Controlling Nonlinear Behavior of a SMRR for Network System Engineering

Controlling Nonlinear Behavior of a SMRR for Network System Engineering

I. S. Amiri*, J. Ali

*1 Institute of Advanced Photonics Science, Nanotechnology Research Alliance, Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Malaysia

Abstract

This research is used to control the nonlinear behavior of silicon microring resonators, MRRs such as chaos and bifurcation. Increasing of nonlinear refractive indices, coupling coefficients and radius of the SMRR leads to descend input power and round trips wherein the bifurcation occurs. As result, bifurcation or chaos behaviors are seen at lower input power of 44 W, where the nonlinear refractive index is n2=3.2×1020 m2/W. Smallest round trips can be seen for the R=40 µm and

generation secured codes in digital information processing.

Light Propagation inside SMRR

Single MRR consists of a single coupler and a micoring resonator. Nonlinearity of the fiber ring is of the Kerr-type wherein the nonlinear refractive index is given by [26-31]

n

0.1 respectively. Signals from the SMRR are passing through a polarizer beam splitter to generate quantum

n n0 n2 I n0 ( 2 )P,

Aeff

(1)

binary codes which are used in wireless network communication.

Keywords: Silicon microring resonator; Bifurcation; Chaos, Coupling coefficient, Nonlinear refractive index

Introduction

Nonlinear behavior of light inside a single MRR occurs when strong pulse of light is inputted into the ring system, used to many applications in signal processing and communication [1-4]. Bifurcation and chaotic signal controls are used in a great number of optical, engineering and biological designed systems [5-11].

Bifurcation can be modified via various control methods [12]. Theoretical studies of such as systems have same concepts with ring cavities, and FabryPerot system [13-15]. Amiri et al. have shown that chaotic signal behavior can be seen after the bifurcation was generated. Amiri et al, showed the nonlinearity behaviors of the PANDA ring resonator system [16-18]. More details of these phenomena have been explained by Afroozeh [19, 20]. One of the phenomena, known as bifurcation has been used in digital coding application [21]. Behavior of light traveling in a nonlinear ring resonator is well described by Yupapin [22]. Controlling of the bifurcation behavior can be implemented by controlling the round trip and input powers of the ring system via variation of the parameters [23-25]. Bifurcation control is not only important in its own right, but also suggests a viable and effective approach for chaos control that can be used to

where n0 and n2 are the linear and nonlinear refractive indices, respectively [32-34]. I and P are the optical intensity and optical field power, respectively [35-38]. The effective mode core area of the fiber is Aeff [39-41]. Schematic of SMRR is illustrated in Fig.1

Fig. 1: Silicon microring resonator (SMRR)

The fiber has a nonlinear refractive index of n2 and a linear absorption coefficient of [42-44]. The intensity coupling coefficient [45-48] of the fiber coupler is , where is a coupling loss of the field amplitude [49-51].

Here the fiber coupler is considered as a point device and is reciprocal [52-54]. The relation between the electric fields E1 and E2, can be expressed using the nonlinear form as [55-57]:

E2 E1x exp{ j(0 NL )},

(2)

where 0

kLn0

and NL

kLn2 1

are expressed as

E

E

2

2

linear and nonlinear phase shift [58, 59], k 2 /

is a

wave number [60, 61] and L is the circumference of the

ring resonator [62]. x exp( L / 2) represents a round

trip loss for the input pulse propagating inside the SMRR [63]. Mathematically, the subsequence Equations of the round trip within the system is given by Eq. (3).

En1 j (1 ) Ein (1 )(1 )xEn exp( j(0 NL )),

(3)

Fig. 2: Bifurcation and chaos behavior of light inside SMRR,

We consider a MRR connected to a single coupler that extracts light from the ring into the output waveguides, as schematically shown in Fig. 1. We ignore reflectivities at the couplerwaveguide interface, which is usually a good approximation due to the same structure of the output waveguides and the coupler [64-67]. Regards to steady situation of the Eq. (3), the output field can be expressed as [68-72]:

where 0.0225and L 80mfor various nonlinear refractive indices: (a): n2=2.2×1020 m2/W, (b): n2=2.4×1020 m2/W, (c):

n2=2.6×1020 m2/W and (d): n2=3.2×1020 m2/W.

Effects of the coupling coefficients on the bifurcation and chaos behavior, in terms of roundtrip and output powers are shown in Fig. 3. Input Gaussian pulse with power of 2W is introduced into the ring system where the radius of the ring is selected to

E 1 E

1

1 x exp( j(0 NL ))

R=15 m. Here, the coupling coefficient is a variable

out

in

. 1 (1 )(1 ) x exp( j(0 NL ))

(4)

parameter that varies from 0.01 to 0.1.

Thus the output power of the light field from Eq. (4) is given by Eq. (5).

Pout

Eout

. E*out

(5)

Equation (5) is mathematical relation used for characterizing of nonlinear effects of the ring resonator system.

Result and Discussion

Figure (2) shows the bifurcation and chaos behavior occurred for various nonlinear refractive indices of the system. The parameters have been fixed to 0=1.55 m, n0=3.37, Aeff=0.30 m2, =0.01 dB km1 and =0.1. The

length of the ring is L=80 m, where the coupling coefficients is 0.0225 and the linear phase shift has been kept to zero. Total round trip of the input pulse inside the ring system is 20000. An increasing of nonlinear refractive index from n2=2.2×1020 m2/W to n2=3.2×1020 m2/W causes the optical nonlinear phenomena to be seen at the lower range of input power

shown in Fig. 2.

Fig. 3: Simulation results of bifurcation behavior generation within a SMRR respect to different value of couple coefficient ( ), where (a): 0.01, (b): 0.03, (c): 0.07 and (d): 0.1

Effects of rings size are shown in Fig. (4). Here the coupling coefficient has been fixed to 0.0225 , where the radius of the SMRR varies from 7 µm to 40 µm.

Fig.4: Simulation results of bifurcation and chaos phenomena within a micro ring resonators respect to different values of ring radius (R).

Optical soliton can be used to generate chaotic filter characteristics when propagating within the SMRR [73- 75]. When the input pulse is introduced into the SMRR as shown in Fig.1, the input optical field (Ein) can be expressed by [76, 77]

Obtained results of the chaotic signals from the SMRR pass through a PBS as shown in Figure (6). In application, the variable quantum binary codes can be generated using the PBS [84]. It means that the localized wavelength or frequency can be used to generate variable codes [85].

T z

, (1)

Binary codes via chaotic signals can be connected into a

Ein A tanhT exp 2L i0t

network communication system shown in Fig. 6 [86].

0 D

z

(2)

Therefore, generated secured quantum binary codes can be transmitted to different users via a wireless networks

Eadd (t) E0 exp 2L i0t

transmitter system [87].

D

0

0

D

D

2

2

Hee A and z are the optical field amplitude and propagation distance, respectively [78]. T is the soliton

pulse propagation time, and

L T 2

is the

dispersion length of the soliton pulse [79]. 2 is the propagation constant. This soliton describes a pulse that

keeps its temporal or spatial width invariance as it propagates along the MRR system [80]. When soliton

peak intensity 2 / T is given, then T0 is known,

2

0

0

0

0

where =n2×k0, is the length scale over which dispersive or nonlinear effects makes the beam become wider or narrower [81]. For the temporal soliton pulse in the micro ring device, a balance should be achieved between the dispersion length (LD) and the nonlinear length (LNL=(1/NL), where and NL are a coupling loss of the field amplitude and nonlinear phase shift [82]. Here

0 kLn0 si the linear phase shifts [83].

The optical power of the dark soliton is fixed to 550 mW, where n0=3.34, n2=2.2×1017 m2 W1,

Aeff=0.50 m2, =0.5 dB mm1, =0.1, with 20,000

roundtrips. The chaotic signals are generated within the ring (R), where R=10 m, =0.9713, shown in Figure 5(a). Gaussian pulse with power of 450 mW and central wavelength of 0=1500 nm is input into the system, where

n2=2.2×1015 m2 W1 and Aeff = 25 m2. In this case

R=17 m, =0.995 and R=17 m, =0.9895 shown in Figure 5(b) and 5(c) respectively.

Fig.5. Simulation results of chaotic signals within the SMRR, where (a): simulated frequency chaotic band, (b) and (c): spatial chaotic signals.

Fig.6: Schematic of a computer wireless networks system, where the transmission of information in the form of binary codes can be implemented using SMRR

Therefore, chaotic signals are generated, whereas the required signals including specific wavelengths or frequencies can be used to perform the secure wireless communication network [88, 89]. In order to increase the capacity of micro ring systems [90-92], more sharp optical pulses with smaller free spectrum range (FSR) are recommended [93-104].

Conclusion

We have presented nonlinear effects of the single ring resonator as optical bifurcation and chaos. Traveling of light inside the proposed ring system is analyzed by manipulating of nonlinear refractive index, coupling coefficient and the radius of the ring resonator. Results have shown that the bifurcation and chaos can be occurred in different roundtrip times and input power. Occurrence of bifurcation at lower input power or smaller round trip is a beneficial effect in order to improve the nonlinear microring system. Therefore, controlling the round trip times and the input power of the system can be used to deal with and control the bifurcation and chaotic signals, where it is used in many applications in photonics communication such as security processing or digital coding implementations. In this study generation of quantum binary codes was perform using chaotic signals which are transmitted via wireless networks and information transmission system.

Acknowledgements

1. S. Amiri would like to thank the Institute of Advanced Photonics Science, Nanotechnology Research Alliance, Universiti Teknologi Malaysia (UTM).

REFERENCES

controlling the chaotic signals using silicon micro ring resonator, in Computer and Communication Engineering (ICCCE) Conference, Malaysia, 2012, 765-769.

1. I. S. Amiri, M. A. Jalil, A. Afroozeh, M. Kouhnavard , J. Ali, and P. P. Yupapin, Controlling Center Wavelength and Free Spectrum Range by MRR Radii, in Faculty of Science Postgraduate Conference (FSPGC), Universiti Teknologi Malaysia, 2010.

2. J. Ali, M. Kouhnavard, A. Afroozeh, I. S. Amiri, M. A. Jalil, and P. P. Yupapin, Optical bistability in a FORR, presented at the ICEM, Legend Hotel, Kuala Lumpur, Malaysia, 2010.

3. M. Kouhnavard, A. Afroozeh, I. S. Amiri, M. A. Jalil, J. Ali, and P. P. Yupapin, New system of Chaotic Signal Generation Using MRR, presented at the The International Conference on Experimental Mechanics (ICEM), Kuala Lumpur, Malaysia, 2010.

4. F. K. Mohamad, N. J. Ridha, I. S. Amiri, J. A. Saktioto, and P.

   P. Yupapin, Effect of Center Wavelength on MRR Performance, presented at the The International Conference on Experimental Mechanics (ICEM), Kuala Lumpur, Malaysia, 2010.

5. J. Ali, M. A. Jalil, I. S. Amiri, and P. P. Yupapin, Effects of MRR parameter on the bifurcation behavior, presented at the Nanotech Malayia, International Conference on Enabling Science & Technology KLCC, Kuala Lumpur, Malaysia 2010.

6. I. S. Amiri, R. Ahsan, A. Shahidinejad, J. Ali, and P. P. Yupapin, Characterisation of bifurcation and chaos in silicon microring resonator, IET Communications, 6(16), 2012, 2671- 2675.

Integrated PANDA-Add/drop and TDMA Systems, International Journal of Engineering Research & Technology (IJERT), 1(5), 2012,

1. A. Afroozeh, I. S. Amiri, J. Ali, and P. P. Yupapin, Determination Of Fwhm For Solition Trapping, Jurnal Teknologi, 552012, 77-83.

2. A. Afroozeh, M. Bahadoran, I. S. Amiri, A. R. Samavati, J. Ali, and P. P. Yupapin, Fast Light Generation Using Microring Resonators for Optical Communication, presented at the National Science Postgraduate Conference NSPC, Universiti Teknologi Malaysia, 2011.

3. J. Ali, M. Kouhnavard, I. S. Amiri, M. A. Jalil, A. Afroozeh, and P. P. Yupapin Security confirmation using temporal dark and bright soliton via nonlinear system, presented at the ICAMN, International Conference, Prince Hotel & Residence, Kuala Lumpur 2010.

4. P. P. Yupapin, M. A. Jalil, I. S. Amiri, I. Naim, and J. Ali, New Communication Bands Generated by Using a Soliton Pulse within a Resonator System, Circuits and Systems, 1(2), 2010, 71-75.

5. J. Ali, H. Nur, S. Lee, A. Afroozeh, I. Amiri, M. Jalil, A. Mohamad, and P. Yupapin, Short and millimeter optical soliton generation using dark and bright soliton, presented at the AMN- APLOC International Conference, Wuhan, China, 2010.

6. I. S. Amiri, A. Nikoukar, A. Shahidinejad, J. Ali, and P. Yupapin, Generation of discrete frequency and wavelength for secured computer networks system using integrated ring resonators, in Computer and Communication Engineering (ICCCE) Conference Malaysia, 2012, 775-778.

nano-waveguide, presented at the ICAMN, International Conference, Prince Hotel, Kuala Lumpur, Malaysia, 2010.

1. I. S. Amiri, M. Nikmaram, A. Shahidinejad, and J. Ali, Cryptography Scheme of an Optical Switching System Using Pico/Femto Second Soliton Pulse, International Journal of Advances in Engineering & Technology (IJAET), 5(1), 2012, 176-184.

2. A. A. Shojaei and I. S. Amiri, Soliton for Radio wave generation, presented at the International Conference for Nanomaterials Synthesis and Characterization (INSC), Kuala Lumpur, Malaysia, 2011.

3. J. Ali, M. Kouhnavard, M. A. Jalil, and I. S. Amiri, Quantum signal processing via an optical potential well, presented at the Nanotech Malaysia, International Conference on Enabling Science & Technology, Kuala Lumpur, Malaysia 2010.

4. J. Ali, A. Mohamad, I. Nawi, I. Amiri, M. Jalil, A. Afroozeh, and P. Yupapin, Stopping a dark soliton pulse within an NNRR, presented at the AMN-APLOC International Conference, Wuhan, China 2010.

5. A. Nikoukar, I. S. Amiri, A. Shahidinejad, A. Shojaei, J. Ali, and P. Yupapin, MRR quantum dense coding for optical wireless communication system using decimal convertor, in Computer and Communication Engineering (ICCCE) Conference, Malaysia, 2012, 770-774.

6. J. Ali, K. Kulsirirat, W. Techithdeera, M. A. Jalil, I. S. Amiri, I. Naim, and P. P. Yupapin, Temporal dark soliton behavior within multi-ring resonators, presented at the Nanotech Malaysia, International Conference on Enabling Science & Technology Malaysia 2010.

7. I. S. Amiri, A. Shahidinejad, A. Nikoukar, J. Ali, and P. Yupapin, A Study oF Dynamic Optical Tweezers Generation For Communication Networks, International Journal of Advances in Engineering & Technology (IJAET), 4(2), 2012, 38-45

8. J. Ali, K. Raman, A. Afroozeh, I. S. Amiri, M. A. Jalil, I. N. Nawi, and P. P. Yupapin, Generation of DSA for security application, presented at the 2nd International Science, Social Science, Engineering Energy Conference (I-SEEC 2010) Nakhonphanom, Thailand, 2010.

9. A. Nikoukar, I. S. Amiri, and J. Ali, Secured Binary Codes Generation for Computer Network Communication, presented at the Network Technologies & Communications (NTC) Conference, Singapore, 2010-2011.

10. A. Afroozeh, I. S. Amiri, M. Kouhnavard, M. Jalil, J. Ali, and

    1. Yupapin, Optical dark and bright soliton generation and amplification, in Enabling Science and Nanotechnology (ESciNano) Conference Malaysia, 2010, 1-3.

11. J. Ali, I. Amiri, A. Jalil, A. Kouhnavard, B. Mitatha, and P. Yupapin, Quantum internet via a quantum processor, presented at the International Conference on Photonics (ICP 2010), Langkawi, Malaysia 2010.

12. A. Afroozeh, I. S. Amiri, A. Samavati, J. Ali, and P. Yupapin, THz frequency generation using MRRs for THz imaging, in Enabling Science and Nanotechnology (ESciNano) Conference Malaysia, 2012, 1-2.

13. J. Ali, K. Raman, M. Kouhnavard, I. S. Amiri, M. A. Jalil, A. Afroozeh, and P. P. Yupapin, Dark soliton array for communication security, presented at the AMN-APLOC International Conference, Wuhan, China, 2011.

14. I. S. Amiri, M. A. Jalil, F. K. Mohamad, N. J. Ridha, J. Ali, and

    1. P. Yupapin, Storage of Atom/Molecules/Photon using Optical Potential Wells, presented at the The International Conference on Experimental Mechanics (ICEM), Kuala Lumpur, Malaysia, 2010.

15. N. J. Ridha, F. K. Mohamad, I. S. Amiri, Saktioto, J. Ali, and P.

    1. Yupapin, Controlling Center Wavelength and Free Spectrum Range by MRR Radii presented at the The International Conference on Experimental Mechanics (ICEM), Kuala Lumpur, Malaysia, 2010.

16. A. Afroozeh, M. Bahadoran, I. S. Amiri, A. R. Samavati, J. Ali, and P. P. Yupapin, Fast Light Generation Using GaAlAs/GaAs Waveguide, Jurnal Teknologi, 572012, 7.

17. J. Ali, I. S. Amiri, M. A. Jalil, M. Hamdi, F. K. Mohamad, N. J. Ridha, and P. P. Yupapin, Proposed molecule transporter system for qubits generation, presented at the Nanotech Malaysia, International Conference on Enabling Science & Technology, Malaysia 2010.

18. I. S. Amiri, S. Babakhani, G. Vahedi, J. Ali, and P. Yupapin, Dark-Bright Solitons Conversion System for Secured and Long Distance Optical Communication, IOSR Journal of Applied Physics (IOSR-JAP), 2(1), 2012, 43-48.

19. I. S. Amiri, K. Raman, A. Afroozeh, M. A. Jalil, I. N. Nawi, J. Ali, and P. P. Yupapin, Generation of DSA for security application, Procedia Engineering, 82011, 360-365.

20. M. A. Jalil, I. S. Amiri, C. Teeka, J. Ali, and P. P. Yupapin, All- optical Logic XOR/XNOR Gate Operation using Microring and Nanoring Resonators, Global Journal of Physics Express, 1(1), 2011, 15-22.

21. J. Ali, A. Afroozeh, I. Amiri, M. Jalil, and P. Yupapin, Wide and narrow signal generation using chaotic wave, presented at the Nanotech Malaysia, International Conference on Enabling Science & Technology Kuala Lumpur, Malaysia, 2010.

22. J. Ali, M. Roslan, M. Jalil, I. Amiri, A. Afroozeh, I. Nawi, and

    1. Yupapin, DWDM enhancement in micro and nano waveguide, presented at the AMN-APLOC International Conference Wuhan, China, 2010.

23. I. Amiri, J. Ali, and P. Yupapin, Security Enhancement of the Optical Signal Communication using Binary Codes Generated by Optical Tweezers, Chinese Journal of Physics, 2013,

24. J. Ali, S. Saktioto, M. Hamdi, and I. S. Amiri, Dynamic silicon dioxide fiber coupling polarized by voltage breakdown, presented at the Nanotech Malaysia, International Conference on Enabling Science & Technology KLCC, Kuala Lumpur, Malaysia, 2010.

25. A. A. Shojaei and I. S. Amiri, DSA for Secured Optical Communication, presented at the International Conference for Nanomaterials Synthesis and Characterization (INSC), Kuala Lumpur, Malaysia, 2011.

26. I. S. Amiri, A. Afroozeh, J. Ali, and P. P. Yupapin, Generation Of Quantum Codes Using Up And Down Link Optical Solition, Jurnal Teknologi, 552012, 97-106.

27. M. Bahadoran, I. S. Amiri, A. Afroozeh, J. Ali, and P. P. Yupapin, Analytical Vernier Effect for Silicon Panda Ring Resonator, presented at the National Science Postgraduate Conference, NSPC Universiti Teknologi Malaysia, 2011.

28. J. Ali, I. S. Amiri, M. A. Jalil, M. Hamdi, F. K. Mohamad, N. J. Ridha, and P. P. Yupapin, Trapping spatial and temporal soliton system for entangled photon encoding, presented at the