1st International Conference on Electrical & Electronic Engineering (ICEEE) 04-06 November 2015, RUET,Rajshabi,Bangladesh
Design of a Photonic Crystal Fiber with Negative Flat Dispersion for Residual Dispersion Compensation Russel Reza Mahmuda,b*, S.M. Abdur Razzaka, Md. Shaikh Salman", Md. Imran Hasanc
aDepartment of EEE, Rajshahi University ofEngineering and Technology, Rajshahi-6204, Bangladesh. b *Department of EEE, Ahsanullah University ofScience and Technology, Dhaka-1208, Bangladesh. CDepartment of ETE, Rajshahi University of Engineering and Technology, Rajshahi-6204, Bangladesh. * Email address:a.b
[email protected]
Abstract- The write-up explains numerical design and analysis of a new photonic crystal fiber (PCF). It performs dispersion (D) in the negative flattened region. The providing bandwidth supports bands of E+S+C+L+U into the infrared region (IF) including the window Ill. The proposed PCF is analyzed for their properties by finite element method (FEM). A perfectly matched layer (PML) boundary is used in FEM. The application of polarization maintaining and residual dispersion compensation (RDC) can be easily performed by the proposed design as it offers high flattened negative average dispersion of (478±8) ps.nm-1.km-1 in the wavelength (A) limits of 1.4 to 1.7 �m (300-nm). The structural parameters' changes caused by the effects, studied to prove the accuracy of the properties of the proposed design, that take place during the fabrication.
-
compensation (DC), the residual dispersion compensation (RDC) is still available in the CSMOF. So, we need to adjust this remaining positive dispersion again. Only an RDC-PCF can nullifY the remaining dispersion. The RDCF provides us highly negative but flattened dispersion property. The RDC PCF should be very short in length and it provides the dispersion property as high as possible for reducing all loss and cost. Focusing on these things, over the last few years, much scholarship on negative but flattened dispersion PCFs has been published by some researchers. For instance, PCFs reported by habib et al. [5] explore negative flattened dispersion of l (465.5 ± 5.25) ps.nm- .km-1 over S-U bands. The main -
Keywords-
Photonic
Crystal
Fiber,
Residual
Dispersion
Compensation, Octagonal Circular Pattern, High Birefringence and Dispersion Compensation.
problem of their designs is hybrid in structure. Besides, studies carried out by Silva et al. [2] demonstrated a PCF with average negative flattened chromatic dispersion (NFCD) of 212 ps.nm-1.km-1 over E-U bands. The main challenges of ref. [2] -
1.
INTRODUCTION
For designing a PCF, tiny air channels are placed in the cladding region that run along the whole length of that PCF. These tiny air channels oblige light to be concentrated and confmed into the main core region [1]. The air channels are placed in an appropriate position depending on their designs. By adjusting and changing the placement, area, dimension of parameters and air holes' number, PCF offers various characteristics like negative flattened dispersion, highly nonlinear coefficient and high birefringence. These characteristics are very much suitable for the application of residual dispersion compensation (RDC), super continuum generation (SCG) and optical sensors based on optical fiber [1]. Anyway, the conventional single-mode optical fiber (CSMOF) which is used in long distance data transmission provides the dispersion property of a positive value of 12 to 22 ps.nm-1.km-1 [1]. Finally, on the receiving side, this value of dispersion increases up to considerably high magnitude to a positive peak when the conventional SMF is used for data transmission over very long distance. As a result, optical pulse spread out may occur in the wavelength division multiplexing (WDM) that creates degradation of the original source signal. In this case, to nullifY this very high positive peak of dispersion, a dispersion compensating fiber (DCF) can be coupled with the SMF into the optical link. But, having applied this dispersion
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are fabrication difficulties arising out of the addition doping of another material 'Ge' in the structure of the core. Again, Franco [6] proposed conventional hexagonal PCF that exhibits very low negative flattened dispersion of -(179±2.1) ps.nm-1.km-1 from the wavelength (A) of 1.48 to 1.675 /lffi. The author in ref. [4] also reported high negative flat dispersion of (455 ± 6) -
ps.nm-1.km-1 for the Ie limits of 1.4 to 1.7 /lm. Though the
designs of [4, 6] are hexagonal but, owing to smaller air holes placed into the inner single structured PCF, the designs become more complex than those of the previously reported PCFs [25]. Besides, out of the hexagonal pattern, equiangular spiral (ES) PCF in decagonal pattern [3] reported average negative flattened dispersion of 393 ps.nm-I.km -I with dispersion -
variation (L1D) of 12 ps.nm-I.km-I covering E-U bands. The
main difficulty of ref. [3] is structural complexity such as ES PCFs structure which is almost impractical to design through the 'stack and draw' conventional fabrication method. Tn this write-up, a new and very simple octagonal circular RDC-PCF structure is proposed. In the cladding position, the design has only circular air holes. The structure is based on the conventional and available material like silica. High negative flattened chromatic dispersion (NFCD) of 470 to 486 1 1 1 1 k ps.nm- . m- with L1D of only ±8 ps.nm- .km- within a wide -
-
band wavelength limits of 1.4 to 1.7 /lm (300-nm) are the main achievement of our proposed RDC-PCF design. This bandwidth supports the telecom window III in IF and covers the bands of E+S+C+L+U.
octagonal circular, the angular displacement of any two ° adjacent air holes is 45 . We have willingly deducted four air d holes (two in the 1 st ring and the rest two in the 2n ring) mentioned as dotted circles near the core region shown in Figure 1 (b). Pitch (A 0.67) /lm and the first ring air holes ( r\ =0.74xA), all the other air holes' diameters in the rest =
IT.
DESIGN METHODOLOGY
The geometry of the proposed octagonal circular (OC) PCF structure with some circular channels of air holes is shown in Fig.1. The central core region is modified to get high birefringence. The sole material of the OC-PCF is silica having many advantages for background material. The RDC-PCF has five rings which are shown in Figure 1 (a). Tn the proposed design, for rings 1, 2, 3, 4 and 5, the total number of air-holes are respectively 6, 14, 24, 32 and 40, whereas, in mutual contrast, a conventional hexagonal PCF has a total of 6, 12, 18, 24 and 30 air holes. The distance created between any two adjacent air holes alone with any axis is called pitch which is denoted hereinafter as ' A '. This ' A ' is the only variable of the proposed OC-PCF structure. So, pitch is related to all other parameters in different mathematical relations. As the design is
rings ( r2 =0.78 xA ) are chosen to optimize the declared values of parameters. Therefore, the proposed RDC-PCF has only two types of air holes' diameters that make the fabrication process very simple. m.
EQUATIONS, SIMULATION RESULTS AND DISCUSSIONS
Very much-commercially available COMS OL software is used for the purpose of simulation based on FEM. Dispersion, hereinafter referred to as D, is the variation of pulse width for the propagation of optical signal in unit distance (i.e., ps.nm-1.km-1). The velocity of light in vacuum, the wavelength and the effective refractive index for real part are represented respectively as C,), and Re(l1et� in the dispersion 2 equation. The unit of the effective area (Ae� is /lm for our results and analysis. We have to put the value of electric field into the equation of maxwell to calculate Aejf: The birefringence (B) needs to be calculated when fiber's summitries are broken. By getting the subtraction results of X Y two X-V polarized modes (l1 et[ and l1 efd, we obtain B. Confinement loss (Le), also called loss of leaky modes, has the unit of dB/m. We can get the effective refractive index (l1efl) after simulation and D, B, Le and Aefl can be calculated by the following equations [1].
D("J,) -("J, / C )[(d2 Re[ '7e[t ])/ d"J,2 ] B IRe( '7,;) - Re( '7:;])1 =
=
Le
(1) (2)
= 8.686 x ko 1m ['7e!! ]
(3)
(A)
(4)
=
[n �E(X, y)12 }xdy l' / n �E(x, y)14 dxdy )
(a)
(a) (b) Fig. 2. Optical field distribution for the fundamental X-polarized (a) and Y polarized (b) modes at popular A of 1.55 Ilm.
(b) Fig. 1. (a) The proposed RDC-PCF in original design of the view of transversal cross-section with all the ring numbers (b) Dimension in geometry of RDC-PCF with optimized structural parameters are elucidated in details.
To analyze the light confinement ability of the proposed RDC-PCF for the fundamental X-V polarized modes, the optical field distributions (OFD) need to be studied under the popular), of 1.55 /lm and those are given in Fig. 2. For the total internal refraction mechanism, the proposed index guiding RDC-PCF has higher refractive index (11) at core than at the cladding. It is observed from the results of simulation that light is very strongly confmed to the central core region of the X-V polarized modes.
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To the best of our literature study, we would like to suggest that high but flattened negative dispersion coefficient versus the wavelength bands should be provided by a true RDC fiber. Tn this erite-up, for the Y-polarized modes within 1.4 to 1.7 flm A limits, the proposed RDC-PCF offers 1 1 (an average of NFCD). In the inner - (478 ± 8) ps.nm- .kmfigure of Fig. 3 showing the flatness of the negative dispersion with optimized parameters for Y-polarized mode (OPY-PM) is shown. Comparison of different structures published in different journals with our proposed RDC-PCF design is shown in Fig. 4 describing 'NFCD' versus 'A' limits. According to the simulation results, the RDC-PCF structure proves higher negative flattened dispersion and wider bandwidth than references [2-5] do. We know that �D of ±8 ps.nm-1.km-1 provides a PCF for the application of RDC within some bands of A. In this write-up, for the proposed RDC-PCF, to achieve very high magnitude of NFCD, we choose the optimum parameters in a simple technique is that the first ring's air holes have the lower value of diameters r1 =0.74xA than others' i.e.
Fig. 5. A against D jor alternation of A from ±(J to 2) )lm when rl and r2 of all air holes' diameters are fixed
r2
=0.78 xA. Another one is the only independent variable and that is i\. = 0.67 flill. 0 ------,---1 -·_·- optimum parameters of Y- polarization mode
E
-100-
,,--470.----�----�-71
�
-200-
"E
::=-300-
c
�.Y
'E c en
�-480
� �
·
c o
-500
l 1,. .1
\ \
-485
-490
.� Q) -400-
C>. !!! . o
·475
1 .4
\\ ."
•
__ .....
.
1.5 1.6 Wavelength ( �m)
Fig. 6. Dispersion's eflects for alternating 1st and 2nd ring air holes' diameters for the ROC-PCF. 1.7
-._._.-._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._.-.-._.
-600 1.4
1.45
1.6 1.55 1.5 Wavelength ()lm )
1.65
17
Fig. 3. The proposed ROC-PCF with OPY-PM for the property of chromatic dispersion against wavelength.
At the time of the fabrication process, the air holes' diameters may change at any percentage which trouble the tolerance levels of the properties of RDC-PCF. So, to ensure the dispersion flatness and other properties, it is very much essential for a ±(0.01 to 0.02) flm variation from its optimum values of parameters (OVP) that should be analyzed. Fig. 5 shows the variation of pitch when r1 and r2 remain constant. It is found from the figure that dispersion changes the value of ±20 ps.nm-1.km-1 from 1.4 to 1.55 flm and that of ±7
ps.nm-1.km-1 from 1.55 to 1.7 flm of the wavelength ranges for the variation of pitch at ±(O.O 1 to 0.02) flm. Therefore, D changes slightly for the pitch variation up to ±0.02 flm. Tn Fig. 6, D changes by only ±(20 to 40) ps.nm-1.km-1 from its previous optimum value within that declared bandwidth for changing r1 and r2 air holes' diameters from ±0.01 to ±0.02 flill when all other parameters are unchanged. For the consideration of D, the alteration caused by the effects of diameter r2 make less changes than those of rl. It is also observed that for all the cases, variation of ±0.02 flill creates more changes than ±O.O lflm tolerance. Alteration of all parameters maintains the NFCD characteristic and it balances the fabrication fluctuation. Fig. 4. The proposed RDC-PCF shows high NFCD against A for the wavelength limits and comparison with structures published in other journals.
Comparing B property of CSMOF with RDC-PCF, the RDC-PCF provides better property for B. It is proved by the
139
results of simulation in Fig. 7 that B of 2.3 x 10-2 to 2.45 X 10-2 can be obtained within the A limits from 1.4 to 1.7 flm. Tn 2 addition, we get effective area of 1.8 to 2.2 flm within the A limits of 1.4 to 1.7 flm at OPY-PM for the RDC-PCF design. Splice loss is generally high for the proposed RDC-PCF providing small effective area. A splice-free interconnection technique is proposed to minimize the splice loss for coupling a PCF with a CSMOF [1]. A good RDC-PCF should also have wavelength against very low Le. Figure 8 shows very low confinement loss (Lc) at a magnitude of 10.4 to 10.3 dB/m and 10.5 to 10.4 dB/m for Y and X polarized modes respectively within the reported wavelength limits. 0.0246 ---�--�-----�--, 0.02440.0242-
� 0.024c w
§ 0.0238
�
iii 0.0236-
I
0.0234
......
r r A, 1 ' 2
=
Optimum
,
,
1.5
,
1.55 1.6 Wavelength ( "m )
(5)
Due to the simple octagonal circular structure, the conventional 'stack and draw' technique can apply to our proposed RDC-PCF structural design [1]. Alternatively, sol gel technique can be used to fabricate the RDC-PCF. Already varied irregular structures [3] have been fabricated applying the sol-gel technique. Tn the discussion for the application chapter, we know that negative flattened dispersion is used both in DC and RDC. For the application of maintaining polarization, high birefringence property is essential. These dual characteristics have appointed the proposed RDC-PCF as an appropriate fiber for broadband residual dispersion compensation and maintenance of polarization application [5].
A correctly formed RDCF with NFCD of -470 to -486 ps.nm-1.km-1 within the A limits of 1.4 to l.7 flill has brought
,
1.65
2 112 2 112 Veil = (k 0AF )(neo - na )
C ONCLUSION
I
0.02321.45
5, refractive index of the circular air holes and the core are represented as I1co and l1a. The air filling fraction is F and is calculated as F=(Ahoz/AcezJ where the area of air holes and RDC-PCF are respectively AhoZe and Acel/. So it is confirmed that the RDC-PCF obviously acts as a single-mode fiber [1].
1.7
Fig. 7. B against A for the RDC-PCF with OVP.
forth better results than the previously published structural designs in the discussion chapter have done. The process of fabrication will be simple as the RDC-PCF is simple in structure for the octagonal circular structure having some circular air holes. To recap, as a conclusion having the appealing features of the proposed RDC-PCF, it is reasonable to say that our proposed RDC-PCF fulfills the requirements of the application of polarization maintaining residual dispersion compensation in high speed optical transmission system. References
10-6� 1.4
[I]
R.R. Mahmud et aI., "Ultraflattened high negative chromatic dispersion over O+E+S+C+L+U bands of a microstructured optical fiber," Optical Engineering, vol. 54,no. 9,pp. 0971051-0971057,2015.
[2]
J. P. d. Silva et aI., "Ge-doped defect-core microstructured fiber design by genetic algorithm for residual dispersion compensation," IEEE Photonics Technology Letters, vol. 22, no. 18, pp. 1337-1339, September 2010.
[3]
M. A. Islam et aI., "Design Optimization of equiangular spiral photonic crystal fiber for large negative flat dispersion and high birefringence," IEEE Journal of Lightwave Technology, vol. 30,no. 22, pp. 3545-3551, November 2012.
[4]
D. C. Tee, et aI., "Photonic Crystal Fiber in Photonic Crystal Fiber for Residual Dispersion Compensation Over E+S+C+L+U Wavelength Bands," IEEE Photonics Journal,vol. 5,no. 3,pp. 7200607,June 2013.
[ 5]
M. S. Habib et aI., "Residual Dispersion Compensation Over S + C + L + U Wavelength Bands Using Highly Birefringent Octagonal Photonic Crystal Fiber," Applied Optics,vol. 53, no. 14, pp. 3057-3062, May 2014.
[6 ]
M. A. R. Franco et aI., "Microstructured optical fiber for residual dispersion compensation over S+C+L+U wavelength bands," IEEE Photonics Technology Letters, vol. 20, no. 9, pp. 751-753, May 2008.
__�__�________�___
1.45
1.5 1.55 1.6 Wavelength C!.tm )
1.65
1.7
Fig. 8. Lc against A with OVP for X-Y polarized modes of the RDC-PCF.
For the mode analysis of the RDC-PCF, we need to compare the fundamental mode with the second mode for Le at the popular A of l.55 flm. The 2nd mode is higher up to 46 dB/m than the fundamental mode (FM). Lc of the second mode is 1025 times higher than the FM. Another way of observing the operating performance for the mode test is the calculation of V-parameter using the equation no. 6. We have obtained the value of V-parameter as less than 2.4 for the entire wavelength boundary of 1.4 to 1.7 flm. Tn equation no.
140
