# Design of a four-branch optical power splitter based on gallium-nitride using rectangular waveguide coupling for telecommunication links

Retno Wigajatri Purnamaningsih, Nji Raden Poespawati, El Hadj Dogheche

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Retno Wigajatri Purnamaningsih, Nji Raden Poespawati, El Hadj Dogheche. Design of a four-branch optical power splitter based on gallium-nitride using rectangular waveguide coupling for telecommunication links. Journal of Engineering, 2019, 2019, pp.7285305. 10.1155/2019/7285305. hal-03138563

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Research Article

# Design of a Four-Branch Optical Power Splitter Based on Gallium-Nitride Using Rectangular Waveguide Coupling for Telecommunication Links

Retno W. Purnamaningsih<sup>1</sup>,<sup>1</sup> Nji R. Poespawati,<sup>1</sup> and Elhadj Dogheche<sup>2</sup>

<sup>1</sup>Department of Electrical Engineering, Universitas Indonesia, Kampus Baru UI, Depok, 16424, Indonesia

<sup>2</sup>Université Polytechnique Hauts de France, CNRS IEMN DOAE, Valenciennes, France

Correspondence should be addressed to Retno W. Purnamaningsih; retno.wigajatri@ui.ac.id

Received 29 April 2019; Accepted 26 June 2019; Published 22 July 2019

Academic Editor: Paolo Colantonio

Copyright © 2019 Retno W. Purnamaningsih et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper reports design of a simple four-branch optical power splitter using five parallel rectangular waveguides coupling in a gallium-nitride (GaN) semiconductor/sapphire for telecommunication links. The optimisation was conducted using the 3D FD-BPM method for long wavelength optical communication. The result shows that, at propagation length of 925 µm, the optical power input was successfully split into four uniform output beams, each with 24% of total input power. It is also shown that the relative output power distribution is almost stable through the C-band range. At the operating wavelength of 1.55 µm, the proposed power splitter has an excess loss lower than 0.2 dB. This study demonstrates the opportunity to develop optical interconnections from UV-Visible to near IR wavelengths.

## 1. Introduction

Optical power splitters play an essential role as a passive component in optical communication. They are functioned for splitting and combining optical signals. Due to the rapid growth of data transmission, several splitter technologies have been proposed to expand data transmission capacity. So far many designs of optical power splitter have been developed, for example, using Y branch and multimode interference (MMI) structure on chip [1–3], photonic crystal [4–6], directional coupler [7], microring [8, 9], and gratings [10].

Gallium-nitride semiconductor has important characteristics, such as mechanical hardness, high-temperature stability, and excellent transparency in telecommunication wavelength [11]. Therefore, III-nitride based devices may operate at much higher optical power levels. Those characteristics make it suitable for the harsh environment. Previous research indicated that III-nitrides have very low-temperature sensitivity, especially in infrared wavelength regions [12]. This is another crucial advantage for applications

in optical communications. Previous research [11] showed that small propagation loss occurred when gallium-nitride (GaN) with aluminium-nitride/gallium-nitride (AlN/GaN) buffer layer were integrated on sapphire substrates.

So far, the development of III-nitride based photonic devices has been focused on the light source [13–15] and photodetectors [16]. However, besides being developed as a light source and photodetectors, III-nitride based waveguide device design has also been developed. The design of the Y junction and MMI structure splitter using GaN/sapphire for long wavelength optical communication systems have been demonstrated [17, 18]. A transferrable monolithic III-nitride photonic circuit for multifunctional optoelectronics has been developed [19]. A photonic circuit for visible light communication has also been reported [20]. GaN-based optical power splitter design for underwater optical wireless communication has also been demonstrated [21, 22]. However, to the best of our knowledge, the design of an optical power splitter based on GaN/sapphire using AlN/GaN buffer layer based on rectangular waveguide coupling for long wavelength telecommunication links has not yet been reported.
This paper reports the design of a simple four-branch power splitter consisting of five identical parallel waveguides which are work based on mode coupling phenomena. The optical power splitter design and analysis relies on numerical calculations using commercial beam propagation software. The program is based on a finite difference beam propagation method (FD-BPM) to solve the paraxial approximation of the Helmholtz equation by applying the boundary conditions. The numerical experimental results of the proposed design are reported.

## 2. Materials and Methods

2.1. Operating Principles. If a waveguide is close enough to its adjacent waveguide, they become coupled and exchange power as a function of propagation direction. According to the scalar coupled mode theory, the field can be represented by a summation of the scalar modes of the individual waveguides. For configuration consists of two identical parallel waveguides, the effective indices of the symmetric and the antisymmetric normal modes can be approximated using conventional coupled mode theory as follows [23]:

$$n_s = n_{eff} + \kappa_{12} \quad (1)$$

$$n_a = n_{eff} - \kappa_{21} \quad (2)$$

where the coupling coefficient is between waveguide 1 and waveguide 2 and vice versa; that is, $\kappa_{12} = \kappa_{21} = \kappa$ and $n_{eff}$ is the effective refractive index. The parameter describing the physics of the power transfer between waveguides is the coupling length, which is related to the difference between symmetric ($n_s$) and antisymmetric ($n_a$) refractive indices; that is,

$$L_c = \frac{\lambda}{2(n_s - n_a)} \quad (3)$$

where $\lambda$ is the wavelength.

2.2. The Proposed Design of Optical Power Splitter. The proposed structure of the waveguide is shown in Figure 1. The GaN structure layer consists of three layers, sapphire, the buffer layer, and GaN. Sapphire (yellow) is used as the wafer, AlN and AlN/GaN (white colour) are used as the buffer layer, GaN (brown colour) is used as the waveguide material, and air (no colour) is used as a cladding material. Figure 2 shows the proposed optical power splitter. The design is based on a conventional structure, five rectangular waveguides, where $C_g$ is the coupling gap between two adjacent waveguides. $L_i$ is the length of the input waveguide and $L_1$ and $L_2$ are the length of waveguides 1 and 2, respectively, while $L_3$ and $L_4$ are the length of waveguide 3 to 4 accordingly. The basis of the design is to obtain a four uniform output power by optimising the waveguide parameter to enable power transfer that occurred between the adjacent waveguides. In this proposed design, the input waveguide is centred with the other four output waveguides. To obtain the desired output distribution, waveguide parameters, coupling gap, and

<figure><img src="image_2.png" /><figcaption>FIGURE 1: The schematic illustration of GaN structure layer in x - y plane.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>FIGURE 2: The schematic structure of the proposed four-branch optical power splitter in x - z plane.</figcaption></figure>

coupling length between the adjacent waveguides should be optimised.

In this design, the wurtzite structure of sapphire was used due to its temperature stability. Compared to other structures, this structure can increase the performances of the splitter. The effective refractive indices of the layers used were from the previous result [11], nTE = 2.279 ± 0.001 and nTM=2.316 ± 0.001. The first step optimised the width and the height of each waveguide to support only one mode of propagation. Next, the coupling gap and coupling length were optimised for TE polarisation. This step was conducted to obtain four separate single modes at the output ports. The numerical experiments were conducted by taking into account the losses and the uniformity of the optical power distribution.
In this proposed design all the waveguides have the same width, thickness, and refractive index. For simplicity, the propagation constant of the fundamental propagation mode of all the waveguides can be assumed to have the same propagation constant, $\beta_i = \beta_1 = \beta_2 = \beta_3 = \beta_4 = \beta$. Since modes in all the waveguides are propagating in the same direction, the propagation constants are always positive, $\beta > 0$. Waveguides 1 and 2 are identical and symmetric, as well as waveguides 3 and 4. Therefore, the amplitudes in waveguides 1 and 2 are the same, as well as waveguides 3 and 4. However to achieve these conditions, the geometrical size of the structure should be optimised. In this design the power is injected only into the input waveguide; hence by applying the boundary conditions input amplitude is equal to 1 at propagation distance $z = 0$, while others are of zero value and the power transfer from input waveguide to the other four waveguides can be calculated. However, due to the complexity of the structure, the numerical analysis method had to be used.

**2.3. Numerical Method for the Propagating Wave.** To accurately design the photonic waveguides devices this requires numerical wave propagation techniques. So far, various numerical methods have been developed to solve Maxwell's equations. One of the most powerful techniques for studying the propagation of light in waveguide-based photonic devices is the beam propagation method (BPM). The BPM is very useful in solving light propagation in photonic waveguides of arbitrary shape. In BPM, a spatial mode is break down into a superposition of plane waves. Each wave propagates a small distance through the design of a waveguide structure. Next, to reconstruct the mode, the plane waves are then added back together. The general three-dimensional scalar Helmholtz equation is as follows [24]:

$$ \nabla^2 E(x, y, z) + k_0^2 n^2(x, y, z) E(x, y, z) = 0 \quad (4) $$

where $k_0$ is the wave number in vacuum. Using the slowly varying envelope approximation the electric field $E(x, z)$ is divided into the slowly varying envelope function $\Phi(x, y, z)$ and a spatially very fast oscillating phase term $\exp(-j\beta z)$ as follows:

$$ E(x, y, z) = \Phi(x, y, z) \exp(-j\beta z) \quad (5) $$

Here, $\beta = kn_{eff}$; $n_{eff}$ is the effective refractive index. In actual calculations, this value is a priori unknown and can be set to the refractive index of the substrate or cladding. Next, by substituting (5) into (4) and dividing both sides of the resultant equation by $\exp(-j\beta z)$ we can obtain

$$ \frac{\partial^2 \Phi}{\partial z^2} - 2j\beta \frac{\partial \Phi}{\partial z} + \nabla_{\perp}^2 \Phi + (k_0^2 n^2 - \beta^2) \Phi = 0 \quad (6) $$

where $\nabla_{\perp} = \partial^2/\partial x^2 + \partial^2/\partial y^2$ is the Laplacian in the lateral directions and (6) can also be written as

$$ 2j\beta \frac{\partial \Phi}{\partial z} - \frac{\partial^2 \Phi}{\partial z^2} = \nabla_{\perp}^2 \Phi + k_0^2 (\varepsilon_r - n_{eff}) \Phi \quad (7) $$

where $\varepsilon_r = n^2$. Next, by neglecting second derivatives, that is, $\partial^2\Phi/\partial z^2 = 0$, (7) is reduced to

$$ 2j\beta \frac{\partial \Phi}{\partial z} = \nabla_{\perp}^2 \Phi + k_0^2 (\varepsilon_r - n_{eff}) \Phi \quad (8) $$

Here, $\partial^2\Phi/\partial z^2$ has been neglected by assuming $|\partial^2\Phi/\partial z^2| \ll 2j\beta|\partial\Phi/\partial z|$. This approximation is called the Fresnel approximation or the paraxial approximation.

For TE mode, $\partial\Phi/\partial y = 0$. The Fresnel equation can be written as follows:

$$ 2j\beta \frac{\partial \Phi}{\partial z} = \partial_x^2 \Phi + k_0^2 (\varepsilon_r - n_{eff}) \Phi \quad (9) $$

Equation (9) can be solved using a finite difference method. The region of interest is divided into a grid of nodes. The selection of the original grid size should be small enough so that the solution converges. The discretisation of the $x$ and $z$ coordinates is according to

$$ \begin{gathered} x = p\Delta x \\ \text{and } z = l\Delta z \end{gathered} \quad (10) $$

where $p$ and $l$ are integers, $\Delta x$ and $\Delta z$ denote the calculation steps in the $x$-axis and $z$-axis directions, respectively, and the propagation step distance $x$ as well as $z$ can be different for each propagation step. Mostly the use of equidistant discretization for the $x$- and $z$-direction is used. The differential equation of (9) can be discretized in $x$ direction; that is, the terms of right hand are expressed as follows:

$$ \begin{aligned} \frac{\partial^2 \Phi}{\partial x^2} &= \frac{1}{\Delta x} \left( \frac{\phi_{p+1} - \phi_p}{(\Delta x)} - \frac{\phi_p - \phi_{p-1}}{(\Delta x)} \right) \\ &= \frac{\phi_{p+1} - 2\phi_p + \phi_{p-1}}{(\Delta x)^2} \end{aligned} \quad (11) $$

$$ k_0^2 (\varepsilon_r - n_{eff}^2) \Phi = k_0^2 (\varepsilon_r (p) - n_{eff}^2) \Phi_p \quad (12) $$

The discretisation of the left-hand side of (9) in the $z$ direction is presented as follows:

$$ \begin{aligned} 2j\beta \frac{\phi_p^{l+1} - \phi_p^l}{(\Delta z)} - \frac{\phi_p - \phi_{p-1}}{(\Delta x)} \frac{\partial \Phi}{\partial z} \\ = \partial_x^2 \Phi + k_0^2 (\varepsilon_r - n_{eff}) \Phi \end{aligned} \quad (13) $$

The subscripts $p$ and $l$ are indices of the sampling points along $x$-direction and $z$-direction, accordingly. The number of grid points along the $x$-axis and $z$-axis directions is $P$ ($p = 1, 2, \dots, P$) and $L$ ($l = 1, 2, \dots, L$), respectively. The term $\phi_p^l$ denotes the discrete values of the field at $x_p = p\Delta x$ and $z_l = l\Delta z$.
<figure><img src="image_4.png" /><figcaption>FIGURE 3: 3D (a) and 2D (b) optical field distribution of the proposed optical power splitter along x − z plane.</figcaption></figure>

Finally, the finite difference expression of E<sub>y</sub>(x, y, z) for
TE mode is as follows:

$$
\begin{align}
& -\alpha_w^{l+1} \phi_{p-1}^{l+1} \nonumber \\
& + \left\{ -\alpha_x^{l+1} + \frac{4j\beta}{\Delta z} - k_0^2 [\varepsilon_r^{l+1}(p) - n_{eff}^2] \right\} \phi_p^{l+1} \nonumber \\
& - \alpha_\epsilon^{l+1} \phi_{p+1}^{l+1} \tag{14} \\
& = -\alpha_w^l \phi_{p-1}^l + \left\{ \alpha_x^l + \frac{4j\beta}{\Delta z} + k_0^2 [\varepsilon_r^l(p) - n_{eff}^2] \right\} \phi_p^l \nonumber \\
& - \alpha_\epsilon^l \phi_{p+1}^l \nonumber
\end{align}
$$

where $\alpha_w = 1/(\Delta x^2)$, $\alpha_\epsilon = 1/(\Delta x^2)$, and $\alpha_\epsilon = 1/-(\Delta x^2)$

Once the initial electric field distribution $\phi_0^l$ ($l = 1, 2, \dots, L$) at the input position is given, the electric field profile $\phi_p^l$ ($p = 1, 2, \dots, P$) can be calculated at any distance $z_i$ by solving the tridiagonal system of linear equations.

**3. Results and Discussion**

The numerical experiments were conducted using OptiBPM
software based on a slowly varying envelope approximation
combined with MATLAB software. The field propagation
calculations through the structure were carried out using
the finite difference beam propagation method (FD-BPM),
which is suitable for the proposed design. In these numerical
experiments, we used the TE polarised field; therefore, a
semivectorial FD-BPM is applied. To obtain the best geo-
metrical value of the proposed splitter, first, the width of
each waveguide was varied from 2 µm up to 5 µm; then the
relative optical power was observed. It was found that the 4
µm waveguide width gave the highest relative optical power
at 0.99. Secondly, by employing this width value, the best
thickness of each waveguide was optimised by varying the
waveguide thickness from 0.5 µm up to 5 µm and observed
the relative output power. It was shown that 4 µm thickness
gave the highest optical power at 0.99. Therefore, the 4 µm
width and 4 µm thickness of each waveguide were chosen.
The following was the optimisation of the gap between

adjacent waveguides by observing power loss for various
gaps, starting at 0.5 µm up to 5 µm. The result showed that
3 µm of gap gave the lowest power loss, at 0.98 a.u. Finally
the optimum length of each waveguide was defined based on
analytic calculation of the coupling length and the coupling
coefficient.

By solving (1) combined with semivector BPM simula-
tions, the value of coupling length L<sub>c</sub> and coupling length κ
can be obtained. The calculated value of L<sub>c</sub> obtained was 254.3
µm with κ=0.0062 µm<sup>-1</sup>. Using this result, the length of each
waveguide was optimised to obtain the uniform distribution
and single mode propagation in each waveguide. It was found
that the best length for the input waveguide is 780 µm, the
output waveguides 1 and 2 are 875 µm, and waveguides 3 and
4 are 825 µm accordingly. It can be noticed that a coupling
gap of 7 µm is needed to obtain an almost equal power
transfer between the waveguides. The total length and width
of the power splitter are 925 µm and 32 µm, respectively.
This size gives the minimum imbalance and lowest excess
loss at 1.55 µm. In Figures 3(a) and 3(b), the map of optical
field distribution through the proposed structure for both
3D and 2D is, respectively, displayed. The different colours
red, yellow, and green represent the level of the optical field.
It is shown that the incoming power is split into an almost
four equal intensities (green colour) in each output branch.
It is also shown that a strong confinement (red colour) was
obtained inside the GaN layer.

Figure 4 shows the mode propagation for $\lambda$ =1550 µm at
several propagation distances, $z = 0$, $z = 675$ µm, and $z = 925$
µm. It should be noted that the optical power begins to split
at $z = 675$ µm; it is then divided into four optical powers at $z$
$= 925$ µm.

Next, to observe the power loss at the telecommunication
wavelength throughout the proposed power splitter, the total
relative optical power at $\lambda$ = 1550 nm along the propagation
z-axis was analysed. The results showed that the total relative
power along the proposed splitter was stable at 0. 98 a.u.,
as shown in Figure 5. Furthermore, the power exchange
between waveguides was explored. Figure 6 shows the power
exchange between input waveguide and waveguide 1. It shows
the power exchange periodically between input waveguide
<figure><img src="image_5.png" /><figcaption>FIGURE 4: 3D normalized optical intensity field distribution at the output ports for various propagation distances, (a) z=0, (b) z=675µm, and (c) z = 925 µm.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 5: The total relative power throughout the proposed power splitter at λ= 1550 nm.</figcaption></figure>

and waveguide 1. At a distance of z = 925 µm, the power is completely transferred from input waveguide to waveguide 1, while at a distance of z = 550 µm half the input power is

transferred. This exchange power mechanism is due to mode coupling that occurred between the waveguides.

To obtain the complete output power distribution, the power transfer mechanism between waveguides was also investigated. The result, among others, is shown in Figure 7, which displayed the optical power transfer between waveguides 1 and 3. It should be noted that the optical input power faded away at z = 780 µm, due to the power transferred to waveguides 1 and 2. By investigating the total relative power throughout the proposed power splitter (Figure 5) and relative power for each waveguide throughout the propagation axis (Figure 7), it can be obtained that the optical power of each output port has an almost uniform splitting ratio of about 24% at each port.

Furthermore, the tolerance value for the structure to anticipate the fabrication error was investigated by varying the coupling gap between the adjacent waveguides. The coupling gap was varied from 6 µm up to 8 µm. The results, among others, are shown in Figure 8. It should be noted that the tolerance range of the coupling gap value should be under 0.5 µm from the best value of 8 µm.
<figure><img src="image_7.png" /><figcaption>FIGURE 6: Exchange of power between input waveguide and waveguide 1.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 7: The relative power as a function of propagation distance (z) for waveguides 1 and 3.</figcaption></figure>

Next, performances of the power splitters are expressed in excess loss, power imbalance, and transmission coefficient. Excess loss is the amount of power lost due to reflection and other material absorption properties. The excess loss was calculated as follows:

$$ \text{Excess Loss} = -10 \log \left( \frac{P_{\text{out}}}{P_{\text{in}}} \right) \quad (15) $$

where $P_{\text{out}}$ and $P_{\text{in}}$ are the total optical output power and the optical input power, respectively. The amount of power imbalance in a splitter is given by the ratio of maximum output power to the minimum output power as defined in (16).

$$ \text{Imbalance} = -10 \log \left( \frac{P_{\text{min}}}{P_{\text{max}}} \right) \quad (16) $$

where $P_{\text{max}}$ is the highest optical power and $P_{\text{min}}$ is the lowest optical power at the four output ports. By using (15) and (16), excess loss and power imbalance of the splitter across

100 nm spectrum of wavelength were calculated at the best geometrical value of the proposed power splitter. The results are presented in Figures 9 and 10 accordingly. Figure 9 shows that, at $\lambda = 1550$ nm, the power splitter has an excess loss of 0.18 dB. It can be noted that the excess loss differences varied $\pm 0.016$ dB across 100 nm spectrum of wavelength. At C-band range (1530–1565 nm), the excess loss varied from 0.18 dB up to 0.19 dB. Due to the guiding mechanism based on mode coupling, it does not involve an interference effect. Therefore, the splitter presents low wavelength sensitivity.

Figure 10 presents the power imbalance of the splitter as a function of wavelength. It can be noticed that, at the operating wavelength, the power imbalance yields are 0.23 dB. Across the C-band range, the power imbalance varied from 0.23 dB up to 0.59 dB. The excess loss and power imbalance of the proposed design are slightly higher in comparison to other optical power splitter designs on slot silicon-gallium nitride waveguide [25].

Next, the transmission coefficient for each output waveguide at the C-band range was observed by calculating it using (17) as follows:

$$ \text{Transmission Coefficient} = -10 \log \left( \frac{P_{\text{ow}}}{P_{\text{in}}} \right) \quad (17) $$

where $P_{\text{ow}}$ and $P_{\text{in}}$ are the power of each output port and power at input port, respectively.

The result is displayed in Figure 11.

Figure 11 displays the transmission coefficient of the splitter across 100 nm spectrum of wavelength. It is found that the transmission coefficient of waveguides 1 and 2 increases from 5.9 dB up to 7.1 dB, while waveguides 3 and 4 decrease from 6.8 dB to 5.8 dB. At the operating wavelength 1.55 $\mu$m, the power splitter divided the input power close to the optimum values.

Furthermore, we investigate the output power of the proposed design across the whole C-band by calculating the normalized transmitted power for $\lambda = 1500–1600$ nm using FD-BPM method. The result is displayed in Figure 12. It should be noted that the normalized transmitted power varies about 0.8 %, from 0.980 to 0.972 over 100 nm spectrum scope.

In the range of C-band (1530-1565 nm), the relative output power distribution varies from 0.980 to 0.977. It means that the design is almost stable through this range. Therefore, it opens an opportunity for future technology.

## 4. Conclusions

A simple 1 × 4 optical power splitter consisting of five parallel rib waveguides based on mode coupling using GaN/sapphire was studied. The optimisation was conducted using FD-BPM and MATLAB at long wavelength optical communication $\lambda = 1550$ nm. The results show that the proposed structure gives an excess loss of 0.18 dB with a power imbalance of 0.23 dB. It is also shown that, at the C-band range, the transmission coefficient of waveguides 1 and 2 increases from 5.9 dB up to 7.1 dB, while waveguides 3 and 4 decrease from 6.8 dB to 5.8 dB. The design is simple; therefore, it is easy to fabricate and can be further developed to be applied in optical communication technology.
<figure><img src="image_9.png" /><figcaption>FIGURE 8: Optical fields profile at the output ports for various coupling gaps (a) 6.5 µm (b) 7 µm and (c) 7.5µm.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>FIGURE 9: The excess loss of the TE mode in the four-branch optical power splitter.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 11: The transmission coefficient of each output port for the TE mode in the four-branch optical power splitter.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>FIGURE 10: The power imbalance of the TE mode in the four-branch optical power splitter.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 12: Relative power distribution for the wavelength range from 1500 nm to 1600 nm.</figcaption></figure>

## Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.
**Additional Points**

We have changed the operating wavelength for telecom-
munication links purposes and investigated the effect of
the coupling gap to the profile of the optical field at the
output ports. Besides, the waveguide parameters and stability
of relative optical power in the C-band range were also
observed.

**Disclosure**

This paper reports an extensive work of our previous paper presented in ICETAS2018 “A GaN/sapphire 1×4 Optical Power Splitter Using Five Rectangular Waveguides for Underwater Application.”

**Conflicts of Interest**

The authors declare that they have no conflicts of interest regarding the publication of this paper.

**Acknowledgments**

This research is supported by Research Grant 2019 (No. NKB-788/UN2.R3.1/HKP.05.00/2019) from RISTEK DIKTI, Indonesia.

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