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Chaotic signal generation and coding using a nonlinear micro

Optics

Optik

Optik 121(2010)120–125

Chaotic signal generation and coding using a nonlinear micro ring resonator

S.Mitatha a ,K.Dejhan a ,P.P.Yupapin b,?,N.Pornsuwancharoen c

Faculty of Engineering,Research Center for Communication and Information Technology,King Mongkut’s Institute of Technology Ladkrabang,Bangkok 10520,Thailand b

Department of Applied Physics,Advanced Research Center for Photonics,Faculty of Science,King Mongkut’s Institute of Technology Ladkrabang,Bangkok 10520,Thailand c

Department of Electronics,Faculty of Industry and Technology,Rajamangala University of Technology Isan,Sakon-nakorn Campus 47160,Thailand

Received 20December 2007;accepted 25May 2008

Abstract

We propose a new digital encoding method using light pulses tracing in a micro ring resonator,where the randomly digital codes can be performed.The chaotic signals can be generated and formed by the logical pulses ‘‘1’’or ‘‘0’’by using the signal quantizing method,which can be randomly coded by controlling the speci?c optical input coupling powers,i.e.coupling coef?cient (k )and ring radii.Simulation results when the ring radius used is 10.0m m,and the other selected parameters are close to the practical device values that are presented and discussed.The random codes can be generated by the random control of coupling powers,which can be transmitted and retrieved via the design ?lters by the speci?c clients.For instance,the controlled input power used is between 2.0and 3.5mW,whereas the quantizing threshold powers and the traveling roundtrips are 0.3–0.4mW and 8000–10,000,respectively.In application,the required information can be generated,and the information can be securely transmitted in the public link.

Keywords:Nonlinear optical communication;Chaotic encoding;Chaotic communication

1.Introduction

Chaotic behavior has been studied as a nonlinear property in areas such as mathematics [1],physics,electronics,and communications [2].They have reported that the nonlinear behaviors can be accorded when the concerned parameters are suitable in similar cases,which is commonly known as a non-periodic behavior

and become the penalty of the system.However,the bene?t of such a property can also be accepted,for instance,the chaotic communication has recently attracted great interest because of its potential applica-tions in secure and con?dential communications,where it uses a noise-like broadband chaotic waveform as a carrier.Furthermore,the chaotic noise has been found useful in several areas of applications such as electronic communication [3],switching and control [4],and optical communication [5].Where the resonator use of the bene?t of such a nonlinear behavior,especially,in

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?Corresponding author.Tel.:+23264339;fax:+23264354.

E-mail address:kypreech@kmitl.ac.th (P.P.Yupapin).

the military purpose for when the information is required to be kept con?dential.In general,the nonlinearity of the system involves behaviors such as chaos,bistability,and bifurcation,which can be generated in the electronic circuit and optical?ber [6,7],laser system[8],and optical waveguide[9].One application is the use of the device known as a micro ring resonator,which can be formed by a waveguide or a ?ber optic that has shown a very promising application. Moreover,when such a device is fabricated within the range of a micrometer scale[10,11],it can be used incorporating a system such as a mobile telephone hand set,computing system,and telecommunication net-works.The secure communication systems based on chaos in a micro ring resonator were proposed by references[12,13].The message coding and the nonlinear effect of the coding process and control chaotic signal encoding were studied.They consist of three methods, such as(1)control input power(mW);(2)control threshold power(mW);and(3)timing control.

The chaotic encoding methods are processed by sampling,quantizing,and chaotic synchronization. The chaotic signal generation and cancellation using a micro ring resonator have been recently reported[7].In this paper,we have proposed the extended details of our previous work,where the other point of view from its applications is the chaotic switching of the optical output which can be formed by the digital codes.The selected input signals can be used to control the required chaotic encoding,which can be distributed into the optical transmission link.The most important advan-tage of the proposed system is the easy implementation compared to the well-known secure communication technique called quantum cryptography[14],which will be extremely dif?cult in the realistic system,while the requirement in terms of security is acceptable.Even-tually,the required information can be retrieved when the decode technique and the tunable?lters are employed by the required clients.The basic theory of a micro ring resonator is reviewed,the chaotic quantiz-ing and coding and control are presented in detail.

2.Operating principles

A simple device schematic diagram is as shown in Fig.1,when the light from a monochromatic light source is launched into a ring resonator with a constant light?eld amplitude(E0)and random phase modulation (f0),which results in a chronological coherence degradation.Hence forth,the input light?eld(E in)can be expressed as

E inetT?E0exp j f0etT(2.1) Eq.(2.2)is given by[7]

E outetT

2?e1àgT

?1à

e1àe1àgTx2Tk

e1àx=

???????????

1àg

p???????????

1àk

T2t4x

???????????

1àg

p???????????

1àk

sin2ef=2T"#

(2.2) In addition,the optical?elds E1and E2represent the right and left hand circulations in a ring resonator, respectively.A close examination of Eq.(2.2)indicates that a ring resonator in the particular case is very similar to a Fabry–Perot cavity,which has an input and output mirror with a?eld re?ectivity,1àk,and a fully re?ecting mirror.Where n0and n2are the linear and nonlinear refractive indices,and the coupling coef?cient is k. Where x?exp(àa L/2)represents a roundtrip losses coef?cient,f0?kLn0and f NL?kLn2|E1|2are the linear and nonlinear phases that shift,respectively; k?2p/l is the wave propagation number in vacuum. This nonlinear behavior of light traveling in a single ring resonator is described.When the parameters of the system are?xed to l0?1.55m m,n0?1.54,A eff?30m m2,the waveguide ring resonator loss(a)is0.5dB/mm.The practical bending loss of the waveguide fabricated by InGaAsP/InP is con?rmed by reference[15],where the propagation loss is as low as1.37.02dB/mm at1.55m m [16],the fractional coupler intensity loss(g)is0.1,and R1?10m m.The coupling coef?cient of the?ber coupler is ?xed to k?0.0225.The nonlinear refractive index used is n2?2.2?10à15m2/W[7],and the data of10,000itera-tions of roundtrips inside the optical micro ring are plotted.We assume that f L?0for simplicity;however, the change in phase is slightly altered by the optical output [9],which means the dispersion can be neglected when the resonant output has occurred.The chaotic signals are generated by using Eq.(2.2),which can be electronically formed by the digital codes as the following details.The quantitatively present logic coding can be expressed by.

uevT?

0::::::::v o3:5mW

1::::::::v X3:5mW

(

(2.3)

Furthermore,when u(v)represents the logic states,v is the signal power.The quantization and re-quantization can be processed by similar transfer characteristics.We assume that the quantizing involved is in?nite,which means that the system input signal is never clipped by saturation of the quantizing.In this case,the correspond-ing transfer functions of the quantizing output to its input can be expressed analytically in terms of the quantizing

Fig.1.A schematic diagram of the micro ring resonator.

S.Mitatha et al./Optik121(2010)120–125121

step size as detailed in references [17,18].The chaotic signals mentioned below can be used to form the digital codes.Fig.2illustrates a ?ow chart of the chaotic encoding procedures.When the program is operated,i.e.‘‘START,’’then the program logical coding begins.Firstly,the reduction of the threshold and maximum powers is required,which are ranged between 3.5and 4mW.Secondly,‘‘Yes’’and ‘‘NO’’form the logics ‘‘1’’and ‘‘0’’,https://www.wendangku.net/doc/3710889288.html,stly,‘‘END’’is the process of the ?nal step.In practice,the design micro ring resonator with its suitable parameters can be used to generate the chaotic signals,which can be electronically coded.For example,the chaotic signals with the optical power ranges are 1.8–1.82,1.84–1.86and 1.88–1.90mW as shown in Fig.3.The signal quantization can be further understood by using the approximation method in which the chaotic signal can be encoded.The quantizing plots of the various input powers are ranged from 1.8to 1.82mW as shown in Fig.3.These plots show the improvement of the approximation method as shown in Fig.3(a–c),and deterioration until or the least-square method in Fig.3(d)is introduced.The signal processing of the output using the approximation method is plotted.Where (a)shows the relationship between the input and output signals;(b)the red line (straight line)is the power reduction with the threshold power of 3.5mW;(c)the signal after threshold power condition uses;and (d)the output signal of when the approximation method

is employed.The logical code with the logic state ‘‘1’’or ‘‘0’’is generated from the previous description,after the chaotic behaviors of the device are characterized;the next step is that random coding can be generated by controlling the input optical power,which then enters into the micro ring device.The required chaotic codes can be electronically generated.However,in application,the ?ber ring resonator parameters and the reliable optical source have become the key conditions.

3.Chaotic coding and control

The chaotic coding generation can be processed as the following.Firstly,the chaotic signals can be generated within the ?ber ring resonator by controlling the optical input power into a ring resonator,which can be speci?ed by the roundtrip numbers,i.e.circulation time.Sec-ondly,the electronically encoding processes are per-formed by the following steps:(i)chaotic coding with the threshold power is marked by using the least-square method;(ii)the clipping signals is introduced;and (iii)the chaotic code generation is completed by using the approximation and sampling methods.The ?rst chaotic code generation is as shown in Fig.4,where Fig.4(a)shows the relationship between the output signals and roundtrips,in which the chaotic behavior occurs when the roundtrips are 10,000,and the optical power is 0.5mW.In Fig.4(b)the threshold power is 3.5mW,and the encoding roundtrips are ranged between 9000and 9050.

The ‘he’clipping signals shown in Fig.4(c–e)are the clipping signals using the least-square method and the chaotic codes using the approximation method.The logic codes are [011110101010110101111010111-010110101010101011110101],which are 50logic codes,and a roundtrip time is found to be 29?10à12s,i.e.ps.

Fig.3.The chaotic signal and coding using the approximation method.

START

Logical Coding

Threshold 0.35mW

Yes

Logic “0”

Logic “1”

END

Fig.2.A diagram of a chaotic coding

algorithm.

Fig. 4.Chaotic codes:[0111101010101101011110101110101-10101010101011110101].

S.Mitatha et al./Optik 121(2010)120–125

122

Similarly,Figs.5–8are the results which are described as the following?gure captions.Fig.5(a),the optical output power is0.5mW,with10,000roundtrips,where the threshold power is0.40mW with the encoding roundtrips that range between9000and9050as shown in Fig.5(b);Fig.5(c)shows the clipping signals,and the least-squares method is applied as shown in Fig.5(d). There are50logic codes obtained with a bit time of 29?10à12s as shown in Fig.5(e).In Fig.6(a)the input optical power is2mW with10,000roundtrips,and the output power is0.5mW(b).The red line is the threshold power,which is0.30mW within the encoding ranges and that range between9000and9025roundtrips.

(c)The clipping signal using the threshold power without the least-squares method,(d)the clipping signals using the threshold power with the least-squares method,(e)the chaotic codes obtained using the approximation method in which there are25logic codes.The roundtrip time is29?10à12s.In Fig.7(a)the input power is2.00mW within10,000roundtrips,the output power is0.5mW.In Fig.7(b)the threshold power is0.30mW,within the encoding ranges between 9000and9025roundtrips.Fig.7(c)and(d)shows the clipping signals without and with least-squares methods.The chaotic codes using the approximation method is as shown in Fig.7(e).There are25logic codes;moreover,the roundtrip time is29?10à12s.In Fig.8(a)the input power is 2.00mW within10,000 roundtrips and the output power is0.5mW.In Fig.8(b) the red line is the threshold power(0.3mW),which is shown within the encoding ranges between8975and 9000roundtrips.The clipping signals without and with the least-squares methods are shown in Fig.8(c–e),which show that the chaotic codes using the approximation

Fig. 5.Chaotic codes:[0000001010100001000000100010100-

00101010101000000101].

Fig.6.Chaotic codes:

[01111110111011110111111011].Fig.7.Chaotic codes:

[01111110111011110111111011]. Fig.8.Chaotic codes:[10111111111101110111101010].

S.Mitatha et al./Optik121(2010)120–125123

method,there are 25logic codes,and the roundtrip time is 29?10à12s.

4.Discussion and conclusion

From Fig.9,the chaotic signals are generated by using the micro ring part,while the chaotic codes (digital codes)are electronically performed by the encryption data.The signals are multiplexed and transmitted via either wire or wireless links to the required receivers.The transmitted signals are received by the users and de-multiplexed,where the synchronously decryption to the encryption data is processed before the chaotic codes being intercepted by the speci?c users via the design chaotic ?lters.Finally,the required signals can be retrieved by the previous scheme,i.e.chaotic cancella-tion [7].Using Eq.(2.2),the simulation results obtained are shown in Fig.10,where Fig.10(a)shows the behaviors of the band stop and band pass ?lters with a ring radius of 12m m,roundtrips of 9050–11,500.In Fig.10(b)and (c),the band stops and band pass ?lters’characteristics of the different ring radii,and the serial rings con?guration are shown.Similarly,the multi-?lter characteristics can be seen in Fig.11.However,the low level of the upper and lower side bands of the signals may cause a problem of low-level signal to noise ratio in real applications.The serial rings results have shown better S/N than the single ring con?gurations.

We have proposed the use of a micro ring resonator to generate the chaotic codes,where the advantages of such a device are (i)the signals are randomly encoded,(ii)easy to design and implement,(iii)the control optical power could be selected,and ?nally (iv)the tunable ?lters can be employed.In an application,such a proposed device can be fabricated and implemented in the communication.For example,a mobile telephone hand set,a computing system,and telecommunication networks.The chaotic signals can be encoded by using the electronically synchronized technique,where the required message can be successfully decoded by

Fig.9.The schematic diagram of the synchronous encryption and the encryption

system.

Fig.10.The chaotic ?lter characteristics and roundtrips of the micro ring at the roundtrips of 20,000,(a)R ?12m m,(b)R ?15m m,(c)R ?12m m in series with R ?15m

Fig.11.The chaotic ?lter characteristics and roundtrips of the output signal using micro ring at the roundtrips of 20,000,(a)R ?16m m,(b)R ?17m m,(c)R ?16m m in series with R ?17m m.

S.Mitatha et al./Optik 121(2010)120–125

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subtracting the chaotic oscillation.This is operated by the receiver on the transmitted signal by using the least-squares method.We have demonstrated that the chaotic signal is logically encoded by using the wave-forms of the transmitter and chaotic signal of the receiver output.Thus,we can conduct a secure transmission of a message by logical coding using the electronic quantizing,and coding by using the micro ring incorporating in the communication transmission. In either case,the completed or generalized chaotic quantizing control and chaotic signals encoding can be applied to the systems for chaotic communications for a long distance communication when the loss in the optical power is the issue of implementation.Therefore, such a proposed technique can overcome the problem of signal degradation because the digital signal can be recovered more easily than the analog ones.In practice, the optical repeater is required into the system,where the signal recovery and noise reduction are required to be taken into account.For further application,the more advantageous method,called quantum chaos,may be the new area of investigation in the near future. References

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