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The document describes two unique photonic crystal fiber (PCF) designs shaped like an S and a U. The S-shaped PCF exhibits zero dispersion at three points within the third optical window, while the U-shaped PCF has zero dispersion at the first optical window. Both designs show birefringence on the order of 10-5 and confinement loss on the order of 10-3. Simulation results show the S-shaped PCF has more suitable properties for applications like sensing.
![S-shaped and U-shaped photonic crystal fiber with
zero dispersion
Abstract—We have investigated two unique design S-shaped
and U-shaped PCF structure. The geometry is chosen such that
the S-shaped PCF structure is diagonally symmetrical whereas
the U-shaped PCF structure is vertically symmetrical. The S-
shaped PCF structure exhibits zero dispersion at three point
within the third optical window. However, the U-shaped PCF
structure reports zero dispersion at first optical window. Besides,
we have studied the other properties like birefringence,
normalized frequency and confinement loss for the designed
fiber. It is to be noted that S- shaped PCF structure was found
more suitable than U- shaped PCF structure for application
purpose.
Index Terms—Dispersion, Birefringence, Confinement loss.
I. INTRODUCTION
Photonic crystal fibers (PCFs) has drawn attention of a lot
of researchers due to some unique properties. Due to the
presence of cladding structure which consists of an array of
micro size air holes, photonic crystal fiber exhibits a different
dispersion behavior from those of conventional optical fiber.
PCFs posses many unique properties, in comparison to the
conventional fibers, such as dispersion [1], high birefringence
[2], endlessly single mode operation [3] and many more. On
the basis of propagation mechanism, PCFs have been classified
into two categories- Index guided PCFs and Photonic band-gap
PCFs. Based on guiding reflection of the light by the
phenomenon of total internal reflection. It consistitues of
hexagonal lattice of air holes or (holes with different
dielectrics), having defects at the center. The defect can be
created by removing one or more holes. The core thus formed
is basically made of Silica. Due to its robustness and its easy
fabrication hexagonal lattice arrangement is highly opted by
the researchers. Moreover, the electric field samples the holes
which originates at the core and induce a lower index cladding
thus the mechanism involved is completely total internal
reflection. Such type of PCFs causes remarkable dispersion
behavior [4]. As we know, the effective mode area completely
depends on the fraction of wavelength ( ) upon pitch factor,
( ). It permits strong as well as weak non-linear coefficients
along which the probability of the shifting of zero-dispersion
point into visible region of the spectra [5]. Dispersion causes
the light pulse to broaden, which results a very popular inter-
symbol interference. It becomes a critical issue when
transmission rate exceeds 10 /Gbits s . To realize dispersion
compensation at random wavelengths, electronic dispersion
compensation is supposed to be a suitable method. Besides,
another way to realize the dispersion compensation is higher
order mode fibers. For instance, an anamolous dispersion
behavior of 60 /ps nm km was observed at a wavelength
of 1080nm [6]. Control of chromatic dispersion of PCFs with
low loss and high birefringence has been one of the important
issue for all the optical community. Moreover, several index
guided PCFs with noticeable dispersion and confinement
properties have been studied [7]. It includes PCF structure with
two defected rings [8], with a defected air hole in the core [9-
10]. PCFs are very flexible in the design of the structure. The
symmetry of the cladding structure or the shape of the core are
destroyed to obtain tailored dispersion and to achieve high
birefringence [12]. Flattened dispersion over wide band have
been realized by a number of micro structure fiber with nano-
scale slots [13]. Dispersion limits the information carrying
capacity of any optical fiber. Flattened dispersion fiber is
effective for optical data transmission over broadband
wavelength range.
We have investigated two unique design of PCFs. The
geometry of the structure is chosen such that one of the design
PCF resembles as S-shaped whereas the other structure
resembles U-shaped. The intension behind studying these two
structures is to study their propagation characteristics. The
designed fiber has shown a very remarkable dispersion
behaviour. The S-shaped PCF structure has reported three zero-
dispersion points within the third optical window. The U-
shaped PCF structure has reported zero-dispersion at first
optical window. Both the designed PCF has reported a higher
birefringence. However, the order of birefringence observed is
5
10
. Both the structure is shown a very low confinement loss.
II. PROPOSED STRUCTURE
In this paper, we have proposed two unique design of PCF. The
geometry of the designed PCF is chosen such that one of them
resembles as S-shaped and other resembles U-shaped. The
geometry of structure is made such that it is diagonally
symmetrical. We have employed OptiFDTD software. The
method utilized is finite difference time-domain. The proposed
U-shaped structure is vertically symmetrical. Controlling
dispersion in PCFs is a vital problem for realistic applications
of fibers. Possibility of getting smaller core and the air glass
index contrast strongly effect the dispersion of a fiber.
Pranaw Kumar, Priyanka Das, Amit Kumar Meher
School of Electronics Engineering
KIIT University, Bhubaneshwar
Kumarpranaw9@gmail.com , dpriyanka752@gmail.com , amit_4693@yahoo.com](https://image.slidesharecdn.com/6778d4b6-d27e-439e-ab65-305b1b000c4c-150613081233-lva1-app6892/85/su_final-1-320.jpg)
![However dispersion coefficient are directly proportional to the
double derivative of the effective refrective index with respect
to the wavelengths. The waveguide dispersion of a fiber can be
calculated using the effective refractive index values as a
function of [13]:
2
2
Re[ ]eff
W
d n
D
c d
(1)
Where c is the velocity of light in vacuum,
Re[ ]effn represents the real part of effective refractive index
and is the operating wavelength.
Birefringence in PCFs occurs due to the effective refractive
index contrast between two orthogonal polarization modes.
However the birefringence (B) can be calculated using the
following relation :
x yB n n (2)
Where xn and yn are the effective refractive index of
transverse magnetic (TM) and transverse electric (TE) waves.
The number of circular air holes in the cladding region
strongly effects the confinement loss. Generally the loss
approaches to zero when the number of air holes is infinite.
The confinement loss ( cL ) can be obtained by using the
formula below :
2*10^ 7 2
[ ]
ln10
c m effL I n
(3)
Where [ ]m effI n represents the imaginary part of the effective
refractive index of the guided mode and is the corresponding
wavelength.
The normalized frequency is one of the most important
property of a fiber. Its value determines the number of modes
propagating inside the fibers. It can be obtained using equation
below [14]:
2 22
( )core effV n n
(4)
Where is the pitch factor, coren and effn are the effective
refractive index and is the corresponding wavelength.
Fig. 1(a) S-shaped PCF structure.
Fig. 1(b) U-shaped PCF structure.
III. SIMULATION RESULTS
In this paper, we have studied two unique design of PCF. It
resembles S-shaped and U-shaped structure. The length and
breadth of the wafer chosen is 32 m and 30 m
respectively. The diameter of the circular air holes is takes
1 m . The pitch factor which is center-to-center spacing is
considered to be 1.2 m .
The proposed design has reported a very low dispersion
value at the first and second optical window. However, the
reported dispersion is below 8 /ps nm km . At the first
optical window, the dispersion reported by S-shaped PCF
structure is almost zero. The designed 'U' shaped PCF structure
has reported a negative dispersion around the first optical
window. However, the zero dispersion point is obtained at the
first optical window. The highest value of dispersion reported
for the designed fiber is 6 /ps nm km .
Fig. 2(a) The curve between dispersion and wavelength of the S-shaped
PCF structure.](https://image.slidesharecdn.com/6778d4b6-d27e-439e-ab65-305b1b000c4c-150613081233-lva1-app6892/85/su_final-2-320.jpg)
![Fig. 2(b) The curve between dispersion and wavelength of U-shaped PCF
structure.
The S-shaped PCF structure has reported a birefringence of
the order
5
10
. Similarly, the U-shaped PCF structure has also
reported birefringence of the order of
5
10
. However, the
birefringence reported for S-shaped PCF structure is higher.
Hence, the PCF structure can be preferred over U-shaped PCF
structure for sensor application.
Fig. 3(a) The curve birefringence and wavelength of the S -shaped
structure.
Fig. 3(b) The curve between birefringence and wavelength of the U -
shaped PCF structure.
The Band loss which is calculated as confinement loss of
the Band PCF which has been calculated for designed PCF.
Both the structure has reported confinement loss of the order of
3
10
. However, the S-shaped PCF structure has reported
comparatively low loss.
Fig. 4(a) The relation between the confinement loss and wavelength of the
S shaped PCF structure.
Fig. 4(b) The relation between confinement loss and wavelength of the S
shaped PCF structure.
As we know that for PCFs if 4.1effV , only one mode can
propagate inside the fiber. It can be shown from values
reported of normalized frequency that the designed fibers
operates endlessly single mode fiber.
Fig. 5 Normalised frequency vrs wavelength plot.
IV. CONCLUSION
Thus we have investigated two PCF design whose
geometry resembles S and U-shaped. Both the structure has
reported a remarkable dispersion behavior. The S-shaped PCF
structure exhibits zero dispersion at three points within the
third optical window. On the other hand, the U-shaped PCF
structure has reported zero dispersion at first optical window.
Both the structure has reported birefringence of same order.
However, the S-shaped PCF structure was found to be more
suitable for sensor application. In fine, it can be said that the S-
shaped PCF structure proves to be more suitable fiber.
REFERENCES
[1] J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blench, W.J.
Wodsworth, P.St. J. Russell, “ Anamolous dispersion in](https://image.slidesharecdn.com/6778d4b6-d27e-439e-ab65-305b1b000c4c-150613081233-lva1-app6892/85/su_final-3-320.jpg)
![photonic crystal fiber”, IEEE Photon Techol. Lett. 12(7), (2000),
807-809.
[2] A. Ortigosa-Blench, J. C. Knight, W.J. Wodsworth, J. Arriaga,
B. J. Mangan, T. A. Birks, ,P.St. J. Russell, “Highly birefringent
photonic crystal fibers”, Opt. Lett. 25, (18), (2000), 1325-1327.
[3] T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single
mode photonic crystal fibers”, Opt. Lett. 22 (13) (1997) 961-
963.
[4] T. M. Monro, P. J. Bennet, N. G. R. Broderick, and D. J.
Richardson, “Holey fibers with random cladding distributions”,
Opt. Lett, vol. 25, pp. 206-208, 2000.
[5] M. J. Steel R. M. Osgood, “Polarization and dispersive
properties of elliptical hole photonic crystal fibers”, J. Lightw.
Technol., vol. 19, no. 4,pp. 495-503, Apr. 2001.
[6] S. Ramachandram, S. Ghatni, J. W. Nicholson, M. F. Yan, P.
Wisk, E. Momberg and F. V. Dimarcello, “Demonstration of
anomalous dispersion in a solid silica based fiber at
1300nm ”, presented at optical fiber communication Conf.
(OFC), Anahein, CA, 2006, paper PDP3.
[7] F. Poletti, V. Finazzi, T. M. Monro, N. G. R. BBrodrieck,V.
Tse, and D. J. Richardson, “Inverse design and fabrication
tolerance of ultra flattemed dispersion holey fibers”, Opt.
Express, Vol. 13, pp. 3728-3736, 2005.
[8] T. L. Wu and C. H Chao, “ A novel Ultra flattened dispersion
photonic crystal fiber”, IEEE Photon Technol. Lett., vol. 17, pp
67-69, 2005.
[9] K. Saitoh, N. Florous, M. Koshiba, “Ultra flattened chromatic
dispersion controllability using a defected core photonic crystal
fiber with low confinemnt losses”, Opt. Express 13 (2005) 8365-
8371.
[10] Pranaw Kumar, R. Kumari, S. K. Parida, A. K. Meher, “ Multi-
core ethanol doped PCF with anomalous dispersion behavior”,
ICECS’15, Coimbtore, Feb-2015
[11] Pranaw Kumar, Chandrani Paul, Amlan Datta, “ A unique
design of photonic crystal fiber for negative dispersion and high
birefringence,” ICCSP’14, (2014) 1363-1368.
[12] W. Guo, J. Kou, F. Xu, Y. Lu, “ Ultra flattened and low
dispersion in engineered microfibers with highly efficient
nonlinearity reduction”, Opt. Express 19 (2011) 15229-15235.
[13] G. Agrawal, Nonlinear Fiber Optics, New York: Academic
1995.
[14] J. D. Jhonpalous, R. D. Meade, J. N. Winn, Photonic Crystals :
modelling the flow of Light, Princeton NJ Preention Univ. press,
1995.](https://image.slidesharecdn.com/6778d4b6-d27e-439e-ab65-305b1b000c4c-150613081233-lva1-app6892/85/su_final-4-320.jpg)
su_final
- 1. S-shaped and U-shaped photonic crystal fiber with zero dispersion Abstract—We have investigated two unique design S-shaped and U-shaped PCF structure. The geometry is chosen such that the S-shaped PCF structure is diagonally symmetrical whereas the U-shaped PCF structure is vertically symmetrical. The S- shaped PCF structure exhibits zero dispersion at three point within the third optical window. However, the U-shaped PCF structure reports zero dispersion at first optical window. Besides, we have studied the other properties like birefringence, normalized frequency and confinement loss for the designed fiber. It is to be noted that S- shaped PCF structure was found more suitable than U- shaped PCF structure for application purpose. Index Terms—Dispersion, Birefringence, Confinement loss. I. INTRODUCTION Photonic crystal fibers (PCFs) has drawn attention of a lot of researchers due to some unique properties. Due to the presence of cladding structure which consists of an array of micro size air holes, photonic crystal fiber exhibits a different dispersion behavior from those of conventional optical fiber. PCFs posses many unique properties, in comparison to the conventional fibers, such as dispersion [1], high birefringence [2], endlessly single mode operation [3] and many more. On the basis of propagation mechanism, PCFs have been classified into two categories- Index guided PCFs and Photonic band-gap PCFs. Based on guiding reflection of the light by the phenomenon of total internal reflection. It consistitues of hexagonal lattice of air holes or (holes with different dielectrics), having defects at the center. The defect can be created by removing one or more holes. The core thus formed is basically made of Silica. Due to its robustness and its easy fabrication hexagonal lattice arrangement is highly opted by the researchers. Moreover, the electric field samples the holes which originates at the core and induce a lower index cladding thus the mechanism involved is completely total internal reflection. Such type of PCFs causes remarkable dispersion behavior [4]. As we know, the effective mode area completely depends on the fraction of wavelength ( ) upon pitch factor, ( ). It permits strong as well as weak non-linear coefficients along which the probability of the shifting of zero-dispersion point into visible region of the spectra [5]. Dispersion causes the light pulse to broaden, which results a very popular inter- symbol interference. It becomes a critical issue when transmission rate exceeds 10 /Gbits s . To realize dispersion compensation at random wavelengths, electronic dispersion compensation is supposed to be a suitable method. Besides, another way to realize the dispersion compensation is higher order mode fibers. For instance, an anamolous dispersion behavior of 60 /ps nm km was observed at a wavelength of 1080nm [6]. Control of chromatic dispersion of PCFs with low loss and high birefringence has been one of the important issue for all the optical community. Moreover, several index guided PCFs with noticeable dispersion and confinement properties have been studied [7]. It includes PCF structure with two defected rings [8], with a defected air hole in the core [9- 10]. PCFs are very flexible in the design of the structure. The symmetry of the cladding structure or the shape of the core are destroyed to obtain tailored dispersion and to achieve high birefringence [12]. Flattened dispersion over wide band have been realized by a number of micro structure fiber with nano- scale slots [13]. Dispersion limits the information carrying capacity of any optical fiber. Flattened dispersion fiber is effective for optical data transmission over broadband wavelength range. We have investigated two unique design of PCFs. The geometry of the structure is chosen such that one of the design PCF resembles as S-shaped whereas the other structure resembles U-shaped. The intension behind studying these two structures is to study their propagation characteristics. The designed fiber has shown a very remarkable dispersion behaviour. The S-shaped PCF structure has reported three zero- dispersion points within the third optical window. The U- shaped PCF structure has reported zero-dispersion at first optical window. Both the designed PCF has reported a higher birefringence. However, the order of birefringence observed is 5 10 . Both the structure is shown a very low confinement loss. II. PROPOSED STRUCTURE In this paper, we have proposed two unique design of PCF. The geometry of the designed PCF is chosen such that one of them resembles as S-shaped and other resembles U-shaped. The geometry of structure is made such that it is diagonally symmetrical. We have employed OptiFDTD software. The method utilized is finite difference time-domain. The proposed U-shaped structure is vertically symmetrical. Controlling dispersion in PCFs is a vital problem for realistic applications of fibers. Possibility of getting smaller core and the air glass index contrast strongly effect the dispersion of a fiber. Pranaw Kumar, Priyanka Das, Amit Kumar Meher School of Electronics Engineering KIIT University, Bhubaneshwar Kumarpranaw9@gmail.com , dpriyanka752@gmail.com , amit_4693@yahoo.com
- 2. However dispersion coefficient are directly proportional to the double derivative of the effective refrective index with respect to the wavelengths. The waveguide dispersion of a fiber can be calculated using the effective refractive index values as a function of [13]: 2 2 Re[ ]eff W d n D c d (1) Where c is the velocity of light in vacuum, Re[ ]effn represents the real part of effective refractive index and is the operating wavelength. Birefringence in PCFs occurs due to the effective refractive index contrast between two orthogonal polarization modes. However the birefringence (B) can be calculated using the following relation : x yB n n (2) Where xn and yn are the effective refractive index of transverse magnetic (TM) and transverse electric (TE) waves. The number of circular air holes in the cladding region strongly effects the confinement loss. Generally the loss approaches to zero when the number of air holes is infinite. The confinement loss ( cL ) can be obtained by using the formula below : 2*10^ 7 2 [ ] ln10 c m effL I n (3) Where [ ]m effI n represents the imaginary part of the effective refractive index of the guided mode and is the corresponding wavelength. The normalized frequency is one of the most important property of a fiber. Its value determines the number of modes propagating inside the fibers. It can be obtained using equation below [14]: 2 22 ( )core effV n n (4) Where is the pitch factor, coren and effn are the effective refractive index and is the corresponding wavelength. Fig. 1(a) S-shaped PCF structure. Fig. 1(b) U-shaped PCF structure. III. SIMULATION RESULTS In this paper, we have studied two unique design of PCF. It resembles S-shaped and U-shaped structure. The length and breadth of the wafer chosen is 32 m and 30 m respectively. The diameter of the circular air holes is takes 1 m . The pitch factor which is center-to-center spacing is considered to be 1.2 m . The proposed design has reported a very low dispersion value at the first and second optical window. However, the reported dispersion is below 8 /ps nm km . At the first optical window, the dispersion reported by S-shaped PCF structure is almost zero. The designed 'U' shaped PCF structure has reported a negative dispersion around the first optical window. However, the zero dispersion point is obtained at the first optical window. The highest value of dispersion reported for the designed fiber is 6 /ps nm km . Fig. 2(a) The curve between dispersion and wavelength of the S-shaped PCF structure.
- 3. Fig. 2(b) The curve between dispersion and wavelength of U-shaped PCF structure. The S-shaped PCF structure has reported a birefringence of the order 5 10 . Similarly, the U-shaped PCF structure has also reported birefringence of the order of 5 10 . However, the birefringence reported for S-shaped PCF structure is higher. Hence, the PCF structure can be preferred over U-shaped PCF structure for sensor application. Fig. 3(a) The curve birefringence and wavelength of the S -shaped structure. Fig. 3(b) The curve between birefringence and wavelength of the U - shaped PCF structure. The Band loss which is calculated as confinement loss of the Band PCF which has been calculated for designed PCF. Both the structure has reported confinement loss of the order of 3 10 . However, the S-shaped PCF structure has reported comparatively low loss. Fig. 4(a) The relation between the confinement loss and wavelength of the S shaped PCF structure. Fig. 4(b) The relation between confinement loss and wavelength of the S shaped PCF structure. As we know that for PCFs if 4.1effV , only one mode can propagate inside the fiber. It can be shown from values reported of normalized frequency that the designed fibers operates endlessly single mode fiber. Fig. 5 Normalised frequency vrs wavelength plot. IV. CONCLUSION Thus we have investigated two PCF design whose geometry resembles S and U-shaped. Both the structure has reported a remarkable dispersion behavior. The S-shaped PCF structure exhibits zero dispersion at three points within the third optical window. On the other hand, the U-shaped PCF structure has reported zero dispersion at first optical window. Both the structure has reported birefringence of same order. However, the S-shaped PCF structure was found to be more suitable for sensor application. In fine, it can be said that the S- shaped PCF structure proves to be more suitable fiber. REFERENCES [1] J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blench, W.J. Wodsworth, P.St. J. Russell, “ Anamolous dispersion in
- 4. photonic crystal fiber”, IEEE Photon Techol. Lett. 12(7), (2000), 807-809. [2] A. Ortigosa-Blench, J. C. Knight, W.J. Wodsworth, J. Arriaga, B. J. Mangan, T. A. Birks, ,P.St. J. Russell, “Highly birefringent photonic crystal fibers”, Opt. Lett. 25, (18), (2000), 1325-1327. [3] T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single mode photonic crystal fibers”, Opt. Lett. 22 (13) (1997) 961- 963. [4] T. M. Monro, P. J. Bennet, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions”, Opt. Lett, vol. 25, pp. 206-208, 2000. [5] M. J. Steel R. M. Osgood, “Polarization and dispersive properties of elliptical hole photonic crystal fibers”, J. Lightw. Technol., vol. 19, no. 4,pp. 495-503, Apr. 2001. [6] S. Ramachandram, S. Ghatni, J. W. Nicholson, M. F. Yan, P. Wisk, E. Momberg and F. V. Dimarcello, “Demonstration of anomalous dispersion in a solid silica based fiber at 1300nm ”, presented at optical fiber communication Conf. (OFC), Anahein, CA, 2006, paper PDP3. [7] F. Poletti, V. Finazzi, T. M. Monro, N. G. R. BBrodrieck,V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerance of ultra flattemed dispersion holey fibers”, Opt. Express, Vol. 13, pp. 3728-3736, 2005. [8] T. L. Wu and C. H Chao, “ A novel Ultra flattened dispersion photonic crystal fiber”, IEEE Photon Technol. Lett., vol. 17, pp 67-69, 2005. [9] K. Saitoh, N. Florous, M. Koshiba, “Ultra flattened chromatic dispersion controllability using a defected core photonic crystal fiber with low confinemnt losses”, Opt. Express 13 (2005) 8365- 8371. [10] Pranaw Kumar, R. Kumari, S. K. Parida, A. K. Meher, “ Multi- core ethanol doped PCF with anomalous dispersion behavior”, ICECS’15, Coimbtore, Feb-2015 [11] Pranaw Kumar, Chandrani Paul, Amlan Datta, “ A unique design of photonic crystal fiber for negative dispersion and high birefringence,” ICCSP’14, (2014) 1363-1368. [12] W. Guo, J. Kou, F. Xu, Y. Lu, “ Ultra flattened and low dispersion in engineered microfibers with highly efficient nonlinearity reduction”, Opt. Express 19 (2011) 15229-15235. [13] G. Agrawal, Nonlinear Fiber Optics, New York: Academic 1995. [14] J. D. Jhonpalous, R. D. Meade, J. N. Winn, Photonic Crystals : modelling the flow of Light, Princeton NJ Preention Univ. press, 1995.