## The analysis of all-optical logic gates based with tunable femtosecond soliton self-frequency shift |

Optics Express, Vol. 22, Issue 7, pp. 8349-8366 (2014)

http://dx.doi.org/10.1364/OE.22.008349

Acrobat PDF (1396 KB)

### Abstract

A type of tunable femtosecond soliton logic gate based on fiber Raman Self-Frequency Shift (SFS) is studied in this paper. The Raman SFSs of femtosecond solitons governed by the Newton’s cradle mechanism in logic gate are analyzed with an Improved Split-Step Fast Fourier Transform (ISSFFT) algorithm. The impact factors of the solitonic pulse frequency shift and temporal time shift, which are included the Third-Order Dispersion (TOD) effect, are investigated. The existing theoretical equation of SFS is modified into a new expression for this type of soliton logic gate. A lower switching power and the small size of the soliton logic gate device is designed to realize the logic functions of AND, NOT, and XOR. The results demonstrate that the logic gate based on SFS is belonged to the asynchronous system and can be achieved with Milli-Watt switching power and good extinction ratio. ISSFFT is effective and accurately to analyze higher-order dispersive and nonlinear effects in the logic gates.

© 2014 Optical Society of America

## 1. Introduction

1. J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical xor gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. **14**, 1436–1438 (2002). [CrossRef]

2. K. Chan, C.-K. Chan, L. K. Chen, and F. Tong, “Demonstration of 20-gb/s all-optical xor gate by four-wave mixing in semiconductor optical amplifier with rz-dpsk modulated inputs,” IEEE Photon. Technol. Lett. **16**, 897–899 (2004). [CrossRef]

3. J. M. Dailey, S. K. Ibrahim, R. J. Manning, R. P. Webb, S. Lardenois, G. D. Maxwell, and A. J. Poustie, “42.6 gbit/s fully integrated all-optical xor gate,” Electron. Lett. **45**, 1047–1049 (2009). [CrossRef]

4. R. Webb, R. Manning, G. Maxwell, and A. Poustie, “40 gbit/s all-optical xor gate based on hybrid-integrated mach-zehnder interferometer,” Electron. Lett. **39**, 79–81 (2003). [CrossRef]

5. S. Randel, A. M. de Melo, K. Petermann, V. Marembert, and C. Schubert, “Novel scheme for ultrafast all-optical xor operation,” J. Lightwave Technol. **22**, 2808–2815 (2004). [CrossRef]

6. I. Kang, M. Rasras, L. Buhl, M. Dinu, S. Cabot, M. Cappuzzo, L. Gomez, Y. Chen, S. Patel, and N. Dutta, “All-optical xor and xnor operations at 86.4 gb/s using a pair of semiconductor optical amplifier mach-zehnder interferometers,” Opt. Express **17**, 19062–19066 (2009). [CrossRef]

7. Y. Feng, X. Zhao, L. Wang, and C. Lou, “High-performance all-optical or/nor logic gate in a single semiconductor optical amplifier with delay interference filtering,” Appl. Opt. **48**, 2638–2641 (2009). [CrossRef] [PubMed]

*ps*) that its response speed is limited. Therefore, a integrated component, based on cascaded multi-SOA-based optical logic gate, may have unbearable response time and can not be applied to the ultra-fast, ultra-short pulse transmission system. The large volume, complex structure and serious polarization dependent also limit its application. The logic gates based on fiber nonlinear effects can overcome above drawbacks because of simple structure, easily integration, fast response (about

*fs*) [8

8. C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L.-S. Yan, and A. E. Willner, “All-optical xor gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett. **17**, 1232–1234 (2005). [CrossRef]

9. J. Wang, Q. Sun, and J. Sun, “All-optical 40 gbit/s csrz-dpsk logic xor gate and format conversion using four-wave mixing,” Opt. Express **17**, 12555–12563 (2009). [CrossRef] [PubMed]

11. R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, “Inelastic collision and switching of coupled bright solitons in optical fibers,” Phys. Rev. E **56**, 2213–2216 (1997). [CrossRef]

13. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. **81**, 3335–3337 (2002). [CrossRef]

14. M. N. Islam, C. E. Soccolich, and D. A. Miller, “Low-energy ultrafast fiber soliton logic gates,” Opt. Lett. **15**, 909–911 (1990). [CrossRef] [PubMed]

16. K. Steiglitz, “Time-gated manakov spatial solitons are computationally universal,” Phys. Rev. E **63**, 016608(2001). [CrossRef]

17. D. Taverner, N. Broderick, D. Richardson, M. Ibsen, and R. Laming, “All-optical and gate based on coupled gap-soliton formation in a fiber bragg grating,” Opt. Lett. **23**, 259–261 (1998). [CrossRef]

18. Y. P. Shapira and M. Horowitz, “Optical and gate based on soliton interaction in a fiber bragg grating,” Opt. Lett. **32**, 1211–1213 (2007). [CrossRef] [PubMed]

13. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. **81**, 3335–3337 (2002). [CrossRef]

19. J. Scheuer and M. Orenstein, “All-optical gates facilitated by soliton interactions in a multilayered kerr medium,” JOSA B **22**, 1260–1267 (2005). [CrossRef]

20. S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial soliton all-optical logic gates,” IEEE Photon. Technol. Lett. **18**, 1287–1289 (2006). [CrossRef]

20. S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial soliton all-optical logic gates,” IEEE Photon. Technol. Lett. **18**, 1287–1289 (2006). [CrossRef]

22. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. **11**, 662–664 (1986). [CrossRef] [PubMed]

23. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. **11**, 659–661 (1986). [CrossRef] [PubMed]

24. C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping zblan fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. **18**, 91–93 (2006). [CrossRef]

25. C. Xu and X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. **28**, 986–988 (2003). [CrossRef] [PubMed]

26. S. Oda and A. Maruta, “All-optical tunable delay line based on soliton self-frequency shift and filtering broadened spectrum due to self-phase modulation,” Opt. Express **14**, 7895–7902 (2006). [CrossRef] [PubMed]

27. J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: experimental demonstrations and applications,” IEEE J. Select. Topics in Quantum Electron. **14**, 713–723 (2008). [CrossRef]

28. J. Lucek and K. Blow, “Optical-intensity dependent switching using soliton self-frequency shift,” Electron. Lett. **27**, 882–884 (1991). [CrossRef]

29. A. Bendahmane, O. Vanvincq, A. Mussot, and A. Kudlinski, “Control of the soliton self-frequency shift dynamics using topographic optical fibers,” Opt. Lett. **38**, 3390–3393 (2013). [CrossRef] [PubMed]

31. K. Zhe, Y. Jin-Hui, L. Sha, X. Song-Lin, Y. Bin-Bin, S. Xin-Zhu, and Y. Chong-Xiu, “Six-bit all-optical quantization using photonic crystal fiber with soliton self-frequency shift and pre-chirp spectral compression techniques,” Chin. Phy. B. **22**, 114211 (2013). [CrossRef]

## 2. Analysis of the solitonic pulse frequency shift and time shift with ISSFFT and modification of the existing theoretical equation in SFS soliton logic gates

### 2.1. Analysis of the pulse frequency shift and time shift in SFS soliton logic gates

*u*,

*ξ*and

*τ*are denoted that normalized amplitude envelope of field, the normalized transmission distance and the normalized delay time, respectively. Parameters

*β*

_{3},

*s*and

*τ*are described as the third-order dispersion, the self-steeping and Raman scattering effect, respectively.

_{R}*δ*

_{3}=

*β*

_{3}/(6 |

*β*

_{2}|

*T*

_{0}),

*s*= 1/(

*ω*

_{0}

*T*

_{0}) and

*τ*=

_{R}*T*/

_{R}*T*

_{0}.

*ω*

_{0}is the center wavelength of the pulse,

*T*

_{0}is the pulse width,

*β*

_{2}is the second-order dispersion parameter which describes the group velocity dispersion (GVD),

*β*

_{3}is TOD parameter and

*T*is relates to the Raman response. In the soliton transmission systems, the constrained relationship between pulse width and peak power of Nth-order solitons is

_{R}32. B. Memarzadeh Isfahani, T. Ahamdi Tameh, N. Granpayeh, and A. R. Maleki Javan, “All-optical nor gate based on nonlinear photonic crystal microring resonators,” JOSA B **26**, 1097–1102 (2009). [CrossRef]

33. P. Andalib and N. Granpayeh, “All-optical ultracompact photonic crystal and gate based on nonlinear ring resonators,” JOSA B **26**, 10–16 (2009). [CrossRef]

*τ*

^{−4}, which is found by G. P. Gordon from (1) through averaging method [22

22. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. **11**, 662–664 (1986). [CrossRef] [PubMed]

34. T. Lakoba and D. Kaup, “Influence of the raman effect on dispersion-managed solitons and their interchannel collisions,” Opt. Lett. **24**, 808–810 (1999). [CrossRef]

*P*

_{0}and

*S*are represented as the peak power of the input pulse and the dispersion management strength respectively. Δ

*f*is frequency shifting in

*Hz*. It is obvious that Eq. (3) is also consistent with Eq. (2) as the dispersion management strength

*S*= 0 and

*N*= 1 (the fundamental soliton or first order soliton) in the dispersion-managed system. The other similarly analytical results have been deduced by Zheltikov [35

35. A. Zheltikov, “Perturbative analytical treatment of adiabatically moderated soliton self-frequency shift,” Phys. Rev. E **75**, 037603 (2007). [CrossRef]

*fs*and is short to Raman oscillation period of 78.5

*fs*.

36. D. Skryabin, F. Luan, J. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science **301**, 1705–1708 (2003). [CrossRef] [PubMed]

30. R. Driben and B. A. Malomed, “Generation of tightly compressed solitons with a tunable frequency shift in raman-free fibers,” Opt. Lett. **38**, 3623–3626 (2013). [CrossRef] [PubMed]

37. R. Driben, B. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From n-soliton fission to soliton chains,” Phys. Rev. A **87**, 063808 (2013). [CrossRef]

36. D. Skryabin, F. Luan, J. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science **301**, 1705–1708 (2003). [CrossRef] [PubMed]

38. A. A. Voronin and A. M. Zheltikov, “Soliton self-frequency shift decelerated by self-steepening,” Opt. Lett. **33**, 1723–1725 (2008). [CrossRef] [PubMed]

*τ*

^{−4}. A bad situation, of which the self-steepening effects lead to soliton remarkably decayed, would be happened in the high-order solitons system [21].

*fs*[21]. Thirdly, a tunable Fabry-perot filter named the Sliding-Frequency Guiding Filter (SFGF) [39

39. P. Mamyshev and L. Mollenauer, “Stability of soliton propagation with sliding-frequency guiding filters,” Opt. Lett. **19**, 2083–2085 (1994). [CrossRef] [PubMed]

40. O. V. Sinkin, R. Holzlhner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. **21**, 61 (2003). [CrossRef]

*z*. The third order or higher of the step size Δ

*z*are error terms, but the coefficient of the third order error term is a constant

*κ*(Δ

*z*)

^{3}. This algorithm is able to amplify the nonlinear effects such as four-wave mixing (FWM) [41]. Logarithmic step size method can be used to analyze the nonlinear effects, which is based on the length of transmission fiber and the loss of optical pulse along the propagation distance to select the step size [42

42. A. Nakamura, “A direct method of calculating periodic wave solutions to nonlinear evolution equations. ii. exact one-and two-periodic wave solution of the coupled bilinear equations,” Journal of the Physical Society of Japan **48**, 1365–1370 (1980). [CrossRef]

*z*and one step of size 2Δ

*z*under a specified standard error. When the error is calculated in the range of standard error, step sizes are kept constant, or step sizes are shortened to reduce the error. Therefore, the accuracy of the nonlinear effects (represented phases in the algorithm) is controlled by eliminated the third order error term

*κ*(Δ

*z*)

^{3}, and calculation accuracy is improved by an order of magnitude.

*fs*, its wavelength is 1.55

*μm*, and

*β*

_{2}is −10.016

*ps*

^{2}/

*km*. The red dash line of the Fig. 2(a) is ignored the Raman scattering and the TOD effects, the black solid line is considered the Raman scattering only, and the blue dot line is considered both the Raman scattering and TOD effects. The TOD effect modulates the tail of soliton pulse into oscillation structure deeply in the time-domain shown in Fig. 2(a) and the soliton spectrum of SFS and TOD in blue color line are divided into two well-resolved frequency peaks in the frequency-domain shown in Fig. 2 (b), which will impact the soliton XOR-gate in later simulation. These results are very consistent with Ref. [21]. The suppression of TOD effect on soliton is also obvious. When the first-order soliton (the soliton power is 232.443

*w*, the pulse width is 256

*fs*) propagates through a 5

*km*standard fiber (

*β*

_{2}is −20

*ps*

^{2}/

*km*and

*τ*is 3

_{R}*fs*), the frequency shift of the soliton is 4.88

*THz*(not considered the TOD effect). If considering the TOD effect, the frequency shift of soliton is 4.19

*THz*(

*β*

_{3}= 0.08

*ps*

^{3}/

*km*). The difference of frequency shift between two cases mentioned above is 0.69

*THz*(which is about 14% of the total amount). Therefore, SFS can not be accurately calculated with the Eq. (2) and Eq. (2) must be modified in order to consider TOD effect.

*kW*,

*T*= 3

_{R}*fs*(

*τ*= 0.106) and 8.2811

_{R}*kW*,

*T*= 0.28

_{R}*fs*(

*τ*= 0.01), respectively. If the fiber loss (

_{R}*α*= 0) is neglected, the full width of pulse at half maximum

*T*is 50

_{FWHM}*fs*(

*T*

_{0}≈ 28.36

*fs*). The wavelength of the carrier is 1550

*nm*. The TOD and the self-steepening effects are ignored (

*δ*= 0 and

*s*= 0). The transmission distance is 1

*m*(about 8 times period of soliton). From Figs. 2 (c and d), the spectral width of the pulse is large enough that the Raman gain amplifies the low-frequency (red) spectral components of the pulse with high-frequency (blue) components of the same pulse when pulse width is in order of

*fs*or shorter. It is obvious that the energy from blue components is continuously transferred to red components. The numerical results in this paper are consistent with Ref. [21], which further prove that our proposed method is reliable. We will show later that the peak power of the second-order soliton can be reduced to order of

*W*by introducing the PCF. If more longer fiber link can be tolerated, the peak power can be reduced to order of

*mW*.

### 2.2. Numerical analysis of SFS and modification of the existing theoretical equation in soliton logic gate

*z*and the pulse width

*T*

_{0}are analyzed in Eq. (1) by ISSFFT. The Δ

*ω*is the difference between the total amount of frequency shift Δ

_{TOD}*ω*(considering the TOD effect) and Δ

*ω*

_{1}(not considering the TOD effect). The first-order solitons (the power is 232.443

*W*) propagate through the standard optical fiber (here the parameter

*β*

_{2}is −20

*ps*

^{2}/

*km*,

*τ*is 3

_{R}*fs*,

*β*

_{3}is 0.08

*ps*

^{3}/

*km*and the length of fiber is 5.13

*km*), the width of the pulse

*T*

_{0}(the half of width at 1/e amplitude) is changed from 256

*fs*to 380

*fs*. The relationship between Δ

*ω*and

_{TOD}*T*

_{0}is shown in Fig. 3(a). The solid line is the simulating datum of ISSFFT, and the dashed line is the math fitting curve. The datum line and the fitting line are well consistent each other.

*y*=

*ax*

^{−7}in Fig. 3(a). It can be similarly found that Δ

*ω*∝

_{TOD}*Z*

^{5/2}when

*z*is changed from 1.065

*km*to 6.065

*km*in Fig. 3(b).

*W*,

*β*

_{2}is −20

*ps*

^{2}/

*km*,

*τ*is 3

_{R}*fs*,

*T*

_{0}is 256

*fs*, and

*z*is 5.13

*km*) except changing the value of parameters

*β*

_{3}from 0.01

*ps*

^{3}

*/km*to 0.13

*ps*

^{3}/

*km*.

### 2.3. Investigations of pulse time’s delay arisen from SFS

*T*

_{0}is 256

*fs*) through the fiber (

*β*

_{2}is −20

*ps*

^{2}/

*km*and

*β*

_{3}is 0.08

*ps*

^{3}/

*km*) into account, we observe the soliton delay in the time-domain with changing the distance

*z*from 106.5

*m*to 606.5

*m*.

### 2.4. The relationship between power and frequency shift of femtosecond solitonic pulses

*Gb*/

*s*bit rates. The parameters of PCF are as follows:

*β*

_{2}is −20

*ps*

^{2}/

*km*,

*β*

_{3}is 0.08

*ps*

^{3}/

*km*,

*T*is 2

_{R}*fs*(3

*fs*), the nonlinear parameter

*γ*is 45.38

*W*

^{−1}

*km*

^{−1}, the length is 60

*m*, the pulse width of soliton is 255.6

*fs*(the duty cycle is 0.0720992), and the power of the first-order soliton in PCF is 6.7W which is very less than the power of the soliton in the G.652 fiber.

*ω*∝

*z*), and the amounts of SFS of 2

*P*

_{0}soliton is much larger than that of

*P*

_{0}(almost an order of magnitude). Therefore, you can increase the value of soliton power to obtain the different widely of frequency shift and to reduce the length of the transmission fiber.

## 3. Operation of SFS-based all-optical soliton logic AND, NOT, and XOR gates

### 3.1. SFS-based all-optical logic AND gate

*P*

_{0}. Field energy of soliton after the coupler can be given by where parameter

*α*is power attenuation coefficient of coupler,

*E*

_{in}_{1}and

*E*

_{in}_{2}are pulse energy of the signal 1 and 2, and

*E*is the energy of output optical pulse after the coupler. Assuming the power attenuation coefficient is 0, the Eq. (5) can be simplified. The two series of pulses are coupled together and the output powers of coupler would be 0, 0.5

_{out}*P*

_{0}, 0.5

*P*

_{0}and 2

*P*

_{0}considered combinations of 0 and 1 from signals. For example, when the inputs of two signal are combined into group of “01”, “10” and “11” respectively, the Eq. (5) can be derived as follows [21]: where the first order of soliton power is

*P*

_{0}and

*P*

_{0}, the frequency of pulse through PCF moves to

*υ*

_{1}(but pulse may not be maintained a soliton, the shape of pulses during transmission would change). When power of pulse is 2

*P*

_{0}, the frequency of pulse moves to

*υ*

_{2}. If detecting optical power with frequency

*υ*

_{2}in detection port, the signal whose frequency is

*υ*

_{2}with only two input ports can be detected with a designed filter. Here, We design the difference of sliding frequency between the input soliton and filter’s frequency exactly matching self-frequency shift which comes from Eq. (4). If the tunable Fabry-perot filter named as SFGF are exactly tuned to frequency of

*υ*

_{2}at export, the pulse in

*υ*

_{2}are gotten to implement the logic AND operation in Fig. 7.

*v*

_{1}and

*v*

_{2}frequencies and the PCF parameters are designed according to Table 1 and Eq. (4).

*P*

_{0}(about 800

*mW*) and the width is spread as drawn in Figs. 8(c) and 8(d), in which the combination signals are “01” or “10”, respectively. (Note : the time axis of Fig. 8(c) doubles that of Figs. 8(a) and 8(e)). But its center frequency

*υ*

_{1}, which is about 193.1

*THz*in Table 1, is not changed. When the combination signals are “11” in Figs. 8(e) and 8(f), the power after coupler is 2

*P*

_{0}(about 24

*W*), the width through the fiber becomes narrow, and there is a certain time’s delay. The width of the spectrum is wider than the incident signal and SFS is increased significantly. The center frequency is moved from 193.1

*THz*to 189.5

*THz*, and the difference of

*υ*

_{1}and

*υ*

_{2}is up to 4.6

*THz*as

*υ*

_{2}is 189.5

*THz*in Table 1.

*υ*

_{1}has a very weak channel crosstalk against

*υ*

_{2}. Considering a SFGF whose bandwidth is 1.2

*THz*, its center frequency should tuned to

*υ*

_{2}, where the center frequency is 189.5

*THz*. If the combination signals are “01” or “10” and logic AND output is “0” in Fig. 8(g), the results of simulation are shown that the optical power after the optical filter is about 56.4

*nW*(−42.5

*dBm*). But the optical power after the optical filter is about 6.9

*W*(38.3

*dBm*) when the logic AND gate output is “1” in Fig. 8(h). The pulse width in output of the logic “0” can be greatly expanded than the logic “1”. The all-optical logic AND gate has a nice performance of the extinction ratio (about 80.8

*dB*).

*τ*=

*k*

_{1}

*Z*

^{2}makes the logic bits breaking away the original sequence. But each pulse has same delay, clock of signal can be extracted from the signal itself. Therefore, SFS-based logic gates have advantage of that it can applicable for asynchronization systems.

*P*

_{0}, 0.5

*P*

_{0}can not maintain the solitonic shape and it decayes into dispersive waves after PCF transmission. The pulse broadening caused by the dispersion waves makes the pulse disappear eventually and power spread into the surrounding to influence the neighbor bits. When the power of pulse after coupler is approximate 2

*P*

_{0}in combination of “11”, there are exist obviously red shifting of the spectrum. The width of pulses become narrow and the peak power of pulses go higher, which are not equal each other due to the nonlinear effects of peripheral power residues. For only a part of frequency of pulse through the filter, the peak power will be weakened. The appropriate bandwidth of optical filter makes appropriate output power. In order to make logic gates can be cascaded to the next gate, we can choose a suitable bandwidth of optical filter which makes the output power of logical “1” is about

*P*

_{0}. The similar treatments can also be done in the other cascade logic gate. The eye diagram of the random sequence in length of 2

^{7}−1 is shown in Fig. 9(c), and the SFS-based all-optical soliton logic AND gate has a good performance. The Q factor is approximately 19.0135, and the minimum bit error rate is about 3.9335

*e*– 81 with further proved by a commercial software package of an Optiwaves System 7.0 in Fig. 9(c).

43. C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science **299**, 368–371 (2003). [CrossRef] [PubMed]

### 3.2. SFS-based all-optical logic NOT gates

*P*

_{0}. The power of signal 1 is

*P*(centre of frequency of input pulses are 193.1

_{s}*THz*). According to Eq. (5), when the input signal is “0” and “1” in Table 1, the pulse power after coupler is as follows:

*P*

_{0}is about 6.74

*W*and

*P*is 1

_{s}*W*, we obtain that

*P*

_{out}_{0}and

*P*

_{out}_{1}is 6.74

*W*and 10.91

*W*(1.5

*P*

_{0}) after coupler, respectively. If the input signal 1 is injected “0”, the center frequency of pulse with shape of a soliton in power

*P*

_{out}_{0}moves to

*υ*

_{1}about 192.8

*THz*in PCF shown by Fig. 10(a). When the input signal 1 is injected “1”, the center frequency of the power

*P*

_{out}_{1}moves to

*υ*

_{2}about 191.36

*THz*(Fig. 10(d)) and has a relatively large delay through the PCF. Then the filter center frequency is tuned to

*υ*

_{1}in the port of receiver, the logic NOT gate can be achieved. Here we can also prove that the results of numerical simulation is correct as follows: According to Eq. (2), the theoretical red-shifting value of the first-order soliton in the normalized form as It is shown that our numerical results of the first-order soliton red-shifting in Eq. (10) agree well with the theoretical value in Eq. (11) as not considering TOD effect.

*P*

_{0}generates little delay to work-off its original position, and the pulses with power

*P*

_{out}_{1}have delay of a logical bit(Fig. 10(c)). The center frequency of two different power pulses differ in 1.44

*THz*. The narrowband filter should be choosen smartly after transmission as we select the center frequency of the SFGF (192.8

*THz*) and a bandwidth of 0.8

*THz*with a lot of numerical calculations. Shown from the final results of output in Fig. 10(d), the device fully realizes logic NOT function. The pulse at the third logical bit in Fig. 10(d) appears lower power (about 364

*mW*), it is due to the interference of pulses. The logic NOT gate has 9

*dB*extinction ratio for the difference between 34.6

*dBm*and 25.6

*dBm*. Using a random sequence of length of (2

^{7}– 1), the eye diagram of the logic NOT gate is given in Fig. 10(d). The value of Q factor is about 3.22652. The minimum bit error rate is about 6.01

*e*– 4. Compared with AND gate, performance of NOT gate have deteriorated for the interference of frequencies (extinction ratio of AND gate is about 80.8

*dB*).

### 3.3. SFS-based all-optical soliton logic XOR gates

*P*

_{0}shown in Table 1. When combinations of input signals are “01” or “10”, the power after coupler is

*THz*. When combination of input signal is “11”, the output of power is

*W*) after coupler. The pulse is formed into the second-order soliton with changing the peak power to 77.1

*W*and shifting the center frequency to 158.57

*THz*shown in Fig. 11(b). The time’s delay is about five logical bits (31.25

*ps*) after PCF. There are still power residues between the frequency (192

*THz*– 194

*THz*), which will interfere all-optical XOR gates decision. When the input signal 1 and 2 of data flow is “10010011” and “01100110” respectively, the output should be “11110101” for XOR gate. The results of numerical simulation are shown in Fig. 11(c). The central frequency and the bandwidth of SFGF is

*υ*

_{1}(192.8

*THz*) and 1

*THz*respectively. Output of the filter is just the result of two signals XOR operation. But the power of output pulse bits is different, especially in the last pulse bit which has lower power compared with other bits and has greatly broadened width. It is shown that the previous pulse of the lower power bit is exactly the second-order soliton at the output of coupler. The second-order soliton has a larger delay than the first-order soliton due to the effect of nonlinear modulation such as XPM. The logic XOR gate extinction ratio is about 6

*dB*. Using a random sequence of length of (2

^{7}– 1), the minimum bit error rate is about 4.01

*e*– 3. Therefore, selecting the appropriate decision threshold will be a key factor for the all-optical XOR gates in the practical application.

*m*. When the logic gates operate on logic function of AND and NOR in this area of length, the frequency difference of two channels may have several

*THZ*or even 10

*THZ*. Then the narrow bandwidth of SFGF is able to distinguish two different channel frequencies easily. The frequency of crosstalk and Cherenkov radiation almost does not affect the performance of logic gates. Numerical studies also show that the two logic gates have a very good extinction ratio. Since there are fissions of second-order soliton in XOR, the XOR performance is worse than the others.

## 4. Conclusion

*fs*, the relatively precise expressions governed by the Newton’s cradle mechanism are simulated with ISSFFT, in which SFS of soliton is given by Eq. (4) and time’s delay of soliton is given by Δ

*τ*=

_{TOD}*k*

_{2}

*β*

_{3}. The tunable SFGF is applied to handle the output of logic gate in asynchronous way, which difference of frequency with soliton is designed exactly matching SFS from Eq. (4). This type logic gates is simple to structure and easy to implement for highly nonlinear effect of PCF. It reduces switch power of the soliton pulse to Milliwatt and makes logic gates more closer to practical application. The SFS based soliton logic gates have good performance in the extinction ratio that AND, NOT and XOR gates are about 80.8

*dB*, 9

*dB*and 6

*dB*, respectively. The clock signal of this asynchronous logic gates can be extracted from the signal itself, which is very suitable for network transmission.

## Acknowledgments

## References and links

1. | J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical xor gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. |

2. | K. Chan, C.-K. Chan, L. K. Chen, and F. Tong, “Demonstration of 20-gb/s all-optical xor gate by four-wave mixing in semiconductor optical amplifier with rz-dpsk modulated inputs,” IEEE Photon. Technol. Lett. |

3. | J. M. Dailey, S. K. Ibrahim, R. J. Manning, R. P. Webb, S. Lardenois, G. D. Maxwell, and A. J. Poustie, “42.6 gbit/s fully integrated all-optical xor gate,” Electron. Lett. |

4. | R. Webb, R. Manning, G. Maxwell, and A. Poustie, “40 gbit/s all-optical xor gate based on hybrid-integrated mach-zehnder interferometer,” Electron. Lett. |

5. | S. Randel, A. M. de Melo, K. Petermann, V. Marembert, and C. Schubert, “Novel scheme for ultrafast all-optical xor operation,” J. Lightwave Technol. |

6. | I. Kang, M. Rasras, L. Buhl, M. Dinu, S. Cabot, M. Cappuzzo, L. Gomez, Y. Chen, S. Patel, and N. Dutta, “All-optical xor and xnor operations at 86.4 gb/s using a pair of semiconductor optical amplifier mach-zehnder interferometers,” Opt. Express |

7. | Y. Feng, X. Zhao, L. Wang, and C. Lou, “High-performance all-optical or/nor logic gate in a single semiconductor optical amplifier with delay interference filtering,” Appl. Opt. |

8. | C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L.-S. Yan, and A. E. Willner, “All-optical xor gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett. |

9. | J. Wang, Q. Sun, and J. Sun, “All-optical 40 gbit/s csrz-dpsk logic xor gate and format conversion using four-wave mixing,” Opt. Express |

10. | B.-E. Olsson and P. A. Andrekson, “Polarization-independent all-optical and-gate using randomly birefringent fiber in a nonlinear optical loop mirror,” in “Optical Fiber Communication Conference and Exhibit, 1998. OFC’98., Technical Digest,” (IEEE), pp. 375–376. |

11. | R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, “Inelastic collision and switching of coupled bright solitons in optical fibers,” Phys. Rev. E |

12. | O. V. Kolokoltsev, R. Salas, and V. Vountesmeri, “All-optical phase-independent logic elements based on phase shift induced by coherent soliton collisions,” J. Lightwave Technol. |

13. | M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. |

14. | M. N. Islam, C. E. Soccolich, and D. A. Miller, “Low-energy ultrafast fiber soliton logic gates,” Opt. Lett. |

15. | M. W. Chbat, B. Hong, M. N. Islam, C. E. Soccolich, and P. R. Prucnal, “Ultrafast soliton-trapping and gate,” J. Lightwave Technol. |

16. | K. Steiglitz, “Time-gated manakov spatial solitons are computationally universal,” Phys. Rev. E |

17. | D. Taverner, N. Broderick, D. Richardson, M. Ibsen, and R. Laming, “All-optical and gate based on coupled gap-soliton formation in a fiber bragg grating,” Opt. Lett. |

18. | Y. P. Shapira and M. Horowitz, “Optical and gate based on soliton interaction in a fiber bragg grating,” Opt. Lett. |

19. | J. Scheuer and M. Orenstein, “All-optical gates facilitated by soliton interactions in a multilayered kerr medium,” JOSA B |

20. | S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial soliton all-optical logic gates,” IEEE Photon. Technol. Lett. |

21. | G. Agrawal, |

22. | J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. |

23. | F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. |

24. | C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping zblan fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. |

25. | C. Xu and X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. |

26. | S. Oda and A. Maruta, “All-optical tunable delay line based on soliton self-frequency shift and filtering broadened spectrum due to self-phase modulation,” Opt. Express |

27. | J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: experimental demonstrations and applications,” IEEE J. Select. Topics in Quantum Electron. |

28. | J. Lucek and K. Blow, “Optical-intensity dependent switching using soliton self-frequency shift,” Electron. Lett. |

29. | A. Bendahmane, O. Vanvincq, A. Mussot, and A. Kudlinski, “Control of the soliton self-frequency shift dynamics using topographic optical fibers,” Opt. Lett. |

30. | R. Driben and B. A. Malomed, “Generation of tightly compressed solitons with a tunable frequency shift in raman-free fibers,” Opt. Lett. |

31. | K. Zhe, Y. Jin-Hui, L. Sha, X. Song-Lin, Y. Bin-Bin, S. Xin-Zhu, and Y. Chong-Xiu, “Six-bit all-optical quantization using photonic crystal fiber with soliton self-frequency shift and pre-chirp spectral compression techniques,” Chin. Phy. B. |

32. | B. Memarzadeh Isfahani, T. Ahamdi Tameh, N. Granpayeh, and A. R. Maleki Javan, “All-optical nor gate based on nonlinear photonic crystal microring resonators,” JOSA B |

33. | P. Andalib and N. Granpayeh, “All-optical ultracompact photonic crystal and gate based on nonlinear ring resonators,” JOSA B |

34. | T. Lakoba and D. Kaup, “Influence of the raman effect on dispersion-managed solitons and their interchannel collisions,” Opt. Lett. |

35. | A. Zheltikov, “Perturbative analytical treatment of adiabatically moderated soliton self-frequency shift,” Phys. Rev. E |

36. | D. Skryabin, F. Luan, J. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science |

37. | R. Driben, B. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From n-soliton fission to soliton chains,” Phys. Rev. A |

38. | A. A. Voronin and A. M. Zheltikov, “Soliton self-frequency shift decelerated by self-steepening,” Opt. Lett. |

39. | P. Mamyshev and L. Mollenauer, “Stability of soliton propagation with sliding-frequency guiding filters,” Opt. Lett. |

40. | O. V. Sinkin, R. Holzlhner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. |

41. | M. Ablowitz and H. Segur, “Solitons, nonlinear evolution equations and inverse scattering. by m. j,” J. Fluid Mech |

42. | A. Nakamura, “A direct method of calculating periodic wave solutions to nonlinear evolution equations. ii. exact one-and two-periodic wave solution of the coupled bilinear equations,” Journal of the Physical Society of Japan |

43. | C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science |

**OCIS Codes**

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(190.5650) Nonlinear optics : Raman effect

(200.4660) Optics in computing : Optical logic

(320.7140) Ultrafast optics : Ultrafast processes in fibers

**ToC Category:**

Optics in Computing

**History**

Original Manuscript: February 4, 2014

Revised Manuscript: March 4, 2014

Manuscript Accepted: March 5, 2014

Published: April 1, 2014

**Citation**

Ming Xu, Yan Li, Tiansheng Zhang, Jun Luo, Jianhua Ji, and Shuwen Yang, "The analysis of all-optical logic gates based with tunable femtosecond soliton self-frequency shift," Opt. Express **22**, 8349-8366 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8349

Sort: Year | Journal | Reset

### References

- J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, S. H. Kim, “All-optical xor gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. 14, 1436–1438 (2002). [CrossRef]
- K. Chan, C.-K. Chan, L. K. Chen, F. Tong, “Demonstration of 20-gb/s all-optical xor gate by four-wave mixing in semiconductor optical amplifier with rz-dpsk modulated inputs,” IEEE Photon. Technol. Lett. 16, 897–899 (2004). [CrossRef]
- J. M. Dailey, S. K. Ibrahim, R. J. Manning, R. P. Webb, S. Lardenois, G. D. Maxwell, A. J. Poustie, “42.6 gbit/s fully integrated all-optical xor gate,” Electron. Lett. 45, 1047–1049 (2009). [CrossRef]
- R. Webb, R. Manning, G. Maxwell, A. Poustie, “40 gbit/s all-optical xor gate based on hybrid-integrated mach-zehnder interferometer,” Electron. Lett. 39, 79–81 (2003). [CrossRef]
- S. Randel, A. M. de Melo, K. Petermann, V. Marembert, C. Schubert, “Novel scheme for ultrafast all-optical xor operation,” J. Lightwave Technol. 22, 2808–2815 (2004). [CrossRef]
- I. Kang, M. Rasras, L. Buhl, M. Dinu, S. Cabot, M. Cappuzzo, L. Gomez, Y. Chen, S. Patel, N. Dutta, “All-optical xor and xnor operations at 86.4 gb/s using a pair of semiconductor optical amplifier mach-zehnder interferometers,” Opt. Express 17, 19062–19066 (2009). [CrossRef]
- Y. Feng, X. Zhao, L. Wang, C. Lou, “High-performance all-optical or/nor logic gate in a single semiconductor optical amplifier with delay interference filtering,” Appl. Opt. 48, 2638–2641 (2009). [CrossRef] [PubMed]
- C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L.-S. Yan, A. E. Willner, “All-optical xor gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett. 17, 1232–1234 (2005). [CrossRef]
- J. Wang, Q. Sun, J. Sun, “All-optical 40 gbit/s csrz-dpsk logic xor gate and format conversion using four-wave mixing,” Opt. Express 17, 12555–12563 (2009). [CrossRef] [PubMed]
- B.-E. Olsson, P. A. Andrekson, “Polarization-independent all-optical and-gate using randomly birefringent fiber in a nonlinear optical loop mirror,” in “Optical Fiber Communication Conference and Exhibit, 1998. OFC’98., Technical Digest,” (IEEE), pp. 375–376.
- R. Radhakrishnan, M. Lakshmanan, J. Hietarinta, “Inelastic collision and switching of coupled bright solitons in optical fibers,” Phys. Rev. E 56, 2213–2216 (1997). [CrossRef]
- O. V. Kolokoltsev, R. Salas, V. Vountesmeri, “All-optical phase-independent logic elements based on phase shift induced by coherent soliton collisions,” J. Lightwave Technol. 20, 1048 (2002). [CrossRef]
- M. Peccianti, C. Conti, G. Assanto, A. De Luca, C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81, 3335–3337 (2002). [CrossRef]
- M. N. Islam, C. E. Soccolich, D. A. Miller, “Low-energy ultrafast fiber soliton logic gates,” Opt. Lett. 15, 909–911 (1990). [CrossRef] [PubMed]
- M. W. Chbat, B. Hong, M. N. Islam, C. E. Soccolich, P. R. Prucnal, “Ultrafast soliton-trapping and gate,” J. Lightwave Technol. 10, 2011–2016 (1992). [CrossRef]
- K. Steiglitz, “Time-gated manakov spatial solitons are computationally universal,” Phys. Rev. E 63, 016608(2001). [CrossRef]
- D. Taverner, N. Broderick, D. Richardson, M. Ibsen, R. Laming, “All-optical and gate based on coupled gap-soliton formation in a fiber bragg grating,” Opt. Lett. 23, 259–261 (1998). [CrossRef]
- Y. P. Shapira, M. Horowitz, “Optical and gate based on soliton interaction in a fiber bragg grating,” Opt. Lett. 32, 1211–1213 (2007). [CrossRef] [PubMed]
- J. Scheuer, M. Orenstein, “All-optical gates facilitated by soliton interactions in a multilayered kerr medium,” JOSA B 22, 1260–1267 (2005). [CrossRef]
- S. V. Serak, N. V. Tabiryan, M. Peccianti, G. Assanto, “Spatial soliton all-optical logic gates,” IEEE Photon. Technol. Lett. 18, 1287–1289 (2006). [CrossRef]
- G. Agrawal, Nonlinear Fiber Optics Principles and Applications (Electronic Industry Press, 2002).
- J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986). [CrossRef] [PubMed]
- F. M. Mitschke, L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef] [PubMed]
- C. L. Hagen, J. W. Walewski, S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping zblan fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18, 91–93 (2006). [CrossRef]
- C. Xu, X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. 28, 986–988 (2003). [CrossRef] [PubMed]
- S. Oda, A. Maruta, “All-optical tunable delay line based on soliton self-frequency shift and filtering broadened spectrum due to self-phase modulation,” Opt. Express 14, 7895–7902 (2006). [CrossRef] [PubMed]
- J. H. Lee, J. van Howe, C. Xu, X. Liu, “Soliton self-frequency shift: experimental demonstrations and applications,” IEEE J. Select. Topics in Quantum Electron. 14, 713–723 (2008). [CrossRef]
- J. Lucek, K. Blow, “Optical-intensity dependent switching using soliton self-frequency shift,” Electron. Lett. 27, 882–884 (1991). [CrossRef]
- A. Bendahmane, O. Vanvincq, A. Mussot, A. Kudlinski, “Control of the soliton self-frequency shift dynamics using topographic optical fibers,” Opt. Lett. 38, 3390–3393 (2013). [CrossRef] [PubMed]
- R. Driben, B. A. Malomed, “Generation of tightly compressed solitons with a tunable frequency shift in raman-free fibers,” Opt. Lett. 38, 3623–3626 (2013). [CrossRef] [PubMed]
- K. Zhe, Y. Jin-Hui, L. Sha, X. Song-Lin, Y. Bin-Bin, S. Xin-Zhu, Y. Chong-Xiu, “Six-bit all-optical quantization using photonic crystal fiber with soliton self-frequency shift and pre-chirp spectral compression techniques,” Chin. Phy. B. 22, 114211 (2013). [CrossRef]
- B. Memarzadeh Isfahani, T. Ahamdi Tameh, N. Granpayeh, A. R. Maleki Javan, “All-optical nor gate based on nonlinear photonic crystal microring resonators,” JOSA B 26, 1097–1102 (2009). [CrossRef]
- P. Andalib, N. Granpayeh, “All-optical ultracompact photonic crystal and gate based on nonlinear ring resonators,” JOSA B 26, 10–16 (2009). [CrossRef]
- T. Lakoba, D. Kaup, “Influence of the raman effect on dispersion-managed solitons and their interchannel collisions,” Opt. Lett. 24, 808–810 (1999). [CrossRef]
- A. Zheltikov, “Perturbative analytical treatment of adiabatically moderated soliton self-frequency shift,” Phys. Rev. E 75, 037603 (2007). [CrossRef]
- D. Skryabin, F. Luan, J. Knight, P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003). [CrossRef] [PubMed]
- R. Driben, B. Malomed, A. Yulin, D. Skryabin, “Newton’s cradles in optics: From n-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013). [CrossRef]
- A. A. Voronin, A. M. Zheltikov, “Soliton self-frequency shift decelerated by self-steepening,” Opt. Lett. 33, 1723–1725 (2008). [CrossRef] [PubMed]
- P. Mamyshev, L. Mollenauer, “Stability of soliton propagation with sliding-frequency guiding filters,” Opt. Lett. 19, 2083–2085 (1994). [CrossRef] [PubMed]
- O. V. Sinkin, R. Holzlhner, J. Zweck, C. R. Menyuk, “Optimization of the split-step fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21, 61 (2003). [CrossRef]
- M. Ablowitz, H. Segur, “Solitons, nonlinear evolution equations and inverse scattering. by m. j,” J. Fluid Mech 244, 721–725 (1992).
- A. Nakamura, “A direct method of calculating periodic wave solutions to nonlinear evolution equations. ii. exact one-and two-periodic wave solution of the coupled bilinear equations,” Journal of the Physical Society of Japan 48, 1365–1370 (1980). [CrossRef]
- C. Luo, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368–371 (2003). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.