)–(d6) are consistent with that of the referenced RZ-DPSK as shown in Fig. 2(d7). The peak powers of the converted RZ-DPSK idlers corresponding to schemes 1–4 are calculated to be
14.43 mW, 33.17 mW, 91.85 mW, and 33.13 mW, respectively. The conversion efficiencies defined by the peak power ratio of converted RZ-DPSK idler to input NRZ-DPSK signal are therefore estimated to be 8.41 dB, 4.79 dB, 0.37 dB, and 4.80 dB for schemes 1–4, respectively. Remarkably, several interesting phenomena can be clearly seen from Fig. 2 for the proposed cSHG/DFG- or cSFG/DFG-based NRZDPSK-to-RZ-DPSK format conversion. First, according to Fig. 2(c3), (c5), and (c9), the pulses of converted RZ-DPSK idlers seem to have a broadened tail compared with the referenced RZ-DPSK as shown in Fig. 2(c11), which can be briefly explained as follows. Fig. 2(c3), (c5), and (c9), respectively, correspond to scheme 1, scheme 2, and scheme 4. For cSHG/DFG- or cSFG/DFG-based NRZ-DPSK-to-RZ-DPSK format
Fig. 2. cSHG/DFG- or cSFG/DFG-based 40 Gb/s NRZ-DPSK-to-RZ-DPSK format conversion: (a1)–(a7) optical spectra; (b1)–(b13) temporal waveforms; (c1)–(c12) eye diagrams; (d1)–(d7) constellation diagrams; (a1)(b1)(b2)(c1)(c2)(d1) NRZ-DPSK signal; (a2)(b3)(d2) pump optical clock; (a3)(b4)(b5)(c3)(c4)(d3) RZ-DPSK idler for scheme 1; (a4)(b6)(b7)(c5)(c6)(d4) RZ-DPSK idler for scheme 2; (a5)(b8)(b9)(c7)(c8)(d5) RZ-DPSK idler for scheme 3; (a6)(b10)(b11)(c9)(c10)(d6) RZ-DPSK idler for scheme 4; (a7)(b12)(b13)(c11)(c12)(d7) referenced RZ-DPSK; (b2)(b5)(b7)(b9)(b11)(b13)(c2)(c4)(c6)(c8)(c10)(c12) are, respectively, the constructive demodulation output of (b1)(b4)(b6)(b8)(b10)(b12)(c1)(c3)(c5)(c7)(c9)(c11) using an FDI.
J. Wang et al. / Optics Communications 281 (2008) 5019–5024
conversion, NRZ-DPSK signal carriers phase information with constant optical power. The control is continuous wave also with constant optical power. The pump optical clock is an ultra-short picosecond pulse train. The pump optical clock participates in the SHG process for scheme 1 and SFG process for scheme 2 and scheme 4, thus the generated second-harmonic wave for scheme 1 and sum-frequency wave for scheme 2 and scheme 4 are all optical pulses. It should be noted that there exist temporal walk-off effects between the second-harmonic wave optical pulse for scheme 1, sum-frequency wave optical pulse for scheme 2 and scheme 4 in the 0.77 lm band and the pump optical clock in the 1.5 lm band due to group-velocity mismatching. In general, the second-harmonic or sum-frequency optical pulse in the 0.77 lm band propagates slower than the pump optical clock in the 1.5 lm band. The walk-off effect causes the temporal separation between the optical pulses in the 0.77 lm band and in the 1.55 lm band, resulting in the accumulation of second-harmonic or sum-frequency optical pulse at the rear edge of pump optical clock. As a result, the generated RZ-DPSK idlers for scheme 1 (Fig. 2(c3)), scheme 2 (Fig. 2(c5)), and scheme 4 (Fig. 2(c9)) have a broadened tail which is asymmetric compared with pump optical clock and referenced RZ-DPSK as shown in Fig. 2(c11). On the contrary, for scheme 3 corresponding to cSFG/DFG with the SFG process occurring between the NRZDPSK signal and CW control, as both NRZ-DPSK signal and CW control have constant optical power, the generated sum-frequency wave in the 0.77 lm band is not optical pulse but with constant optical power. Therefore, there is negligible walk-off effect for scheme 3 and the converted RZ-DPSK idler as shown in Fig. 3(c7) experiences no broadening and distortion which is symmetric. The pulse widths of converted RZ-DPSK idlers for scheme 1–4 shown in Fig. 3(c3), (c5), (c7), and (c9) are calculated to be 6.35 ps, 7.91 ps, 4.98 ps, and 7.81 ps, respectively. It is apparent that RZ-DPSK idlers for scheme 1, scheme 2, and scheme 4 are slightly broadened compared with pump optical clock (5 ps), while the RZ-DPSK idler for scheme 3 has almost the same pulse width as the pump optical clock. It is reasonable to give a suggested order of
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superiority in schemes 1–4 as ‘‘scheme 3 > scheme 1 > scheme 4 > scheme 2”, according to the pulse widths of converted idlers for schemes 1–4 (4.98 ps < 6.35 ps < 7.81 ps < 7.91 ps). Second, it is interesting to find that the optical phases of converted RZ-DPSK idlers shown in Fig. 2(d3), (d4), (d5), and (d6) seem to slightly shift compared with input NRZ-DPSK signal shown in Fig. 2(d1). The possible explanation can be found as follows. For cSHG/DFG processes (scheme 1), the DFG process is slightly phase mismatched (DkDFG1 6¼ 0) as the SHG process is perfectly phase matched (DkSHG1 = 0). Similarly, for cSFG/DFG processes (schemes 2–4), the DFG process is also slightly phase mismatched (DkDFG2 6¼ 0, DkDFG3 6¼ 0, DkDFG4 6¼ 0) as the SFG process is perfectly phase matched (DkSFG2 = 0, DkSFG3 = 0, DkSFG4 = 0). It is well known that the phase mismatching in the cascaded second-order nonlinear interactions will induce nonlinear phase shift. Therefore, the slight phase mismatching of the DFG process in cSHG/DFG (scheme 1) or in cSFG/DFG (schemes 2–4) will cause nonlinear phase shift. As a result, the optical phases of the converted RZ-DPSK idlers shown in Fig. 2(d3), (d4), (d5), and (d6) corresponding to schemes 1–4 are slightly shifted compared with input NRZ-DPSK signal shown in Fig. 2(d1). To further verify the explanation, Fig. 3 depicts the constellation diagrams of converted RZ-DPSK idlers on the mandatory assumption that the DFG process in schemes 1–4 is also phase matched (DkDFG1 = DkDFG2 = DkDFG3 = DkDFG4 = 0). As can be clearly seen from Fig. 3a–d, it is found that there is no phase shift. As a matter of fact, the DFG process is always slightly phase mismatched in cSHG/DFG or cSFG/DFG when SHG or SFG is phase matched, thus slight phase shift is introduced as shown in Fig. 2(d3), (d4), (d5), and (d6). Note that the slight phase shift actually does not affect the NRZ-DPSK-to-RZ-DPSK format conversion. In fact, the nonlinear phase shift due to DFG phase mismatching only causes the absolute phase shift. For RZ-DPSK modulation format, the phase information only depends on the relative phase shift. The absolute shift of optical phase does not affect the relative phase shift. As shown in Fig. 2(d3), (d4), (d5), and (d6), in spite of the absolute shift of optical phase, the relative phase shift is still kept to be binary values of ‘‘0” and ‘‘p ” which does not affect the implementation of NRZ-DPSK-to-RZ-DPSK format conversion. To further confirm the successful realization of NRZ-DPSK-toRZ-DPSK format conversion, the phase distribution with respect to the time scale is also analyzed as shown in Fig. 4. It can be clearly seen that the converted idlers for schemes 1–4 as shown in Fig. 4b–e have the inverse phase distribution as the input NRZ-DPSK signal as shown in Fig. 4a. Such interesting phenomenon can easily be ascribed to the minus sign () in Eqs. (1)–(4). As the data information in DPSK is represented by the relative phase change between consecutive data bits, it is verified that the phase distribution of the converted idlers for schemes 1–4 accords well with that of the input NRZ-DPSK signal. In other words, the converted idler successfully preserves the phase information of the input signal. Note that all the obtained optical spectra, temporal waveforms, eye diagrams, and phase distribution in Figs. 2 and 4 for NRZ-DPSK and RZ-DPSK are in accordance with those presented in [36].
4. Discussion
Fig. 3. Constellation diagrams of converted RZ-DPSK idlers on the mandatory assumption that the DFG process for schemes 1–4 is also phase matched (DkDFG1 = DkDFG2 = DkDFG3 = DkDFG4 = 0) as the SHG or SFG in cSHG/DFG or cSFG/ DFG is phase matched. (DkSHG1 ¼ 0; DkSFG2 ¼ 0; DkSFG3 ¼ 0; DkSFG4 ¼ 0). (a) Scheme 1; (b) scheme 2; (c) scheme 3; (d) scheme 4.
With further improvement, scheme 1 can also perform simultaneous multi-channel NRZ-DPSK-to-RZ-DPSK format conversion, i.e. n-channel NRZ-DPSK signals and one-channel pump optical clock produce n-channel RZ-DPSK idlers. Scheme 2 also has the potential to realize channel-selective and multicasting NRZ-DPSK-to-RZDPSK format conversions. For channel-selective format conversion, multi-channel NRZ-DPSK signals are employed. Due to the limitation of the SFG QPM condition, only one-channel NRZ-DPSK signal
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temporal waveforms, eye diagrams, constellation diagrams, and phase distribution are studied in detail to confirm the successful realization of NRZ-DPSK-to-RZ-DPSK format conversion. In addition, it is worth noting that simultaneous multi-channel format conversion, channel-selective format conversion, and multicasting format conversion can all potentially be implemented with the proposed schemes. Acknowledgements This research was supported by the National Natural Science Foundation of China under Grant No. 60577006, and by the program for New Century Excellent Talents in University (NCET-040694). References
Fig. 4. Phase distribution with respect to the time scale: (a) input NRZ-DPSK signal; (b) converted RZ-DPSK idler for scheme 1; (c) converted RZ-DPSK idler for scheme 2; (d) converted RZ-DPSK idler for scheme 3; (e) converted RZ-DPSK idler for scheme 4.
can be selected and converted to the corresponding RZ-DPSK idler simply by properly adjusting the pump wavelength. For multicasting format conversion, one-channel NRZ-DPSK signal, one-channel pump optical clock, and multiple CW controls generate multichannel RZ-DPSK idlers. Scheme 3 also enables channel-selective and multicasting NRZ-DPSK-to-RZ-DPSK format conversions. However, the selected signal channel is determined by the CW control wavelength for channel-selective format conversion, while multiple pumps are required for multicasting format conversion. Scheme 4 also provides the possibility of simultaneous multi-channel format conversion similar to scheme 1. Moreover, the pump and control wavelengths can be set apart from both input signal and converted idler, thus none of the communication channels is occupied. Note that it is preferable to select proper scheme according to the requirement of practical applications. In addition to NRZDPSK-to-RZ-DPSK format conversion, it is also possible to further perform other PPLN-based advanced all-optical format conversions, including NRZ-to-CSRZ, RZ-to-CSRZ, CSRZ-to-RZ, NRZDPSK-to-CSRZ-DPSK, and RZ-DPSK-to-CSRZ-DPSK [35,37]. All these potential functions are attractive for effectively enhancing the flexibility of optical networks. 5. Conclusion In conclusion, four kinds of all-optical NRZ-DPSK-to-RZ-DPSK format conversion at 40 Gb/s are proposed and simulated by using cSHG/DFG or cSFG/DFG in a PPLN waveguide. The optical spectra,
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Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Proposal and simulation for all-optical format conversion between differential phase-shift keying signals based on cascaded second-order nonlinearities Jian Wang, Junqiang Sun *, Xinliang Zhang, Deming Liu, Dexiu Huang Wuhan National Laboratory for Optoelectronics, College of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, PR China
a r t i c l e
i n f o
Article history: Received 16 April 2008 Received in revised form 22 June 2008 Accepted 22 June 2008
PACS: 42.65.k 42.65.Wi Keywords: Nonlinear optics All-optical signal processing All-optical format conversion Cascaded second-harmonic generation and difference-frequency generation (cSHG/ DFG) Cascaded sum- and difference-frequency generation (cSFG/DFG) Periodically poled lithium niobate (PPLN) Differential phase-shift keying (DPSK)
a b s t r a c t We propose and simulate simple realizations of all-optical format conversion between differential phaseshift keying (DPSK) signals based on cascaded second-order nonlinearities in a periodically poled lithium niobate (PPLN) waveguide. Four kinds of 40 Gb/s all-optical format conversion from non-return-to-zero differential phase-shift keying (NRZ-DPSK) to return-to-zero differential phase-shift keying (RZ-DPSK) are investigated based on cascaded second-harmonic generation and difference-frequency generation (cSHG/DFG) or cascaded sum- and difference-frequency generation (cSFG/DFG). The optical spectra, temporal waveforms, eye diagrams, constellation diagrams, and time-related phase distribution are analyzed, which indicate successful implementation of NRZ-DPSK-to-RZ-DPSK format conversion. The obtained results also confirm the phase preservation characteristic of PPLN. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction In future optical networks, different modulation formats may be selectively employed depending on the network scales and applications. Compared to conventional cost-effective on–off keying (OOK) modulation formats such as non-return-to-zero (NRZ) and return-to-zero (RZ), differential phase-shift keying (DPSK) modulation formats including NRZ-DPSK and RZ-DPSK are robust against fiber nonlinear effects and capable of improving the receiver sensitivity by a factor of 3 dB. Moreover, DPSK has preferably exhibited better performance than OOK for long-haul transmission systems [1]. All-optical format conversion is considered to be an important technology in all-optical signal processing to enhance the flexibility of optical networks. So far, there have been various reports on format conversion between OOK signals, especially from NRZ to RZ using semiconductor optical amplifier (SOA)-based loop mirror [2] and Mach–Zehnder interferometer (MZI) [3]. However, all-optical format conversion from NRZ-DPSK to RZ-DPSK has not yet been reported before. * Corresponding author. Tel.: +86 27 8779 2242 804; fax: +86 27 8779 2225. E-mail address: [email protected] (J. Sun). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.06.068
Recently, a promising candidate called periodically poled lithium niobate (PPLN) waveguide has attracted an increased attention in all-optical signal processing for its distinct advantages of ultrafast response, negligible spontaneous emission noise, and complete transparency to bit rate and modulation format [4]. Up to now, various PPLN-based all-optical signal processing applications have been reported showing impressive operation performance, including all-optical wavelength conversions [5–16], all-optical logic gates [17–29], all-optical format conversions [30–35], etc. We have previously suggested and numerically verified PPLN-based all-optical NRZ-to-RZ format conversion [30,31]. In this Paper, we propose and investigate simple realizations of four kinds of alloptical NRZ-DPSK-to-RZ-DPSK format conversions by using the cascaded second-order nonlinearities in a PPLN. The phase preservation characteristic of PPLN is also verified.
2. Principle of operation Fig. 1 shows the schematic diagram and illustrates the operation principle of the proposed PPLN-based NRZ-DPSK-to-RZ-DPSK format conversion. It is expected that PPLN is capable of
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Remarkably, the normalized complex amplitude of the converted idler has a linear relationship with the input signal for all the above four kinds of cSHG/DFG or cSFG/DFG processes according to Eqs. (1)–(4). The linear relationship between the idler and signal indicates that the converted idler can preserve the phase information carried by the input signal. Moreover, the optical power of the idler depends both on the input signal and pump. As a result, it is interesting to find that NRZ-DPSK signal and synchronized pump optical clock will produce RZ-DPSK idler, which corresponds to the NRZ-DPSK-to-RZ-DPSK format conversion from the signal to the idler as shown in Fig. 1f. The above four kinds of operation regimes are, respectively, referred to as schemes 1–4 for description simplicity.
PPLN
(a) DFG Signal Pump SHG (b) Idler SH
Control SFG Signal (c) Pump
Control DFG SFG Idler Signal (d) SF
DFG Idler SF
DFG Signal SFGControl Idler (e) Pump SF
Pump
3. Theoretical model and simulation results
(f) NRZ-DPSK Signal Pump RZ-DPSK Idler
NRZ-DPSK-to-RZ-DPSK 0 1 1 0
0
0
Demodulation (FDI) 1 1 0 0
Fig. 1. Schematic diagram and operation principle of PPLN-based NRZ-DPSK-to-RZDPSK format conversion.
performing all-optical format conversion from NRZ-DPSK to RZDPSK as shown in Fig. 1a. According to either cascaded second-harmonic generation and difference-frequency generation (cSHG/ DFG) or cascaded sum- and difference-frequency generation (cSFG/DFG), there exist four kinds of operation regimes for the proposed NRZ-DPSK-to-RZ-DPSK format conversion. Note that NRZDPSK signal and synchronized pump optical clock are employed in the cSHG/DFG processes, and another continuous-wave (CW) control is needed in the cSFG/DFG processes. (1) cSHG/DFG: The pump optical clock is set at the SHG quasiphase matching (QPM) wavelength of PPLN. As shown in Fig. 1b, the pump taking part in SHG is converted into second-harmonic wave, which simultaneously interacts with the signal to yield a new idler wave via DFG. Under the non-depletion approximation, the normalized complex amplitude of the idler wave (Ai) can be derived by
Ai / A2P AS
ð1Þ
where AS and AP denote the normalized complex amplitudes of the input signal and pump, respectively. (2) cSFG/DFG with SFG occurring between the signal and pump: As shown in Fig. 1c, the signal and pump participate in SFG to generate a sum-frequency wave. At the same time, the sum-frequency wave mixes with the CW control to produce a new idler wave by the subsequent DFG. We can deduce a similar expression as
Ai / AS AP AC
ð2Þ
where AC represents the normalized complex amplitude of the CW control. (3) cSFG/DFG with SFG occurring between the signal and control: As shown in Fig. 1d, we can obtain following relationship written by
Ai / AS AC AP
oAP oAP i o 2 AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jSHG1 AP ASH expðiDkSHG1 zÞ 2 2 oz ot ot ð5aÞ oASH oASH i o2 ASH 1 þ aSH ASH þ b1SH þ b2SH 2 2 oz ot ot2 i ¼ xSH jSHG1 AP AP expðiDkSHG1 zÞ 2 þ ixSH jDFG1 AS Ai expðiDkDFG1 zÞ
ð4Þ
ð5bÞ
2
oAS oAS i o AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jDFG1 Ai ASH expðiDkDFG1 zÞ 2 2 oz ot ot ð5cÞ oAi oAi i o2 Ai 1 þ b1i þ b2i 2 þ ai Ai ¼ ixi jDFG1 AS ASH expðiDkDFG1 zÞ 2 oz ot 2 ot ð5dÞ Scheme 2:
oAS oAS i o 2 AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jSFG2 AP ASF expðiDkSFG2 zÞ 2 2 oz ot ot ð6aÞ 2
oAP oAP i o AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jSFG2 AS ASF expðiDkSFG2 zÞ 2 2 oz ot ot ð6bÞ 2
oASF oASF i o ASF 1 þ aSF ASF þ b1SF þ b2SF 2 2 oz ot ot2 ¼ ixSF jSFG2 AS AP expðiDkSFG2 zÞ þ ixSF jDFG2 AC Ai expðiDkDFG2 zÞ
ð6cÞ
2
oAC oAC i o AC 1 þ b1C þ b2C 2 þ aC AC ¼ ixC jDFG2 Ai ASF expðiDkDFG2 zÞ 2 2 oz ot ot ð6dÞ
ð3Þ
(4) cSFG/DFG with SFG occurring between the pump and control: As shown in Fig. 1e, similar formula can be obtained by
Ai / AP AC AS
For the proposed four approaches (schemes 1–4) of NRZ-DPSKto-RZ-DPSK format conversion, under the slowly varying envelope approximation, where the electric field amplitude changes slowly relative to the fast optical carrier frequency, we can derive the following coupled-mode equations for scheme 1 (Eq. (5)), scheme 2 (Eq. (6)), scheme 3 (Eq. (7)), and scheme 4 (Eq. (8)) describing the well-known cSHG/DFG and cSFG/DFG processes [30,31]. Scheme 1:
2
oAi oAi i o Ai 1 þ ai Ai ¼ ixi jDFG2 AC ASF expðiDkDFG2 zÞ þ b1i þ b oz ot 2 2i ot 2 2 ð6eÞ
J. Wang et al. / Optics Communications 281 (2008) 5019–5024
Scheme 3: 2
oAS oAS i o AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jSFG3 AC ASF expðiDkSFG3 zÞ oz ot 2 2 ot ð7aÞ oAC oAC i o2 AC 1 þ b1C þ b2C 2 þ aC AC ¼ ixC jSFG3 AS ASF expðiDkSFG3 zÞ 2 2 oz ot ot ð7bÞ oASF oASF i o2 ASF 1 þ aSF ASF þ b1SF þ b2SF 2 2 oz ot ot 2 ¼ ixSF jSFG3 AS AC expðiDkSFG3 zÞ þ ixSF jDFG3 AP Ai expðiDkDFG3 zÞ
ð7cÞ
oAP oAP i o2 AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jDFG3 Ai ASF expðiDkDFG3 zÞ 2 2 oz ot ot ð7dÞ oAi oAi i o 2 Ai 1 þ ai Ai ¼ ixi jDFG3 AP ASF expðiDkDFG3 zÞ þ b1i þ b oz ot 2 2i ot2 2 ð7eÞ Scheme 4:
oAP oAP i o2 AP 1 þ b1P þ b2P 2 þ aP AP ¼ ixP jSFG4 AC ASF expðiDkSFG4 zÞ 2 2 oz ot ot ð8aÞ oAC oAC i o2 AC 1 þ b1C þ b2C 2 þ aC AC ¼ ixC jSFG4 AP ASF expðiDkSFG4 zÞ 2 2 oz ot ot ð8bÞ oASF oASF i o2 ASF 1 þ aSF ASF þ b1SF þ b2SF 2 2 oz ot ot 2 ¼ ixSF jSFG4 AP AC expðiDkSFG4 zÞ þ ixSF jDFG4 AS Ai expðiDkDFG4 zÞ
ð8cÞ
2
oAS oAS i o AS 1 þ b1S þ b2S 2 þ aS AS ¼ ixS jDFG4 Ai ASF expðiDkDFG4 zÞ 2 2 oz ot ot ð8dÞ oAi oAi i o 2 Ai 1 þ b1i þ b2i 2 þ ai Ai ¼ ixi jDFG4 AS ASF expðiDkDFG4 zÞ 2 oz ot 2 ot ð8eÞ Where
! ok 1 dn ; j ¼ S; P; C; SH; SF; i nj kj b1j ¼ ¼ oxx¼xj c dk k¼kj k3j d2 n o2 k b2j ¼ ¼ ; j ¼ S; P; C; SH; SF; i 2 ox 2pc2 dk2 x¼xj k¼kj sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 jSHG1 ¼ deff ; jDFG1 ¼ deff cnS ni nSH Aeff cn2P nSH Aeff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 jSFG2 ¼ deff ; jDFG2 ¼ deff cnS nP nSF Aeff cnC ni nSF Aeff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 ; jDFG3 ¼ deff jSFG3 ¼ deff cnS nC nSF Aeff cnP ni nSF Aeff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2l0 2l0 jSFG4 ¼ deff ; jDFG4 ¼ deff cnP nC nSF Aeff cnS ni nSF Aeff 2p nSH nP 1 DkSHG1 ¼ kSH 2kP ¼ 2p 2 K kSH kP K 2p nSH nS ni 1 DkDFG1 ¼ kSH kS ki ¼ 2p K kSH kS ki K 2p nSF nS nP 1 DkSFG2 ¼ kSF kS kP ¼ 2p K kSF kS kP K 2p nSF nC ni 1 DkDFG2 ¼ kSF kC ki ¼ 2p K kSF kC ki K
ð9Þ ð10Þ
ð11Þ ð12Þ ð13Þ ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ
2p nSF nS nC 1 DkSFG3 ¼ kSF kS kC ¼ 2p K kSF kS kC K 2p nSF nP ni 1 DkDFG3 ¼ kSF kP ki ¼ 2p K kSF kP ki K 2p nSF nP nC 1 DkSFG4 ¼ kSF kP kC ¼ 2p K kSF kP kC K 2p nSF nS ni 1 DkDFG4 ¼ kSF kS ki ¼ 2p K kSF kS ki K
5021
ð19Þ ð20Þ ð21Þ ð22Þ
In the above equations, AS, AP, AC, ASH, ASF and Ai, as functions of the position z and time t, denote the normalized complex amplitudes of the signal, pump, control, second-harmonic wave, sumfrequency wave, and converted idler wave, respectively. b1j and b2j are the first and second derivatives of the propagation constant kj with respect to the angular frequency x, evaluated at xj (j = S, P, C, SH, SF, i). aj is the waveguide propagation loss coefficient. jSHG1, jDFG1, DkSHG1, and DkDFG1, respectively refer to the SHG coupling coefficient, DFG coupling coefficient, SHG phase mismatching, and DFG phase mismatching for scheme 1. jSFG2, jDFG2, DkSFG2, and DkDFG2, respectively denote the SFG coupling coefficient, DFG coupling coefficient, SFG phase mismatching, and DFG phase mismatching for scheme 2, while those for scheme 3 are represented by jSFG3, jDFG3, DkSFG3, and DkDFG3, and those for scheme 4 are known as jSFG4, jDFG4, DkSFG4, and DkDFG4. Aeff is the effective nonlinear interaction area. nj (j = S, P, C, SH, SF, i) are the refractive indexes for different optical waves. The parameter l0 is the permeability and c is the light velocity in vacuum. deff = d33 2/p is the effective nonlinear coefficient. K is the microdomain period of the periodically poled structure in the PPLN waveguide. The above coupled-mode Eqs. (5)–(8) can be numerically solved using the finite difference beam propagation method [10,11]. In the following simulations, a 50 mm long PPLN is assumed. It has a microdomain period of 18.8 lm and a QPM wavelength of 1543.2 nm. The waveguide propagation losses of 0.35 dB/cm in the 1.5 lm band and 0.70 dB/cm in the 0.77 lm band are considered, i.e. aS = aP = aC = ai = 0.35 dB/cm and aSH = aSF = 0.70 dB/cm. The input signal is considered as a 40 Gb/s 27 1 pseudo-random binary sequence (PRBS) NRZ-DPSK. The synchronized 40 GHz pump optical clock has a hyperbolic-secant pulse type and a 5 ps pulse width. For scheme 1, the signal (kS) and pump (kP) wavelengths are set at 1550.0 and 1543.2 nm. The signal (PS) and pump (PP) peak powers are assumed to be 100 and 200 mW. For scheme 2, kS = 1550.0 and kP = 1536.5 nm are considered to satisfy the SFG QPM condition. The CW control (kC) is tuned at 1555.0 nm. PS = 100 and PP = 200 mW are assumed. The optical power of the CW control (PC) is assumed to be 100 mW. For scheme 3, kS = 1550.0, kC = 1536.5 and kP = 1555.0 nm as well as PS = 100, PC = 100 and PP = 200 mW are considered. For scheme 4, kP = 1550.0, kC = 1536.5 and kS = 1555.0 nm together with PP = 200, PC = 100 and PS = 100 mW are assumed. Fig. 2 clearly depicts the simulation results for four kinds of NRZDPSK-to-RZ-DPSK format conversion. Fig. 2(a1) and (a2) show the optical spectra of input 40 Gb/s NRZ-DPSK signal and synchronized 40 GHz pump optical clock. Note that the signal central wavelength is changed to1555.0 nm for scheme 4, while the pump central wavelength is changed to 1543.2 nm for scheme 1, 1555.0 nm for scheme 3, and 1550.0 nm for scheme 4. Fig. 2(a3)–(a6) plot the optical spectra of the converted idler corresponding to schemes 1–4, respectively. It can be seen that the converted idler spectra are similar to the referenced RZ-DPSK spectrum as shown in Fig. 2(a7). The referenced 40 Gb/s RZ-DPSK adopted has a duty cycle of 1/3, corresponding to a pulse width of 8.33 ps. Fig. 2(b1)–(b13) and (c1)–(c12) display the temporal waveforms and eye diagrams of NRZ-DPSK-to-RZ-DPSK format conversion. It should be noted
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that Fig. 2(b2)(b5)(b7)(b9)(b11)(b13)(c2)(c4)(c6)(c8)(c10)(c12) are, respectively, the constructive demodulation output of Fig. 2(b1) (b4)(b6)(b8)(b10)(b12)(c1)(c3)(c5)(c7)(c9)(c11) by using a fiber delay interferometer (FDI) with a relative time delay of 25 ps between two fiber arms. It is found that the temporal waveforms and eye diagrams of the converted idler for schemes 1–4 as shown in Fig. 2(b4)–(b11) and (c3)–(c10) are also agreement with those of the referenced RZ-DPSK as shown in Fig. 2(b12)(b13) and (c11)(c12). Fig. 2(d1)–(d7) illustrate the constellation diagrams of different optical waves, from which it can be concluded that the constellation diagrams of the converted idler for schemes 1–4 as shown in Fig. 2(d3)–(d6) are consistent with that of the referenced RZ-DPSK as shown in Fig. 2(d7). The peak powers of the converted RZ-DPSK idlers corresponding to schemes 1–4 are calculated to be
14.43 mW, 33.17 mW, 91.85 mW, and 33.13 mW, respectively. The conversion efficiencies defined by the peak power ratio of converted RZ-DPSK idler to input NRZ-DPSK signal are therefore estimated to be 8.41 dB, 4.79 dB, 0.37 dB, and 4.80 dB for schemes 1–4, respectively. Remarkably, several interesting phenomena can be clearly seen from Fig. 2 for the proposed cSHG/DFG- or cSFG/DFG-based NRZDPSK-to-RZ-DPSK format conversion. First, according to Fig. 2(c3), (c5), and (c9), the pulses of converted RZ-DPSK idlers seem to have a broadened tail compared with the referenced RZ-DPSK as shown in Fig. 2(c11), which can be briefly explained as follows. Fig. 2(c3), (c5), and (c9), respectively, correspond to scheme 1, scheme 2, and scheme 4. For cSHG/DFG- or cSFG/DFG-based NRZ-DPSK-to-RZ-DPSK format
Fig. 2. cSHG/DFG- or cSFG/DFG-based 40 Gb/s NRZ-DPSK-to-RZ-DPSK format conversion: (a1)–(a7) optical spectra; (b1)–(b13) temporal waveforms; (c1)–(c12) eye diagrams; (d1)–(d7) constellation diagrams; (a1)(b1)(b2)(c1)(c2)(d1) NRZ-DPSK signal; (a2)(b3)(d2) pump optical clock; (a3)(b4)(b5)(c3)(c4)(d3) RZ-DPSK idler for scheme 1; (a4)(b6)(b7)(c5)(c6)(d4) RZ-DPSK idler for scheme 2; (a5)(b8)(b9)(c7)(c8)(d5) RZ-DPSK idler for scheme 3; (a6)(b10)(b11)(c9)(c10)(d6) RZ-DPSK idler for scheme 4; (a7)(b12)(b13)(c11)(c12)(d7) referenced RZ-DPSK; (b2)(b5)(b7)(b9)(b11)(b13)(c2)(c4)(c6)(c8)(c10)(c12) are, respectively, the constructive demodulation output of (b1)(b4)(b6)(b8)(b10)(b12)(c1)(c3)(c5)(c7)(c9)(c11) using an FDI.
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conversion, NRZ-DPSK signal carriers phase information with constant optical power. The control is continuous wave also with constant optical power. The pump optical clock is an ultra-short picosecond pulse train. The pump optical clock participates in the SHG process for scheme 1 and SFG process for scheme 2 and scheme 4, thus the generated second-harmonic wave for scheme 1 and sum-frequency wave for scheme 2 and scheme 4 are all optical pulses. It should be noted that there exist temporal walk-off effects between the second-harmonic wave optical pulse for scheme 1, sum-frequency wave optical pulse for scheme 2 and scheme 4 in the 0.77 lm band and the pump optical clock in the 1.5 lm band due to group-velocity mismatching. In general, the second-harmonic or sum-frequency optical pulse in the 0.77 lm band propagates slower than the pump optical clock in the 1.5 lm band. The walk-off effect causes the temporal separation between the optical pulses in the 0.77 lm band and in the 1.55 lm band, resulting in the accumulation of second-harmonic or sum-frequency optical pulse at the rear edge of pump optical clock. As a result, the generated RZ-DPSK idlers for scheme 1 (Fig. 2(c3)), scheme 2 (Fig. 2(c5)), and scheme 4 (Fig. 2(c9)) have a broadened tail which is asymmetric compared with pump optical clock and referenced RZ-DPSK as shown in Fig. 2(c11). On the contrary, for scheme 3 corresponding to cSFG/DFG with the SFG process occurring between the NRZDPSK signal and CW control, as both NRZ-DPSK signal and CW control have constant optical power, the generated sum-frequency wave in the 0.77 lm band is not optical pulse but with constant optical power. Therefore, there is negligible walk-off effect for scheme 3 and the converted RZ-DPSK idler as shown in Fig. 3(c7) experiences no broadening and distortion which is symmetric. The pulse widths of converted RZ-DPSK idlers for scheme 1–4 shown in Fig. 3(c3), (c5), (c7), and (c9) are calculated to be 6.35 ps, 7.91 ps, 4.98 ps, and 7.81 ps, respectively. It is apparent that RZ-DPSK idlers for scheme 1, scheme 2, and scheme 4 are slightly broadened compared with pump optical clock (5 ps), while the RZ-DPSK idler for scheme 3 has almost the same pulse width as the pump optical clock. It is reasonable to give a suggested order of
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superiority in schemes 1–4 as ‘‘scheme 3 > scheme 1 > scheme 4 > scheme 2”, according to the pulse widths of converted idlers for schemes 1–4 (4.98 ps < 6.35 ps < 7.81 ps < 7.91 ps). Second, it is interesting to find that the optical phases of converted RZ-DPSK idlers shown in Fig. 2(d3), (d4), (d5), and (d6) seem to slightly shift compared with input NRZ-DPSK signal shown in Fig. 2(d1). The possible explanation can be found as follows. For cSHG/DFG processes (scheme 1), the DFG process is slightly phase mismatched (DkDFG1 6¼ 0) as the SHG process is perfectly phase matched (DkSHG1 = 0). Similarly, for cSFG/DFG processes (schemes 2–4), the DFG process is also slightly phase mismatched (DkDFG2 6¼ 0, DkDFG3 6¼ 0, DkDFG4 6¼ 0) as the SFG process is perfectly phase matched (DkSFG2 = 0, DkSFG3 = 0, DkSFG4 = 0). It is well known that the phase mismatching in the cascaded second-order nonlinear interactions will induce nonlinear phase shift. Therefore, the slight phase mismatching of the DFG process in cSHG/DFG (scheme 1) or in cSFG/DFG (schemes 2–4) will cause nonlinear phase shift. As a result, the optical phases of the converted RZ-DPSK idlers shown in Fig. 2(d3), (d4), (d5), and (d6) corresponding to schemes 1–4 are slightly shifted compared with input NRZ-DPSK signal shown in Fig. 2(d1). To further verify the explanation, Fig. 3 depicts the constellation diagrams of converted RZ-DPSK idlers on the mandatory assumption that the DFG process in schemes 1–4 is also phase matched (DkDFG1 = DkDFG2 = DkDFG3 = DkDFG4 = 0). As can be clearly seen from Fig. 3a–d, it is found that there is no phase shift. As a matter of fact, the DFG process is always slightly phase mismatched in cSHG/DFG or cSFG/DFG when SHG or SFG is phase matched, thus slight phase shift is introduced as shown in Fig. 2(d3), (d4), (d5), and (d6). Note that the slight phase shift actually does not affect the NRZ-DPSK-to-RZ-DPSK format conversion. In fact, the nonlinear phase shift due to DFG phase mismatching only causes the absolute phase shift. For RZ-DPSK modulation format, the phase information only depends on the relative phase shift. The absolute shift of optical phase does not affect the relative phase shift. As shown in Fig. 2(d3), (d4), (d5), and (d6), in spite of the absolute shift of optical phase, the relative phase shift is still kept to be binary values of ‘‘0” and ‘‘p ” which does not affect the implementation of NRZ-DPSK-to-RZ-DPSK format conversion. To further confirm the successful realization of NRZ-DPSK-toRZ-DPSK format conversion, the phase distribution with respect to the time scale is also analyzed as shown in Fig. 4. It can be clearly seen that the converted idlers for schemes 1–4 as shown in Fig. 4b–e have the inverse phase distribution as the input NRZ-DPSK signal as shown in Fig. 4a. Such interesting phenomenon can easily be ascribed to the minus sign () in Eqs. (1)–(4). As the data information in DPSK is represented by the relative phase change between consecutive data bits, it is verified that the phase distribution of the converted idlers for schemes 1–4 accords well with that of the input NRZ-DPSK signal. In other words, the converted idler successfully preserves the phase information of the input signal. Note that all the obtained optical spectra, temporal waveforms, eye diagrams, and phase distribution in Figs. 2 and 4 for NRZ-DPSK and RZ-DPSK are in accordance with those presented in [36].
4. Discussion
Fig. 3. Constellation diagrams of converted RZ-DPSK idlers on the mandatory assumption that the DFG process for schemes 1–4 is also phase matched (DkDFG1 = DkDFG2 = DkDFG3 = DkDFG4 = 0) as the SHG or SFG in cSHG/DFG or cSFG/ DFG is phase matched. (DkSHG1 ¼ 0; DkSFG2 ¼ 0; DkSFG3 ¼ 0; DkSFG4 ¼ 0). (a) Scheme 1; (b) scheme 2; (c) scheme 3; (d) scheme 4.
With further improvement, scheme 1 can also perform simultaneous multi-channel NRZ-DPSK-to-RZ-DPSK format conversion, i.e. n-channel NRZ-DPSK signals and one-channel pump optical clock produce n-channel RZ-DPSK idlers. Scheme 2 also has the potential to realize channel-selective and multicasting NRZ-DPSK-to-RZDPSK format conversions. For channel-selective format conversion, multi-channel NRZ-DPSK signals are employed. Due to the limitation of the SFG QPM condition, only one-channel NRZ-DPSK signal
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temporal waveforms, eye diagrams, constellation diagrams, and phase distribution are studied in detail to confirm the successful realization of NRZ-DPSK-to-RZ-DPSK format conversion. In addition, it is worth noting that simultaneous multi-channel format conversion, channel-selective format conversion, and multicasting format conversion can all potentially be implemented with the proposed schemes. Acknowledgements This research was supported by the National Natural Science Foundation of China under Grant No. 60577006, and by the program for New Century Excellent Talents in University (NCET-040694). References
Fig. 4. Phase distribution with respect to the time scale: (a) input NRZ-DPSK signal; (b) converted RZ-DPSK idler for scheme 1; (c) converted RZ-DPSK idler for scheme 2; (d) converted RZ-DPSK idler for scheme 3; (e) converted RZ-DPSK idler for scheme 4.
can be selected and converted to the corresponding RZ-DPSK idler simply by properly adjusting the pump wavelength. For multicasting format conversion, one-channel NRZ-DPSK signal, one-channel pump optical clock, and multiple CW controls generate multichannel RZ-DPSK idlers. Scheme 3 also enables channel-selective and multicasting NRZ-DPSK-to-RZ-DPSK format conversions. However, the selected signal channel is determined by the CW control wavelength for channel-selective format conversion, while multiple pumps are required for multicasting format conversion. Scheme 4 also provides the possibility of simultaneous multi-channel format conversion similar to scheme 1. Moreover, the pump and control wavelengths can be set apart from both input signal and converted idler, thus none of the communication channels is occupied. Note that it is preferable to select proper scheme according to the requirement of practical applications. In addition to NRZDPSK-to-RZ-DPSK format conversion, it is also possible to further perform other PPLN-based advanced all-optical format conversions, including NRZ-to-CSRZ, RZ-to-CSRZ, CSRZ-to-RZ, NRZDPSK-to-CSRZ-DPSK, and RZ-DPSK-to-CSRZ-DPSK [35,37]. All these potential functions are attractive for effectively enhancing the flexibility of optical networks. 5. Conclusion In conclusion, four kinds of all-optical NRZ-DPSK-to-RZ-DPSK format conversion at 40 Gb/s are proposed and simulated by using cSHG/DFG or cSFG/DFG in a PPLN waveguide. The optical spectra,
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