Comparative Study of Triple-Clad Dispersion-Shifted

J. Opt. Commun. 2015; aop

Vikram Palodiya* and Sanjeev Kumar Raghuwanshi

Comparative Study of Triple-Clad Dispersion-Shifted, Dispersion-Flattened and Dispersion-Compensated Fiber for Broadband Optical Network Application DOI 10.1515/joc-2015-0017 Received February 27, 2015; accepted October 21, 2015

Abstract: In this paper, comprehensive analyses of tripleclad fibers are presented. The geometry of multiple-clad fibers has been considered as a four-layer cylindrical structure. The geometry consists of a core and three claddings. We have analyzed and compared different types of tripleclad refractive index profiles on the basis of dispersion, mode distribution and propagation constant. To enhance the optical characteristics of these three fibers, we have developed a combined formulation which is applicable for single-clad, double clad and triple-clad optical fibers. In optical fibers, two or more claddings are required for dispersion shifting, dispersion flattening and other specialized applications. Thus, an analysis of design dispersion-shifted, dispersion-flattened and dispersion-compensated fibers is presented. We have used a boundary match method for evaluating propagation wave vectors and guided modes. Keywords: triple-clad fiber, dispersion-shifted fiber, dispersion-flattened fiber, dispersion-compensated fiber PACS. 42.81.Gs, 42.50.Nn, 42.81.Bm

1 Introduction The number of internet users is increasing day by day in the world and as a result the demand for data communication is growing rapidly. Ultra-wideband transmission media are required in order to provide largebandwidth, high-speed communications for a much larger number of users. Optical fiber-based high-speed communications require low-dispersion and large-bandwidth optical medium [1, 2]. The focus of those studies was *Corresponding author: Vikram Palodiya, Department of Electronics Engineering, Indian School of Mines, Dhanbad, India, E-mail: [email protected] Sanjeev Kumar Raghuwanshi, Department of Electronics Engineering, Indian School of Mines, Dhanbad, India, E-mail: [email protected]

on reducing the total dispersion of single-mode fiber (SMF) at 1,550 nm where the loss is lowest for silica fibers. There were two main trends in those studies: one, to reduce the linewidth and stabilize the laser center wavelength, and two, to reduce the dispersion at this wavelength. It was found that the fiber designed for a high-speed data communication system generally exhibits a near-zero dispersion in a certain spectral window [3]. To meet the requirements of low-dispersion fibers, we discuss triple-clad optical fibers of three different types and present an analytical study of their dispersion characteristics. For the first type of triple-clad singlemode dispersion-shifted fiber (DSF) [4], refractive index distribution is the technique, in which, by increasing the refractive index difference between core and cladding and by reducing the core radius, the wavelength of zero dispersion can be shifted into the 1,550-nm window. The increase in material dispersion is greater than expected due to the increased doping material concentration in the core [5, 6]. However, the waveguide dispersion can be modified by designing a suitable refractive index profile and geometrical structure so as to balance the material dispersion effect. The dispersion due to material and waveguide takes an algebraic value, thus they can be designed so as to take opposite values that cancel each other. A different way to reduce the dispersion in optical fiber using advanced design techniques is to determine the design of dispersion flatten fibers (DFFs) [7], where the dispersion is flat over the wavelength range from 1,300 to 1,600 nm, adjusted by the refractive index profile of the core of optical fibers. Another type of optical fiber, which would be required for compensating the dispersion effect of optical signal after transmission over a length of optical fiber, is the dispersioncompensated fiber (DCF) [8], whose dispersion factor is many times larger than that of the SMF with an opposite sign. This can be designed by setting the total dispersion to the required compensated dispersion and thus the waveguide dispersion can be found over the required operating range. We discuss in this paper the dispersion characteristics of triple-clad DSF, DFF and DCF [9–12]. A triple-clad fiber was initially studied by Cozens and Boucouvalas as

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V. Palodiya and S. K. Raghuwanshi: Comparative Analyses of Triple-Clad Fibers

an optical coupler for sensing [13]. Dispersion curves for a particular coaxial structure were first theoretically obtained with the resonance technique [14] and later by solving the transcendental equation [15]. Detailed studies were carried out on the transmission characteristics of three types of triple-clad optical fibers with different refractive index profiles [16], and on the modal dispersion and field distribution during the single-mode propagation [17]. The advantages of triple-clad fibers are that more perfect dispersion-flattened and dispersion-shifted characteristics can be achieved by adjusting some parameters, which can overcome the difficulties that W-profile optical fibers encounter [18, 19]. The fiber characteristic dispersion, modes and propagation constant can be plotted together for DSF, DFF and DCF. Therefore, by adjusting the parameters practically, the dispersion and guided modes can easily be optimized. The objective of this work is to examine the effect of change in refractive index profile on the mode and dispersion of triple-clad optical fiber for different communication applications. In this paper, we focus our study on the dispersion, dispersion slope and normalized propagation constant in triple-clad SMFs, which we have determined successfully. We have also used a theoretical approach to calculate the chromatic dispersion and modes. We change the refractive index profile; the three different structures compare the cutoff condition for single-mode propagation. The paper is organized as follows: in Section 2, we discuss the refractive index profile and design parameters of different types of triple-clad fibers. In Section 3, we derive the mathematical equation for calculating the dispersion and propagation constants for different types of triple-clad fibers. The calculations of dispersion and the propagation constant relation using weak guidance condition are presented. In Section 3, numerical results and discussion are also given. Finally, the paper ends with a conclusion given in Section 4.

2 Design of triple-clad fibers In this section we discuss the relationship between geometrical parameters and the refractive index profile of different triple-clad fibers. We also analyze the effect of the change in the core and cladding radius on the guiding characteristics of fibers. Figure 1(a) shows the geometrical view of triple-clad fibers. Figure 1(b), 1(c) and 1(d) shows the refractive index distribution in triple-clad profile of DSF, DFF and DCF, respectively. The geometry consists of four layers, the first layer is the core and the other three layers are cladding; r0 is the radius of the core

Figure 1: (a) Geometry of triple-clad fiber, (b) the refractive index profile of dispersion-shifted fiber, (c) the refractive index profile of dispersion-flattened fiber and (d) the refractive index profile of dispersion-compensated fiber.

and r1 , r2 and r3 are radius of cladding of corresponding layers, as shown in the figure. The outer cladding layer is assumed to expand to infinity in radial direction. This assumption for guided mode means the field decreases exponentially in the radial direction. The refractive index distribution in profile for DSF is n0 > n2 > n3 > n1 , for DFF is n0 > n3 > n2 > n1 and for DCF is n1 > n3 > n0 > n2 . The material used in optical fiber fabrication is silica based, such as SiO2 , GeO2 − SiO2 and F − SiO2 , etc. Sellmeier coefficients of the materials are used for specified materials to calculate the refractive indices. The design parameters for the three different fibers are shown in Table 1. Table 1: Parameters for the designed fibers. Fiber

Core n0

Clad 1 n1

Clad 2 n2

Clad 3 n3

Fiber b Fiber c Fiber d

r0 = 3.2 μm r0 = 2.9 μm r0 = 5.3 μm

r1 = 3.8 μm r1 = 3.5 μm r1 = 6.0 μm

r2 = 4.3 μm r2 = 4.5 μm r0 = 7.4 μm

r3 = ∞ r3 = ∞ r3 = ∞

3 Theoretical analysis of triple-clad optical fiber In this section the modal analysis based on boundarymatching technique for the proposed structure, as illustrated in Figure 1, is presented. The refractive indices of the structure are



8 n0 , > > < n1 , nðrÞ = > n2 , > : n3 ,

0 < r < r1 , r1 < r < r2 , r2 < r < r3 , r3 < r,

ð1Þ

where r is the radius. Using the refractive index profile, the effective index can be calculated: ni = β=k, where β0 and k are propagation constant and free space wave number, respectively. As shown in Figure 1, the radius of the core, first cladding, second cladding and third cladding is, respectively, given by r0 , r1 , r2 and r3 . In this proposed structure the radius and refractive index of the core and all cladding have specific refractive indices, which also control the dispersion, propagation constant and other characteristics of multi-clad fiber. Here we use the weak guidance approximation and consider that the tangential electric and magnetic field components and their derivatives are continuous at the various interfaces along with some simple mathematical steps [14]. We can write the following characteristic equations: for double-clad waveguide, Jm ðU1 Þ − Im ðW3 Þ − Km ðW3 Þ 0 0 Im ðU2 Þ Km ðU2 Þ − Km ðW4 Þ U1 J′ ðU1 Þ − W3 I′ ðW3 Þ − W1 K′ ðW3 Þ 0 m m m U2 K′ ðU2 Þ − W2 K′ ðW4 Þ 0 U2 I′ ðU2 Þ m

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ffi β1 − k 2 n20 ; W2 = a2 β22 − k 2 n21 ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi W3 = a3 β23 − k 2 n22 W1 = a1

m

3

ð5Þ

where β1 , β2 and β3 are the propagation constants of the guided waves in the core, first and second cladding layers, which are given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 2 b1 n20 − n2 + n2 ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi β3 = k 2 b3 n22 − n2 + n2 β1 =

β2 =

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 2 ðb2 ðn21 − n2 Þ + n2 Þ;

ð6Þ Hence the normalized frequency for all layers can be expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffi n20 − n2 ; qffiffiffiffiffiffiffiffiffiffiffiffiffi V3 = a3 k n22 − n2

V1 = a1 k

V2 = a2 k

qffiffiffiffiffiffiffiffiffiffiffiffiffi n21 − n2 ;

ð7Þ

and the effective V of the multiple-clad fibers can be defined as Veff = a1 k

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2nððn0 − n1 Þ + ðn1 − n3 Þ + ðn2 − nÞÞ

ð8Þ

m

ð2Þ for triple-clad waveguide, Jm ðU1 Þ Im ðW3 Þ 0 I′m ðW3 Þ 0 0 U J′ ðU Þ W I′ ðW Þ 3 m 3 1 m 1 0 W′3 I′m W′3 0 0

Km ðW3 Þ Km W′3

0

0

− Im ðU2 Þ Im U′3

− Km ðU2 Þ Km U′3

0

0

− U′2 I′m U′2 U′2 I′m U′2

− U′2 K′m U′2 U′2 K′m U′2

0 − W1 K′m ðW3 Þ − W′3 K′m W′3 0

where Jm , Ym are the Bessel functions; Im , Km are the modified Bessel functions. The transverse propagation constant of the guided light wave u=a and v=a in the core and cladding regions, respectively, are given for the core, first and second cladding layers corresponding to subscripts 1, 2 and 3, respectively, of the triple-clad index profile fibers as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ffi U1 = a1 ðk 2 n20 − β21 Þ; U2 = a2 k 2 n1 − β2 ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi U3 = a3 k 2 n22 − β23

The waveguide dispersion factors of different fiber layers can be obtained as

ð4Þ

0 − Km ðW4 Þ 0 0 − W4 K′m ðW4 Þ 0

ð3Þ

n − n d2 ðV bÞ n − n d2 ðV bÞ 0 1 1 1 2 2 V1 V2 ; DW2 = − ; 2 λc λc dV1 dV22 n − n d2 ðV bÞ 2 3 V3 DW3 = − λc dV32 DW1 = −

ð9Þ where the normalized waveguide dispersion coefficient is V ðd2 ðVbÞ=dV 2 Þ. For triple-clad fibers we have the following three normalized waveguide dispersion parameters:


4


2 V1 d2 ðV1 bÞ U1 = 2 × V1 dV12

pffiffiffiffiffiffi 2 2 1 pffiffiffiffiffiffi K0 ð1 − 2K0 Þ + W1 + U12 K0 K0 − 1 K0 K0 + W1 W1 ð10Þ V2 d2 ðV2 bÞ U2 2 =2 × 2 V2 dV2

pffiffiffiffiffi 2 2 1 pffiffiffiffiffi K1 ð1 − 2K1 Þ + W2 + U22 K1 K1 − 1 K1 K1 + W2 W2 ð11Þ 2 V3 d2 ðV3 bÞ U3 = 2 × 2 V3 dV3

pffiffiffiffiffi 2 2 1 pffiffiffiffiffi 2 W3 + U3 K3 K2 ð1 − 2K2 Þ + K2 − 1 K2 K2 + W3 W3 ð12Þ K0 =

K1 ðW1 Þ K1 ðW2 Þ K1 ðW3 Þ ; K1 = ; K2 = K0 ðW1 Þ K0 ðW2 Þ K0 ðW3 Þ

ð13Þ

where Bessel Ki is the ith-order modified Bessel function finally obtained using the superposition of the total dispersion of multiple-clad fibers. Hence, we can say that pulse broadening per unit length for unit spectral width is called dispersion. The total dispersion is the total effect of material and waveguide dispersion: DTOTAL = DMAT + DW1 + DW2 + DW3

ð14Þ

DMAT depends upon the material taken for the construction of the optical fiber. DW is the parameter that depends upon the structure of the fiber. According to the definitions of total dispersion coefficient D [20], the expressions of total dispersion coefficient D and its slope S can be obtained as follows:

λ d2 dBV N3 Δ d2 ðBV Þ D= − 1 + Δ ð15Þ − V C dλ2 dV dV 2 c λ

λ d2 dBV 1 d2 n3 dBV − 1 + Δ 1 + Δ S= − C dλ3 dV c dλ2 dV ð16Þ 3 3 N3 Δ 2 d ðBV Þ N3 Δ d ðBV Þ + V + 2 V dV 3 dV 2 c λ2 c λ2 where N3 = n3 − λdn3 =dλ is the group index of the outer cladding and dm n3 =dλm (m = 1, 2, 3) can be calculated by Sellmeier formula [21].

4 Calculated results and analysis In this section we discuss the simulated results. We consider the dispersion behavior of the proposed three structures.

These simulations are based on the structure parameters and distribution of refractive index profile of different fibers. The formulation is mentioned in the previous section. The simulation results are illustrated to present the effect of the variation of the optical and geometrical parameters of dispersion, mode distribution and normalized propagation constant for the triple-clad fibers. Compare the result of three different types of triple-clad DSF, DFF and DCF fibers. The optical fibers were analyzed on the basis of transmission properties including dispersion, dispersion slope, propagation constant and mode distribution. The figures we obtained are classified into two categories including propagation constant-related quantities and dispersion quantities of proposed triple-clad fibers. This section has three parts on fibers of three different profiles. The first part includes simulation result analysis of DSF, the second part includes simulation result analysis of DFF and the third part includes simulation result analysis of DCF.

4.1 Dispersion-shifted fiber This section presents a novel triple-clad DSF design for broadband application. The refractive index profile of DSF is shown in Figure 1(b). Figure 2 shows the variation of the normalized propagation constant and mode as a function of the wavelength for two lower order modes. The fiber shows good performance for the LP01 mode in a wavelength range of 1,400–1,600 nm.

Figure 2: Normalized propagation constant vs. wavelength for the LP01 and LP11 mode of DSF.

The cut-off condition occurs at a wavelength less than 2,000 nm for the LP01 mode and at 980 nm for LP11 mode. The rest of the mode has a lower wavelength than the LP11 mode. This DSF is a single-mode fiber in a



Figure 3: Variation dispersion vs. wavelength for the fundamental mode of DSF.

wavelength range of 1, 000 nm < λ < 2, 000 nm. Figure 3 shows the dispersion vs. wavelength for DSF. The DSF gives the best result in a range between 1,500 and 1,600 nm wavelengths. The total dispersion is 0.02 ps/nm km at a wavelength of 1,550 nm.

5

Figure 5: Dispersion vs. wavelength for the LP01 mode of DFF.

fiber for the wavelength range of 900–1,900 nm. The fundamental mode exists within this range. Figure 5 shows the variation of dispersion in opposition to wavelength. The dispersion is less than 1 ps/nm km.

4.3 Dispersion-compensated fiber 4.2 Dispersion-flattened fiber A fiber in which the dispersion is low over a broad wavelength range is called DFF. The single-mode DFF has been studied, and its designs offer a flattened dispersion property. DFFs were designed for use in a wide wavelength range, such as 1,400–1,600 nm. The LP01 and LP11 mode of the fiber depends on a variation of propagation constant against wavelength as shown in Figure 4 for all modes. DFF is a single-mode

For the RI profile of DCF shown in Figure 1(c), the DCF shows negative dispersion at the wavelength of 1,550 nm. The guiding characteristics of DCF are only for some lower order mode. In Figure 6 the cut-off wavelengths for the earliest modes,LP01 , LP11 and LP21 , in the order of wavelengths are 1,580, 1,540 and 1,420 nm, respectively.

Figure 6: Normalized propagation constant vs. wavelength for the LP01 , LP11 and LP21 modes of DCF.

Figure 4: Normalized propagation constant vs. wavelength for the LP01 and LP11 mode of DFF.

The DCF was used for single-mode transmission in the wavelength range of 1,540–1,600 nm. This fiber shows the dispersion slope for some lower order mode in Figure 7. The fiber shows a large negative dispersion for fundamental


6


3.

4.

5.

6.

7. Figure 7: Dispersion vs. wavelength for the LP01 mode of DCF. 8.

mode LP01 : –390 ps=nm km at the wavelength of 1,550 nm. Dispersion is a change in wavelength at certain wavelength ranges. For the wavelength range of 1,554–1,556 nm, the dispersion change obtained is –312 to –400 ps=nm km.

9. 10.

5 Conclusion

11.

In this paper we have analyzed triple-clad single-mode fibers designed for dispersion-shifted, -flattened and -compensated fibers. We present mathematical formulations for triple-clad fibers, which help to study the transmission characteristics of single-mode fibers. We have obtained designspecific refractive index profiles to carry out the desired propagation constant and dispersion characteristics for lower order modes. The dispersion-shifted fiber offers zero dispersion at a wavelength of 1,550 nm. Thus, smaller pulses are spread over long-distance optical transmission. The dispersion-flattened fiber offers a flat dispersion of 1 ps=nm km for the wavelength range of 1,490–1,553 nm. The dispersioncompensated fiber gives a negative dispersion of –390 ps=nm km at a wavelength of 1,550 nm. The dispersioncompensated fiber gives the dispersion compensation for the fundamental mode.

12.

13. 14.

15. 16.

17. 18.

19.

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