OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 9 — May. 2, 2005
  • pp: 3355–3370
« Show journal navigation

A phase insensitive all-optical router based on nonlinear lenslike planar waveguides

Eduardo F. Mateo and Jesús Li ñares  »View Author Affiliations


Optics Express, Vol. 13, Issue 9, pp. 3355-3370 (2005)
http://dx.doi.org/10.1364/OPEX.13.003355


View Full Text Article

Acrobat PDF (430 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present the design of an all-optical router based on the properties of both propagation and interaction of Gaussian beams in lenslike planar guides. Variational results of single co- and counterpropagation are derived and used to design three integrated optical devices, that is, a header extraction device, an optical bistable device and a data routing device, which perform an ultrafast, phase-insensitive and fiber compatible routing operation in the optical domain.

© 2005 Optical Society of America

1. Introduction

The development and perspectives of the Internet Era have represent, an enormous challenge in the task of giving solutions to the continuous growth of bandwidth requirements in communication networks [1

1. G. Stix, “The triumph of light,” Scientific American, January (1998).

].

In the context of fiber-based optical networks, the all-optical data processing plays a major role for future ultrafast communications schemes where bit-rates up to the Terabit barrier will be necessary; thus, operating at a ultra-high speed requires all-optical devices capable to operate in such a way that the entire optical signal routing, switching, processing and so on, can be made in the optical domain. In OTDM asynchronous packet transmission (for instance the IP protocol), a header is usually added to each data packet carrying information in order to identify the destination of the data; accordingly, the header recognition and separation process as well as the routing of the data packet to a proper output port as a function of the binary value of the header, must be one of the first steps towards routing architectures in the all-optical domain [2

2. B. Olsson, L. Rau, and J. Blumenthal, “WDM to OTDM multiplexing using an ultrafast all-optical wavelength converter,” IEEE Photon. Technol. Lett. 13, 1905 (2001). [CrossRef]

, 3

3. J. Blumenthal, B. Olsson, G. Rossi, T. E. Dimmick, L. Rau, M. Masanovic, O. Lavrova, R. Doshi, O. Jerphagnon, J. E. Bowers, V. Kaman, L. A. Coldren, and J. Barton, “All-optical label swapping networks and technologies,” J. Lightwave Technol. 18, 2058 (2000). [CrossRef]

].

Results about all-optical routing have been previously reported based on TOADs (Terahertz optical asymmetric demultiplexers) [4

4. I. Glesk, K.I. Kang, and P. R. Prucnal, “Ultrafast photonic packet switching with optical control,” Opt. Express 1, 126 (1997). [CrossRef] [PubMed]

], NOMLs (Nonlinear optical mirror loops) [5

5. K. H. Park and T. Mizumoto, “All-optical address extraction for optical routing,” Opt. Eng. , 38, 1848 (1999). [CrossRef]

], logic gates [6

6. V. W. S. Chan, K. L. Hall, E. Modiano, and K. A. Rauschenbach, “Architectures and technologies for high-speed optical data networks,” J. Lightwave Technol. 16, 2146 (1998). [CrossRef]

] or Bragg gratings [7

7. H. J. Lee, J. B. Yoo, V. K. Tsui, and K. H. Fong, “A simple all-optical label detection and swapping technique incorporating a fiber Bragg grating filter,” IEEE Photon. Technol. Lett. 13, 635 (2001). [CrossRef]

]; for such a devices, the interference phenomena is present and, in consequence, they show a strong phase-sensitivity as well as a high requirements for coherent interactions between data and/or control signals; moreover, the presence of undesirable factors in long-distance optical transmission such as: depolarization properties of optical fibers, finite coherence time of sources or nonlinear dispersive effects, could make difficult a coherent processing in all-optical networks [8

8. D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A 32, 2270 (1985). [CrossRef] [PubMed]

].

In this work we present a new strategy to route optical data packets in a phase-insensitive way. The routing configuration (introduced in section 2) is based on the intensity amplification of the header bits and on the properties of the nonlinear propagation and interactions of optical beams in integrated devices; these devices are composed by nonlinear lenslike waveguides and linear integrated multilenses connected to optical fibers. By means of the variational method, the evolution equations for the parameters of a single Gaussian beam propagation and for coand counterpropagating Gaussian beams are obtained in a nonlinear lenslike waveguide, which can be made by means of a linear film deposited on a parabolic-shaped curved substrate with third-order nonlinear properties (section 3).

The phase-insensitive character of the proposed routing system allows, on the one hand, an efficient routing operation for wavelength demultiplexed signals (without modifying the device characteristics) and on the other hand, it makes sure the robustness of the device when mechanical and/or thermal instabilities are present. Finally, it must be remarked that the data packet is considered here as a low power signal along the whole routing process and therefore it represents a key advantage over soliton processing devices for all-optical networks [11

11. F. Garzia, C. Sibilia, and M. Bertolotti, “All-optical serial switcher,” Opt. Quantum Electron. 32, 781 (2000). [CrossRef]

].

2. Phase-insensitive router: principles of operation

As the specific design of the integrated devices, implementing the whole routing operation, will be detailed later, let us introduce the basis of the proposed phase-insensitive routing mechanism sketched in Fig. 1. The primary aim is to route, in an all-optical way, the data packet onto two different optical ports (fiber 1 and 2) depending on the value of the header bit.

Fig. 1. Sketch of the intensity-dependent routing operation where HE-D represents the Header Extraction Device, OB-D is the Optical Bistable Device and DR-D is the Data Routing Device. In figure (A) is represented the operation under the presence of a 1-valued header bit whereas in figure (B) is represented the operation for a 0-valued header bit.

Let us start with the routing mechanism for a 1-valued header bit. The first device, labelled as HE-D (Header Extraction Device), performs the extraction of the header from data train by means of the power-dependent swing effect experimented by optical beams in the nonlinear lenslike waveguide; therefore, by a suitable design of the waveguide parameters and the initial conditions of the optical beams, the data and header bits can be coupled onto two optical fibers. Next, the header bit is added, by means of a directional coupler, to an OB-D (Optical Bistable Device) which is fed with a secondary continuous wave, labelled as feed, placing the bistable device on the proper power value (point L); in consequence, when the high power header bit is added, the bistable device jumps to a high transmission state (point H), which is stable due to hysteresis, and it provides an output continuous wave of high power, labelled as pump; this pump wave is subsequently amplified by means of an optical fiber amplifier in order to achieve an optimal power value. Finally, both the pump wave and the data packet are injected onto the DR-D (Data Routing Device) where the presence of the high intensity pump wave induces a cross-amplitude modulation on the low power data wave, which changes its normal trajectory; obviously, a proper designing of the lenslike parameters and the integrated multilenses will be required to achieve an optimal coupling of the data packet onto the output fiber 2.

Otherwise, when the header bit is 0-valued and accordingly the OB-D has been reseted to its operation point L, the OB-D gives a low output power value, which does not contribute to cross-amplitude modulation in the DR-D and therefore, the injected data packet trajectory does not present any modification on its trajectory in a such a way that they will be coupled onto fiber 1.

It is important to remark that the three devices involved in the routing operation are designed under the same technology and accordingly the modulation, power values and compatibility with optical fibers are kept unchanged in all the process. For the sake of simplicity, we have just introduced the fundamental mechanism of a single-bit operation with an initial amplified header bit, however, in section 7 is shown how to implement a N-bit routing mechanism with a low power modulation for the header and data bits (more realistic case), by means of a synchronized differential amplification of the header bits and a cascaded configuration of several single-bit routing devices.

3. Propagation and interaction of Gaussian beams in nonlinear lenslike waveguides

The main physical processes involved in the proposed routing device are the nonlinear propagation and nonlinear interactions of optical beams in lenslike nonlinear waveguides. We will derivate in this section, by means of the variational method, the corresponding nonlinear evolution equations containing the following particular cases: the single beam linear and nonlinear propagation, for the design of the HE-D; the coherent counterpropagation of beams, for the design of the OB-D; and incoherent copropagation of beams for the design of the DR-D.

Let us consider a planar step-index waveguide constituted by a nonlinear curved glass substrate of refractive index ns2+3χRe(3) 2, where χRe(3) is the real part of the third order nonlinear optical susceptibility and is the module of the optical field amplitude. The curved substrate, whose linear refractive index is ns , is shaped by a parabolic surface represented by the function f(x)=x 2/l 2; next, a linear film is deposited on the substrate with a maximum thickness t 0 at x=0; finally, nc2 is the cladding index. A sketch of the waveguide is shown in Fig. 2. The linear refractive index profile of the planar waveguide can be written as follows: nl2(x,y)=n02(y)+Δn 2(x,y), where n02(y) is the linear index profile at x=0 and Δn 2(x,y)=ns2-nf2 for 0≤yf(x), represents the index perturbation due the substrate curvature; finally, the nonlinearity distribution is characterized by χRe(3) (x,y)=χRe(3) for -∞≤yf(x).

Fig. 2. Transverse view of the waveguide.

It is wellknown that the real vector amplitude of the total optical field ⃗ satisfies the following scalar equation:

2(r,t)=μ02t2[ε0nl2(x,y)+3ε0χRe(3)(x,y)2].
(1)

Now, let us consider a set of two TE waves with central frequency ω0 and unperturbed propagation constants β1 and β2, that is,

(x,y,z,t)=12φ(y)[ψ1(x,z)exp(iβ1z)+ψ2(x,z)exp(iβ2z)]exp(iω0t)+cc.
(2)

For the case of incoherently interacting copropagating beams [8

8. D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A 32, 2270 (1985). [CrossRef] [PubMed]

], and coherent counterpropagation of parallel polarized beams [12

12. J. H. Marburger and F. S. Felber, “Theory of a lossless nonlinear Fabry-Perot interferometer,” Phys. Rev. A 17, 335 (1978). [CrossRef]

], the derivation of the propagation equations for the nonlinear envelopes ψα is made up by considering only the terms synchronized with the propagation constants β 1 and β 2, after inserting Eq. (2) into Eq. (1), and by performing a z-spatial averaging. For the counterpropagating case, there will be terms oscillating with ±3β 0 which vanish after a z-spatial averaging; likewise, in the case of incoherent copropagation, there will be a beams superposition with random phases, therefore only the terms corresponding with the sum of the beam intensities are conserved. In short, by considering the above assumptions, and by taking into account the expression of the linear index profile, we obtain, after multiplying by φ*(y) and integrating along the y-direction [13

13. R. A. Sammut, C. Pask, and Q. Y. Li, “Theoretical study of spatial solitons in planar waveguides,” J. Opt. Soc. Am. B 10, 485 (1993). [CrossRef]

], the following expressions for ψα (x, z),

2iβαψαz+2ψαx2+k2[Δn(x,y)φ2dy]ψα+
34k2[χRe(3)(x,y)φ4dy](ψα2+Jψ3α2)ψα=0,
(3)

with J=0 for a single-beam propagation, J=1 for the copropagating case and J=2 for the counterpropagating one.

The integrals of Eq. (3) can be solved by taking into account the perturbative condition (lx), as it is shown in reference [15

15. E. F. Mateo and J. Liñares, “All-optical integrated logic gates based on intensity-dependent transverse modal coupling,” Opt. Quantum Electron. 35, 1221 (2003). [CrossRef]

], and by taking into account the general expression for the fundamental mode of a step-index planar waveguide, which can be found, for instance, in reference [14

14. R. G. Hunsperger, Integrated optics: Theory and technology (Springer-Verlag, Berlin, 1991).

]. Accordingly, the above equations can be rewritten as follows,

2iβαψαz+2ψαx2G2x2ψα+k2n˜k0(1+Q2x2)(ψα2+Jψ3α2)ψα=0,
(4)

By following the variational formalism [10

10. E. F. Mateo, J. Liñares, and C. Montero, “Intrinsic bistability achieved by transverse modal coupling in a nonlinear integrated device,” J. Opt. A: Pure Appl. Opt. 4, 562 (2002). [CrossRef]

, 16

16. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys.Rev. A 27, 3135 (1983). [CrossRef]

] let us choose a Gaussian multiparametric trial function in order to solve Eq. (4), that is,

ψα(x,z)=E0αexp[(xxα)2a2wα2]exp[iβαρα(xxα)2+iVα(xxα)].
(5)

The four z-dependent parameters for each envelope are: the normalized beam widths (z), the inverse curvature radius ρα (z), the beam peak position xα (z) and the transverse local wave number Vα (z); a is the initial beam width, therefore wα (z=0)=1, and E is the maximum field amplitude.

After a long but straightforward calculations, the following coupled equations for the relevant Gaussian parameters are obtained:

d2wαdτ21wα3+gwα+12pα1wα2(1qwα2+Q2xα2)+2Jp3α1wα2×
(1+w3α2wα2)32(K0αqK1α+Q2K2α)exp[2(xαx3α)2a2wα2+a2w3α2]=0,
(6)
d2xαdτ2+gxα2pαqxα1wα+J2p3α(D0αqD1α)exp[2(xαx3α)2a2wα2+a2w3α2]=0,
(7)
Vα=βαdxαdτ,
(8)

where τ=2z/βαa 2, g=14G2a4, q=18Q2a2, pα=k 2 ñk 0 E0α2 a 2/2√2 (note that pα is a parameter which is proportional to the power of the beams), and

K0α=14(xαx3α)2a2wα2+a2w3α2,K1α=2w3α23wα2w3α2wα2+w3α2,
K2α=4x3α(wα2x3α+w3α2xα)wα2+w3α2+4(wα2x3α+w3α2xα)2(xαx3α)2a2(wα2+w3α2)3
+5(wα2x3α+w3α2xα)+wα2w3α2(xαx3α)2(wα2+w3α2)2.
(9)
D0α=(xαx3α)(wα2+w3α2)32,D1α=8w3α2(wα2x3α+w3α2xα)(wα2+w3α2)52
4(xαx3α)(wα2+w3α2)524(wα2x3α+w3α2xα)2(xαx3α)a2(wα2+w3α2)72.
(10)

Let us describe briefly the main effects involved in the light propagation inside the structure sketched in Fig.(2). As expected from Eq. (6) the g(G)-factor induces a linear lenslike effect depending on the linear substrate-film index difference and the curvature of the parabolic interface; moreover, the global self-focusing effect is modulated by the Gaussian intensity distribution depending on the power of the beam pα . The Q(q)-factor involves a double effect: by one hand, it compensates the linear gradient effect due the reduction of the index difference between the film and the substrate (since the index of the substrate is increased with the intensity), and by the other hand, it modulates the self-focusing effect as a function of the peak displacement increasing its influence in regions where the field is more present in the substrate. According to the first effect, the oscillatory behaviour of the beam peak displacement, which is induced by a gradient index distribution (swing effect), is in turn modulated as a function of the beam intensity/power (as Eq. (7) shows), and in consequence the period of oscillation is modified. This property is one of the key results of this work (as it will be shown in the HE-D design) since it does not take place in usual nonlinear lenses, where the focusing and/or swing properties are intensity-independent.

4. Design of the header extraction device

We will design an all-optical planar waveguide header recognizer, based on the commented power dependence of the period of the swing of the beam. The device will operate with two different power states, that is, a low power state (data packet) and a high power state (header bit); the design of the device must verify that the beams corresponding to these states be well spatially-resolved to achieve an optimal output coupling onto two different optical fibers. It is assumed that the low power state will undergo a linear propagation, that is p~0; and the high power state will be chosen as a quasi-self-trapping state, that is, a state where the Gaussian beam presents small variations of its width around the initial value.

Fig. 3. Top view of the header extraction device where the variational evolution of the header (solid) and data (dashed) Gaussian beam widths are shown.

The variational propagation equations for a single beam are derived by choosing p 2=0 in Eqs. (6) and (7); thus by denoting with (wh, xh ) the parameters of the header Gaussian beam with power p 1=ph , we obtain the following evolution equations:

d2whdτ21wh3+gwh+12ph1wh2(1qwh2+Q2xh2)=0,
(11)
d2xhdτ2+gxh2pqxh1wh=0.
(12)

On the other hand, the evolution equations for the data wave (wd, xd ) are derived from Eqs. (6) and (7) by considering a linear propagation of the data Gaussian beam (p 1=pd ≪1) and again p 2=0, that is,

d2wddτ21wd3+gwd=0,
(13)
d2xddτ2+gxd=0.
(14)

For the header Gaussian beam, the above-mentioned nonlinear quasi-self-trapping state is obtained as follows: if we consider a non-displaced Gaussian beam (δ=0), we can calculate the value of power pst for self-trapping: wh (pst,xh =0, z)=1, from Eq. (11) (see for example [16

16. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys.Rev. A 27, 3135 (1983). [CrossRef]

, 19

19. M. Desaix, D. Anderson, and M. J. Lisak, “Variational approach to collapse of optical pulses,” Opt. Soc. Am. B 8, 2082 (1991). [CrossRef]

]), that is,

pst=2(1g)1q=164G2α48Q2α2.
(15)

When this power value is used for displaced Gaussian beams (δ≠0) a quasi-selftrapping beam is obtained such as it is showed in Fig.3 (solid line).

By launching both the data and header Gaussian beams with an initial displacement δ, oscillating trajectories (swing effect) are obtained, and therefore spatial periods of oscillation can be defined for the corresponding trajectories, that is, Λd for the data Gaussian beam (obtained from Eq. (14)) and Λh for the header Gaussian beam (obtained from Eq. (12) with pst ). A simple condition for achieving a maximum spatial separation between the beams is obtained under the following condition: Λh=2Λl (see Fig.3). Now, we must calculate these periods and, as the g(G) and q(Q) factors depend on the waveguide parameters, the first step will be to obtain a proper design of the waveguide in order to enlarge the nonlinear contribution to the swing effect and so increase the difference between Λh and Λ l ; for that, we have considered a substrate formed by a porous nonlinear glass [20

20. R. J. Gehr, G. L. Fisher, and R. W. Boyd, “Nonlinear-optical response of porous-glass-based composite materials,” J. Opt. Soc. Am. B 14, 2310 (1997). [CrossRef]

] and a film formed by an organic material with the following characteristics: ns =1.500 and nf =1.540 at λ=0.532 µm, nc =1.000, t 0=2.40 µm and l=400.0 µm1/2; moreover, we have taken an initial peak displacement δ=40µm.

It can be easily derived from Eq. (14) that the peak trajectory of the data beam is given by the solution xd (τ)=δ cos(g 1/2 τ), therefore the linear period is

Λl=2πg12=4πGa2.
(16)

On the other hand, the initial beam width a of the beams is taken as a designing parameter; thus, from the numerical solutions of Eqs. (11) and (12), and by taking into account Eqs. (15) and the expression (16), we can find the value of a which fulfills the condition for the swing periods. The numerical result was a=6.87 µmand therefore with the following factors g=3.40×10-3, q=5.82×10-4 and pst =1.994.

In Figs. 4-(a) and (b) it is shown the evolution of the Gaussian widths of the linear and quasi-self-trapped beams, respectively.

Fig. 4. Variational results for the data (A) and header (B) beam propagation.

5. Design of the optical bistable device

In Fig. 5 it is shown the integrated device proposed for optical bistability. The device is made up by an nonlinear planar waveguide with the same characteristics that the one designed for the HE-D unless the curvature of the of the substrate-film interface, which, for the sake of simplicity, has been chosen as planar (l≫) (otherwise, it could arise undesired multistable loops [21

21. E. F. Mateo and J. Liñares, “Third order nonlinear integrated device based on an effective graded-index waveguide for all-optical multistability,” Fiber and Int. Optics. To be published (2005). [CrossRef]

]); in addition, two linear subsystems (input and feedback ones) formed by integrated-lenses and optical single-mode fibers are included. A reflective element, with reflectance R, is incorporated to the feedback subsystem, in order to obtain the optical counterpropagation. Finally, the regressive (feedback) beam is collected by the input lens providing, by means of a directional coupler, the output power value.

Fig. 5. Sketch of the bistable device showing the propagation behaviour of the counterpropagating beams in cases of low (A) and high (B) transmission output.

Let us denote as p+1≡pin and w+1 the power parameter and beam width of the forward beam, and p-1 and w-1 the power parameter and the width of the backward (feedback) beam (see Fig. 5). As it was mentioned above, for optical bistability we will consider an homogeneous planar waveguide (l≫) and in consequence g=Q=q=0; likewise, collinear beams are assumed, where x +1=x -1=0.0. Under such assumptions, the variational equations (6) for the counterpropagating beams (J=2) are now given, with the new notation, by,

d2w+1dτ21w+13+12p+11w+12+22p11w+12(1+w12w+12)32=0,
(17)
d2w1dτ21w13+12p11w12+22p+11w12(1+w+12w12)32=0.
(18)

η3(p+1,p1)=2w+1(z2,p+1,p1)1+w+12(z2,p+1,p1),
(19)

p1=η3(p+1,p1)Rp+1.
(20)

η0(p1,p+1)=2w1(z1,p1,p+1)1+w12(z1,p1,p+1),
(21)

where,

pout=p1η0(p+1,p1).
(22)

In short, we must solve the equations system given by Eqs. (17) and (18) with the implicit condition given by Eq. (20), in order to obtain the final pin-pout results. For that, we solve the equations system for the beam widths, starting from an initial value of p -1, and iteratively we find the value or values (since there will be multivalued point due to the bistability) of p -1 which fulfills the condition (20) for a given value pin ; iteration is based on the searching of roots of Eq. (20).

In Fig. 6 it is shown the result of the bistable calculus, for a reflectivity of R=1.0 and a propagation distance of |z 2-z 1|=2.1 mm. The propagation behaviour of the bistable operation (points A and B), it is shown in Figs. 5-A and -B respectively, extracted from the solutions of the equations (17) and (18).

Fig. 6. Optical bistability plot showing the bi-valued points for routing operation at pin =0.55, where A is the output power value for a header bit “0”, and B is for the header value “1”.

As it is shown in the bistability plot, we must fix the power of the bistability feed input (feed in Fig. 1) equal to pin=pfeed =0.55, therefore, when the header bit is added to the bistable feed power, the output switches to a high transmission state providing an output power value (in normalized units) pout =0.3. This value must be amplified since (as we will see later), the pump signal for the DR-D must fulfill the quasi-self-trapping condition (pst ~2) in the same way that in the header extraction device. It is important to stress here that the the power parameters p depend on the waveguide structure via the averaged third order susceptibility; in this way, we have considered the same waveguide parameters and material configuration which allows us to talk in terms of power parameters instead of real power values.

6. Design of the data routing device

We will perform the design of the device devoted to the derivation of the data as a function of the bistable output, which in turn, depends on the header bit value. The main task is to achieve an optimal coupling of the data packet wave onto two different optical fibers (output channels) depending on the presence or absence of the pump wave generated by the header bit. The pump wave, as in the HE-D, is propagated in a quasi-self-trapping state and it will induce changes on the refractive index, due third order nonlinearity, which will affect on the data packet wave by modifying its beam width and peak trajectory. The most important aim is to avoid the cross-talk between the output channels, that is, the presence of part of the data wave in its non-corresponding optical fiber; therefore, the coupling efficiency of the data packet in its corresponding channel must by sufficiently high and moreover, a fully negligible coupling efficiency in its non-corresponding optical fiber must be achieved. On the other hand, the pump wave must not increase in a relevant way the data transmission power in order the preserve the data power values in a linear regime. This requirement is important for a cascaded system where the output signals are used as input signals of new devices.

By considering again, as in section 4, that the power of the data sufficiently low for making sure a linear regime, that is, p d0=p d1~0, let us rewrite the evolution equations (6) and (7) for the data and pump beams for both the case of absence (header bit 0) and presence (header bit 1) of pump. For the first case we have that,

d2wd0dτ21wd03+gwd0=0,d2xd0dτ2+gxd0=0,Vd0=β0dxd0dτ.
(23)

For the second case,

d2wp1dτ21wp13+gwp1+12pp11wp12(1qwp12+Q2xp12),
d2xp1dτ2+gxp12pp1qxp11wp1=0,Vp1=β0dxp1dτ.
(24)

Moreover, the evolution equations for the data wave width in the presence of pump are given by,

d2wd1dτ21wd13+gwd1+
+2pp11wd12(1+wp12wd12)32(K0+qK1QK2)exp[2(xd1xp1)2a2wd12+a2wp12]=0,
(25)

where the values of the K-functions are given by Eqs. (9) with the proper notation. Finally, the peak displacement and the wave number of data beam in the presence of pump are given by,

d2xd1dτ2+gxd1+12pp1(D0qD1)exp[2(xd1xp1)2a2wd12+a2wp12]=0,
Vd1=β0dxd1dτ,
(26)

where the functions D 0 and D 1 are given by Eqs. (10).

Fig. 7. Integrated device performing the data routing under the absence (A) and presence (B) of the pump wave. The variational evolution of the pump (dashed) and data (solid) are shown for each case.

It is clear, from the above assumptions that the data wave in the absence of pump will not experiment any peak displacement since it is launched along the symmetry z-axis of the substrate-film curved interface; therefore, it will couple onto an output optical fiber at x=0; however, when the pump wave is present, the data wave will interact with the high power pump wave modifying its propagation, that is, the data beam will undergo a peak displacement; moreover, as in the HE-D, the pump wave will experiment a swing effect due to its initial peak shifting respect to x=0.

We start the calculation by choosing a separation of the output fibers equal to δ ; therefore, in the presence of pump, the data wave will be optimally coupled onto fiber 2 if the following conditions are fulfilled at plane z 3, that is

awd1(z3)=wg,xd1(z3)=δ.
(27)

For the sake of simplicity we have not imposed any restriction on the wave number V d1 at the plane z 3.

Now, by taking into account the transformation relationships for an output multilens with one EFT-module, and by considering the above expressions, we have the following expressions for the values of the Gaussian parameters of the data wave at the plane z 2, that is,

awd1(z2)=2Bk1wg,Vd1(z2)=kδB.
(28)

Finally, by taking the product of the above expressions, the Gaussian beam parameters of the data wave under the presence of the pump wave and the B parameter of the output multilens must fulfill the following condition

awd1(z2)Vd1(z2)=2δwg=10,B/k=12awd1(z2)wg.
(29)

It is important to stress that the Gaussian parameters at the plane z2 for both the pump wave and the data wave in the absence of pump, are now completely determined by the condition (29) since it will fix both the length of the nonlinear waveguide and consequently the parameters of the output multilens.

Therefore, the value of the beam width, peak displacement and wave number of the data wave without pump are now given by,

awd0(z3)=2Bk1awd0(z2)=wd1(z2)wgwd0(z2),xd0(z3)=0,Vd0(z3)=0,
(30)

and the pump wave parameters at the plane z 3 are given are given by,

awp1(z3)=2Bk1awp1(z2)=wd1(z2)wgwp1(z2),xp1(z3)=Bkxp1(z2)=12awd1(z2)wgVp1(z2),
Vp1(z3)=kBxp1(z2)=2awd1(z2)wgxp1(z2).
(31)

By solving the system of equations (24), (25) and (26) for the quasi-selftrapping power for the pump wave, that is p p1=pst (given by the equation (15)), we find the distance of propagation which makes sure the condition (29), that is z 2-z 1=25.84 mm. Once the optimal distance value has been obtained, we calculate, from Eqs. (23), the values for the Gaussian parameters of the data beam in the absence of pump. In Fig. 8 are shown the plots derived from the results from the design, where it can be observed the quantitative evolution of the beams for each routing operation.

ψσ(x)=214(πa2wσ2)14exp[(xxσ)2a2wσ2]exp[iVσ(xxσ)],
(32)

Fig. 8. Propagation plots (top view) for the data routing operation. (A) Data wave propagation under the absence of pump (header bit “0”); (B) Data and pump wave propagation under the presence of pump (header bit “1”).
φg(x)=214(πwg2)14exp[(xΔ)2wg2].
(33)

ησ=ψσ(x)φg(x)dx2=2awσwga2wσ2+wg2exp[12a2wσ2wg2Vσ2+4(xσΔ)2a2wσ2+wg2],
(34)

Table 1. Transverse coupling efficiencies of the data and pump beams onto the output optical fibers.

table-icon
View This Table

As the results show, the data packet is transmitted through each fiber with a high efficiency (higher than the 85 %) for each case; on the other hand, the most important result is that the cross-talk of the transmission is negligible since the coupling efficiencies of data packet on the non-corresponding channel are lower than 0.0001 %; in addition, the pump wave presents an optical coupling efficiency onto both channels about 10 %; although it is not negligible, it is enough to preserve the data packet free of nonlinear effects for further incorporation to cascaded devices.

7. Cascaded configuration for N-port routing.

The implementation of a single-bit routing module, presented above, routes the data signal onto two different output channels. It is the first step towards a general multi-port routing operation as a function of a generalized header composed by an array of bits. The header encoding in a N-bit binary format, allows the routing of the data packet towards 2N output ports, and the routing path must be determined by the header binary value.

Fig. 9. Scheme of the cascaded configuration for multi-bit header routing where a [0,1] header routes the data packet onto its correspondent output channel.

8. Conclusions

An integrated optical system has been fully designed for a phase-insensitive all-optical routing operation. By means of the variational method, we have obtained the evolution equations for the characteristic parameters of single, co- and counter-propagating Gaussian beams in a nonlinear lenslike waveguide. Starting from these results and in connection with the theory and design of integrated waveguiding multilenses, three integrated all-optical devices devoted to header bit extraction, bistability and data routing, have been designed under a unique technology. The optical system proposed shows a robust, phase-insensitive and fiber compatible single-bit routing operation. Finally, by connecting several integrated optical systems of this kind in a cascaded way a N-bit router can be implemented.

Appendix

In this work the design of the integrated multilens is based on one or two modules performing, each one of them, an Exact Fourier Transform (EFT) of the input beam. The configuration, for instance, of a multilens with two modules and their characteristic parameters are shown in Fig.10.

Fig. 10. Sketch of a multilens with two EFT modules.

Let us define each EFT module j=1,2 as a planar integrated multilens composed by mj plane-convex lenses of thickness tj and aperture Aj separated a distance lj with effective indexes Ni and No inside and outside of each lens. It can be demonstrated (explicit calculus is found in reference [17

17. J. Liñares, C. Montero, and D. Sotelo, “Theory and design of an integrated optical sensor based on planar waveguiding lenses,” Opt. Commun. 180, 29 (2000). [CrossRef]

]) that each module j produces, at zj -planes, an Exact Fourier Transform of the Gaussian beam at z j-1-planes if the following conditions are fulfilled,

Notj=Nilj,mjcos1(1tjNifj)=π2,
(A.1)

where fj are the focal lengths of each plane-convex lens, that is:

fj=NoNiNo1tj[tj2+(Aj2)2].
(A.2)

Now, by defining the Gaussian beam width, peak displacement and wave number at planes zj (see Fig.10) as wj, xj and Vj respectively, the following relationships, for a single EFT module, are obtained for the transformation of the beam parameters:

awj=2Bjk1awj1,xj=BjkVj1andVj=kBjxj1,
(A.3)

where,

Bj=[2tjfjNitj2No2].
(A.4)

Finally, by combining the expressions (A.3) it can be easily obtained the following relationships for two EFT modules, that is:

aw2=B2B1aw0,x2=B2B1x0andV2=B1B2V0.
(A.5)

Acknowledgments

This work was supported by contract TIC2003-08992, Ministerio de Ciencia y Tecnología (Spain).

References and links

1.

G. Stix, “The triumph of light,” Scientific American, January (1998).

2.

B. Olsson, L. Rau, and J. Blumenthal, “WDM to OTDM multiplexing using an ultrafast all-optical wavelength converter,” IEEE Photon. Technol. Lett. 13, 1905 (2001). [CrossRef]

3.

J. Blumenthal, B. Olsson, G. Rossi, T. E. Dimmick, L. Rau, M. Masanovic, O. Lavrova, R. Doshi, O. Jerphagnon, J. E. Bowers, V. Kaman, L. A. Coldren, and J. Barton, “All-optical label swapping networks and technologies,” J. Lightwave Technol. 18, 2058 (2000). [CrossRef]

4.

I. Glesk, K.I. Kang, and P. R. Prucnal, “Ultrafast photonic packet switching with optical control,” Opt. Express 1, 126 (1997). [CrossRef] [PubMed]

5.

K. H. Park and T. Mizumoto, “All-optical address extraction for optical routing,” Opt. Eng. , 38, 1848 (1999). [CrossRef]

6.

V. W. S. Chan, K. L. Hall, E. Modiano, and K. A. Rauschenbach, “Architectures and technologies for high-speed optical data networks,” J. Lightwave Technol. 16, 2146 (1998). [CrossRef]

7.

H. J. Lee, J. B. Yoo, V. K. Tsui, and K. H. Fong, “A simple all-optical label detection and swapping technique incorporating a fiber Bragg grating filter,” IEEE Photon. Technol. Lett. 13, 635 (2001). [CrossRef]

8.

D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A 32, 2270 (1985). [CrossRef] [PubMed]

9.

A. E. Kaplan, “Optical bistability that is due to mutual self-action of counterpropagating beams of light,” Opt. Lett. 6, 360 (1981). [CrossRef] [PubMed]

10.

E. F. Mateo, J. Liñares, and C. Montero, “Intrinsic bistability achieved by transverse modal coupling in a nonlinear integrated device,” J. Opt. A: Pure Appl. Opt. 4, 562 (2002). [CrossRef]

11.

F. Garzia, C. Sibilia, and M. Bertolotti, “All-optical serial switcher,” Opt. Quantum Electron. 32, 781 (2000). [CrossRef]

12.

J. H. Marburger and F. S. Felber, “Theory of a lossless nonlinear Fabry-Perot interferometer,” Phys. Rev. A 17, 335 (1978). [CrossRef]

13.

R. A. Sammut, C. Pask, and Q. Y. Li, “Theoretical study of spatial solitons in planar waveguides,” J. Opt. Soc. Am. B 10, 485 (1993). [CrossRef]

14.

R. G. Hunsperger, Integrated optics: Theory and technology (Springer-Verlag, Berlin, 1991).

15.

E. F. Mateo and J. Liñares, “All-optical integrated logic gates based on intensity-dependent transverse modal coupling,” Opt. Quantum Electron. 35, 1221 (2003). [CrossRef]

16.

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys.Rev. A 27, 3135 (1983). [CrossRef]

17.

J. Liñares, C. Montero, and D. Sotelo, “Theory and design of an integrated optical sensor based on planar waveguiding lenses,” Opt. Commun. 180, 29 (2000). [CrossRef]

18.

J. Liñares and M. C. Nistal, “Single local mode propagation though ion-exchanged waveguide elements with quasi-abrupt transitions,” Jpn. J. Appl. Phys. 35, L1596 (1996). [CrossRef]

19.

M. Desaix, D. Anderson, and M. J. Lisak, “Variational approach to collapse of optical pulses,” Opt. Soc. Am. B 8, 2082 (1991). [CrossRef]

20.

R. J. Gehr, G. L. Fisher, and R. W. Boyd, “Nonlinear-optical response of porous-glass-based composite materials,” J. Opt. Soc. Am. B 14, 2310 (1997). [CrossRef]

21.

E. F. Mateo and J. Liñares, “Third order nonlinear integrated device based on an effective graded-index waveguide for all-optical multistability,” Fiber and Int. Optics. To be published (2005). [CrossRef]

22.

J. Liñares, G. C. Righini, and J. E. Alvarellos, “Modal coupling analysis for integrated optical components in glass and lithium niobate,” App. Opt. 31, 5292 (1992). [CrossRef]

OCIS Codes
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(200.4560) Optics in computing : Optical data processing
(230.1150) Optical devices : All-optical devices

ToC Category:
Research Papers

History
Original Manuscript: January 11, 2005
Revised Manuscript: April 18, 2005
Published: May 2, 2005

Citation
Eduardo Mateo and Jesús Liñares, "A phase insensitive all-optical router based on nonlinear lenslike planar waveguides," Opt. Express 13, 3355-3370 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-9-3355


Sort:  Journal  |  Reset  

References

  1. G. Stix, �??The triumph of light,�?? Scientific American, January (1998)
  2. B. Olsson, L. Rau, and J. Blumenthal,�??WDM to OTDM multiplexing using an ultrafast all-optical wavelength converter,�?? IEEE Photon. Technol. Lett. 13, 1905 (2001). [CrossRef]
  3. J. Blumenthal, B. Olsson, G. Rossi, T. E. Dimmick, L. Rau, M. Masanovic, O. Lavrova, R. Doshi, O. Jerphagnon, J. E. Bowers, V. Kaman, L. A. Coldren, and J. Barton, �??All-optical label swapping networks and technologies,�?? J. Lightwave Technol. 18, 2058 (2000). [CrossRef]
  4. I. Glesk, K.I. Kang, and P. R. Prucnal, �??Ultrafast photonic packet switching with optical control,�?? Opt. Express 1, 126 (1997). [CrossRef] [PubMed]
  5. K. H. Park, and T. Mizumoto, �??All-optical address extraction for optical routing,�?? Opt. Eng., 38, 1848 (1999). [CrossRef]
  6. V. W. S. Chan, K. L. Hall, E. Modiano and K. A. Rauschenbach, �??Architectures and technologies for high-speed optical data networks,�?? J. Lightwave Technol. 16, 2146 (1998). [CrossRef]
  7. H. J. Lee, J. B. Yoo, V. K. Tsui, and K. H. Fong, �??A simple all-optical label detection and swapping technique incorporating a fiber Bragg grating filter,�?? IEEE Photon. Technol. Lett. 13, 635 (2001). [CrossRef]
  8. D. Anderson, and M. Lisak, �??Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,�?? Phys. Rev. A 32, 2270 (1985). [CrossRef] [PubMed]
  9. A. E. Kaplan, �??Optical bistability that is due to mutual self-action of counterpropagating beams of light,�?? Opt. Lett. 6, 360 (1981). [CrossRef] [PubMed]
  10. E. F. Mateo, J. Liñares, and C. Montero, �??Intrinsic bistability achieved by transverse modal coupling in a nonlinear integrated device,�?? J. Opt. A: Pure Appl. Opt. 4, 562 (2002). [CrossRef]
  11. F. Garzia, C. Sibilia, and M. Bertolotti, �??All-optical serial switcher,�?? Opt. Quantum Electron. 32, 781 (2000). [CrossRef]
  12. J. H. Marburger, and F. S. Felber, �??Theory of a lossless nonlinear Fabry-Perot interferometer,�?? Phys. Rev. A 17, 335 (1978). [CrossRef]
  13. R. A. Sammut, C. Pask, and Q. Y. Li, �??Theoretical study of spatial solitons in planar waveguides,�?? J. Opt. Soc. Am. B 10, 485 (1993) [CrossRef]
  14. R. G. Hunsperger, Integrated optics: Theory and technology (Springer-Verlag, Berlin, 1991).
  15. E. F. Mateo, and J. Liñares, �??All-optical integrated logic gates based on intensity-dependent transverse modal coupling,�?? Opt. Quantum Electron. 35, 1221 (2003). [CrossRef]
  16. D. Anderson, �??Variational approach to nonlinear pulse propagation in optical fibers,�?? Phys.Rev. A 27, 3135 (1983). [CrossRef]
  17. J. Liñares, C. Montero, and D. Sotelo, �??Theory and design of an integrated optical sensor based on planar waveguiding lenses,�?? Opt. Commun. 180, 29 (2000). [CrossRef]
  18. J. Liñares, M. C. Nistal, �??Single local mode propagation though ion-exchanged waveguide elements with quasi-abrupt transitions,�?? Jpn. J. Appl. Phys. 35, L1596 (1996). [CrossRef]
  19. M. Desaix, D. Anderson, M. J. and Lisak, �??Variational approach to collapse of optical pulses,�?? Opt. Soc. Am. B 8, 2082 (1991). [CrossRef]
  20. R. J. Gehr, G. L. Fisher, R. W. and Boyd, �??Nonlinear-optical response of porous-glass-based composite materials,�?? J. Opt. Soc. Am. B 14, 2310 (1997). [CrossRef]
  21. E. F. Mateo, and J. Liñares, �??Third order nonlinear integrated device based on an effective graded-index waveguide for all-optical multistability,�?? Fiber and Int. Optics. To be published (2005). [CrossRef]
  22. J. Liñares, G. C. Righini, and J. E. Alvarellos,�??Modal coupling analysis for integrated optical components in glass and lithium niobate,�?? App. Opt. 31, 5292 (1992). [CrossRef]

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.

CrossCheck Deposited