The Design and Fabrication of a Highly Dispersive
Photonic Crystal Fiber for Phased Array Antenna
Systems
Harish Subbaraman, Peiyan Cao, Maggie Yihong Chen*, Ray T. Chen
Microelectronic Research Center, Department of Electrical and Computer Engineering,
The University of Texas at Austin, Austin, Texas 78758.
* Omega Optics, Inc, 10435 Burnet RD. STE 108, Austin, TX 78758
A highly dispersive photonic crystal fiber is designed and fabricated with maximum
chromatic dispersion value of about -4400 ps/nm/km around 1.55 µm wavelength region
and a full width at half maximum (FWHM) of 40 nm. The fiber is based on the working
principle of a dual concentric-core PCF, wherein, the structure with central and outer
doped cores behaves like a directional coupler. Modal field redistribution between the
cores causes the effective refractive index to change rapidly with wavelength, thus,
resulting in a very high dispersion value around the phase matched wavelength of 1.55 µm.
Such a highly dispersive photonic crystal fiber can be used as true time delay elements in
Phased Array antenna (PAA) Systems.
Copyright
OCIS codes: 060.2280
1
1. Introduction
Phased Array antennas (PAA), as shown in Fig. 1 are a group of antennas in which the relative
phase between the elements are varied in such a manner that the radiation pattern of the array
prefers one direction to the other, i.e. they are highly directional. PAAs find numerous
applications on both the civilian and military systems such as radar, satellite communication,
mobile communication, GPS, missile guidance etc. In order to have a squint-free operation,
utilization of true time delay (TTD) circuits become mandatory. Based on the techniques used,
TTD circuits can be broadly classified into electrical TTD and optical TTD systems. Although
electrical TTD systems have a long established history, their bulkiness and susceptibility to
Electromagnetic Interference (EMI) make them less interesting compared to their optical
counterparts. Apart from low weight, size and low EMI features, optical TTDs offer a much
wider bandwidth of operation.
There have been many optical TTD systems demonstrated in the past such as bulk optical
TTD1,2, WDM based TTD3,4, holographic TTD5, acousto-optic TTD6-8, chirped fiber grating
TTD9, 10, fiber prism based TTD11-13. In terms of size, volume and ease of use, fiber prism based
TTD techniques stand out. However, these TTD systems use conventional dispersion
compensating fibers (DCF). These fibers have relative low dispersion parameter, D ~ -100
ps/nm/km14, and therefore larger lengths of such fibers are required to obtain a larger time delay.
Since the first working model was demonstrated in the year 1996, photonic crystal fibers
(PCFs)15, fibers with an array of periodic air-holes running down the length of the fiber, have
gained an increasing popularity due to their unique properties such as endlessly single-mode
operation16, high non-linearity17, ultralow loss18,19, and so on. PCF structures can be designed to
2
have higher negative dispersion values compared to conventional DCFs20-22. These highly
dispersive photonic crystal fibers (HDPCF) have a potential for high dispersion applications such
as dispersion compensation to reduce the length, payload, and loss.20 Another important
application for highly dispersive PCFs is for true-time delay elements in the phased array
antenna systems. This was demonstrated by Jiang et al.25-27. By using PCFs as true time delay
elements, the fiber’s total length can be decreased proportionally, leading to compact device
structures suitable for air-borne and space-borne applications. Various groups from all over the
world have been working on tweaking the peculiar properties of PCFs in order to achieve high
negative dispersion coefficients20, 22 and low loss structures. Although most of the methods have
been able to achieve very high negative dispersion values, the bandwidth is strictly limited. This
paper presents the design and fabrication of a dual concentric core PCF28 to achieve a very high
negative dispersion coefficient of about -4400 ps/nm/km, with a HWFM of 40 nm. A cross
section of the fabricated fiber is shown in Fig. 2 . d1 denotes the diameter of the inner core and;
d3 denotes the diameter of the negatively doped rods (not visible as they are very slightly
negatively doped compared to the background) in the second ring which forms the second core;
d2 denotes the diameter of the air hole rings that form the inner cladding. The rest of the air hole
rings, with a diameter of d4 (third-tenth rings) form the outer cladding region. The period of the
structure is given by Λ. The structure presented here has a high dispersion value which is an
improvement by a factor of 2 over previous designs27, and is a suitable candidate for applications
requiring compact systems for broadband phased array antennas.
2. Theory and design of a dual concentric- core PCF
The mechanism of a dual concentric-core PCF is very similar to that of a directional coupler.28
First, we introduce the coupled mode theory on the dual core PCFs.22 The central core and the
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outer core behave like two parallel waveguides and the high dispersion is from the coupling
between the two waveguides. By expanding the propagation constants, β, of the modes in the
isolated waveguides around the phase matched frequency using Taylor’s series, we get28
d
 i ( )   ( p )  (   p ) i
d
  p
(   p ) 2 d 2  i

2
d 2
(1)
  p
where i = 1, 2 represents the inner and the outer waveguide respectively and ωp represents the
phase matched frequency. From the coupled mode theory, we know that the coupling of the
individual modes can generate two super-modes, whose propagation constants can be written
as28
/  
1
{[ 1 ( )   2 ( )]  [ 1 ( )   2 ( )]2  4 2 }
2
(2)
where  is the coupling constant between the two waveguides. We can insert Eq. (1) into Eq. (2)
and differentiate the result twice with respect to angular frequency. Supposing that the two
waveguides’
d 2
d 2
are all very small numbers (this term is mainly determined by the
  p
material dispersion of waveguide, and so it must be a very small term), we get the group velocity
dispersion as

(   p ) d1 d 2 2
d 2/ 
1 d1 d 2 2
2


(

)

[
(

)

1
]
d 2
4 d
d
4 2
d
d
2
The dispersion parameter is normally written as29
4
3
(3)
2
 d neff
2c d 2 B
D
 2
c d2
 d 2
(4)
Using Eq. (3) and Eq. (4) we get,
2
 dn1 dn2 2  2 (   p ) dn1 dn2 2
D
(

) [ 2
(

)  1]3 / 2
2
2c d d

p
d d
(5)
From Eq. (5), we see that the dispersion value reaches its maximum value when  is
equal to p and is given by
DMax  
 dn1 dn2 2
(

)
2c d
d
(6)
The full width at half maximum (FWHM) can be derived from Eq. (5) and Eq. (6) as
  0.766 
2 p dn1 dn2 1
(

)

d d
(7)
From Eq. (6) and Eq. (7), we see that the dispersion value mainly depends on the
coupling constant κ and the difference of dn / d between the inner and the outer core. The
bandwidth is dependent on the phase match wavelength (p), the coupling constant κ and the
difference of dn / d between the inner and the outer core.
There is a trade off between the maximum dispersion value and FWHM. If we multiply
Eq. (6) with Eq. (7), we can get a dispersion-bandwidth product that is independent of the
coupling constant (). This product can be defined as a Figure of Merit for our structure.
5
DMax    0.766 
 p dn1 dn2

c d d
(8)
The parameters of the fiber were carefully chosen to make the respective modes have a phase
match at a wavelength (P) close to 1.55 µm. The redistribution of modal fields with a variation
in wavelength is shown in Fig. 3. When the wavelength is shorter than phase match wavelength
(<p) the field is essentially confined in the inner core (Fig. 3(a)). Around the phase match
wavelength (p), a part of the field is in the inner core and a part is in the outer core (Fig.
3(b)). When the wavelength is longer than phase match wavelength (>p), most of the power
spreads to the outer core and is effectively guided in the outer core (Fig. 3(c)). This modal field
redistribution makes the effective index change greatly with the wavelength and thus, near the
phase match wavelength, the dispersion of the dual concentric core fiber will be very high.
3. Design parameters and fabrication
The PCFs were fabricated using stack and draw technique30. The background index of
silica is 1.444. The inner and outer cores are made of Ge, and As doped silica rods with a
refractive index of 2%, -0.7% respectively. Due to limits set by manufacturability, the period,
was chosen to be 2.0 m. The inner core diameter, d1/Λ, was chosen to be 1.2, followed by an
inner cladding made up of air holes with d2/Λ = 0.75, and then by an outer core with d3/Λ = 0.41.
The outer cladding is made up of air hole rings with diameter d4/Λ = 0.41. BandSolve31 software
was used to simulate the structure. Fig. 4 shows the variation of neff versus wavelength. It can be
seen that, at the phase match wavelength around 1.55 m, the effective index changes rapidly
with wavelength. This is the reason for high dispersion of the structure. Eq. (4) was used to
calculate the dispersion of the fiber and the resulting curve is shown in Fig. 5. The variation of D
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with respect to a change in period was also calculated and the results are shown in Fig. 6. It can
be seen that there is a great shift in the peak dispersion when the period is changed by +/- 0.1
m. Therefore, the period and all the parameters have to be strictly controlled during the fiberdrawing process.
An inter-media fiber coupler was used from single mode fiber to a taper fiber, followed
by coupling from tapered fiber to the PCF. This way, the total coupling loss can be brought down
to less than 3dB. The difficulty in fabricating structures with a period less than 2 m come from
the fact that, at such small periods, it becomes difficult to maintain the shape of air holes and that
the small period makes the inner core’s diameter very small ~ 1.5 µm, making the coupling from
a standard single mode fiber to this fiber difficult. This kind of broadband, highly negative
dispersion fiber can be used as a dispersion compensating fiber covering the entire C (1525–
1565nm) band.
4. Conclusion
We have designed and fabricated a doped dual concentric-core photonic crystal fiber. By
choosing period = 2.0 µm, we got a dual concentric core pure silica photonic crystal fiber design
with a maximum chromatic dispersion value of about -4400 ps/nm/km and FWHM around 40
nm in the 1.55 µm wavelength window. This kind of broadband highly dispersive photonic
crystal fiber can be used in applications requiring compact phased array antennas.
7
References
1. D. Dolfi, J.P. Huignard, and M. Baril, “Optically controlled true-time delays for
phased array antenna”, SPIE, Vo. 1102, pp. 152, 1989.
2. Dolfi, F. Michel-Gabriel, S. Bann, and J.P. Huignard, “Two-dimensional optical
architecture for true-time-delay beam forming in a phased-array antenna”, Optics
Letters, Vol. 16, pp. 255, 1991
3. P.M. Freitag, S.R. Forrest, “A coherent optically controlled phased array antenna
system”, IEEE Microwave and Guided Wave Letters, vol. 3, pp. 292, 1993
4. L. Xu, R. Taylor, and S.R. Forrest, “True-time delay phased array antenna feed system based
on optical heterodyne techniques”, IEEE Photonics Technology Letters, vol. 8, pp. 160, 1996
5. Z. Fu and R. Chen, “Highly packing density optical true-time delay lines for phased
array antenna applications”, Recent Research Developments Series, pp. 1, Dec.
1998
6. W. D. Jemison, and P. R. Herczfeld, “Acousto-optically controlled true-time
delay”, IEEE Microwave and Guided Wave Letters, vol. 3, pp. 72, 1993
7. L. H. Gesell, R. E. Feinleib, J. L. Lafuse, and T. M. Turpin, “Acousto-optic control
of time delays for array beam steering, SPIE, vol. 2155, 194, 1994
8. E. N. Toughlian, and H. Zmuda, “A ph0tonic variable RF delay line for phased array
antennas”, Journal of Lightwave Technology, vol. 8, pp. 1824, 1990
9. J. L. Cruz, B. Ortega, M. V. Andres, B. Gimeno, D. Pastor, J. Capmany, and L.
8
Dong, “Chirped fiber gratings for phased array antenna”, Electronics Letters, vol.
33, pp. 545, 1997
10. J. L. Corral, J. Marti, S. Regidor, J. M. Fuster, R. Laming, and M. J. Cole,
“Continuously variable true time-delay optical feeder for phased-array antenna
employing chirped fiber gratings”, IEEE Trans. Microwave and Tech., vol. 45, pp.
1531, 1997
11. R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell,
D. G. Cooper, “Fiber-optic prism true time-delay antenna feed”, IEEE Photonics
Technology Letter, vol. 11, pp. 1347-1349, 1993
12. R. Soref, “Optical dispersion technique for time-delay beam steering”, Appl. Opt.
Vol. 31, pp. 7395-7397, 1992
13. S. T. Johns, D. A. Norton, C. W. Keefer, R. Erdmann, R. A. Soref, “Variable time
delay of microwave signals using high dispersion fibre”, Electronics Letters, vol.
29, pp. 555, (1993)
14. B. Jopson, and A. Gnauck, “Dispersion compensation for optical fiber systems,” IEEE
Comm. Mag. 33, 96-102 (1995).
15. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical
fiber with photonic crystal cladding,” Opt. Lett. 21, 1547-1549 (1996).
16. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal
fiber,” Opt.Lett. 22, 961-963 (1997).
17. Z. Yusoff, J. H. Lee, W. Belardi, T. M. Monro, P. C. Teh, and D. J. Richardson, “Raman
effects in a highly nonlinear holey fiber: amplification and modulation,” Opt. Lett. 27, 424-426
(2002).
9
18. K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow Loss and Long Length Photonic
Crystal Fiber,” J. Lightw.Technol. 22, 7-10 (2004).
19. M. Koshib, and K. Saitoh, “Simple evaluation of confinement losses in holey fibers,” Opt.
Comm. 253, 95-98 (2005).
20. S. K. Varshney, K. Saitoh, and M. Koshiba, “A Novel Design for Dispersion Compensating
Photonic Crystal Fiber Raman Amplifier,” IEEE Photon. Technol. Lett. 17, 2062-2064 (2005).
21. Y. Jiang, T. Ling, L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Highly dispersive photonic
crystal waveguides and their applications in optical modulators and true-time delay lines,” Proc.
Of. SPIE. 6128, 61280Y (2006).
22. S. K. Varshney, T. Fujisawa, K. Saitoh, and M. Koshiba, “Design and analysis of a
broadband dispersion compensating photonic crystal fiber Raman amplifier operating in Sband,” Opt. Express. 14, 3528-3540 (2006).
23. B. J. Mangan, F. Couny, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, M. Banham, M.
W. Mason, D. F. Murphy, E. A. M. Brown, and H. Sabert, “Slope-matched dispersioncompensating photonic crystal fibre,” Lasers and Electro-Optics, 2004. (CLEO). (Conference on
Vol. 2, 16-21 May 2004), 1069-1070.
24. Y. Jiang, Z. Shi, B. Howley, X. Chen, M. Y. Chen, and R. T. Chen, “Delay Time Enhanced
Photonic Crystal Fiber array for Wireless Communications using 2-D X-band Phased-Array
Antennas,” Opt. Engineering. 44, No.12 (2005).
25. Y. Jiang, B. Howley, Z. Shi, Q. Zhou, R. T. Chen, M. Y. Chen, G. Brost, and C. Lee,
“Dispersion-Enhanced Photonic Crystal Fiber Array for a True Time-Delay Structured X-Band
Phased Array Antenna,” IEEE Photon. Technol. Lett. 17, 187-189 (2005).
10
26. Y. Jiang, Z. Shi, B. Howley, and R. T. Chen, “Highly Dispersive Photonic Crystal Fibers for
True-Time-Delay Modules of an X-band Phased Array Antenna,” Proc. Of SPIE. 5360, 253-258
(2004).
27. F. Gérôme, J. L. Auguste, and J. M. Blondy, “Design of dispersion-compensating fibers
based on a dual-concentric-core photonic crystal fiber,” Opt. Lett. 29, 2725-2727 (2004).
28. U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion
compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111-2113 (1995).
29. J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K.
Thyagarajan, and B. P. Pal, “ Conception, Realization, and Characterization of a Very High
Negative Chromatic Dispersion Fiber,” Opt.Fiber.Technology. 8, 89-105 (2002).
30. Bjarklev, J. Broeng, A. S. Bjarklev, Photonic crystal fibers, Kluwer Academic
Publishers (2003).
31. RSoft Photonics CAD Suite, Version 5.1.7.
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Fig. 1. Schematic of a Phased Array antenna system.
12

d2
d4
d1
d3
Fig. 2. Cross section of the fabricated Photonic Crystal Fiber.
13
Fig. 3 (a) Mode profile at <p
(b) Mode profile at p
14
(c) Mode profile at >p
1.425
1.424
n eff
1.423
1.422
1.421
1.420
1.419
1.48
1.50
1.52
1.54
1.56
1.58
1.60
1.62
1.64
Wavelength (m)
Fig. 4. Variation of neff with Wavelength
15
1.66
1.68
0
D (ps/nm/km)
-1000
-2000
-3000
-4000
-5000
1.48
1.50
1.52
1.54
1.56
1.58
1.60
1.62
Wavelength (m)
Fig. 5. Relationship between dispersion value D and Wavelength.
16
0
 = 1.9m
 = 2.0m
-1000
Dispersion (ps/nm/km)
 = 2.1m
-2000
-3000
-4000
-5000
1.40
1.45
1.50
1.55
1.60
1.65
Wavelength (m)
Fig. 6. Variation of D with Period ().
17
1.70
1.75
List of figure captions:
Fig. 1. Schematic of a Phased Array antenna system.
Fig. 2. Cross section of the fabricated Photonic Crystal Fiber.
Fig. 3 (a). Mode profile at <p
Fig. 3 (b). Mode profile at p
Fig. 3 (c). Mode profile at >p
Fig. 4. Variation of neff with Wavelength.
Fig. 5. Relationship between dispersion value D and Wavelength.
Fig. 6. Variation of D with Period (
18