## Abstract

We propose a novel all-optical wavelength auto-router based on spatial solitons. By using the swing effect of spatial solitons in a Kerr-type nonlinear medium, the proposed nonlinear waveguide structure could function as a self-routing wavelength division multiplexer (WDM). It could be a potential key component in the applications of ultra-high-speed and ultra-high-capacity optical communications and optical data processing systems.

© 2004 Optical Society of America

## 1. Introduction

Demands for ultra-high-speed and ultra-high-capacity optical communications and optical data processing systems are increasing dramatically. There is a lot of interests in all-optical ultrafast photonic devices using nonlinear optical effect for applications to optical communications and optical signal processing systems [1]. Nonlinear optical waveguide structures are attractive to construct these all-optical devices with low-operational power because of high-optical power density and diffractionless propagation in waveguides due to the confinement of light in a small core area. Controlling light by light can avoid any electrooptic conversion process and can increase the photonic device speed and efficiency. In the past, several all-optical nonlinear waveguide devices have been proposed and implemented.

More and more attention now has been focused on the investigation of the optical waves propagating in the Kerr-type nonlinear media since, under suitable conditions, the diffraction and self-focusing effects can balance each other, and the optical beams, called spatial solitons, can propagate a long distance without changing their spatial shapes [2]. Recently, some papers have been proposed for the possible applications of the all-optical devices base on the spatial solitons, for example, all-optical switches, all-optical logic gates, and all-optical modulators [3–9]. These all-optical devices utilizing the interaction properties of spatial solitons were first proposed for single wavelength operation. In this paper, we propose a new all-optical wavelength auto-router based on the spatial solitons. It is well-known that multiwavelengths are at the basis of WDM networks. WDM is one promising approach that can be used to exploit the huge bandwidth of optical fiber. By utilizing WDM in optical fiber networks, the ultra-high-speed and ultra-high-capacity optical communication systems can be achieved by dividing the optical fiber bandwidth into several nonoverlapping wavelength bands, each of which may be accessed at peak electronic rates by an end user [10]. In this paper, numerical results show that the proposed nonlinear waveguide structure could really function as an all-optical wavelength auto-router based on the spatial solitons. It would be a potential key component in the application of WDM optical communication systems.

## 2. Analysis

The proposed nonlinear waveguide structure of the all-optical wavelength auto-router is shown in Fig. 1. It is divided into four sections: the inclined linear waveguide section, the straight nonlinear waveguide section, the uniform nonlinear medium section, and the output nonlinear waveguide section. The lengths of the four sections are *L*
_{1}, *L*
_{2}, *L*
_{3}, and *L*
_{4}, respectively. The widths of the inclined linear waveguide, the straight nonlinear waveguide, and the output nonlinear waveguide are denoted *w*
_{1}, *w*
_{2}, and *w*
_{3}, respectively. In the input section, the inclined linear waveguide is used to launch the signal beam and the inclined angle is denoted *θ*. In the straight nonlinear waveguide section, the spatial solitons will be excited. Owing to the strong perturbation of the linear-nonlinear interfaces, the spatial solitons will swing in this region [11]. In the uniform nonlinear medium section, the spatial solitons will be self-routing when the input wavelength increases. In the output section, the nonlinear waveguides are used to couple out the spatial solitons excited by the input signal beams. The separation between each output guide is sufficiently large to prevent mutual coupling. For simplicity, we consider the case of TE waves propagating along the structure as:

where *k*
_{0} is the wave number in the free space, *ω* is the angular frequency, *β* is the effective refractive index, and we have taken the field to be homogeneous in the y direction. Taking into account the slowly varying envelope approximation, we obtain the following equation for *E*(*x*, *z*):

where the subscripts *f*, *c*, and *u* are used to denote the guiding film, the cladding, and the uniform nonlinear medium, respectively. For a Kerr-type nonlinear medium [12], the square of the refractive index ${n}_{i}^{2}$ can be expressed as:

where *n*_{i}
_{0} is the linear refractive index of the nonlinear medium and *α* is the nonlinear coefficient (*α* = 0 , for the linear medium). All the refractive indices in the proposed structure are *n*_{i}
= *n*
_{c0} in the cladding of the structure, *n*_{i}
= *n*
_{f0} in the inclined linear waveguide, *n*_{i}
= $\sqrt{{n}_{f0}^{2}+\alpha {\left|E\right|}^{2}}$ in the straight nonlinear waveguide and the output nonlinear waveguides, and *n*_{i}
= $\sqrt{{n}_{u0}^{2}+\alpha {\left|E\right|}^{2}}$ in the uniform nonlinear medium section.

## 3. Numerical results and discussions

In this section, we use the finite difference beam propagation method (FD-BPM) [13] to simulate the propagation phenomena of the signal beam propagating along the structure. For the calculations, we use the following numerical data: *n*
_{c0}=*n*
_{u0} =1.55 , *n*
_{f0}=1.56 , *w*
_{1}=*w*
_{3}=3*μm* , *w*
_{2}=15*μm* , *L*
_{1}=50*μm* , *L*
_{4}=500*μm* , *L*
_{3}=1000*μm* , and
*α* = 63786*μm*
^{2} /*V*
^{2} [12]. We denote Δ*d* the position shift of the input signal beam propagating throughout the uniform nonlinear medium section and *λ*_{i}
the wavelength of the input signal beam. As shown in Fig. 2, we plot the position shift Δ*d* as a function of the wavelength*λ*_{i}
, of the input signal beam. Figure 2(a) shows that the position shift Δ*d* is plotted as a function of the input wavelength *λ*_{i}
,in 1310*nm* spectral region and Fig. 2(b) shows that the position shift Δ*d* is plotted as a function of the input wavelength*λ*_{i}
, in 1550*nm* spectral region. The numerical results show that the position shift is increasing as the input wavelength is increasing and the linearity is very well. Figure 3 shows the transmission efficiency *P*_{0}
/*P*_{i}
(*P*_{i}
, the input signal power, *P*_{0}
the output signal power) of the input signal beam propagating throughout the output section. The numerical results show that the transmission efficiency is very high, more than 94%. When the incoming signal beams enter the straight nonlinear waveguide, they will excite spatial solitons. Because the signal beams are launched in an inclined angle, the particle-like spatial solitons [14] will swing in the straight nonlinear waveguide region and collide on the linear-nonlinear interfaces. Owing to the strong perturbation of the linear-nonlinear interfaces, the total reflection angle of each soliton with different wavelength will be different and the optical path of each soliton will also be different. These particle-like spatial solitons will swing in the straight nonlinear medium region. The scheme is based on the interesting property of a spatial soliton propagating in a Kerr-type nonlinear medium. We can use the results shown in Figs. 2–3 to design a new 1×N all-optical wavelength auto-router. We show some numerical examples as follows. First, we show a numerical example of a 1×13 all-optical wavelength auto-router with the input wavelength in 1310*nm* spectral region. Because for the conventional single-mode optical fiber, when the wavelength of the input light wave in 1310*nm* spectral region, the dispersion is near zero and the transmission loss is very low. The numerical results are shown in Figs. 4(a) and 5(a). Figure 4(a) shows the evolutions of the input signal beams propagating along the structure with the wavelength of the input signal beams in 1310*nm* spectral region. When the input wavelength increases, the output signal beams will be switched from one output guide to another. The spatial distributions of the input signal beam with different wavelengths at the end of the uniform nonlinear medium section is shown in Fig. 5(a). Second, we show a numerical example of a 1×13 all-optical wavelength auto-router with the input wavelength in 1550*nm* spectral region. Because for the dispersion shifted single-mode optical fiber, when the wavelength of the input light wave in 1550*nm* spectral region, the dispersion is near zero and the transmission loss is very low. The numerical results are shown in Figs. 4(b) and 5(b). Fig. 4(b) shows the evolutions of the input signal beams propagating along the structure with the wavelength of the input signal beams in 1550nm spectral region. When the input wavelength increases, the output signal beams will be switched from one output guide to another. The spatial distribution of the input signal beams with different wavelengths at the end of the output is shown in Fig. 5(b). Tab. 1(a) and Tab. 1(b) show the transmission efficiency with respect the input wavelength in 1310*nm* and 1550*nm* spectral region, respectively. The numerical results show that the transmission efficiency is higher than 94%.

wavelength (nm) |
P_{o}
/P_{i}
(%) | |
---|---|---|

λ
_{1}
| 1530 | 96.51 |

λ
_{2}
| 1534 | 96.51 |

λ
_{3}
| 1538 | 96.33 |

λ
_{4}
| 1541 | 96.76 |

λ
_{5}
| 1544 | 96.97 |

λ
_{6}
| 1547 | 95.35 |

λ
_{7}
| 1550 | 95.06 |

λ
_{8}
| 1553 | 94.82 |

λ
_{9}
| 1556 | 94.66 |

λ
_{10}
| 1559 | 94.58 |

λ
_{11}
| 1563 | 94.62 |

λ
_{12}
| 1567 | 94.81 |

A3 | 1570 | 95.20 |

## 4. Conclusions

In this paper, we propose a nonlinear waveguide structure that realizes all-optical auto-routing directly controlled by the wavelength of the input signal. The optimization of the all-optical wavelength auto-router comes through the choice of the suitable input power and the inclined angle, the straight nonlinear waveguide length, and the uniform nonlinear medium length. This is a very adaptive all-optical wavelength auto-router. By properly choosing these parameters, we can easily design an all-optical wavelength auto-router with the wavelengths in the desired spectral region. The numerical results show that it is possible to obtain well distinguishable output signal beams and high transmission efficiencies (more than 94%), so realizing the desired wavelength routing function, without distortion or power loss. The relative merits of the proposed all-optical auto-router with respect to similar devices based on spatial solitons are the simple structure, the high transmission efficiency, and no control beam. It is very suitable for integration of device components into circuits. It would be a potential key component in the applications of ultra-high-speed and ultra-high-capacity optical communications and optical data processing systems.

## Acknowledgments

The author would like to thank Min-Lun Huang for his helpful discussions. This work was supported by National Science Council R.O.C. under Grant No. 93-2215-E-151-003.

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