Quantum key distribution using the localized soliton pulses via a wavelength router in the optical network

Quantum key distribution using the localized soliton pulses via a wavelength router in the optical network

ARTICLE IN PRESS Optik Optics Optik 121 (2010) 1111–1115 www.elsevier.de/ijleo Quantum key distribution using the localized soliton pulses via a w...

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Optik

Optics

Optik 121 (2010) 1111–1115 www.elsevier.de/ijleo

Quantum key distribution using the localized soliton pulses via a wavelength router in the optical network N. Pornsuwancharoena, U. Dunmeekaewa, P.P. Yupapinb, a

Department of Electronic Engineering, Faculty of Industry and Technology, Rajamangala University of Technology Isan, Sakonnakon 47160, Thailand b Advanced Research Center for Photonics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand Received 29 August 2008; accepted 19 December 2008

Abstract We propose a new system of a continuous variable quantum key distribution via a wavelength router in the optical networks. A large bandwidth signal is generated by a soliton pulse propagating within the micro ring resonator, which is allowed to form the continuous wavelength with large tunable channel capacity. There are two forms of localized soliton pulses proposed. Firstly, the required information is transmitted via the localized temporal soliton pulse. Secondly, the continuous variable quantum key distribution is formed by using the localized spatial soliton pulse via a quantum router and networks, which is formed by using and optical add/drop multiplexer incorporating in the network. The localized soliton pulses are available for add/drop signals to/from the optical network, where the high security and capacity information can be performed. r 2009 Elsevier GmbH. All rights reserved. Keywords: Continuous variable; QKD; Quantum router; Quantum network; Perfect security

1. Introduction Quantum key distribution (QKD) is only form of information that can be provided the perfect communication security. The use of QKD has been proposed in many research works, whereas the applications in different forms such as point to point link [1], optical wireless [2], satellite [3], long distance [4] and network [5] have been reported. However, a more reliable system for network security is needed. The system that can be provided the ability of serving both in high capacity and security is required. The concept of continuous variable Corresponding author. Fax: +66 2 3264 354.

E-mail address: [email protected] (P.P. Yupapin). 0030-4026/$ - see front matter r 2009 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2008.12.034

in the form of dense wavelength multiplexing is introduced to overcome such a problem. By using the continuous variable concept, the continuous QKD can be formed and available for a large demand. There are some works proposed the use of continuous variable QKD with quantum router and network [6,7]. However, the requirement of large bandwidth signal and dense wavelength multiplexing become the practical problems. Recently, Yupapin et al. [8] have shown that the continuous wavelength can be generated by using a soliton pulse in a micro ring resonator, which can be used to overcome such problems. In this work, we propose the system that uses two types of localized soliton pulses to form the high capacity and security communication in the optical network. The generation

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of the localized soliton pulses for continuous variable application is demonstrated. The detail of QKD via a wavelength router is described.

2. Operating principle An optical soliton is recognized as a powerful laser pulse, which can be used to enlarge the optical bandwidth when propagating within the nonlinear micro ring resonator. Moreover, the soliton self-phase modulation (SPM) keeps the large output gain. When the soliton pulse is introduced into the multi-stage micro an ring resonators as shown in Fig. 1(a), the input optical field (Ein) is given by     T z exp (1) E in ¼ A sec h T0 2LD where A and z are the optical field amplitude and propagation distance, respectively. T is a soliton pulse propagation time, and LD ¼ T 20 =jb2 ji is the dispersion length of the soliton pulse. b2 is propagation constant. This solution describes a pulse that keeps its temporal width invariance as it propagates, and thus is called a temporal soliton. When a soliton peak intensity ðjb2 =gT 20 jÞ is given, then T0 is known. For instance,

when the soliton pulse is input into a micro ring resonator at wavelength of 1.55 mm, with a 12 W peak power, then T0 ¼ 50 ns. This is a pulse of about 2 mm (in z). For the soliton pulse in the micro ring device, a balance should be achieved between the dispersion length (LD) and the nonlinear length (LNL ¼ (1/gfNL), where g and fNL are a coupling loss of the field amplitude and nonlinear phase shift, respectively. They are the length scales over which dispersive or nonlinear effects makes the beam becomes wider or narrower. For a soliton pulse, there is a balance between dispersion and nonlinear lengths, hence LD ¼ LNL .   n2 P (2) n ¼ n0 þ n 2 I ¼ n0 þ Aeff where n0 and n2 are the linear and nonlinear refractive indexes, respectively. I and P are the optical intensity and optical power, respectively. The effective mode core area of the device is given by Aeff. For the micro ring and nano ring resonators, the effective mode core areas range from 0.50 to 0.1 mm2 [9]. When a soliton pulse is input and propagated within a micro ring resonator as shown in Fig. 1(a), which can be a series micro ring resonators. The resonant output is formed, thus, the normalized output of the light field can be expressed as

2 3   2 E out ðtÞ2 ð1  ð1  gÞx Þk   4  5 pffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffi  E ðtÞ  ¼ ð1  gÞ 1  in ð1  x 1  g 1  kÞ2 þ 4x 1  g 1  k sin2 f

(3)

2

Fig. 1. Schematic of a localized soliton pulse generation system (a) and (b) a schematic of a quantum router and network system, where Rs; ring radii and ks, ks1, ks2 are the coupling coefficients.

The close form of Eq. (3) indicates that a ring resonator in the particular case to very similar to a Fabry–Perot cavity, which has an input and output mirror with a field reflectivity, (1k), and a fully reflecting mirror. Where k is the coupling coefficient, and x ¼ expðaL=2Þ represents a roundtrip loss coefficient, f0 ¼ kLn0 and fNL ¼ kLn2 jE in j2 are the linear and nonlinear phase shifts, respectively, k ¼ 2p=l is the wave propagation number in a vacuum. Where L and a are a waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the result as shown in Eq. (3), similarly, when the output field is connected and input into the other ring resonators. Generally, there are two pairs of the possible polarization entangled photons formed within the ring device, which they are represented by the four polarization orientation angles as [01, 901], [1351 and 1801]. These can be formed by using the optical component called the polarization rotatable device and PBS. In this concept, we assume that the polarized photon can be performed by using the proposed arrangement. Where each pair of the transmitted qubits can be randomly formed the entangled photon pairs. To begin this

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into the polarized state by the delay circuit as jFi ¼ ½j1; His þ expðifs Þj2; V is   ½j1; Hii þ expðifi Þj2; V ii  þ ½j2; His þ expðifs Þj3; V is   ½j2; Hii þ expðifi Þj2; V ii  ¼ ½j1; His j1; Hii þ expðifi Þj1; His j2; V ii  þ expðifs Þj2; V is j1; Hii þ exp½iðfs þ fi Þj2; V is j2; V ii þ j2; His j2; Hii þ expðifi Þj2; His j3; V ii þ expðifs Þj3; V is j2; Hii þ exp½iðfs þ fi Þj3; V is j3; V ii Fig. 2. Shows a schematic of a continuous wavelength generation (a), and (b) a schematic of an entangled photon pair generation via a nonlinear four wave mixing (FWM) type in a ring resonator. The Bell’s state is propagating to a rotatable polarizer and then is split by a beam splitter (PBS) flying to detector D1 and D2, where their visibility are measured.

concept, we introduce the technique that can be used to create the entangled photon pair (qubits) as shown in Fig. 2, a polarization coupler that separates the basic vertical and horizontal polarization states corresponds to an optical switch between the short and the long pulses. We assume those horizontally polarized pulses with a temporal separation of Dt. The coherence time of the consecutive pulses is larger than Dt. Then the following state is created by Eq. (4). jFip ¼ j1; His j1; Hii þ j2; His j2; Hii

(4)

In the expression jk; Hi; k is the number of time slots (1 or 2), where denotes the state of polarization [horizontal jHi or vertical jV i], and the subscript identifies whether the state is the signal (s) or the idler (i) state. In Eq. (4), for simplicity we have omitted an amplitude term that is common to all product states. We employ the same simplification in subsequent equations in this paper. This two-photon state with jHi polarization shown by Eq. (4) is input into the orthogonal polarization-delay circuit shown schematically. The delay circuit consists of a coupler and the difference between the round-trip times of the micro ring resonator, which is equal to Dt. The micro ring is tilted by changing the round trip of the ring is converted into jV i at the delay circuit output. That is the delay circuits convert jk; Hi to be rjk; Hi þ t2 expðifÞjk þ 1; V i þ rt2 expði2 fÞjk þ 2; Hi þ r2 t2 expði3 fÞjk þ 3; V i where t and r is the amplitude transmittances to cross and bar ports in a coupler. Then Eq. (4) is converted

(5)

By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the following polarization entangled state as jFi ¼ j2; His j2; Hii þ exp½iðfs þ fi Þj2; V is j2; V ii

(6)

We assume that the response time of the Kerr effect is much less than the cavity round-trip time. Because of the Kerr nonlinearity of the optical device, the strong pulses acquire an intensity dependent phase shift during propagation. The interference of light pulses at a coupler introduces the output beam, which is entangled. Due to the polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. The entangled photons of the nonlinear ring resonator are separated to be the signal and idler photon probability. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity.

3. Results and discussion In operation, the large bandwidth within the micro ring device can be generated by using a soliton pulse input into the nonlinear micro ring resonator. The schematic diagram of the proposed system is as shown in Fig. 1. The localized soliton pulse is generated by using the schematic in Fig. 1(a), whereas the required signals can be performed the secure communication network as shown in Fig. 1(b). In order to begin this concept, a soliton pulse with 20 ns pulse width, peak power at 500 mW is input into the system. The suitable ring parameters are used, for instance, ring radii R1 ¼ 10 mm, R2 ¼ 5 mm, and R3 ¼ 2.5 mm. In order to make the system associate with the practical device [10,11], the selected parameters of the system are fixed to l0 ¼ 1.55 mm, n0 ¼ 3.34 (InGaAsP/InP), Aeff ¼ 0.50, 0.25 and 0.12 mm2 for a micro ring and nano ring, respectively, a ¼ 0.5 dB mm1, g ¼ 0.1. The coupling coefficient (kappa, k) of the micro ring resonator ranged

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from 0.50 to 0.975. The nonlinear refractive index is n2 ¼ 2.2  1017 m2/W. In this case, the wave guided loss used is 0.5 dB mm1. As shown in Fig. 3, the signal is chopped (sliced) into a smaller signal spreading over the spectrum as shown in Fig. 3, which is shown that the large bandwidth(continuous variable) is formed within the first ring device. The compress bandwidth with smaller group velocity is obtained within the ring R2. The amplified gain is obtained within a nano ring device (i.e. ring R3). The localized light pulse situation can be formed by using the constant9remaining) gain condition, where a small group velocity is seen. The

Fig. 3. Results obtained when light is stored (temporal localized) within a nano ring device with 40,000 roundtrips, the pulse width is 3 ps, the ring radii are R1 ¼ 10 mm, R2 ¼ 5 mm, R3 ¼ 4 mm, and the coupling coefficient is 0.90.

attenuation of the optical power within a nano ring device is required in order to keep the constant output gain, where the next round input power is attenuated and kept the same level with the R2 output as shown in Fig. 4. This means that the remaining power of the light pulse (i.e. localized soliton) can be absorbed the coupling loss and distributed into the employed system. The localized soliton concept is formed when the constant gain of the tuned light pulse is achieved as shown in Fig. 4. Since, we have found that the tuned light pulse gain recovery can be obtained by connecting the nano ring device into the system (i.e. R2), therefore, the coupling loss is included due to the different core effective areas between micro and nano ring devices, which is given by 0.1 dB. However, we have already described that the other ring parameters are also very important to keep localized light pulse behavior. We can conclude that the tuned light pulse can be stored or localized in the nano ring device when the output gain is reached a constant value which is time independence, as shown in Figs. 4–6. By using Eq. (3), the output gain of light pulse within a ring R3 is obtained. The output gain of a ring R3 can be attenuated and reached the value that can be used for the next storing input power, which is shown in Fig. 4. The main parameters that can provide the constant are k31, k32 and the output power. In principle, the soliton behavior known as SPM is performed when the balance between the dispersion and nonlinear length phase shift is presented, which is induced the soliton pulse gain recovery. When light pulse is slow down and completely stopped within a ring

Fig. 4. Plot of the temporal soliton within a nano ring device, with the pulse width (Dt) is 2 ps, the coupling coefficient is 0.90.

Fig. 5. Plot of the temporal soliton within a nano ring device, with the pulse width (Dt) is 2 ps, the coupling coefficient is 0.90.

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Fig. 6. Plot of the spatial soliton within a nano ring device, with the optical spectral width (Dl) is 1 pm, the coupling coefficient is 0.95.

R3, the localized or stored light pulse time of 2 ps (1012 s) is achieved. In application, both temporal and spatial soliton pulses can be kept (stored) within the nano waveguide as shown in Figs. 4–6, which can be used to form the classical signal and quantum key in the optical network. In Fig. 6, several soliton pulses with different wavelengths can be generated, which can be formed more channel capacity by using the wavelength division multiplexing (WDM). This means that the secure communication with high capacity can be realized by using the proposed system.

4. Conclusion We have shown that a large bandwidth of the arbitrary wavelength of light pulse can be generated and compressed to store within a nano waveguide. The tuned pulse can be slow down and localized coherently when the matching between dispersion and nonlinear length is exhibited, whereas the soliton SPM pulse exhibits the gain constant within the soliton period. The selected light pulse can be localized and used to perform the secure communication network. The classical information and security code can be formed by using the temporal and spatial soliton pulses, respectively. Furthermore, the applications such as quantum repeater, quantum entangled photon source and quantum logic gate can also be available, which can be fulfilled the concept of quantum computer and networks.

Acknowledgments This research was supported by the ‘‘Industry and University Cooperative Research Center (I/UCRC) in HDD Components, the Faculty of Engineering, Khon Kaen University and National Electronics and Computer Technology Center (NECTEC), National Science and Technology Development Agency’’, Thailand.

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