# An Ultrashort Wavelength Multi/Demultiplexer via Rectangular Liquid-Infiltrated Dual-Core Polymer Optical Fiber

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design Principle and Theoretical Modeling

_{1}is the diameter of the blue air hole filled with benzene (n = 1.366). Benzene is a highly toxic carcinogen. How to quickly and easily detect benzene in the environment and food is very important [69]. Therefore, the sensing characteristics of polymer devices based on filled benzene will be considered in future work. The distance of hole to hole can be expressed as period Λ, the air-filling ratio is d/Λ. The refractive index of background material is set as 1.49.

_{0}z) and the envelope term of ϕ(x, y, z) of slow change in the axial direction, n

_{0}is a refractive index in the cladding. Then, E(x, y, z) is stated as

**H**. We find that $n\ne {n}_{0}$ if the fields vary in the transverse direction to propagation. Light propagation in various kinds of waveguides can be analyzed by the above method.

_{x}and n

_{y}represent the effective refractive index of x-polarization and y-polarization, respectively.

_{λ1}and L

_{λ2}satisfy the following Equation (9) or (10), a polymer coupler can separate two wavelengths λ

_{1}and λ

_{2}transmitted in a core [4].

## 3. Simulated Results and Analysis

_{1}= 0.4 μm as shown in Figure 2. It is observed that the coupling length is increased when period Λ is increased for a constant air-filling ratio d/Λ. Moreover, the coupling length of y-polarization is higher than the coupling length of x-polarization. Since the x-axis is parallel to the core A and core B, the coupling length of the y-polarization is smaller than that of the x-polarization. Furthermore, we can clearly see that coupling length is decreased when air-filling ratio d/Λ is increased for the same value of period Λ. This is because the restriction of the outer cladding to the light wave is enhanced as the air-filling ratio increases. For the coupler with excellent performance, not only the strong coupling effect between core A and core B but also the good extinction ratio should be considered [4]. Based on the above considerations, we decided to use the y-polarization for the polymer optical fiber couplers.

_{1}= 0.4 μm, d/Λ = 0.9, the coupling length of y-polarized mode is shown as a function of period Λ in Figure 4, in which it is observed that the coupling length is increased if period Λ is increased. As the period increases, the coupling between the cores becomes weaker. Meanwhile, the coupling length of y-polarization decreases with increasing operating wavelength.

_{λ2}:L

_{λ1}by changing d

_{1}from 0.3 to 0.8 for different period Λ and d/Λ = 0.9. The one wavelength is 0.52 μm and 0.57 μm, and the other wavelength is 0.57 μm or 0.65 μm. Therefore, we obtain three couplers, named coupler 1, 2, and 3. In order to obtain an excellent coupling effect, we choose d/Λ = 0.9, Λ = 0.9 μm as the optimal parameters. When d/Λ = 0.9, Λ = 0.9 μm, and d

_{1}= 0.4 μm, L

_{0.57}: L

_{0.65}and L

_{0.52}:L

_{0.57}for couplers cannot satisfy Equation (9) or (10); L

_{0.52}:L

_{0.65}for coupler is 7:4. In order to obtain the ultrashort coupler, we analyze the influence of parameter d

_{1}on the length of the coupler through Figure 5c. Finally, the couplers 1 to 3 are L

_{0.52}:L

_{0.65}= 2:1, L

_{0.57}:L

_{0.65}= 3:2, and L

_{0.52}:L

_{0.57}= 3:2, respectively.

_{1}= 0.48 μm, Λ = 0.9 μm, and d/Λ = 0.9. It is observed that birefringence of coupler filled with liquid is higher than birefringence of coupler without liquid. Figure 7 shows the variation of confinement loss with filling material for d

_{1}= 0.48 μm, Λ = 0.9 μm, and d/Λ = 0.9. It can be seen that the confinement loss of the coupler without liquid is higher the confinement loss of the coupler with filled liquid. Therefore, the coupler with filled liquid has lower confinement loss and higher birefringence than the coupler without liquid.

_{1}and λ

_{2}according to the simulation results by BPM. The fundamental modes of y-direction at λ

_{1}and λ

_{2}are imported into the core A or core B in Figure 1. Figure 8 shows the propagation distance dependence of the normalized power. We observed that the separation of two wavelengths of λ

_{1}and λ

_{2}for couplers 1 to 3 are achieved at the distances of 183.6 μm, 288 μm, and 799.5 μm, respectively shown as the blue line in Figure 8. Obviously, the three polymer optical fiber couplers can operate as wavelength MUX/DEMUX at the wavelength of 0.52/0.65-μm, 0.57/0.65-μm, and 0.52/0.57-μm, respectively.

_{1}= 0.48 μm, Λ = 0.9 μm, and d/Λ = 0.9. It shows the mode-field distribution of the odd- and even- mode in two vertical directions. Moreover, the difference propagation constants and phase difference change of odd- and even-mode in transmission results in a power transfer between two cores [74].

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Cross-section of the proposed polymer optical fiber. The enlarged view of the core region is shown in the illustration.

**Figure 5.**d

_{1}dependence of the different coupling ratios, (

**a**) when d/Λ = 0.9, (

**b**) when d/Λ = 1.0, and (

**c**) when d/Λ = 1.1.

**Figure 8.**The propagation distance dependence of the normalized power for the three couplers, (

**a**) at the wavelength of 0.52/0.65-μm, (

**b**) at the wavelength of 0.57/0.65-μm, and (

**c**) at the wavelength of 0.52/0.57-μm.

**Figure 9.**(

**a**) Even-mode of x-direction, (

**b**) odd-mode of x-direction, (

**c**) even-mode of y-direction, (

**d**) odd-mode of y-direction for coupler.

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**MDPI and ACS Style**

Xu, Q.; Li, K.; Copner, N.; Lin, S.
An Ultrashort Wavelength Multi/Demultiplexer via Rectangular Liquid-Infiltrated Dual-Core Polymer Optical Fiber. *Materials* **2019**, *12*, 1709.
https://doi.org/10.3390/ma12101709

**AMA Style**

Xu Q, Li K, Copner N, Lin S.
An Ultrashort Wavelength Multi/Demultiplexer via Rectangular Liquid-Infiltrated Dual-Core Polymer Optical Fiber. *Materials*. 2019; 12(10):1709.
https://doi.org/10.3390/ma12101709

**Chicago/Turabian Style**

Xu, Qiang, Kang Li, Nigel Copner, and Shebao Lin.
2019. "An Ultrashort Wavelength Multi/Demultiplexer via Rectangular Liquid-Infiltrated Dual-Core Polymer Optical Fiber" *Materials* 12, no. 10: 1709.
https://doi.org/10.3390/ma12101709