Investigation on optical wavelength conversion based on SPM using triangular-shaped pulses

Optik 127 (2016) 3049–3054

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Investigation on optical wavelength conversion based on SPM using triangular-shaped pulses Jin Yuan, Tigang Ning, Jing Li ∗ , Li Pei, Hongyao Chen, Chan Zhang, Yueqin Li Key Lab of All Optical Network and Advanced Telecommunication Network of EMC. Beijing Jiaotong University, Beijing 100044, China

a r t i c l e

i n f o

Article history: Received 9 October 2015 Accepted 7 December 2015 Keywords: Triangular-shaped pulse SPM Wavelength conversion

a b s t r a c t A photonic triangular-shaped pulse train is generated based on optical subcarrier modulation and harmonic fitting. After modulated by an amplitude modulator, a single symmetrical triangle-shaped pulse is extracted to investigate the optical wavelength conversion caused by the self-phase modulation effect in a high nonlinear fiber (HNLF). Then two frequency shifts are induced and gradually separated from the original pulse frequency. The energy has been transferred to the two new frequencies efficiently and wavelength conversion is realized. It is also found that the wavelength conversion is proportional to the input power level of the triangular-shaped pulse, the fiber length and nonlinear coefficient of the HNLF and the spectra intensity evolution over time. © 2015 Elsevier GmbH. All rights reserved.

1. Introduction All-optical signal processing technology is an important part of optical communication network, which has become the focus among the domestic and foreign researches currently. According to this situation, various research achievements about the generation of triangular-shaped optical pulses have been proposed. All-optical pulse shaping using mode-locked lasers as the light source is the most common approach to obtain the symmetrical triangular-shaped optical pulses [1,2]. The continuous wave lasers can also be served as light source to achieve symmetrical triangular-shaped pulse. For instance, Dai et al. carried out a versatile waveform generator based on frequency comb generation [3,4]. Li et al. reported and analyzed a generator based on harmonic fitting [5]. As the symmetrical triangular-shaped optical pulse train is characterized by its linear up-and-falling edges in the time domain, it can be used for various applications in optical signal processing and manipulation, which are important for future all-optical networks [6–10]. For example, optical triangular -shaped pulse, combined with cross-phase-modulation (XPM) in the fiber, can be used for all-optical conversion of time-division multiplexed (TDM) to wavelength-division multiplexed (WDM) signals and partial regeneration of signals [6]. This is only true if onoff-keying (OOK) signals are used. However, now OOK signals seem to be mostly replaced by phase and amplitude encoded signals. In

∗ Corresponding author. Tel.: +86 13681429960. E-mail address: [email protected] (J. Li). http://dx.doi.org/10.1016/j.ijleo.2015.12.015 0030-4026/© 2015 Elsevier GmbH. All rights reserved.

Ref. [7], through using XPM with a triangular pump pulse in an HNLF and subsequent propagation in a linear dispersive medium, alloptical techniques of frequency conversion, pulse compression and optical signal copying in both the time and frequency domains can be realized. In Ref. [8], a novel technique of doubling optical pulses based on a combination of the nonlinear shift induced by a triangular pump pulse through XPM in a nonlinear Kerr medium and the subsequent propagation is proposed. The technique could have applications in devices performing optical signal manipulating and processing function in telecommunications, lasers and other areas of optics. In Ref. [9], Parmigiani et al. experimentally demonstrated an all-optical pulse retiming scheme based on chirping the signal to be retimed using XPM incorporating parabolic pulses generated in a linear fashion through pulse shaping in a super-structured fiber Bragg grating. In Ref. [10], by using the temporal characteristics of the triangular-shaped optical pulses incorporating the optical nonlinear effects, triangular-shaped optical pulses could efficiently implement all-optical wavelength conversion. It has achieved a two-fold improvement in the performance of a wavelength convert based on self-phase modulation (SPM) in fiber and offset filtering. As wavelength conversion can play an important role in all-optical networks due to the significant increase in flexibility and potential reduction, researches are conducted internationally. In this letter, we firstly propose a periodic symmetrical triangular-shaped pulse train generator based on harmonic fitting incorporating optical grating dispersion-induced power fading. Then an amplitude modulator (AM) and a non-return-to-zero pulse generator (NRZPG) is used to sieve a single symmetrical triangularshaped pulse from the pulse train. Subsequently, we simulate the

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In order to remove the undesired harmonic in Eq. (3), =−(2k + 1) /(8˝2 ),(k = 0,1,2,. . .. . .) must be satisfied. Thus, the dispersion of the CFBG must meet the following requirement [12]: Dg Lg =

Fig. 1. Schematic setup of the pulses generation and wavelength conversion.

optical wavelength conversion phenomenon caused by the SPM effect in an HNLF. For symmetrical triangle-shaped pulse, only two frequency shifts are induced by the SPM effect, without other frequency components generation. In this way, the energy has been transferred to the two new frequencies efficiently. This means that the triangular-shaped pulse has apparent advantages over the traditional Gaussian-shaped or hyperbolic secant pulses.

4˝2 20



+

E1 (t) =

2V

=

3 Ein (t) 

8



an exp jn˝t

2V

(1)

n=−3

where, Ein (t) = Ein exp(jωo t) denotes the optical field at the input of the DP-MZM (Ein and ω0 are the amplitude and angular frequency, respectively). VLO (t) = VLO sin˝t denotes the RF modulated signal (VLO and ˝ = 2f are the amplitude and angular frequency, respectively). V represents the half-wave switching voltage of the DP-MZM. The amplitude weighting factor of each order optical sideband is an = [2−2(−1)n ]Jn (m), where Jn (•) is the Bessel function of the first kind of order n. Then considering the dispersion of the chirped fiber Bragger grating (CFBG), the optical field at the output of the CFBG can be expressed as [11] E2 (t) ∝

3 



1 an exp jn˝t + j n2 ˝2 2

(4)

J32 (m) J12

(m)



cos 6˝t

(5)

As is known, the Fourier expansion of ideal triangular-shaped waveform can be expressed as

2.1. The generation of triangular-shaped pulses

    ⎫ ⎧ VLO VLO ⎪ ⎬ ⎨ exp j 2V cos(˝t) − exp −j 2V sin(˝t) ⎪ Ein (t)     8 ⎪ ⎭ ⎩ − exp −j VLO cos(˝t) + exp j VLO sin(˝t) ⎪

I2 (t) ∝ IDC + cos 2˝t +

∞  i=1

Fig. 1 shows the schematic setup of triangular-shaped pulses generation and the method to realize wavelength conversion. In this proposal, optical triangular-shaped pulse train was generated using optical carrier suppression incorporating optical grating dispersion-induced power fading. By operating a dual-drive Mach – Zehnder modulator (DD-MZM) to work at push – pull mode and bias at the minimum transmission point (MTTP), optical carrier suppression modulation was realized. The parameter m = VLO /2V is defined as the modulation index. According to [11], optical field at the output of DP-MZM can be shown as:

, k = 0, 1, 2, . . .. . .

where, 0 and c represents central wavelength and speed of light in vacuum. After the undesired 4th-order harmonic in Eq. (3) has been suppressed, the remaining effective frequency components constitute the main components of the symmetrical triangularshaped pulses. Then substituting a1 = 4J1 (m), a3 = 4J3 (m) into Eq. (3), I2 (t) can be calculated as

T (t) ∝

2. Theory

(2k + 1) c2

1 (2i − 1)

2

cos [(2i − 1) ωt] = cos (ωt)

1 1 cos (3ωt) + cos(5ωt) + · · · 9 25

(6)

Fig. 2 gives the relationship between m and J2k−1 (•). Note that when modulation index m is adjusted to m = 2.305, J2 3(m)/J2 1(m)=1/9 can be obtained. Comparing Eq. (5) with Eq. (6), we can conclude that the weight of every order harmonic of optical field intensity is identical with the Fourier expansion of ideal triangularshaped waveform. To further illustrate the shape evolution of optical intensity before and after inserting the CFBG, Fig. 3 shows the temporal simulation waveform of optical intensity [5]. It is obvious that the temporal waveform of the optical intensity before the CFBG reflection is not triangular-shaped. This is because before the CFBG is imported, the 4th-order harmonic component of the optical intensity may destroy the entire temporal characteristics. After inserting the CFBG, dispersion-induced power fading can eliminate the effect caused by the 4th-order harmonic. Thus, the high-quality periodic triangular pulse will be generated as shown by the solid line. In order to facilitate the observation of the symmetrical triangular-shaped pulse wavelength conversion caused by the SPM effect in the HNLF, the generated continuous periodic triangularshaped optical pulse train of E2 (t) should be taken a single pulse for research. By instilling E2 (t) and the NRZ pulse generated by a NRZPG to an AM, the single pulse can be obtained. In this case, the single pulse width of the NRZPG time-domain waveform and

 (2)

n=−3

where, =(−2 0/2c)Dg Lg . Dg Lg denotes the dispersion of the CFBG. Lg , Dg represents fiber length and dispersion parameter, respectively. The corresponding optical field intensity can be written as

 1 2 a + 2 0

I2 (t) ∝



3 

n=1

  a2n

−





a21 cos 2˝t +a23





cos 6˝t





− 2a1 a3 cos 4˝2 cos 4˝t









Undesired

Desired

(3)

Fig. 2. Bessel function of the first kind of order 2k − 1, J2k − 1 (m) versus modulation index, m.

J. Yuan et al. / Optik 127 (2016) 3049–3054

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The input intensity field of symmetrical triangular pulse and Gaussian pulse can be written as: u(0, T )Triangular = {

 u(0, T )Gauss = exp

Fig. 3. Shape evolution of optical intensity Iout (t) before and after CFBG reflection.

the triangular-shaped pulse should be same. A USBSG is used to acquire the desired pulses generated by the NRZPG. Thereafter, the single symmetrical triangle-shaped optical pulse is amplified by an erbium-doped fiber amplifier (EDFA), and then entered the HNLF, in which the wavelength conversion phenomenon of the single pulse caused by the SPM effect can be observed.

−

T2



(8)

2T02

Fig. 4(a) shows the input intensity curves of a symmetrical triangle-shaped pulse with a full width of 50 ps and a Gaussian pulse with a similar pulse width. Fig. 4(b) shows the corresponding frequency chirp curves of the two pulses caused by the SPM. As can be seen from Fig. 4(b), in a larger context of the center, the frequency chirp of the Gaussian pulse is linear. Different from that of the Gaussian pulse, the frequency chirp of the symmetrical triangleshaped pulse is constant across the up-and-falling edge of the pulse. Thus, for symmetrical triangle-shaped pulse, only two frequency shifts of ±ıω are induced by the SPM effect, and the magnitudes of the ±ıω become larger with the increase of the peak power or the transmission distance. The two newly generated frequency components are gradually separated from the original pulse frequency, without the generation of other frequency components. In this way, the energy has been transferred to the two new frequencies efficiently and wavelength conversion is achieved. 3. Simulation and discussion

2.2. Theoretical analysis of spectral changes It is well known that the theory of the wavelength conversion is based on the frequency shifting effect of SPM in an HNLF, which can be mathematically described by [13]: ı (t) = −

2 ∂nl ∂ = −l p0 u (0, t) ∂t ∂t

(7)

where ıω(t) denotes the SPM frequency shift induced on the signal, and l are the nonlinear coefficient and length of the HNLF, P0 is the peak power of the triangular-shaped pulse, and U = Vexp(i␾NL ) is its corresponding normalized pulse envelope. The change of ıω over time is frequency chirp, which will lead the optical pulse transmitted in the fiber to generate new frequency components, thereby causing spectral broadening. According to Eq. (7), the frequency chirp is proportional to the length and nonlinear coefficient of the HNLF, the optical pulse power, and the rate of change of optical intensity over time. As different waveforms possess different frequency chirps, triangular-shaped pulse and Gaussian pulse are taken for example to discuss the impact of SPM on the pulse propagation as a comparison.

To investigate the mechanism, simulations are performed according to the schematic setup as shown in Fig. 1. An optical signal from a CW laser at central wavelength of 1550 nm and line-width of 0.8 MHz is sent to a DD-MZM. The DD-MZM has insertion loss of 5.5 dB, half-wave switching voltage of 4 V and extinction ratio of 25 dB. The driving frequency of the signal from the local oscillator (LO) is tuned up to10 GHz, and the DD-MZM is biased at the minimum transmission (MITP). By adjusting the magnitude of the driving signal from the LO, modulation index m can be tuned to 2.305. Subsequently, the achieved signal is transmitted by a CFBG. When the driving frequency is fRF = 10 GHz, the required grating dispersion is Dg Lg = 389.94 ps/nm. According to the fiber grating dispersion coefficient definition D = T/(Lg ) and the time a light transmits a round trip in a grating is T = 2Lg neff /c, the dispersion coefficient proves to be Dg = 2neff / c, where  denotes the wavelength bandwidth of the CFBG and neff ≈ 1.46 represents the effective refractive index[14]. When Dg Lg = 389.94 ps/nm, the desired Chirp coefficient of the CFBG is C = /Lg = 0.25 nm/cm. Finally, a CFBG with Chirp coefficient C = 0.25 nm/cm, length Lg = 8 cm and modulation depth ın = 0.0005 is selected to applied

Fig. 4. (a) The input intensity curves of symmetric triangular pulse and Gaussian pulse and (b) the corresponding frequency chirps induced by SPM effect.

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Fig. 5. Simulated results of optical intensity at fRF = 10 GHz: (a) temporal waveform and (b) optical spectrum.

Fig. 6. Simulated results of optical intensity of the single symmetrical triangle-shaped pulse: (a) temporal waveform, and (b) optical spectrum.

in the program. In this case, the repetition rate of the generated triangular pulse is f = 2fRF = 20 GHz, and the corresponding period of the waveform is 50 ps. The temporal waveform and the corresponding optical spectrum of output optical field intensity I2 (t) are presented in Fig. 5. As shown in Fig. 5(b), the sideband power difference between the ±1st-order and the ±3rd-order sidebands is approximately 9.5 dB, which satisfies J2 3(m)/J2 1(m) = 1/9. The 7th-order and higher order sidebands are negligible small. After modulated by the AM, the temporal waveform and optical spectrum of the generated single symmetrical triangle-shaped pulse are shown in Fig. 6. The full width of the single pulse is 50 ps. In order to analyze the pulse wavelength conversion phenomenon induced by the SPM effect, the single triangular-shaped pulse is then transmitted into an HNLF, which possesses a length of 0.1 km, a dispersion of −0.31 ps/nm/km at 1550 nm and a nonlinear coefficient of 19 W−1 /km. The solid line in Fig. 7 shows the spectra of the triangular-shaped pulse at the output of the HNLF for a wavelength conversion of 1.55 nm. The input power of the signal is 15.85 dBm. Since we used first two harmonics fitting to obtain the triangular-shaped pulse train in our scheme, some unwanted frequencies still existed. In order to minimize the unwanted frequencies, we can use more harmonics with higher order to generate triangular-shaped pulse train. As a contrast, a Gaussian pulse with similar pulse width is used to replace the single triangular-shaped pulse to realize the wavelength conversion. It is found that the Gauss pulse needs a lower average input power of 14.22 dBm to achieve the similar peak wavelength conversion. However, during the course of the wavelength conversion of the Gauss pulse, many undesired frequency components are generated as the dash line shown in Fig. 7. This makes the spectra more messy, even no

significant difference exist among the primary and the side peaks. These finally lead to more energy loss. As the nonlinear coefficient of the HNLF can be expressed as = 2␲n2 /(Aeff ), the value of can be adjusted by changing the effective mode area of the HNLF. Setting ␥ to 19 W−1 /km and adjusting the magnitude of input average power of the symmetrical triangle-shaped pulse, spectra broadening of the triangle-shaped pulse at different input average powers can be observed at the output of the HNLF. Fig. 8 shows the optical spectra of the triangleshaped pulse at different input average powers of 6.85 dBm, 10.85 dBm, 12.85 dBm and 14.85 dBm. It is shown that when the input pulse power is larger, the wavelength conversion of the

Fig. 7. Simulated spectra of the triangular and Gaussian pulses with the same input pulse widths after transmitted in the HNLF.

J. Yuan et al. / Optik 127 (2016) 3049–3054

Fig. 8. Optical spectra of the triangle-shaped pulse at different input average powers within an HNLF.

symmetrical triangle-shaped pulse is more obvious. When the input power of the signal is too small, the SPM effect is too weak that the newly generated pulses are even without any frequency shifts. When the input power is increased to a certain extent, the spectrum frequency shift of the symmetrical triangle-shaped pulse will become irregular; many undesired frequency components are generated between the two new frequency components, which will lead to the main pulse peak power reduction and the spectrum becomes cluttered. Fig. 9 has shown the wavelength conversion for different input power levels. Keeping the parameters of HNLF constant as l = 0.1 km and = 19 W−1 /km. The driving frequency of the signal from the LO is fRF = 10 GHz. With the increase of the input power, the wavelength conversion of the signal has showed significant growth. When the input power of the triangularshaped pulse is 15.85 dBm, the displacement of the wavelength conversion has reached 1.55 nm. According to the previous analysis, departing from the input power level, the wavelength conversion is also related to the fiber length, nonlinear coefficient and the change of optical intensity over time. Next, the proposed factors influencing the frequency shift displacement will be analyzed. Fig. 10 shows the wavelength conversion of the symmetric triangular-shaped pulse with different lengths and nonlinear coefficients of HNLF. In the simulation, the input power of the triangular-shaped pulse is 15.85 dBm. In Fig. 10(a), the nonlinear coefficient is tuned to 19 W−1 /km. By changing the length of the HNLF, different wavelength conversion can be achieved. It is obvious that with larger HNLF length, the

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Fig. 9. Wavelength conversion of symmetric triangular pulse with different input power.

wavelength conversion of the symmetrical triangular-shaped pulse is more distinct. In Fig. 10(b), an HNLF with length of 0.1 km is used in simulation. When is varied from 11 W−1 /km to 19 W−1 /km, the wavelength conversion increases from 0.9 nm to 1.55 nm. Moreover, the wavelength conversion with the length and nonlinear coefficient of HNLF showed a nearly linear relationship, which has proved that the temporal waveform at the input of the HNLF is the ideal symmetrical triangular pulse. According to Eq. (6), the wavelength conversion is related to the optical intensity evolution over time which is depended on the width of the triangular-shaped pulse. The optical intensity evolution over time varies with the change of full width of the pulse. By tuning the frequency of the signal from OL, different pulse widths can be obtained. In addition, the dispersion of the CFBG should be adjusted according to the driving frequency. Table 1 has given the LO signal frequency f and the Dg Lg of CFBG corresponding to different pulse width of T. Fig. 11 gives the wavelength conversion of symmetric triangular pulse with different driving frequencies. As shown in Fig. 11, by setting the coefficients l and of the HNLF fixed values as l = 0.1 km and = 19 W − 1/km, when the input power of the triangular-shaped pulse is 15.85 dBm, the relation between the wavelength conversion and the driving frequency fRF can be observed at the output of the HNLF. The picture has shown that the wavelength conversion of symmetric triangular pulse goes up linearly with the increase of the driving frequency. It is also proved that the temporal waveform at the input of the HNLF is an ideal symmetrical triangular pulse.

Fig. 10. Wavelength conversion of symmetric triangular pulse with different (a) length and (b) nonlinear coefficient of HNLF.

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Table 1 LO signal frequency f and the Dg Lg of CFBG corresponding to different pulse width of T when generating symmetric triangular pulse. T (ps) 16.66 20 25 33.34 50 100

f (GHz) 30 25 20 15 10 5

Dg Lg (ps/nm) 43.36 62.44 97.56 173.43 390.22 1560.88

up-and-falling edge of the triangular-shaped pulse. Thus we can increase the repetition rate of the pulse train or enhance the power of the pulses to enlarge the wavelength conversion. If we filter one of the frequencies in the output of the optical fiber, the frequency shift can be realized, but is accompanied by another frequency component energy loss. Acknowledgments This work is jointly supported by the National Natural Science Foundation of China (61525501, (61471033, (61405007), and the National Natural Science Foundation of Beijing (no. 4154081) References

Fig. 11. Wavelength conversion of symmetric triangular pulse with different driving frequencies.

4. Conclusion In conclusion, we have demonstrated an approach for triangular-shaped pulse train generation based on harmonic fitting. In the scheme, by inserting a CFBG with accurate dispersion, the undesired harmonics can be suppressed. After sieving a single pulse from the generated periodic symmetrical triangle-shaped pulse, it is more feasible to observe the optical wavelength conversion caused by the SPM in HNLF. Due to the SPM effect, it is also found that the central wavelength of the new generated pulse is gradually separated from the original with the increase of the input power level of the triangular-shaped pulse, the fiber length and nonlinear coefficient of the HNLF, and the spectra intensity evolution over time. After all, a wavelength conversion of 1.55 nm can be achieved. The wavelength shift is related to the slope of the

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