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A general rule for designing multibranch high-order mode converter.

1. INTRODUCTION

In recent years, within the field of optical communications, there has been considerable interest in all-optical networks [1-3]. The advantages of all-optical networks are both the tremendous expansion of the bandwidth and the low end-to-end delay [4]. For all-optical networks, more and more attention now has been focused on the investigation of all-optical devices [5-7]. The multibranch waveguides are the key component in the applications of integrated optics. By coupling effect, the multibranch waveguides can be designed to operate as switches [8], wavelength-selective filter [9], and logic gates [10]. The design of mode converter [11-14] is another good guide for all-optical devices. Zhang et al. [15] experimented and fabricated a TE mode converter. Wu [16] had been made a novel multimode interference coupler with exponentially tapered waveguide. Kuo et al. [17] proposed the mode theory in metamaterial.

In this paper, we propose a general rule that can be used to design an all-optical high-order mode converter composed of a pair of multibranch optical waveguides with a sort-of hybrid combination. The high-order mode converter is a novel type of mode-controlling optical device structure based on multi-mode interference. A special case proposed in this paper is a ten-order mode converter for a multimode waveguide. The device would be used in the complement operation in all-optical data computing system. We use the modal theory [18-21] to analyze the proposed structure rigorously. For reducing the calculational processes, we presented the general design principles to study this structure. The well-established finite-difference time-domain beam propagation method (FD-BPM) [22-24] was used to simulate the proposed device. The numerical results show that the proposed devices could really function as the all-optical mode converter.

2. ANALYSIS

In this section, we had used the multibranh waveguide to construct a quality all-optical high-order mode converter. This mode converter can be used to transform the order of the input modes into the desired mode-order in a multibranch waveguides. The multibranch waveguide can be divided into three sections from bottom to top: the straight-line section (three-layer waveguide), the coupled separating-waveguide section (multilayer waveguides with interaction layers), and the isolated separating-waveguide section (multilayer waveguides isolated from one another), as shown in Figure 1. The cladding and substrate layers are assumed to extend to infinity in the +x and -x directions, respectively. The major significance of this assumption is that there are no reflections in the x direction to be concerned with, expect for those occurring at interfaces. The separating-waveguide section can be approximated by straight waveguide segments step by step. These step-waveguide segments can be analyzed by the method proposed in Refs. [18-21].

Figure 2 shows the high-order mode converter. The mode splitter separates the input modes, and the mode combiner combines the separated modes. The role of the tapered waveguides located in the middle is to transform the shapes of mode profiles adiabatically. A simple and general rule had been presented under condition that each guiding channel of multibranch waveguide had a regular variation in width. The method combined the modal theory of multilayer planar optical waveguide with the effects of mode localization and adiabatic propagation. For simplicity, there are the same indices of refraction in the cladding, substrate and interaction layers. In this structure, the width of the widest channel [W.sub.0] must be satisfied the following inequalities:

K (K - 1)[DELTA]W < [2.sub.W0] < [[[lambda].sub.0]/[([n.sup.2.sub.f] - [n.sup.2.sub.c]).sup.1/2]] (1)

where [[lambda].sub.0] is the input wavelength, [DELTA]W the channel-width difference, and K the branch number. Each guiding channel can be characterized by a given width [W.sub.i] = [W.sub.0] - (i - 1)[DELTA]W (i = 1, 2, 3, ..., K), and the sum of widths of all guiding channels can be written as:

[W.sub.t] = [K.summation over (i=1)] [W.sub.i] (2)

The effective design of [DELTA]W must satisfy the condition that the ratio of [W.sub.t] to [W.sub.0] is more than and tends toward K - 1. A different uncoupled propagation constant in each guiding channel is an essential condition. Because all of the materials in this structure are linear media, the different uncoupled propagation constant in each guiding channel can be achieved by different widths or different refractive index. The branching angle [theta] between the each adjacent guiding channel are the same. The good approximation of branching angle has to be satisfied the following inequality:

[theta] [less than or equal to] [tan.sub.-1] [[K x [DELTA]W]/[4.3 (K - 1) x [W.sub.t]]] (3)

In multibranch waveguide, the final distances of each pair of adjacent guiding channels relate with uncoupled propagation constants of each guiding channel. The final distances D of each adjacent guiding channel can be calculated by mode theory [18-21]. The lengths of [L.sub.2] and [L.sub.4] can be determined by the branching angle and the final distances. For matching the condition of adiabatic propagation and avoiding significant intermode scattering, the branching angle has to be sufficiently small [14]. However, a very small branching angle will result in a huge structure of this device. The above principles had provided a simple and direct idea to design the all-optical high-order mode converter.

3. NUMERICAL RESULTS AND DISCUSSIONS

In this section, we use the finite-difference beam-propagation method to simulate the electric field propagating along the mode converter. A special case of this structure had been examined in this work. Figure 3 shows the ten-order mode converter structure. The propagation phenomena of the signal beam propagating along the structure had been studied. Figure 4 shows the ten-order mode converter for a multimode waveguide. The numerical data have been calculated with the values: the input wavelength [[lambda].sub.0] =1550 nm, the guiding channel refractive index [n.sub.f] =1.57, background refractive index [n.sub.c] = [n.sub.s] = [n.sub.l] = 1.55, branching angle [theta] = 0.01[degrees], [W.sub.t] = 28.48 [micro]m, [W.sub.0] = 3.1 [micro]m, [DELTA]W = 0.056 [micro]m, [L.sub.1] = [L.sub.3] = 5 mm, [L.sub.2] = [L.sub.4] = 45 mm, and [L.sub.3] = 0.5 mm. The layers M = 21 in the separating-waveguide section. This device can be used to transform the order of the input modes into the desired mode-order in a multibranch waveguides. The input modes had been separated in mode splitter section, and the separated modes had been combined in mode combiner section. The input modes and output modes have the complement relations in this ten-order mode converter. Beam propagations shown in Figures 4(a)-(j) illustrate the mode converter operation. When the [TE.sub.00] launched from the input waveguide section propagates along this structure, we can get a [TE.sub.90] mode at output port, as shown in Figure 4(a). Also, a TE10 mode is converted into a TE80 mode, as shown in Figure 4(b); [TE.sub.20] mode is converted into a [TE.sub.70], as shown in Figure 4(c); [TE.sub.30] mode is converted into a [TE.sub.60], as shown in Figure 4(d); TE40 mode is converted into a [TE.sub.50], as shown in Figure 4(e); [TE.sub.50] mode is converted into a [TE.sub.40], as shown in Figure 4(f); TE60 mode is converted into a [TE.sub.30], as shown in Figure 4(g); TE70 mode is converted into a [TE.sub.20,] as shown in Figure 4(h); [TE.sub.80] mode is converted into a [TE.sub.10], as shown in Figure 4(i); [TE.sub.90] mode is converted into a [TE.sub.00], as shown in Figure 4(j). The transmission efficiency [P.sub.0]/[P.sub.i] ([P.sub.i] the input signal power, [P.sub.0] the output signal power) of the input signal beam propagating throughout the output section is shown in Tab. 1. The numerical results showed that the transmission efficiency is very high, more than 90%. So all input modes of the given waveguide are converted in reverse older for the mode-older converter. The functional performance of this device would finish the complement operation in all-optical data computing system.

4. CONCLUSIONS

In this paper, we propose a general rule that can be used to design multibranch high-order mode converters. We used the modal theory to analyze the proposed structure rigorously and presented the general principles. A numerical example of the ten-order mode converter had been presented. The device would be used in the complement operation in all-optical data computing system. The numerical results show that the proposed devices could really function as the all-optical mode converter. It would be developed to quantify the applications in and be beneficial to ultra-high-speed and ultra-high-capacity all-optical data processing systems.

ACKNOWLEDGMENT

This work was partly supported by the National Science Council R.O.C. and under Grant No. 100-2221-E-151-033.

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Yaw-Dong Wu (1), *, Chih-Wen Kuo (2), Shih-Yuan Chen (2), and Mao-Hsiung Chen (2)

(1) Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan, R.O.C.

(2) Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, R.O.C.

* Corresponding author: Yaw-Dong Wu (ydwu@cc.kuas.edu.tw).

Received 14 October 2011, Accepted 29 December 2011, Scheduled 26 March 2013

Table 1. The transmission efficiency [P.sub.0]/[P.sub.i]
as a function of the ten-order mode converter.

Input signal   Output signal   [P.sub.0]/[P.sub.i] (%)

[TE.sub.00]     [TE.sub.90]             90.7
[TE.sub.10]     [TE.sub.80]             91.2
[TE.sub.20]     [TE.sub.70]             95.4
[TE.sub.30]     [TE.sub.60]             97.5
[TE.sub.40]     [TE.sub.50]             90.9

Input signal   Output signal   [P.sub.0]/[P.sub.i] (%)

[TE.sub.50]     [TE.sub.40]             90.5
[TE.sub.60]     [TE.sub.30]             97.6
[TE.sub.70]     [TE.sub.20]             96.9
[TE.sub.80]     [TE.sub.10]             97.1
[TE.sub.90]     [TE.sub.00]             98.2
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Author:Wu, Yaw-Dong; Kuo, Chih-Wen; Chen, Shih-Yuan; Chen, Mao-Hsiung
Publication:Progress In Electromagnetics Research
Article Type:Report
Geographic Code:9TAIW
Date:Jun 1, 2013
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