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

Optics Express, Vol. 13, Issue 9, pp. 3355-3370 (2005)

http://dx.doi.org/10.1364/OPEX.13.003355

Acrobat PDF (430 KB)

### 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

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]

## 2. Phase-insensitive router: principles of operation

*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.

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

*ℰ*

^{2}, where

*ℰ*is the module of the optical field amplitude. The curved substrate, whose linear refractive index is

*n*

_{s}, 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,

*x,y*)=

*y*)+Δ

*n*

^{2}(

*x,y*), where

*y*) is the linear index profile at

*x*=0 and Δ

*n*

^{2}(

*x,y*)=

*y*≤

*f*(

*x*), represents the index perturbation due the substrate curvature; finally, the nonlinearity distribution is characterized by

*x,y*)=

*y*≤

*f*(

*x*).

*ℰ*⃗ satisfies the following scalar equation:

_{1}and β

_{2}, that is,

*β*

_{1}=

*β*

_{2}=

*β*

_{0}for the copropagating case and

*β*

_{2}=-

*β*

_{1}for the counterpropagating case;

*φ*(

*y*) is the unperturbed normalized linear amplitude of the fundamental mode, that is, (∫

*φ**

*φ*d

*y*=1); and

*ψ*

_{α}(

*x, z*) (with

*α*=1, 2) are the

*z*-slowly varying nonlinear envelopes of the beams. This factorization is made under the assumption of a negligible nonlinear effect on the modal amplitude (linear modal amplitude assumption).

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]

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

*ψ*

_{α}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 ±3

*β*

_{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]

*ψ*

_{α}(

*x, z*),

*J*=0 for a single-beam propagation,

*J*=1 for the copropagating case and

*J*=2 for the counterpropagating one.

*l*≫

*x*), 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]

*β*

_{0}is the solution of the dispersion equation for the step-index waveguide. Moreover,

*G, Q*and

*ñ*

_{0}, which depend on the modal parameters

*ξ*

_{s}(

*p*in the notation of reference [14]) and

*φ*

_{0}(modal amplitude value in

*y*=0), take the following values:

*G*

^{2}=

*k*

^{2}(

*l*

^{2},

*ñk*

_{0}=

*ξ*

_{s}and

*Q*

^{2}=4

*ξ*

_{s}/

*l*

^{2}. The

*G*-factor can be regarded as a linear (effective) gradient index parameter (linear lenslike behaviour) whereas the

*Q*-factor is an effective gradient nonlinear index parameter (power-dependent lenslike behaviour).

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

*z*-dependent parameters for each envelope are: the normalized beam widths

*wα*(

*z*), the inverse curvature radius

*ρ*

_{α}(

*z*), the beam peak position

*x*

_{α}(

*z*) and the transverse local wave number

*V*

_{α}(

*z*);

*a*is the initial beam width, therefore

*w*

_{α}(

*z*=0)=1, and

*E*

_{0α}is the maximum field amplitude.

*τ*=2

*z/βαa*

^{2},

*p*

_{α}

*=k*

^{2}

*ñk*

_{0}

*a*

^{2}/2√2 (note that

*p*

_{α}is a parameter which is proportional to the power of the beams), and

*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

*p*

_{α}. 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

*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.

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]

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]

*p*

_{2}=0 in Eqs. (6) and (7); thus by denoting with (

*w*

_{h}

*, x*

_{h}) the parameters of the header Gaussian beam with power

*p*

_{1}=

*p*

_{h}, we obtain the following evolution equations:

*w*

_{d}

*, x*

_{d}) are derived from Eqs. (6) and (7) by considering a linear propagation of the data Gaussian beam (

*p*

_{1}=

*p*

_{d}≪1) and again

*p*

_{2}=0, that is,

*δ*=0), we can calculate the value of power

*p*

_{st}for self-trapping:

*w*

_{h}(

*p*

_{st}

*,x*

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

*δ*≠0) a quasi-selftrapping beam is obtained such as it is showed in Fig.3 (solid line).

*δ*, oscillating trajectories (swing effect) are obtained, and therefore spatial periods of oscillation can be defined for the corresponding trajectories, that is, Λ

_{d}for the data Gaussian beam (obtained from Eq. (14)) and Λ

_{h}for the header Gaussian beam (obtained from Eq. (12) with

*p*

_{st}). A simple condition for achieving a maximum spatial separation between the beams is obtained under the following condition: Λ

_{h}=2Λ

_{l}(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 Λ

_{h}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]

*n*

_{s}=1.500 and

*n*

_{f}=1.540 at λ=0.532

*µ*m,

*n*

_{c}=1.000,

*t*

_{0}=2.40

*µ*m and

*l*=400.0 µm

^{1/2}; moreover, we have taken an initial peak displacement

*δ*=40

*µ*m.

*x*

_{d}(

*τ*)=

*δ*cos(

*g*

^{1/2}

*τ*), therefore the linear period is

*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

*p*

_{st}=1.994.

## 5. Design of the optical bistable device

*p*

_{in}, is characterized by a low and high transmission states of optical power at the output of the device (

*p*

_{out}), which are joined by an hysteresis loop in the plane

*p*

_{in}

*-p*

_{out}.

*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]

*x*-direction; next, after the beam propagation along the nonlinear planar waveguide, the light is coupled onto the optical fiber, with a reflective end, by means of a second integrated multilens, which is specularly identical to the input one. At low power values the optical beam will arrive diffracted to the second multilens (plane

*z*

_{2}) and, as it performs the inverse beam transformation of the first multilens, a diffracted beam will be coupled inefficiently onto the optical fiber (as it is shown in Fig. 5, which provides a poor feedback and consequently a poor output transmission. As the optical power is increased the beam tends to a self-confinement regime; in this case, the second multilens will couple the nonlinear envelope to the optical fiber in a more efficient way, which provides an intense reflected beam and therefore, a high transmission output. Under this condition, the cross-action of the nonlinear counterpropagating beams creates an state of

*waves-guiding-waves*which keeps a quasi-self-trapped state even when the input power is reduced, making sure a high transmission behaviour, within an hysteresis loop, such as it is required in an optical bistable behaviour.

*p*+1≡

*p*

_{in}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,

**4**, 562 (2002). [CrossRef]

*z*

_{3}, is given, as a function of the forward beam width at plane

*z*

_{2}, by the following expression,

*w*

_{+1}at

*z*

_{2}is given by Eqs. (17) and (18) after a propagation distance |

*z*

_{2}-

*z*

_{1}|. Next, the power value of the backward beam is calculated by taking into account the transverse modal coupling and the reflection onto the output fiber, that is,

*p*-1 and the transverse modal coupling of the backward beam at the plane

*Z*

_{0}, that is,

*p*

_{in}

*-p*

_{out}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

*p*

_{in}; iteration is based on the searching of roots of Eq. (20).

*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).

*feed*input (feed in Fig. 1) equal to

*p*

_{in}

*=p*

_{feed}=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)

*p*

_{out}=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 (

*p*

_{st}~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

*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,

*w*

_{p1}~1. First let us advance the results on the design and the structure of the device and later we will present the calculations. In Figs. 7 are shown both the device and the variational propagation of the two states under a top view of the beam widths (taken as 1/e of the peak amplitudes).

*a*=6.87. The input fibers are separated a distance

*δ*=5

*w*

_{g}, where

*w*

_{g}is the modal radius of the fiber mode, which is assumed to be equal to the modal radius of the modal amplitude of the planar waveguide which takes the value,

*w*

_{g}=1.33

*µ*m; the distance

*δ*is chosen as short as possible to maximize the interaction between the pump and data waves in an also short propagation distances (

*z*

_{2}-

*z*

_{1}); moreover, the input fibers are placed in such a way that the input data channel is at

*x*=0, that is

*x*

_{d0}(

*z*

_{1})=

*x*

_{d1}(

*z*

_{1})=0 and the pump channel is at

*x=-δ*; thus, the input multilens, designed with 2 EFT modules (see appendix A), shifts the pump wave a value

*x*

_{p1}(

*z*

_{1})=

*B*

_{2}

*δ/B*

_{1}=5

*a*at the plane

*z*

_{1}(see Fig. 7-(B)), as they show the multilenses transformation laws given by Eqs. (A.5).

*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.

*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

*V*

_{d1}at the plane

*z*

_{3}.

*z*

_{2}, that is,

*B*parameter of the output multilens must fulfill the following condition

*z*

_{3}are given are given by,

*p*

_{p1}=

*p*

_{st}(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.

*ψ*

_{σ}at the plane

*z*

_{3}where the subindex σ gives account of the notation (

*σ*=

*d*0,

*d*1,

*p*1),

*φ*

_{f}of an optical fiber displaced a value Δ respect to the

*x*-axis, is expressed as follows,

*z*

_{3}by the following expression [22

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]

*δ*for fiber 2. Finally, these are the results for the transverse modal coupling on each fiber for the propagating waves in both operation states,

## 7. Cascaded configuration for N-port routing.

^{N}output ports, and the routing path must be determined by the header binary value.

**4**, 562 (2002). [CrossRef]

## 8. Conclusions

## Appendix

*j*=1,2 as a planar integrated multilens composed by

*m*

_{j}plane-convex lenses of thickness

*t*

_{j}and aperture

*A*

_{j}separated a distance

*l*

_{j}with effective indexes

*N*

_{i}and

*N*

_{o}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]

*j*produces, at

*z*

_{j}-planes, an Exact Fourier Transform of the Gaussian beam at

*z*

_{j-1}-planes if the following conditions are fulfilled,

*f*

_{j}are the focal lengths of each plane-convex lens, that is:

*z*

_{j}(see Fig.10) as

*w*

_{j}

*, x*

_{j}and

*V*

_{j}respectively, the following relationships, for a single EFT module, are obtained for the transformation of the beam parameters:

## Acknowledgments

## 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. |

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. |

4. | I. Glesk, K.I. Kang, and P. R. Prucnal, “Ultrafast photonic packet switching with optical control,” Opt. Express |

5. | K. H. Park and T. Mizumoto, “All-optical address extraction for optical routing,” Opt. Eng. , |

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. |

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. |

8. | D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A |

9. | A. E. Kaplan, “Optical bistability that is due to mutual self-action of counterpropagating beams of light,” Opt. Lett. |

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. |

11. | F. Garzia, C. Sibilia, and M. Bertolotti, “All-optical serial switcher,” Opt. Quantum Electron. |

12. | J. H. Marburger and F. S. Felber, “Theory of a lossless nonlinear Fabry-Perot interferometer,” Phys. Rev. A |

13. | R. A. Sammut, C. Pask, and Q. Y. Li, “Theoretical study of spatial solitons in planar waveguides,” J. Opt. Soc. Am. B |

14. | R. G. Hunsperger, |

15. | E. F. Mateo and J. Liñares, “All-optical integrated logic gates based on intensity-dependent transverse modal coupling,” Opt. Quantum Electron. |

16. | D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys.Rev. A |

17. | J. Liñares, C. Montero, and D. Sotelo, “Theory and design of an integrated optical sensor based on planar waveguiding lenses,” Opt. Commun. |

18. | J. Liñares and M. C. Nistal, “Single local mode propagation though ion-exchanged waveguide elements with quasi-abrupt transitions,” Jpn. J. Appl. Phys. |

19. | M. Desaix, D. Anderson, and M. J. Lisak, “Variational approach to collapse of optical pulses,” Opt. Soc. Am. B |

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 |

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. |

**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

- G. Stix, �??The triumph of light,�?? Scientific American, January (1998)
- 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]
- 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]
- I. Glesk, K.I. Kang, and P. R. Prucnal, �??Ultrafast photonic packet switching with optical control,�?? Opt. Express 1, 126 (1997). [CrossRef] [PubMed]
- K. H. Park, and T. Mizumoto, �??All-optical address extraction for optical routing,�?? Opt. Eng., 38, 1848 (1999). [CrossRef]
- 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]
- 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]
- 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]
- A. E. Kaplan, �??Optical bistability that is due to mutual self-action of counterpropagating beams of light,�?? Opt. Lett. 6, 360 (1981). [CrossRef] [PubMed]
- 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]
- F. Garzia, C. Sibilia, and M. Bertolotti, �??All-optical serial switcher,�?? Opt. Quantum Electron. 32, 781 (2000). [CrossRef]
- J. H. Marburger, and F. S. Felber, �??Theory of a lossless nonlinear Fabry-Perot interferometer,�?? Phys. Rev. A 17, 335 (1978). [CrossRef]
- 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]
- R. G. Hunsperger, Integrated optics: Theory and technology (Springer-Verlag, Berlin, 1991).
- 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]
- D. Anderson, �??Variational approach to nonlinear pulse propagation in optical fibers,�?? Phys.Rev. A 27, 3135 (1983). [CrossRef]
- 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]
- 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]
- M. Desaix, D. Anderson, M. J. and Lisak, �??Variational approach to collapse of optical pulses,�?? Opt. Soc. Am. B 8, 2082 (1991). [CrossRef]
- 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]
- 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]
- 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.