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Dispersion characteristics of all-glass photonic crystal fibers
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Dispersion characteristics of all-glass photonic crystal fibers Sanjaykumar Gowre a,∗ , Sudipta Mahapatra a , S.K. Varshney a , P.K. Sahu b a b
Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Khargapur 721302, India School of Electrical Sciences, Indian Institute of Technology, Bhubaneswar 751013, India
a r t i c l e
i n f o
Article history: Received 20 June 2012 Accepted 12 November 2012 Keywords: All-glass PCF Dispersion Doping and endlessly single mode
a b s t r a c t In this paper, we numerically investigate all-glass photonic crystal fiber (AGPCF) structure using finite difference time domain method. The proposed PCF structure exhibit improved endlessly single-mode behavior and tunable dispersion properties. The proposed structure consists of fluorine-doped rods in the cladding region which might reduce the deformation of air-holes as in air-hole cladding PCF structures. By varying the doping concentration, the optical characteristics can be varied and makes it possible to achieve several improved PCF designs. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction The rapid development of photonic crystal fiber (PCF) [1] since the last decade has created strong requirements for novel optical components that can handle functions such as dispersion compensation [2–4], flattened dispersion [6–8] and exhibit endlessly single-mode property [5]. Their artificial crystal-like structure results in a number of unique and unusual properties, such as single-mode operation from UV to IR spectral regions, large mode areas with core diameters larger than 20 m2 , highly nonlinear performance, tunable dispersion, and a numerical aperture ranging from arbitrarily low value to 0.9, impossible to achieve in classical step index fibers. Therefore, PCFs offer exciting potentials for key enabling technologies in optical communication systems. To realize the potentials of photonic crystals, however, it is important to understand how photonic crystal structures can be engineered to meet the stringent requirements of optical communication systems. For example, a fundamental challenge for high bit-rate applications is to achieve significant dispersive affects with a large enough bandwidth that is sufficient to cover the signal of interest. In this paper, we present all-glass photonic crystal fiber structure in order to achieve endlessly single-mode regime and to have large dispersion that can be used for dispersion compensation. In addition to this, we also carry out loss analysis using the finite difference time domain method and the result shows that the loss is in between that of single-mode fiber and conventional photonic crystal fiber. Moreover, a new structure with different air-hole
diameters in different layers is proposed to get flattened dispersion of the order of ±0.2 ps/nm/km over a wavelength range of 1400–1650 nm. The organization of the paper is as follows: Section 2, following the introduction, briefly presents the design of the conventional PCF and the all-glass PCF. Section 3 compiles different results including the loss analysis to show the superiority of the proposed design and Section 4 concludes the paper. 2. All-glass PCF design Two of the major limitations of conventional photonic crystal fibers are deformation of air-holes and emergence of additional airholes during the fabrication of the fiber [9]. The main objective of this work is to circumvent these problems while ensuring that the fiber exhibits improved endlessly single-mode property and tunable dispersion characteristics. Fig. 1(a) depicts the photonic crystal fiber with a triangular lattice of holes, each having a diameter d and pitch . In the center, an air hole is omitted creating a central high index defect serving as the fiber core. In order to remove the drawbacks associated with the air-hole PCF, we have proposed a all-glass photonic crystal fiber structure shown in Fig. 1(b) with a triangular lattice of rods of fluorine doped silica, which replace the air-holes in a conventional PCF [10]. The proposed structure has an additional design parameter in terms of doping concentration in addition to the diameter of the silica rods, pitch and refractive index. 3. Theory, design and simulation results
∗ Corresponding author. Tel.: +91 8951855685. E-mail addresses: [email protected] (S. Gowre), [email protected] (S. Mahapatra), [email protected] (S.K. Varshney), [email protected] (P.K. Sahu).
3.1. V-parameter The properties of standard optical fibers are parameterized by the V parameter (normalized frequency) and the entire concept is
0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.11.036
Please cite this article in press as: S. Gowre, et al., Dispersion characteristics of all-glass photonic crystal fibers, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.036
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Fig. 1. Photonic crystal fiber structures (a) air-hole PCF, (b) proposed all-glass PCF with doped silica rods in cladding.
Fig. 3. Effect of doping concentration on V parameter.
very close to the heart of a majority of the optical fiber community. The cut-off properties and the endlessly single-mode (ESM) phenomena of PCFs can also be qualitatively understood within this framework. For an operating wavelength, if the value of V parameter is less than or equal to 2.405, the fiber is said to be operating in the single-mode region in standard optical fiber literature. The tradition of parametrizing the optical properties in terms of the V parameter stems from analysis of the step-index fiber (SIF). The SIF is characterized by the core radius , the core index nco , and the cladding index ncl , which all enter into the parameter VSIF given by
in the single-mode region irrespective of the operating wavelength. This property is not achievable with single-mode fiber. We have investigated the effect of the doping concentration on refractive index and found that as doping concentration is increased, there is an increase in the refractive index [10]. The allglass photonic crystal fiber structure also shows this property. It has the advantage of having the cut-off V parameter less than for a higher value of d/, i.e., 0.46 with a doping concentration of 1.8%. A higher value of d/ simplifies the fabrication process. At the same time, the all-glass photonic crystal fiber shows endlessly single-mode property. For all-glass photonic crystal fiber structure, the value of the effective V parameter is less than that of the air hole PCF as there is a low refractive index contrast between core and cladding for the same value of d/. Fig. 2(b) shows the effective V parameter of all-glass photonic crystal fiber for different values of d/. We can examine the above said low values of V parameter for same value of d/ for air-hole PCF and all-glass PCF by comparing Fig. 2(a) and Fig. 2(b). For d/ of 0.4, the value of V parameter is 2.6 for all-glass PCF, whereas for air-hole PCF it is 2.8 for a value / of 10. Further, we have investigated the effect of fluorine doping on the V parameter. A doped silica rod with a diameter of 0.4 m and = 1 m is used and is compared with the conventional PCF. As shown in Fig. 3, for AHPCF the V parameter value is more than the cut-off value (3.142) for / equal to 10. This indicates that the PCF is no more working in the single-mode region, whereas for our proposed all-glass PCF structure with 1.8% doping concentration, the V parameter value is less than the cut-off value up to a / value of 50. As doping concentration is increased from f = 1.8% to f = 13.5%, there is increase in the V parameter value as refractive index contrast between core and cladding increases. So, we have an additional design parameter in doping concentration, while designing endlessly single-mode PCF. This signifies that by keeping the values of d/ and constant, it is possible to design PCF for endlessly single-mode applications only by varying the doping concentration.
VSIF =
2
n2co − n2cl
(1)
Following Eq. (1), for a given value of operating wavelength, the values of core radius () and refractive index contrast between core and cladding are adjusted in such a way that the value of V parameter is less than 2.405, which is the required condition for the fiber to be in the single-mode region. In the context of PCFs, it is also natural to consider a V parameter. However, using Eq. (1), it is not possible to analyze PCFs, as it has not taken pitch (), and diameter (d) into consideration. The photonic crystal fiber is rather analyzed by Eq. (2) given below [5]. V=
2aeff
n2co − n2FSM =
U2 + W 2
(2)
where U and W are known as normalized transverse phase and attenuation constants, given by U=
2aeff
n2co − n2eff ,
W=
2aeff
n2eff − n2FSM
(3)
In the above equation, aeff is the effective core radius given by aeff = √ / 3, nco is the core refractive index, nFSM is the cladding index, neff is the index of the fundamental guided mode, and is operating wavelength. Fig. 2(a) gives the variation in the cut-off V parameter versus / for different values of d/. It shows that for values of d/ below 0.425, the effective V parameter value of conventional photonic crystal fiber is less than indicating that the fiber is operating
Fig. 2. Effective V parameter for different values of d/ (a) air-hole PCF, (b) proposed all-glass PCF with 1.8% doping concentration.
3.2. Dispersion Chromatic dispersion is a variation in the velocity of light (group velocity) with a variation in the wavelength. This variation in velocity causes the pulses of a modulated laser source to broaden when traveling through the fiber; up to a point where pulses overlap and bit error rate increases. As this increase in bit error rate interferes with both the quality and speed of the signal, chromatic dispersion (CD) is a major limiting factor in high-speed transmission. A finite difference time domain (FDTD) method is be used to analyze the chromatic dispersion property with the help of RSoft’s BandSOLVE software package. Fig. 4 shows the chromatic dispersion of the proposed all-glass PCF structure for different values
Please cite this article in press as: S. Gowre, et al., Dispersion characteristics of all-glass photonic crystal fibers, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.036
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Fig. 4. Chromatic dispersion of proposed all-glass photonic crystal fiber.
of d/, ranging from 0.3 to 0.6. The doping concentration used is 13.5%. As shown in Fig. 4, the ZDW is 1.22 m for d/ of 0.3, 1.26 m for d/ = 0.4, 1.29 m for d/ = 0.5, 1.3 m for d/ = 0.6. It is also possible to shift the zero dispersion wavelengths at any desired wavelength by making suitable changes in structure, refractive index, number of air-holes, as in conventional PCF. We observe that here it is possible to shift the zero dispersion wavelength to a desired value due to the fact that the waveguide dispersion is more dominant than material dispersion. This is also possible in conventional PCF, but our proposed all-glass PCF structure has an additional design parameter in doping concentration, which can be used to shift the dispersion to any desired value. For AHPCF, ZDW is at 2 m and by varying the doping concentration from 1.8% to 7.9%, we can get the desired ZDW at 1.32 m, 1.35 m and 1.4 m respectively as shown in Fig. 5. A variety of dispersion compensating techniques has been investigated previously to cancel the large anomalous dispersion of the standard single-mode fibers (SMF’s) at 1550 nm wavelength. Among them, the dispersion compensating fiber technique (DCF) has been shown to be attractive for femto-second pulse transmission; because, a carefully selected DCF with a precisely adjusted fiber length is able to cancel all of the second-order dispersion and effectively suppress much of the third-order dispersion. In optical fiber one often uses DCM for compensating chromatic dispersion. As shown in Fig. 6, for doping concentration of 4.1% and 7.9%, the chromatic dispersion at 1.55 m is −400 ps/nm/km, and −322 ps/nm/km respectively. Therefore, we can design a photonic crystal fiber structure for desired chromatic dispersion which can be used as dispersion compensation unit in optical communication. We know that the dispersion of single-mode fiber at 1.55 m is 17 ps/nm/km and dispersion of all-glass PCF with doping
Fig. 5. Effect of doping concentration on dispersion. For air-hole PCF, ZDW = 2 m, with 1.8% doping, ZDW = 1.32 m, with 4.9% doping concentration, ZDW = 1.35 m, with 7.9% doping concentration, ZDW = 1.4 m.
3
Fig. 6. Dispersion compensation at 1.55 m using proposed all-glass PCF structure.
concentration of 4.1% and 7.9% are −400 ps/nm/km and −322 ps/nm/km respectively. The length of the dispersion compensating fiber is given by [4] LDCF =
80 × 17 DDCF
(4)
Using the above equation, the length of the dispersion compensating fiber is 3.4 km and 4.22 km respectively, for the proposed all-glass PCF. 3.3. Loss analysis A PCF has a potential to achieve lower losses than conventional single-mode fiber, as it does not suffer from concentration fluctuation induced scattering loss, which is due to the doped material in fiber. Since the first trial fabrication of PCF, its optical attenuation has been reduced rapidly over the past several years. The spectral loss of a PCF is given by [11,12], ˛() =
A() + B() + C1 exp 4
C 2
D 2
+ D1 exp −
+ E() + F() (5)
The six terms on the right-hand side of Eq. (5) contribute to the loss coefficient. The first term is the Rayleigh scattering loss, the second term is the imperfection loss, the third term is the ultraviolet absorption loss, the fourth term is the Infrared absorption loss, the fifth term is the absorption loss due to other impurities, and the sixth term is the confinement loss. Because both PCF and SMF are mainly based on silica material, the infrared and ultraviolet absorption loss characteristics, which are due to the electronics and vibrational resonances, are assumed to be the same. Therefore, both these losses of photonic crystal fiber can be disregarded. The confinement loss, which is a loss component peculiar to photonic crystal fiber, can be ignored if we properly design the number of hexagonally packed rings and their dimensions.
Fig. 7. Comparisons of loss in different PCF, SMF with modified all-glass PCF.
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4 Table 1 Loss comparison. Parameters
Fabricated PCF (K. Tajima et al.)
Fabricated PCF (J. Zhou et al.)
Conventional SMF
Modified AGPCF
Loss (dB/km) ( = 1.31 m) Loss (dB/km) ( = 1.55 m) Rayleigh scattering coefficient (dB/km m4 ) Imperfection loss (dB/km) OH absorption loss (dB/km) ( = 1.31 m) OH absorption loss (dB/km) ( = 1.55 m)
2.72 1.97 2.3 1.49 – 0.12
0.44 0.28 1.0 0.08 0.008 0.005
0.35 0.2 1.0 <0.01 <0.01 <0.01
0.4 0.23 1.0 0.05 0.05 0.03
0.36 m, 2 ring 0.75 m, 3 ring 0.82 m, 4 ring 0.47 m, and 5, 6, 7 rings is 0.53 m. The pitch is 0.89 m. Fig. 9 shows the simulated chromatic dispersion of the proposed PCF structure for different values of the air hole diameter d. The chromatic dispersion is almost flattened in 1440–1660 nm wavelength range of the order of ±0.2 ps/nm/km, which is very low. 4. Conclusion
Fig. 8. Proposed structure with 5 cores.
We have proposed a all-glass photonic crystal fiber structure and analyzed it for the endlessly single-mode property. Also we have studied dispersion related properties and carried out the loss analysis. Results indicate that the losses at 1.55 m and 1.31 m are in between single-mode fiber and photonic crystal fiber as fabricated by Zhou et al. [13]. The results illustrate that our proposed structure has an additional design parameter in doping concentration. We have also proposed a structure with different hole diameters in different layers to get flattened dispersion over a wide wavelength range. Acknowledgement This work is supported by Visveswaraya Technological University, Belgaum, Karnataka State, under award number VTU/Aca/2009-10/A-9/11621. References
Fig. 9. Chromatic dispersion of proposed structure.
From Table 1 and Fig. 7we can conclude that except imperfection loss, almost all types of losses in the modified all-glass photonic crystal fiber are comparable. As our proposed modified all-glass photonic crystal fiber has doped material in the cladding instead of air-holes, the various losses are between that of holey fibers made up of pure silica and single-mode fibers. Fig. 7 shows the losses at 1310 nm and 1550 nm for two different fabricated photonic crystal fibers, single-mode fiber and modified all-glass photonic crystal fiber. 3.4. Dispersion flattened fiber Photonic crystal fibers having minimum non-zero dispersion over the wide spectral window region are essential for the multichannel operation of dense wavelength multiplexed systems and minimizing the nonlinear four wave mixing effects. The structure shown in Fig. 8 is used to get flattened dispersion over a wide wavelength range. As shown in Fig. 8, there are 4 missing air-holes apart from the central core. The diameter of the air-holes in the 1 ring is
[1] P.St.J. Russell, Micro-structured optical fibers, Science 299 (2003) 358–362. [2] R.K. Sinha, S.K. Varshney, Dispersion properties of photonic crystal fibers, Microw. Opt. Technol. Lett. 37 (April) (2003) 129–132. [3] Y. Ni, L. Zhang, L. An, J. Peng, C. Fan, Dual-core photonic crystal fiber for dispersion compensation, IEEE Photon. Technol. Lett. 16 (June (6)) (2004) 1516–1518. [4] F. Gérome, J.L. Auguste, J.M. Blondy, Design of dispersion-compensating fibers based on a dual-concentric-core photonic crystal fiber, Opt. Lett. 29 (December) (2004) 2725–2727. [5] T.A. Birks, J.C. Knight, P.St.J. Russell, Endlessly single-mode photonic crystal fiber, Opt. Lett. 22 (13) (1997) 961–963. [6] A. Ferrando, E. Silvestre, P. Andres, Designing the properties of dispersionflattened photonic crystal fibers, Opt. Express 9 (December (13)) (2001) 687–697. [7] W. Reeves, J. Knight, P. Russell, Demonstration of ultra-flattened dispersion in photonic crystal fibers, Opt. Express 10 (July (14)) (2002) 609–613. [8] K. Saitoh, M. Koshiba, T. Hasegawa, E. Sasaoka, Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion in photonic crystal fibers, Opt. Express 11 (April (8)) (2003) 843–851. ˛ P. Szarniak, R. Buczynski, T. Szoplik, Comparing character[9] D. Pysz, R. Stepien, istics and prospects of fabrication of multicomponent photonic crystal fibers with different lattice structures, Proc. SPIE 5576 (2004) 78–84. [10] S.K.C. Gowre, S. Mahapatra, P.K. Sahu, J.C. Biswas, Design and analysis of modified photonic crystal fiber structure, in: IEEE International Conference on Industrial and Information System-2007, 8–11 August, Peradeniya University, Kandy, Sri-Lanka, 2007. [11] K. Tajima, J. Zhou, K. Nakajima, K. Sato, Ultra low loss and long length photonic crystal fibers, in: OFC2003, PD1, Atlanta, GA, USA, March, 2003. [12] K. Tajima, J. Zhou, K. Kurokawa, K. Nakajima, Low water peak photonic crystal fiber, in: ECOC2003, Th4.1.6, Rimini, Italy, September, 2003. [13] J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, I. Sankawa, Progress on low loss photonic crystal fibers, Opt. Fiber Technol. 11 (2005) 101–110.
Please cite this article in press as: S. Gowre, et al., Dispersion characteristics of all-glass photonic crystal fibers, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.036
ARTICLE IN PRESS Optik xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Dispersion characteristics of all-glass photonic crystal fibers Sanjaykumar Gowre a,∗ , Sudipta Mahapatra a , S.K. Varshney a , P.K. Sahu b a b
Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Khargapur 721302, India School of Electrical Sciences, Indian Institute of Technology, Bhubaneswar 751013, India
a r t i c l e
i n f o
Article history: Received 20 June 2012 Accepted 12 November 2012 Keywords: All-glass PCF Dispersion Doping and endlessly single mode
a b s t r a c t In this paper, we numerically investigate all-glass photonic crystal fiber (AGPCF) structure using finite difference time domain method. The proposed PCF structure exhibit improved endlessly single-mode behavior and tunable dispersion properties. The proposed structure consists of fluorine-doped rods in the cladding region which might reduce the deformation of air-holes as in air-hole cladding PCF structures. By varying the doping concentration, the optical characteristics can be varied and makes it possible to achieve several improved PCF designs. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction The rapid development of photonic crystal fiber (PCF) [1] since the last decade has created strong requirements for novel optical components that can handle functions such as dispersion compensation [2–4], flattened dispersion [6–8] and exhibit endlessly single-mode property [5]. Their artificial crystal-like structure results in a number of unique and unusual properties, such as single-mode operation from UV to IR spectral regions, large mode areas with core diameters larger than 20 m2 , highly nonlinear performance, tunable dispersion, and a numerical aperture ranging from arbitrarily low value to 0.9, impossible to achieve in classical step index fibers. Therefore, PCFs offer exciting potentials for key enabling technologies in optical communication systems. To realize the potentials of photonic crystals, however, it is important to understand how photonic crystal structures can be engineered to meet the stringent requirements of optical communication systems. For example, a fundamental challenge for high bit-rate applications is to achieve significant dispersive affects with a large enough bandwidth that is sufficient to cover the signal of interest. In this paper, we present all-glass photonic crystal fiber structure in order to achieve endlessly single-mode regime and to have large dispersion that can be used for dispersion compensation. In addition to this, we also carry out loss analysis using the finite difference time domain method and the result shows that the loss is in between that of single-mode fiber and conventional photonic crystal fiber. Moreover, a new structure with different air-hole
diameters in different layers is proposed to get flattened dispersion of the order of ±0.2 ps/nm/km over a wavelength range of 1400–1650 nm. The organization of the paper is as follows: Section 2, following the introduction, briefly presents the design of the conventional PCF and the all-glass PCF. Section 3 compiles different results including the loss analysis to show the superiority of the proposed design and Section 4 concludes the paper. 2. All-glass PCF design Two of the major limitations of conventional photonic crystal fibers are deformation of air-holes and emergence of additional airholes during the fabrication of the fiber [9]. The main objective of this work is to circumvent these problems while ensuring that the fiber exhibits improved endlessly single-mode property and tunable dispersion characteristics. Fig. 1(a) depicts the photonic crystal fiber with a triangular lattice of holes, each having a diameter d and pitch . In the center, an air hole is omitted creating a central high index defect serving as the fiber core. In order to remove the drawbacks associated with the air-hole PCF, we have proposed a all-glass photonic crystal fiber structure shown in Fig. 1(b) with a triangular lattice of rods of fluorine doped silica, which replace the air-holes in a conventional PCF [10]. The proposed structure has an additional design parameter in terms of doping concentration in addition to the diameter of the silica rods, pitch and refractive index. 3. Theory, design and simulation results
∗ Corresponding author. Tel.: +91 8951855685. E-mail addresses: [email protected] (S. Gowre), [email protected] (S. Mahapatra), [email protected] (S.K. Varshney), [email protected] (P.K. Sahu).
3.1. V-parameter The properties of standard optical fibers are parameterized by the V parameter (normalized frequency) and the entire concept is
0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.11.036
Please cite this article in press as: S. Gowre, et al., Dispersion characteristics of all-glass photonic crystal fibers, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.036
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2
Fig. 1. Photonic crystal fiber structures (a) air-hole PCF, (b) proposed all-glass PCF with doped silica rods in cladding.
Fig. 3. Effect of doping concentration on V parameter.
very close to the heart of a majority of the optical fiber community. The cut-off properties and the endlessly single-mode (ESM) phenomena of PCFs can also be qualitatively understood within this framework. For an operating wavelength, if the value of V parameter is less than or equal to 2.405, the fiber is said to be operating in the single-mode region in standard optical fiber literature. The tradition of parametrizing the optical properties in terms of the V parameter stems from analysis of the step-index fiber (SIF). The SIF is characterized by the core radius , the core index nco , and the cladding index ncl , which all enter into the parameter VSIF given by
in the single-mode region irrespective of the operating wavelength. This property is not achievable with single-mode fiber. We have investigated the effect of the doping concentration on refractive index and found that as doping concentration is increased, there is an increase in the refractive index [10]. The allglass photonic crystal fiber structure also shows this property. It has the advantage of having the cut-off V parameter less than for a higher value of d/, i.e., 0.46 with a doping concentration of 1.8%. A higher value of d/ simplifies the fabrication process. At the same time, the all-glass photonic crystal fiber shows endlessly single-mode property. For all-glass photonic crystal fiber structure, the value of the effective V parameter is less than that of the air hole PCF as there is a low refractive index contrast between core and cladding for the same value of d/. Fig. 2(b) shows the effective V parameter of all-glass photonic crystal fiber for different values of d/. We can examine the above said low values of V parameter for same value of d/ for air-hole PCF and all-glass PCF by comparing Fig. 2(a) and Fig. 2(b). For d/ of 0.4, the value of V parameter is 2.6 for all-glass PCF, whereas for air-hole PCF it is 2.8 for a value / of 10. Further, we have investigated the effect of fluorine doping on the V parameter. A doped silica rod with a diameter of 0.4 m and = 1 m is used and is compared with the conventional PCF. As shown in Fig. 3, for AHPCF the V parameter value is more than the cut-off value (3.142) for / equal to 10. This indicates that the PCF is no more working in the single-mode region, whereas for our proposed all-glass PCF structure with 1.8% doping concentration, the V parameter value is less than the cut-off value up to a / value of 50. As doping concentration is increased from f = 1.8% to f = 13.5%, there is increase in the V parameter value as refractive index contrast between core and cladding increases. So, we have an additional design parameter in doping concentration, while designing endlessly single-mode PCF. This signifies that by keeping the values of d/ and constant, it is possible to design PCF for endlessly single-mode applications only by varying the doping concentration.
VSIF =
2
n2co − n2cl
(1)
Following Eq. (1), for a given value of operating wavelength, the values of core radius () and refractive index contrast between core and cladding are adjusted in such a way that the value of V parameter is less than 2.405, which is the required condition for the fiber to be in the single-mode region. In the context of PCFs, it is also natural to consider a V parameter. However, using Eq. (1), it is not possible to analyze PCFs, as it has not taken pitch (), and diameter (d) into consideration. The photonic crystal fiber is rather analyzed by Eq. (2) given below [5]. V=
2aeff
n2co − n2FSM =
U2 + W 2
(2)
where U and W are known as normalized transverse phase and attenuation constants, given by U=
2aeff
n2co − n2eff ,
W=
2aeff
n2eff − n2FSM
(3)
In the above equation, aeff is the effective core radius given by aeff = √ / 3, nco is the core refractive index, nFSM is the cladding index, neff is the index of the fundamental guided mode, and is operating wavelength. Fig. 2(a) gives the variation in the cut-off V parameter versus / for different values of d/. It shows that for values of d/ below 0.425, the effective V parameter value of conventional photonic crystal fiber is less than indicating that the fiber is operating
Fig. 2. Effective V parameter for different values of d/ (a) air-hole PCF, (b) proposed all-glass PCF with 1.8% doping concentration.
3.2. Dispersion Chromatic dispersion is a variation in the velocity of light (group velocity) with a variation in the wavelength. This variation in velocity causes the pulses of a modulated laser source to broaden when traveling through the fiber; up to a point where pulses overlap and bit error rate increases. As this increase in bit error rate interferes with both the quality and speed of the signal, chromatic dispersion (CD) is a major limiting factor in high-speed transmission. A finite difference time domain (FDTD) method is be used to analyze the chromatic dispersion property with the help of RSoft’s BandSOLVE software package. Fig. 4 shows the chromatic dispersion of the proposed all-glass PCF structure for different values
Please cite this article in press as: S. Gowre, et al., Dispersion characteristics of all-glass photonic crystal fibers, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.036
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Fig. 4. Chromatic dispersion of proposed all-glass photonic crystal fiber.
of d/, ranging from 0.3 to 0.6. The doping concentration used is 13.5%. As shown in Fig. 4, the ZDW is 1.22 m for d/ of 0.3, 1.26 m for d/ = 0.4, 1.29 m for d/ = 0.5, 1.3 m for d/ = 0.6. It is also possible to shift the zero dispersion wavelengths at any desired wavelength by making suitable changes in structure, refractive index, number of air-holes, as in conventional PCF. We observe that here it is possible to shift the zero dispersion wavelength to a desired value due to the fact that the waveguide dispersion is more dominant than material dispersion. This is also possible in conventional PCF, but our proposed all-glass PCF structure has an additional design parameter in doping concentration, which can be used to shift the dispersion to any desired value. For AHPCF, ZDW is at 2 m and by varying the doping concentration from 1.8% to 7.9%, we can get the desired ZDW at 1.32 m, 1.35 m and 1.4 m respectively as shown in Fig. 5. A variety of dispersion compensating techniques has been investigated previously to cancel the large anomalous dispersion of the standard single-mode fibers (SMF’s) at 1550 nm wavelength. Among them, the dispersion compensating fiber technique (DCF) has been shown to be attractive for femto-second pulse transmission; because, a carefully selected DCF with a precisely adjusted fiber length is able to cancel all of the second-order dispersion and effectively suppress much of the third-order dispersion. In optical fiber one often uses DCM for compensating chromatic dispersion. As shown in Fig. 6, for doping concentration of 4.1% and 7.9%, the chromatic dispersion at 1.55 m is −400 ps/nm/km, and −322 ps/nm/km respectively. Therefore, we can design a photonic crystal fiber structure for desired chromatic dispersion which can be used as dispersion compensation unit in optical communication. We know that the dispersion of single-mode fiber at 1.55 m is 17 ps/nm/km and dispersion of all-glass PCF with doping
Fig. 5. Effect of doping concentration on dispersion. For air-hole PCF, ZDW = 2 m, with 1.8% doping, ZDW = 1.32 m, with 4.9% doping concentration, ZDW = 1.35 m, with 7.9% doping concentration, ZDW = 1.4 m.
3
Fig. 6. Dispersion compensation at 1.55 m using proposed all-glass PCF structure.
concentration of 4.1% and 7.9% are −400 ps/nm/km and −322 ps/nm/km respectively. The length of the dispersion compensating fiber is given by [4] LDCF =
80 × 17 DDCF
(4)
Using the above equation, the length of the dispersion compensating fiber is 3.4 km and 4.22 km respectively, for the proposed all-glass PCF. 3.3. Loss analysis A PCF has a potential to achieve lower losses than conventional single-mode fiber, as it does not suffer from concentration fluctuation induced scattering loss, which is due to the doped material in fiber. Since the first trial fabrication of PCF, its optical attenuation has been reduced rapidly over the past several years. The spectral loss of a PCF is given by [11,12], ˛() =
A() + B() + C1 exp 4
C 2
D 2
+ D1 exp −
+ E() + F() (5)
The six terms on the right-hand side of Eq. (5) contribute to the loss coefficient. The first term is the Rayleigh scattering loss, the second term is the imperfection loss, the third term is the ultraviolet absorption loss, the fourth term is the Infrared absorption loss, the fifth term is the absorption loss due to other impurities, and the sixth term is the confinement loss. Because both PCF and SMF are mainly based on silica material, the infrared and ultraviolet absorption loss characteristics, which are due to the electronics and vibrational resonances, are assumed to be the same. Therefore, both these losses of photonic crystal fiber can be disregarded. The confinement loss, which is a loss component peculiar to photonic crystal fiber, can be ignored if we properly design the number of hexagonally packed rings and their dimensions.
Fig. 7. Comparisons of loss in different PCF, SMF with modified all-glass PCF.
Please cite this article in press as: S. Gowre, et al., Dispersion characteristics of all-glass photonic crystal fibers, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.036
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ARTICLE IN PRESS S. Gowre et al. / Optik xxx (2013) xxx–xxx
4 Table 1 Loss comparison. Parameters
Fabricated PCF (K. Tajima et al.)
Fabricated PCF (J. Zhou et al.)
Conventional SMF
Modified AGPCF
Loss (dB/km) ( = 1.31 m) Loss (dB/km) ( = 1.55 m) Rayleigh scattering coefficient (dB/km m4 ) Imperfection loss (dB/km) OH absorption loss (dB/km) ( = 1.31 m) OH absorption loss (dB/km) ( = 1.55 m)
2.72 1.97 2.3 1.49 – 0.12
0.44 0.28 1.0 0.08 0.008 0.005
0.35 0.2 1.0 <0.01 <0.01 <0.01
0.4 0.23 1.0 0.05 0.05 0.03
0.36 m, 2 ring 0.75 m, 3 ring 0.82 m, 4 ring 0.47 m, and 5, 6, 7 rings is 0.53 m. The pitch is 0.89 m. Fig. 9 shows the simulated chromatic dispersion of the proposed PCF structure for different values of the air hole diameter d. The chromatic dispersion is almost flattened in 1440–1660 nm wavelength range of the order of ±0.2 ps/nm/km, which is very low. 4. Conclusion
Fig. 8. Proposed structure with 5 cores.
We have proposed a all-glass photonic crystal fiber structure and analyzed it for the endlessly single-mode property. Also we have studied dispersion related properties and carried out the loss analysis. Results indicate that the losses at 1.55 m and 1.31 m are in between single-mode fiber and photonic crystal fiber as fabricated by Zhou et al. [13]. The results illustrate that our proposed structure has an additional design parameter in doping concentration. We have also proposed a structure with different hole diameters in different layers to get flattened dispersion over a wide wavelength range. Acknowledgement This work is supported by Visveswaraya Technological University, Belgaum, Karnataka State, under award number VTU/Aca/2009-10/A-9/11621. References
Fig. 9. Chromatic dispersion of proposed structure.
From Table 1 and Fig. 7we can conclude that except imperfection loss, almost all types of losses in the modified all-glass photonic crystal fiber are comparable. As our proposed modified all-glass photonic crystal fiber has doped material in the cladding instead of air-holes, the various losses are between that of holey fibers made up of pure silica and single-mode fibers. Fig. 7 shows the losses at 1310 nm and 1550 nm for two different fabricated photonic crystal fibers, single-mode fiber and modified all-glass photonic crystal fiber. 3.4. Dispersion flattened fiber Photonic crystal fibers having minimum non-zero dispersion over the wide spectral window region are essential for the multichannel operation of dense wavelength multiplexed systems and minimizing the nonlinear four wave mixing effects. The structure shown in Fig. 8 is used to get flattened dispersion over a wide wavelength range. As shown in Fig. 8, there are 4 missing air-holes apart from the central core. The diameter of the air-holes in the 1 ring is
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Please cite this article in press as: S. Gowre, et al., Dispersion characteristics of all-glass photonic crystal fibers, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.11.036