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Highly birefringent TOPAS based single mode photonic crystal fiber with ultra-low material loss for Terahertz applications
Optical Fiber Technology 53 (2019) 102031
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Highly birefringent TOPAS based single mode photonic crystal fiber with ultra-low material loss for Terahertz applications Bikash Kumar Paula,b,c,
T
⁎,1
, Kawsar Ahmeda,b
a
Department of Information and Communication Technology, Mawlana Bhashani Science and Technology University, Santosh-1902, Tangail, Bangladesh Group of Biophotomatiχ, Bangladesh c Department of Software Engineering (SWE), Daffodil International University (DIU), Sukrabad, Dhaka 1207, Bangladesh b
A R T I C LE I N FO
A B S T R A C T
Keywords: Effective material loss Birefringence Power fraction Effective area Single mode PCF Terahertz waveguides
In this article, a polarization maintaining single mode photonic crystal fiber (PCF) has been suggested for Terahertz wave propagation. The proposed PCF is circular shape where five layers cladding vicinity encircles the two layers core region. The air holes of the core part are arranged in porous manner and elliptical shape. These types of air holes destroy the structural symmetry of the reported PCF and increase the level of birefringence. Optical properties of the proposed PCF are investigated by utilizing very popular pretending method that introduces as full vectorial finite element method (FEM). Several guiding mechanisms such as effective material loss (EML), birefringence, effective area, V-parameter, and power fraction are calculated by varying distinctive geometrical parameters and effects. The proposed PCF reveals ultra-low EML of 0.053 cm−1 and ultra-high birefringence of 1.34 × 10−02 at f = 1 THz. In addition, effective area and power fraction of the reported PCF are 2.36 × 10−07 m2 and 52% at the same operating frequency.
1. Introduction Last few decades Terahertz (THz) radiation or wave based technologies have a conveyed massive change in distinctive scientific areas such as sensing, communications, imaging, defense-security, drug testing, spectroscopy, bio-medical engineering and bio-sensing applications that create the attention of researchers and pioneers. The THz wave generation and detection techniques are also advanced with the change of period. The frequency range of THz wave is covered from 0.1 to 10 THz. This range is satisfied the gap between microwave band and infrared rays [1,2]. It remains the challenge to design a flexible, concise, and low-loss THz waveguides because of huge absorption loss occurs in this frequency range. Most of the THz methods are depended on free space for transmission of wave. But various kinds of losses including path loss and material loss have happened in the free space propagation of THz radiation. The metallic waveguides, parallel-plate waveguides, bare metal wires, metallic slot waveguides, dielectric waveguides, subwavelength fibers, and porous polymer fibers have reported due to subdue these limitations of THz wave transmission [3,4]. The modal field is tightly confined at the metallic waveguides but it suffers from high material loss and dispersion characteristics. The
attenuation loss of metallic slot tubes is higher from the metallic tubes. Besides, the parallel-plate waveguides show zero dispersion and lowloss properties that lead to use these waveguides in imaging and signal processing applications [5]. But the ohmic and divergence loss are the main limitation of these wave guides [3]. The bare metal wires are minimized the ohmic loss but these wires are endured from radiation loss [6]. These sub-wavelength fibers reveal comparatively low material loss from the other waveguides. Main drawback of the fiber is most of the optical fields go through external side of the core vicinity. For this reason, the sub-wavelength fibers are produced resolute coupling with the environment [7]. The porous polymer fibers are considered as best compare with the among reported wave guides. These fibers exhibit low loss and provide design flexibility from the other waveguides. Birefringence is another important characteristic of porous fibers that shows better performance in sensing and filtering applications [8]. This property can be enhanced by breaking symmetry of the fiber cladding and establish asymmetry to the fiber core [9]. The elliptical air holes are utilized to increase the birefringence. Various kinds of hosting materials including Teflon [10], poly tetrafluoro ethylene [11], and Topas [4] are mainly used due to increasing the guiding properties of THz wave based photonic crystal fiber (PCF). The cyclic-olefin
⁎
Corresponding author at: Department of Information and Communication Technology (ICT), Mawlana Bhashani Science and Technology University (MBSTU), Santosh, Tangail 1902, Bangladesh. E-mail address: [email protected] (B.K. Paul). 1 ORCID: https://orcid.org/0000-0002-4414-2751. https://doi.org/10.1016/j.yofte.2019.102031 Received 23 March 2019; Received in revised form 3 October 2019; Accepted 9 October 2019 1068-5200/ © 2019 Elsevier Inc. All rights reserved.
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
3. Result and discussion
copolymer (COC) Topas is recommended as the best among these background materials. Distinctive appealing properties are making its unique from the other materials. These attributes are the constant refractive index, low material loss, insensitivity to humidity, and low dispersion [1]. It is noted that PCFs are used for different domain of applications such as gas, chemical temperature, pressure sensor [12–14], nonlinear application [15–17]. From the earlier period, the researchers have suggested different types of PCF due to minimize the material loss and maximize the birefringence attributes. Chen and Tam [18] proposed a super cell structure for THz wave transmission that exhibited the birefringence of 1 × 10−02 at the 1 THz operating frequency. They were not indicated effective area and V-parameter of the proposed fiber. Li et al. [19] reported a hexagonal PCF (H-PCF) where cladding vicinity arranged by circular and elliptical air cavities. This structure revealed birefringence in the order of 10−03 in the range of 0.1–5 THz activation operating frequency. But, the authors were not calculated effective absorption loss, effective area, power fraction, and mode characteristics of the reported H-PCF. Islam et al. [20] suggested a diamond-core porous fiber for polarization maintaining applications that exhibited the material loss and birefringence of 0.11 cm−1 and 8.45 × 10−03 at f = 1 THz. The absorption loss of the PCF was higher and not preferable for communications. Moreover, the V-parameter and power fraction characteristics not indicated in this article. In the year of 2016, Wu et al. [1] proposed a micro structured PCF which revealed the birefringence of 0.98 × 10−02 at the 4 THz pumping frequency. The material loss, effective area, power fraction, and V-parameter didnot calculate for the proposed PCF. Islam et al. [21] reported a PCF as well as obtained the absorption loss and power fraction of 0.08 cm−1 and 38% respectively at the 1 THz operating frequency. The effective material loss (EML) of the proposed PCF was also high. Now, in this paper, we have suggested a circular shape photonic crystal fiber due to decaying these limitations of among the previously reported articles [1,18–21]. The core and cladding territories of proposed PCF are formed by elliptical and circular air holes respectively. The proposed PCF shows single mode characteristics in the entire considered frequency range. In addition, the EML, power fraction, and effective area of the suggested PCF are 0.053 cm−1, 52%, and 2.36 × 10−07 m2 accordingly gain at the 1 THz pumping frequency. So, the proposed PCF is massively efficient for sensing and communication by its excellent features.
For the periodic structure FEM based numerical analysis is highly used. Here COMSOL Multiphysics version 4.2 is employed to carry out the propagation characteristics of the proposed terahertz waveguide. In the beginning of the simulation study, a circular body PML is applied here for boundary condition. Moreover, incorporated with finer mesh analysis number of vertex elements, boundary elements, elements are 636, 9196, 107,220 respectively with carrying minimum element quality 0.6117 found. Finer analysis is subdivided the whole complex geometrical structure into triangular region then mapping to calculate more accurately. It is noted that the convergence error of 6.89 × 10−9 has been found at the operating wavelength of f = 1 THz. When light propagating through the whole length of the fiber some loss are arises. EML is one of the major losses which cause the operating signal energy dissipation. EML of the proposed PCF can be numerated by Eq. (1) according to the article [22].
α eff =
2 αmo 1 ε ⎛ ∫A nαmat |E |dA ⎞ −1 = ⎜⎛ 0 ⎟⎞ ⎜ mat ⎟ cm ∫All Sz dA αmat 2 ⎝ μ0 ⎠ ⎝ ⎠
(1)
where αmo and αmat are denoting loss of fundamental mode and loss causes from material absorption. Here ε0 and μ0 are the relative permittivity and permeability of vacuum respectively. The αmat is the bulk material absorption loss, n = 1.45 is the refractive index of the material, electric field component is represented by E; poynting vector by z; component by Sz. In this work, EML has been investigated in several steps. For analyzing EML, first step is discussed with different porosity at the innermost core region of the proposed fiber. Here 55%, 60% and 65% core porosity has been enumerated for different core diameter for 1 THz activating frequency in Fig. 2. Core diameter is properly adapted around the proposed fiber core diameter. Fig. 1 tells that red green and blue curve are presenting 55%, 60% and 65% core porosity. The variation of core diameter from 404 µm to 424 µm produces different EML level at 1 THz. EML level 0.052–0.065, 0.059–0.072 and 0.068–0.80 are acquired for 55%, 60% and 65% core porosity respectively. All porosity curves are gradually step up with the increment of operating wavelength. Such behavior occurs because higher core porosity allows high optical power transmission through the fiber core. Now curve provides clear perception about EML and gained 0.052 cm−1 EML for 65% core porosity and 404 µm core diameter. Now it can be clearly mentioned that EML of the proposed PCF is comparatively lower than previously reported article [23]. Fiber core has been constituted with elliptical air hole. These air holes can be revolved based on their unique coordinated in associated with semi-major and semi-minor axis. Therehave no occur severe changes in case of EML for different orientation of core air hole angles which are clearly presented in Fig. 3. On the basis of above
2. Fiber design theory The proposed PCF is consisted of five rings circular lattice formed in association with circular types of air hole. All air holes are utilized here by playing the role of dielectric medium. The fiveringsare constitutedby applying perfectly circular type’s air holes with identical diameter value. Moreover, an interesting arithmetic sequence has beenfound for determine the number of air holes. The sequence is followed by an = a1 + (n − 1) × r where n is the ring number and r = 8. Cladding region air holes diameter is denoted by d1 = 244 µmand in the same region center to center distance is commonly known as pitch. Here outermost cladding region pitch is denoted by Ʌ = 320 µm. The diameter of the proposed PCF is 1770 µm. The cladding region is completely bounded by the anisotropic circular perfectly matched layer (CPML) which absorbs unwanted incident electromagnetic radiation. The innermost core segment is modeled with air holes. The 1st layer consists of 6 and 2nd consists of 12 holes. The distance from one center to another center is Ʌc with the value of Ʌc = 80 µm. The hosting material of the proposed PCF is material cyclic olefin copolymer (COC), with a commercial name of TOPAS®. TOPAS® is chosen here for high performance in terahertz waveguide due to its bulk absorption material loss is very low. For fiber modeling and numerical investigation commercially available software COMSOL Multiphyics® version 4.2 has been used.
Fig. 1. Transverse cross-sectional end face two dimensional (2D) view of proposed Circular PCF: (a) cladding region and (b) core region. 2
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
Fig. 2. Normalized effective material loss (EML) a function of different core diameter at 1 THz. Fig. 4. Normalized effective material loss (EML) a function of eccentricity as a core air hole rotation angle at 1 THz for 55%, 60%, and 65% core porosity respectively.
Fig. 3. Normalized effective material loss (EML) a function of different core air hole rotation angle at 1 THz. Fig. 5. Normalized effective material loss (EML) a function of operating frequency for 55%, 60%, and 65% core porosity over 0.80 THz to 1.20 THz.
investigation at f = 1THz frequency, it can be conclude that for 65% core porosity maximum light propagated through the core region which ensures low level of loss. Eccentricity is another fundamental geometric parameter for elliptical air hole. Eccentricity is the measurement of the how nearly circular the ellipse. It is expressed by the following relationship given by Eq. (2).
e=
1−
b2 a2
All investigated results tell that EML for 65% porosity is best suited due to comparatively lower order of EML. Other crucial parameter of the PCFs is power fraction. It defines the total amount of flow over the THz waveguide. The amount of power fraction can be estimated by the following Eq. (3)
(2)
η′ =
where a represents semi major and b represents semi minor axis respectively. EML is a function of eccentricity derived for the activation frequency f = 1THz has been plotted in Fig. 4. The eccentricity has varied around the optimum parameters from 0.4 to 0.6. In this investigated module, the results are resembled with Figs. 2 and 3. Now a wider range of frequency spectrum has been applied to observe the behaviors of the proposed PCF. For this task frequency range 0.80–1.20 THz has been applied successfully. In Fig. 5 EML as a function of applied frequency has been plotted for three different core porosities. Here it clearlydemonstrates that higher core porosity offers more excellent power flower over the THz waveguide and diminishes EML. Higher porosity reduces the degree of material employed in the innermost core area. As a result an optical electromagnetic optical wave experienced with less interaction the PCF material TOPAS®. Here core porosities of 55%, 60% and 65% are shows the EMLof 0.052 cm−1, 0.059 cm−1 and 0.068 cm−1 at 1 THz pumping frequency respectively.
∫X Sz dA ∫All Sz dA
(3)
where X in the numerator defines the area of the region of interest, and the denominator defines is the total area. The background material TOPAS® has a constant refractive index of 1.53 over boarder frequency range spectrum reported in article [23]. Fig. 6 represents simultaneouslycore diameter variation and core porosity variation by keeping other geometrical fixed in frequency condition f = 1THz. Figure also reportsthat on an average 47–53% power fraction have been occurred during the variation (405–425 µm) of core diameter. It clearly indicates that due to increasing core diameter less amount of power flow occurs. During this investigation time modal parameter (V-parameter) has also been studied and plotted in Fig. 7 with the help of the following Eq. (4).
V=
2πrf c
2 2 ncore − ncladding ≤ 2.405
(4)
where ncore, ncladdingare mapping the effecting refractive index of core 3
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
Fig. 6. Normalized effective material loss (EML) a function of operating frequency for 55%, 60%, and 65% core porosity over 0.80–1.20 THz.
Fig. 8. Power fraction is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
Fig. 7. Normalized effective material loss (EML) a function of operating frequency for 55%, 60%, and 65% core porosity over 0.80–1.20 THz.
Fig. 9. V parameter is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
and cladding region respectively. The r is the radios of core region, f is the operated frequency and c is the light velocity in free space. During this overall investigation study V parameter is ranging from 1.95 to 2.38. It can mention that if V is under 2.405 then it persist in single mode region. Besides this, intermodal dispersion can be elevated for single mode propagation. So our proposed fiber is strongly favorable in this condition. Wide range of frequency has been applied to check the power fraction. The power fraction is a function of operating THz frequency is plotted in Fig. 8. The investigation study has done over 0.08–1.20 THz range. In applied frequency spectrum, the power fraction remains unchanged. More than 50% power fraction is produced here for optimum PCF structure. As a result 400 GHz flat band power fraction derived which is very necessary for broadband transmission by minimizing EML. At the same time V parameter inspection has been carried out which is very important for practical applications. Expanding Eq. (4) the V parameter has been diagrammed in Fig. 9. The V parameter is sharply upraises and making positive slope over 1.4–2.6 for 0.08–1.2 THz respectively. PCF remains in single mode region up to 1.14 THz region. After 1.14 THz the fiber experienced with multimode behaviors. Now it clearly expresses that single mode or long haul communication is possible from the PCF by facilitating 340 GHz bandwidth. It is known that the refractive indices of two orthogonal polarization directions are different in a birefringent fiber. The birefringence of a
fiber can be calculated by the following Eq. (5). x Birefringence = neff − neffy
(5)
x and neffy are effective refractive index for x and y polarization where neff respectively. The traditional polarization-maintaining fibers like Bowtie or PANDA fibers [24] have a modal birefringence up to 5 × 10−4 by using mechanical stress to core, and they have been applied to overcome this type of random polarization limitation [25]. It has been expressed that due to the intrinsically high index contrast, the PCFs can retain larger birefringence than the traditional PM fibers. Currently, published PCFs are called PM PCFs and have been fabricated as well as have yielded a birefringence as 3.9 × 10−3 at the wavelength of 1.55 μm [26].This result is improved by our proposed structure that exhibits the birefringence orders of 1.34 × 10−2 which is depicted in Fig. 10. From this figure, it can be seen that frequency dependent birefringence increases according to the increment of frequency up to 1 THz and slightly decreases up to rest of the frequencies and vice versa. For the finite number of air holes in cladding region, the light can propagate among the air hole that is called the confinement loss (CL) or leakage loss. To calculate the confinement loss, an efficient boundary condition is required, that introduces no reflection at boundary. Circular PMLs are the most effective absorption boundary condition for this type of purpose [27]. The leakage loss is computed with the imaginary portion of the effective index according to the Eq. (6).
4
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
Fig. 10. V parameter is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
f dB Confinement Loss (CL) ⎡ ⎤ = 8.686 × 2π Im (neff ) c ⎣m⎦
Fig. 12. Effective mode area is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
enhancement of frequencies up to 1 THz and reduces rest of the frequencies, and the value of effective mode area is about 2.1 × 10−7 m2 at 1 THz frequency which is higher than [29]. Effective mode area due to fiber’s global diameters variation does not vary and its shape abruptly. From above discussions, it can be clearly expressed that our proposed PCF will be effective for transmission systems. Table 1 represents the comparisons among proposed PCF and prior PCFs. It is nicely exhibited that our proposed PCF shows excellent performance than recent designed PCFs. Besides, the effective material loss (EML) of the proposed fiber is comparatively very low about 0.053 cm−1 at1 THz activation frequencies compare to Ref. [20,22–23]. Due to low loss exhibition of proposed fiber makes it suitable in THz radiation propagation. Now, from the experimental and technical point of view, fabrication is the most important task and challenging also. The proposed P-HPCF fabrication process may be easy to fabricate using Sol-gel technique [30] because it can fabricate any shapes and sizes of air holes. Its design flexibility makes it unique compare to others fabrication technique. So our proposed P-PCF can be successfully fabricated applying the most well-known technique called Sol-gel technique.
(6)
where f is the operating frequency and Im is the imaginary part of the effective refractive index. Fig. 11 describes the relationship between the leakage/confinement loss and frequency for x-polarized mode detailed around 1.2 THz frequencies. From this figure, it is also noticed that the confinement loss linearly alleviates with the increment of frequency that is effectible for long haul communication systems [23]. Increasing frequency forms a relatively high index difference between core region and cladding region. In addition, light is tightly absorbed in the core region and for this reason, CL decreases. It is also found that the xpolarization effective mode offers smaller CLcompare to that of the ypolarization mode. The confinement loss at 1 THz frequency is about 1.9 × 10−2 (dB/m). At longer wavelength, the mode power weakly confines in the core region, as a result the guiding waves spread largely. So in this step effective area of the fiber are determined by using Eq. (7).
Aeff =
[∫ I (r ) rdr ]2 [∫ I 2 (r ) dr ]2
(7)
where I (r ) = |Et is representing the electric field intensity. In this situation, the propagating modes retain larger effective mode area [28]. Fig. 12 represents effective mode area as a function of frequency. The effective mode area of the fiber decreases according to the
|2
4. Conclusions A circular shape PCF has been proposed and numerically investigated in this paper. The reported PCF is designed for THz wave transmission. Two different sizes and shapes air cavities are used to design this PCF structure. Various geometrical parameters including diameters of circular air holes; major and minor axis of the elliptical air holes has fluctuated to examine the optical properties of the suggested PCF. The core porosity and eccentricity effects are also considered to calculate the guiding parameters. The reported PCF shows ultra-high birefringence in the order of 1.34 × 10−02 and ultra-low absorption loss of 0.053 cm−1 at the 1 THz activation frequency. The V-parameter Table 1 Comparison among several fundamental properties of the proposed THz waveguide with the existing standard PCF structures.
Fig. 11. Confinement loss is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure. 5
References
f (THz)
Birefringence
EML (cm−1)
Ref. [18] Ref. [20] Ref. [1] Ref. [23] Ref. [30] Ref. [22] Proposed PCF
1 1 4 1 1 1 1
1 × 10−02 8.45 × 10−03 0.98 × 10−02 – – – 1.34 × 10−2
– 0.110 – 0.085 0.076 0.066 0.053
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
indicates that proposed fiber is single mode. High power fraction attribute mentions lower EML. In addition, effective area of the proposed PCF is also high that ensures the high data rate transmission. Finally, the reported PCF is very effective for polarization maintaining and long distance communication applications.
[13]
[14]
Declaration of Competing Interest
[15]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[16]
[17]
Appendix A. Supplementary data
[18] [19]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.yofte.2019.102031.
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Optical Fiber Technology journal homepage: www.elsevier.com/locate/yofte
Highly birefringent TOPAS based single mode photonic crystal fiber with ultra-low material loss for Terahertz applications Bikash Kumar Paula,b,c,
T
⁎,1
, Kawsar Ahmeda,b
a
Department of Information and Communication Technology, Mawlana Bhashani Science and Technology University, Santosh-1902, Tangail, Bangladesh Group of Biophotomatiχ, Bangladesh c Department of Software Engineering (SWE), Daffodil International University (DIU), Sukrabad, Dhaka 1207, Bangladesh b
A R T I C LE I N FO
A B S T R A C T
Keywords: Effective material loss Birefringence Power fraction Effective area Single mode PCF Terahertz waveguides
In this article, a polarization maintaining single mode photonic crystal fiber (PCF) has been suggested for Terahertz wave propagation. The proposed PCF is circular shape where five layers cladding vicinity encircles the two layers core region. The air holes of the core part are arranged in porous manner and elliptical shape. These types of air holes destroy the structural symmetry of the reported PCF and increase the level of birefringence. Optical properties of the proposed PCF are investigated by utilizing very popular pretending method that introduces as full vectorial finite element method (FEM). Several guiding mechanisms such as effective material loss (EML), birefringence, effective area, V-parameter, and power fraction are calculated by varying distinctive geometrical parameters and effects. The proposed PCF reveals ultra-low EML of 0.053 cm−1 and ultra-high birefringence of 1.34 × 10−02 at f = 1 THz. In addition, effective area and power fraction of the reported PCF are 2.36 × 10−07 m2 and 52% at the same operating frequency.
1. Introduction Last few decades Terahertz (THz) radiation or wave based technologies have a conveyed massive change in distinctive scientific areas such as sensing, communications, imaging, defense-security, drug testing, spectroscopy, bio-medical engineering and bio-sensing applications that create the attention of researchers and pioneers. The THz wave generation and detection techniques are also advanced with the change of period. The frequency range of THz wave is covered from 0.1 to 10 THz. This range is satisfied the gap between microwave band and infrared rays [1,2]. It remains the challenge to design a flexible, concise, and low-loss THz waveguides because of huge absorption loss occurs in this frequency range. Most of the THz methods are depended on free space for transmission of wave. But various kinds of losses including path loss and material loss have happened in the free space propagation of THz radiation. The metallic waveguides, parallel-plate waveguides, bare metal wires, metallic slot waveguides, dielectric waveguides, subwavelength fibers, and porous polymer fibers have reported due to subdue these limitations of THz wave transmission [3,4]. The modal field is tightly confined at the metallic waveguides but it suffers from high material loss and dispersion characteristics. The
attenuation loss of metallic slot tubes is higher from the metallic tubes. Besides, the parallel-plate waveguides show zero dispersion and lowloss properties that lead to use these waveguides in imaging and signal processing applications [5]. But the ohmic and divergence loss are the main limitation of these wave guides [3]. The bare metal wires are minimized the ohmic loss but these wires are endured from radiation loss [6]. These sub-wavelength fibers reveal comparatively low material loss from the other waveguides. Main drawback of the fiber is most of the optical fields go through external side of the core vicinity. For this reason, the sub-wavelength fibers are produced resolute coupling with the environment [7]. The porous polymer fibers are considered as best compare with the among reported wave guides. These fibers exhibit low loss and provide design flexibility from the other waveguides. Birefringence is another important characteristic of porous fibers that shows better performance in sensing and filtering applications [8]. This property can be enhanced by breaking symmetry of the fiber cladding and establish asymmetry to the fiber core [9]. The elliptical air holes are utilized to increase the birefringence. Various kinds of hosting materials including Teflon [10], poly tetrafluoro ethylene [11], and Topas [4] are mainly used due to increasing the guiding properties of THz wave based photonic crystal fiber (PCF). The cyclic-olefin
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Corresponding author at: Department of Information and Communication Technology (ICT), Mawlana Bhashani Science and Technology University (MBSTU), Santosh, Tangail 1902, Bangladesh. E-mail address: [email protected] (B.K. Paul). 1 ORCID: https://orcid.org/0000-0002-4414-2751. https://doi.org/10.1016/j.yofte.2019.102031 Received 23 March 2019; Received in revised form 3 October 2019; Accepted 9 October 2019 1068-5200/ © 2019 Elsevier Inc. All rights reserved.
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
3. Result and discussion
copolymer (COC) Topas is recommended as the best among these background materials. Distinctive appealing properties are making its unique from the other materials. These attributes are the constant refractive index, low material loss, insensitivity to humidity, and low dispersion [1]. It is noted that PCFs are used for different domain of applications such as gas, chemical temperature, pressure sensor [12–14], nonlinear application [15–17]. From the earlier period, the researchers have suggested different types of PCF due to minimize the material loss and maximize the birefringence attributes. Chen and Tam [18] proposed a super cell structure for THz wave transmission that exhibited the birefringence of 1 × 10−02 at the 1 THz operating frequency. They were not indicated effective area and V-parameter of the proposed fiber. Li et al. [19] reported a hexagonal PCF (H-PCF) where cladding vicinity arranged by circular and elliptical air cavities. This structure revealed birefringence in the order of 10−03 in the range of 0.1–5 THz activation operating frequency. But, the authors were not calculated effective absorption loss, effective area, power fraction, and mode characteristics of the reported H-PCF. Islam et al. [20] suggested a diamond-core porous fiber for polarization maintaining applications that exhibited the material loss and birefringence of 0.11 cm−1 and 8.45 × 10−03 at f = 1 THz. The absorption loss of the PCF was higher and not preferable for communications. Moreover, the V-parameter and power fraction characteristics not indicated in this article. In the year of 2016, Wu et al. [1] proposed a micro structured PCF which revealed the birefringence of 0.98 × 10−02 at the 4 THz pumping frequency. The material loss, effective area, power fraction, and V-parameter didnot calculate for the proposed PCF. Islam et al. [21] reported a PCF as well as obtained the absorption loss and power fraction of 0.08 cm−1 and 38% respectively at the 1 THz operating frequency. The effective material loss (EML) of the proposed PCF was also high. Now, in this paper, we have suggested a circular shape photonic crystal fiber due to decaying these limitations of among the previously reported articles [1,18–21]. The core and cladding territories of proposed PCF are formed by elliptical and circular air holes respectively. The proposed PCF shows single mode characteristics in the entire considered frequency range. In addition, the EML, power fraction, and effective area of the suggested PCF are 0.053 cm−1, 52%, and 2.36 × 10−07 m2 accordingly gain at the 1 THz pumping frequency. So, the proposed PCF is massively efficient for sensing and communication by its excellent features.
For the periodic structure FEM based numerical analysis is highly used. Here COMSOL Multiphysics version 4.2 is employed to carry out the propagation characteristics of the proposed terahertz waveguide. In the beginning of the simulation study, a circular body PML is applied here for boundary condition. Moreover, incorporated with finer mesh analysis number of vertex elements, boundary elements, elements are 636, 9196, 107,220 respectively with carrying minimum element quality 0.6117 found. Finer analysis is subdivided the whole complex geometrical structure into triangular region then mapping to calculate more accurately. It is noted that the convergence error of 6.89 × 10−9 has been found at the operating wavelength of f = 1 THz. When light propagating through the whole length of the fiber some loss are arises. EML is one of the major losses which cause the operating signal energy dissipation. EML of the proposed PCF can be numerated by Eq. (1) according to the article [22].
α eff =
2 αmo 1 ε ⎛ ∫A nαmat |E |dA ⎞ −1 = ⎜⎛ 0 ⎟⎞ ⎜ mat ⎟ cm ∫All Sz dA αmat 2 ⎝ μ0 ⎠ ⎝ ⎠
(1)
where αmo and αmat are denoting loss of fundamental mode and loss causes from material absorption. Here ε0 and μ0 are the relative permittivity and permeability of vacuum respectively. The αmat is the bulk material absorption loss, n = 1.45 is the refractive index of the material, electric field component is represented by E; poynting vector by z; component by Sz. In this work, EML has been investigated in several steps. For analyzing EML, first step is discussed with different porosity at the innermost core region of the proposed fiber. Here 55%, 60% and 65% core porosity has been enumerated for different core diameter for 1 THz activating frequency in Fig. 2. Core diameter is properly adapted around the proposed fiber core diameter. Fig. 1 tells that red green and blue curve are presenting 55%, 60% and 65% core porosity. The variation of core diameter from 404 µm to 424 µm produces different EML level at 1 THz. EML level 0.052–0.065, 0.059–0.072 and 0.068–0.80 are acquired for 55%, 60% and 65% core porosity respectively. All porosity curves are gradually step up with the increment of operating wavelength. Such behavior occurs because higher core porosity allows high optical power transmission through the fiber core. Now curve provides clear perception about EML and gained 0.052 cm−1 EML for 65% core porosity and 404 µm core diameter. Now it can be clearly mentioned that EML of the proposed PCF is comparatively lower than previously reported article [23]. Fiber core has been constituted with elliptical air hole. These air holes can be revolved based on their unique coordinated in associated with semi-major and semi-minor axis. Therehave no occur severe changes in case of EML for different orientation of core air hole angles which are clearly presented in Fig. 3. On the basis of above
2. Fiber design theory The proposed PCF is consisted of five rings circular lattice formed in association with circular types of air hole. All air holes are utilized here by playing the role of dielectric medium. The fiveringsare constitutedby applying perfectly circular type’s air holes with identical diameter value. Moreover, an interesting arithmetic sequence has beenfound for determine the number of air holes. The sequence is followed by an = a1 + (n − 1) × r where n is the ring number and r = 8. Cladding region air holes diameter is denoted by d1 = 244 µmand in the same region center to center distance is commonly known as pitch. Here outermost cladding region pitch is denoted by Ʌ = 320 µm. The diameter of the proposed PCF is 1770 µm. The cladding region is completely bounded by the anisotropic circular perfectly matched layer (CPML) which absorbs unwanted incident electromagnetic radiation. The innermost core segment is modeled with air holes. The 1st layer consists of 6 and 2nd consists of 12 holes. The distance from one center to another center is Ʌc with the value of Ʌc = 80 µm. The hosting material of the proposed PCF is material cyclic olefin copolymer (COC), with a commercial name of TOPAS®. TOPAS® is chosen here for high performance in terahertz waveguide due to its bulk absorption material loss is very low. For fiber modeling and numerical investigation commercially available software COMSOL Multiphyics® version 4.2 has been used.
Fig. 1. Transverse cross-sectional end face two dimensional (2D) view of proposed Circular PCF: (a) cladding region and (b) core region. 2
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
Fig. 2. Normalized effective material loss (EML) a function of different core diameter at 1 THz. Fig. 4. Normalized effective material loss (EML) a function of eccentricity as a core air hole rotation angle at 1 THz for 55%, 60%, and 65% core porosity respectively.
Fig. 3. Normalized effective material loss (EML) a function of different core air hole rotation angle at 1 THz. Fig. 5. Normalized effective material loss (EML) a function of operating frequency for 55%, 60%, and 65% core porosity over 0.80 THz to 1.20 THz.
investigation at f = 1THz frequency, it can be conclude that for 65% core porosity maximum light propagated through the core region which ensures low level of loss. Eccentricity is another fundamental geometric parameter for elliptical air hole. Eccentricity is the measurement of the how nearly circular the ellipse. It is expressed by the following relationship given by Eq. (2).
e=
1−
b2 a2
All investigated results tell that EML for 65% porosity is best suited due to comparatively lower order of EML. Other crucial parameter of the PCFs is power fraction. It defines the total amount of flow over the THz waveguide. The amount of power fraction can be estimated by the following Eq. (3)
(2)
η′ =
where a represents semi major and b represents semi minor axis respectively. EML is a function of eccentricity derived for the activation frequency f = 1THz has been plotted in Fig. 4. The eccentricity has varied around the optimum parameters from 0.4 to 0.6. In this investigated module, the results are resembled with Figs. 2 and 3. Now a wider range of frequency spectrum has been applied to observe the behaviors of the proposed PCF. For this task frequency range 0.80–1.20 THz has been applied successfully. In Fig. 5 EML as a function of applied frequency has been plotted for three different core porosities. Here it clearlydemonstrates that higher core porosity offers more excellent power flower over the THz waveguide and diminishes EML. Higher porosity reduces the degree of material employed in the innermost core area. As a result an optical electromagnetic optical wave experienced with less interaction the PCF material TOPAS®. Here core porosities of 55%, 60% and 65% are shows the EMLof 0.052 cm−1, 0.059 cm−1 and 0.068 cm−1 at 1 THz pumping frequency respectively.
∫X Sz dA ∫All Sz dA
(3)
where X in the numerator defines the area of the region of interest, and the denominator defines is the total area. The background material TOPAS® has a constant refractive index of 1.53 over boarder frequency range spectrum reported in article [23]. Fig. 6 represents simultaneouslycore diameter variation and core porosity variation by keeping other geometrical fixed in frequency condition f = 1THz. Figure also reportsthat on an average 47–53% power fraction have been occurred during the variation (405–425 µm) of core diameter. It clearly indicates that due to increasing core diameter less amount of power flow occurs. During this investigation time modal parameter (V-parameter) has also been studied and plotted in Fig. 7 with the help of the following Eq. (4).
V=
2πrf c
2 2 ncore − ncladding ≤ 2.405
(4)
where ncore, ncladdingare mapping the effecting refractive index of core 3
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
Fig. 6. Normalized effective material loss (EML) a function of operating frequency for 55%, 60%, and 65% core porosity over 0.80–1.20 THz.
Fig. 8. Power fraction is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
Fig. 7. Normalized effective material loss (EML) a function of operating frequency for 55%, 60%, and 65% core porosity over 0.80–1.20 THz.
Fig. 9. V parameter is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
and cladding region respectively. The r is the radios of core region, f is the operated frequency and c is the light velocity in free space. During this overall investigation study V parameter is ranging from 1.95 to 2.38. It can mention that if V is under 2.405 then it persist in single mode region. Besides this, intermodal dispersion can be elevated for single mode propagation. So our proposed fiber is strongly favorable in this condition. Wide range of frequency has been applied to check the power fraction. The power fraction is a function of operating THz frequency is plotted in Fig. 8. The investigation study has done over 0.08–1.20 THz range. In applied frequency spectrum, the power fraction remains unchanged. More than 50% power fraction is produced here for optimum PCF structure. As a result 400 GHz flat band power fraction derived which is very necessary for broadband transmission by minimizing EML. At the same time V parameter inspection has been carried out which is very important for practical applications. Expanding Eq. (4) the V parameter has been diagrammed in Fig. 9. The V parameter is sharply upraises and making positive slope over 1.4–2.6 for 0.08–1.2 THz respectively. PCF remains in single mode region up to 1.14 THz region. After 1.14 THz the fiber experienced with multimode behaviors. Now it clearly expresses that single mode or long haul communication is possible from the PCF by facilitating 340 GHz bandwidth. It is known that the refractive indices of two orthogonal polarization directions are different in a birefringent fiber. The birefringence of a
fiber can be calculated by the following Eq. (5). x Birefringence = neff − neffy
(5)
x and neffy are effective refractive index for x and y polarization where neff respectively. The traditional polarization-maintaining fibers like Bowtie or PANDA fibers [24] have a modal birefringence up to 5 × 10−4 by using mechanical stress to core, and they have been applied to overcome this type of random polarization limitation [25]. It has been expressed that due to the intrinsically high index contrast, the PCFs can retain larger birefringence than the traditional PM fibers. Currently, published PCFs are called PM PCFs and have been fabricated as well as have yielded a birefringence as 3.9 × 10−3 at the wavelength of 1.55 μm [26].This result is improved by our proposed structure that exhibits the birefringence orders of 1.34 × 10−2 which is depicted in Fig. 10. From this figure, it can be seen that frequency dependent birefringence increases according to the increment of frequency up to 1 THz and slightly decreases up to rest of the frequencies and vice versa. For the finite number of air holes in cladding region, the light can propagate among the air hole that is called the confinement loss (CL) or leakage loss. To calculate the confinement loss, an efficient boundary condition is required, that introduces no reflection at boundary. Circular PMLs are the most effective absorption boundary condition for this type of purpose [27]. The leakage loss is computed with the imaginary portion of the effective index according to the Eq. (6).
4
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
Fig. 10. V parameter is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
f dB Confinement Loss (CL) ⎡ ⎤ = 8.686 × 2π Im (neff ) c ⎣m⎦
Fig. 12. Effective mode area is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure.
enhancement of frequencies up to 1 THz and reduces rest of the frequencies, and the value of effective mode area is about 2.1 × 10−7 m2 at 1 THz frequency which is higher than [29]. Effective mode area due to fiber’s global diameters variation does not vary and its shape abruptly. From above discussions, it can be clearly expressed that our proposed PCF will be effective for transmission systems. Table 1 represents the comparisons among proposed PCF and prior PCFs. It is nicely exhibited that our proposed PCF shows excellent performance than recent designed PCFs. Besides, the effective material loss (EML) of the proposed fiber is comparatively very low about 0.053 cm−1 at1 THz activation frequencies compare to Ref. [20,22–23]. Due to low loss exhibition of proposed fiber makes it suitable in THz radiation propagation. Now, from the experimental and technical point of view, fabrication is the most important task and challenging also. The proposed P-HPCF fabrication process may be easy to fabricate using Sol-gel technique [30] because it can fabricate any shapes and sizes of air holes. Its design flexibility makes it unique compare to others fabrication technique. So our proposed P-PCF can be successfully fabricated applying the most well-known technique called Sol-gel technique.
(6)
where f is the operating frequency and Im is the imaginary part of the effective refractive index. Fig. 11 describes the relationship between the leakage/confinement loss and frequency for x-polarized mode detailed around 1.2 THz frequencies. From this figure, it is also noticed that the confinement loss linearly alleviates with the increment of frequency that is effectible for long haul communication systems [23]. Increasing frequency forms a relatively high index difference between core region and cladding region. In addition, light is tightly absorbed in the core region and for this reason, CL decreases. It is also found that the xpolarization effective mode offers smaller CLcompare to that of the ypolarization mode. The confinement loss at 1 THz frequency is about 1.9 × 10−2 (dB/m). At longer wavelength, the mode power weakly confines in the core region, as a result the guiding waves spread largely. So in this step effective area of the fiber are determined by using Eq. (7).
Aeff =
[∫ I (r ) rdr ]2 [∫ I 2 (r ) dr ]2
(7)
where I (r ) = |Et is representing the electric field intensity. In this situation, the propagating modes retain larger effective mode area [28]. Fig. 12 represents effective mode area as a function of frequency. The effective mode area of the fiber decreases according to the
|2
4. Conclusions A circular shape PCF has been proposed and numerically investigated in this paper. The reported PCF is designed for THz wave transmission. Two different sizes and shapes air cavities are used to design this PCF structure. Various geometrical parameters including diameters of circular air holes; major and minor axis of the elliptical air holes has fluctuated to examine the optical properties of the suggested PCF. The core porosity and eccentricity effects are also considered to calculate the guiding parameters. The reported PCF shows ultra-high birefringence in the order of 1.34 × 10−02 and ultra-low absorption loss of 0.053 cm−1 at the 1 THz activation frequency. The V-parameter Table 1 Comparison among several fundamental properties of the proposed THz waveguide with the existing standard PCF structures.
Fig. 11. Confinement loss is a function of operating frequency over 0.80–1.20 THz regime for optimum design structure. 5
References
f (THz)
Birefringence
EML (cm−1)
Ref. [18] Ref. [20] Ref. [1] Ref. [23] Ref. [30] Ref. [22] Proposed PCF
1 1 4 1 1 1 1
1 × 10−02 8.45 × 10−03 0.98 × 10−02 – – – 1.34 × 10−2
– 0.110 – 0.085 0.076 0.066 0.053
Optical Fiber Technology 53 (2019) 102031
B.K. Paul and K. Ahmed
indicates that proposed fiber is single mode. High power fraction attribute mentions lower EML. In addition, effective area of the proposed PCF is also high that ensures the high data rate transmission. Finally, the reported PCF is very effective for polarization maintaining and long distance communication applications.
[13]
[14]
Declaration of Competing Interest
[15]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[16]
[17]
Appendix A. Supplementary data
[18] [19]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.yofte.2019.102031.
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