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Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass
Optical Fiber Technology 18 (2012) 220–225
Contents lists available at SciVerse ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass Ireneusz Kujawa a, Ryszard Buczynski a,b,⇑, Tadeusz Martynkien c, Marek Sadowski c, Dariusz Pysz a, Ryszard Stepien a, Andrew Waddie d, Mohammad R. Taghizadeh d a
Glass Laboratory, Institute of Electronic Materials Technology, Wolczynska 133, 01-919, Warsaw, Poland Faculty of Physics, University of Warsaw, Pasteura 7, 02-093 Warsaw, Poland Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland d School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK b c
a r t i c l e
i n f o
Article history: Received 1 December 2011 Revised 8 March 2012 Available online 26 June 2012 Keywords: Photonic crystal fibers Birefringent fibers Fiber sensors Soft glass
a b s t r a c t We present a dual mode, large core highly birefringent photonic crystal fiber with a photonic cladding composed of elliptical holes ordered in a rectangular lattice. The fiber is made of borosilicate glass and has a regular set of elliptical holes with an aspect ratio of 1.27 and a filling factor near 0.5. The group birefringence (G) and effective mode area were measured at 1550 nm for the fundamental mode and were found to equal 2 104 and 20 lm2 respectively. We discuss the influence of structural parameters including the ellipticity of the air holes and the aspect ratio of the rectangular lattice on the birefringence and on the fundamental and second modes of the fiber. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction The development of highly birefringent fibers remains one of the most promising applications of photonic crystal fibers (PCFs). It is well known that photonic crystal fibers (PCFs) can exhibit much higher birefringence values than their conventional counter parts such as bow tie and panda type optical fibers. Since the birefringence in PCFs results from the asymmetric distribution of the refractive index in the fiber cross-section, not form stress induced phenomena, they are highly sensitive to temperature variations [1] and, therefore, good candidates for various mechanical sensors such as strain, stress or pressure [2]. There are several methods proposed to break symmetry and achieve the asymmetric distribution of the field in PCFs including elliptical cores [3], small air holes in the core [4], varied sizes of circular holes in the cladding [5,6] and adding large air holes outside the cladding [7]. A lot of interest has also been focused on PCFs with elliptical holes in a hexagonal or rectangular lattice [8,9]. This solution offers extremely high birefringence, however the practical development of these types of structure suffers from a number of technological difficulties [10]. A successful demonstration of a polymer PCF with elliptical holes made from polymethyl methacrylate (PMMA) using an extrusion method was reported by Issa ⇑ Corresponding author at: Faculty of Physics, University of Warsaw, Pasteura 7, 02-093 Warsaw, Poland. Fax: +48 22 5546822. E-mail address: [email protected] (R. Buczynski). 1068-5200/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yofte.2012.04.004
et al. [11]. This polymer PCF exhibited a birefringence on the order of 104 at 850 nm. Recently two groups reported the successful development of PCFs with elliptical holes using soft [12] and silica glasses [13]. In most of work to date, the major focus has been on the realization of the maximum birefringence that it is possible to obtain in the photonic structures. As a result, the proposed structures posses a very small core and high coupling losses are expected. On the other hand, large mode fibers offer a likely route to single mode performance and high birefringence. Several groups have reported the use of step-index two-mode highly birefringent fibers as a good candidate for multi-parameter sensors for the simultaneous measurement of strain and temperature [14], the very sensitive measurement of strain or temperature individually [15,16] or the measurement of the acousto-optic frequency shift [17]. The two mode highly birefringent fiber can work as an interferometer using two spatial modes as the two interferometer arms – in this configuration the group delay is similar, while the difference in the phase delays is large [18]. The use of a photonic crystal fiber allows the development of two-mode fibers for a wide wavelength range [19]. Two mode photonic crystal fibers have been successfully used as inteferometric strain sensors at wavelengths from 650 nm to 1300 nm [20], as an interferometric torsion sensor [21], a tunable acousto-optic filter from 700 to 1700 nm [22] and as a temperature sensor [23]. In this paper we present a large core fiber design with elliptical holes on a rectangular lattice in the cladding. In order to increase
221
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
the mode area, the core is created by omitting the 4 central holes in the structures.
2. Influence of hole ellipticity on fiber properties The total birefringence of the squeezed lattice fibers is a combination of the birefringence induced by the rectangular lattice and the birefringence induced by the ellipticity of the air holes in the cladding. To study the influence of hole ellipticity, we have simulated a test structure with a rectangular lattice and various hole shapes with a constant minor axis diameter of 0.88 lm and major axis lengths between 0.88 lm and 1.2 lm (Fig. 1). We assume that the photonic crystal fiber is composed of four rings of air holes ordered in a rectangular lattice with lattice constants of Kx = 2.6 lm and Ky = 1.6 lm. The core of the fiber is formed by omitting the four central holes in the structure. In the simulations we consider the fundamental as well as second guided modes. The simulations were performed using the finite element method in Comsol 3.4 [24]. The effective refractive indices of the guided modes were calculated taking into account the material dispersion of the glass. Uniaxial perfectly matched layer (UPML) boundary conditions were used to determine the confinement loss of the selected guided modes in the fibers. These simulations show that the
Fig. 1. The scheme of core and first two rings in photonic cladding in the photonic crystal fiber with rectangular lattice and various shapes of air-holes from circular with the diameter of 0.88 lm (dotted line) to elliptical with the diameter of major and minor axis of 1.2 lm and 0.88 lm, respectively (solid line).
×10-4
considered structures are capable of effectively guiding up to 2 modes. Based on the calculated refractive index properties, the phase birefringence B, defined as the difference between the propagation constants bx and by of the two orthogonally polarized components (LPx01 and LPy01 for the fundamental mode/LPx11 and LPy11 for the second mode), is calculated according to the formula:
B ¼ nx ny ¼
k ðb by Þ 2p x
ð1Þ
Whilst the group birefringence G is defined as:
G¼Bk
dB dk
ð2Þ
We observe that the ellipticity of the air holes has consequences for the birefringence ratio between the first and second modes. For circular holes (e = 1), the birefringence of the second mode LP11 is higher than that of the fundamental mode LP01 – independent of the hole diameter. In addition, the observed change in the birefringence with increasing ellipticity of the air holes is different for the fundamental and second modes. The phase birefringence of the
Fig. 3. Phase birefringence vs. ellipticity of air-holes for fundamental LP11 (a) and higher mode LP11 (b) for a wavelength of 1200 nm.
×10-4
e=1 e=1.15 e=1.2 e=1.25 e=1.3 e=1.35
Fig. 2. Calculated phase (B) and group (G) birefringence for fundamental LP01 and second mode LP11 of the PCF structures with various shape of air-holes: e denotes aspect ration between fast and slow axis of elliptical holes. Rectangular lattice has lattice constant of Kx = 1.25 lm and Ky = 2.25 lm.
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
Loss [dB/m]
222
LP11y
LP11x
e=1.2 e=1.25 LP01
e=1.3
x
wavelength [µm]
LP01y
wavelength [µm]
Fig. 4. Calculated confinement loses of guided fundamental (thin lines) and second (thick lines) modes in PCFs with different aspect ratio of elliptical holes e = 1.2, 1.25 and 1.3. Material loses are not taken into account.
fundamental mode (LP01) increases with ellipticity, (Fig. 2a) whereas the phase birefringence of the second mode (LP11) decreases with ellipticity (Fig. 2b). Based on those simulations we can determine a target ellipticity of the air-holes, where the birefringence of both the fundamental and second modes are equal for a particular wavelength of illumination (Fig. 3). This property has important consequences for the characterization of the fiber and the determination of the measurement mode, since the confinement losses of the LP11 modes are one order of magnitude higher than for the fundamental mode (Fig. 4).
3. Development of large core birefringent PCF with elliptical airholes A borosilicate glass (NC-21A) is used for the PCF development. This multi-component glass, synthesized in-house at ITME, has an oxide composition by weight of 55.0% SiO2, 1.0% Al2O3, 26.0% B2O3, 3.0% Li2O, 9.5% Na2O, 5.5% K2O and 0.8% As2O3. This glass is well suited for the development of complex fiber structures with the stack and draw technology due to its very good rheological properties [12,25,26]. The main physical properties of NC21A are: refractive index nD = 1.533, density q = 2.50 g/cm3, coefficient of thermal expansion a20-300 = 82 107 K1, glass transition temperature Tg = 500 °C and softening point DTM = 530 °C. The transmission of NC-21A glass is limited to the range 380–2700 nm with a relatively high attenuation of 4 dB/m.
For the preform assembly, we used rectangular cross-section glass capillaries (Fig. 5c) with an axis aspect ratio of 0.33 and linear filling factors of fx = 0.90 and fy = 0.75 ordered in a rectangular lattice. The rectangular capillaries are drawn by a fiber drawing tower to a size of 2 by 4 mm. As a preform for these capillaries, a rectangular tube built from two L-shaped glass profiles fused in a furnace at a temperature slightly above the glass softening point was used. It is well known that the lattice geometry used at the PCF preform stage influences the shape of the air-holes formed during the fiber drawing process (Fig. 5). Choosing a rectangular lattice at the preform stage therefore results in elliptical air-holes during drawing of the subpreform rods. The core of the fiber is formed with four rectangular rods and surrounded by four concentric rings of elliptical rods. During sub-preform and fiber drawing, we use a low-speed drawing process to ensure a homogenous heat distribution in the subpreform and a relatively low pulling temperature of 730 °C to preserve the ellipticity of the air holes. The drawing process, performed on a fiber drawing tower, uses a feeding speed of 1.5 mm/ min and a pulling speed of 0.6 m/min. Accurate control and adjustment of these drawing parameters is essential to obtaining elliptical holes, since the subpreform air-holes tend to become circular. For our final fiber we chose a rectangular cross-section which allows easy identification of the main axis and simplifies the orientation and avoids twisting of the fiber during measurement. The fabricated fibers have lattice constants of Kx = 2.6 lm and Ky = 1.6 lm for main axes X and Y respectively (Fig. 6). The size of the elliptical holes varies slightly depending on the location in the structure
Fig. 5. Subpreform of large core birefringent PCF with rectangular air-holes – general view (a), core area (b) and rectangular-like microcapillary – the preform component (c).
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
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Fig. 6. SEM photograph of PCF with elliptical air-holes in the cladding (a) rectangular cross-section of the fiber, (b) photonic cladding, and (c) rectangular core.
(Fig. 6c). This is due to too high a preform temperature during fiber drawing corresponding to too low a glass viscosity. Under these conditions, small differences in the inner dimensions of the preform capillaries result in pressure differences and, consequently, an increase in the diameter of some of the holes. Most of the enlarged holes are located in the outside of the ring structure which correlates well with the temperature gradient in the structural preform during drawing. These imperfections don’t significantly degrade the fiber birefringence, attenuation or modal properties. The distortion of the rectangular lattice results form some irregularities of rectangular-like capillaries obtained during individual capillary drawing process (Fig. 5c) These imperfections resulted in lattice shifts during sub-preform drawing process (Fig. 5b) and it couldn’t be further corrected during final fiber drawing process. The holes have minor and major axes of dx = 1.12 lm and dy = 0.88 lm, respectively, yielding linear filling factors of fx = 0.43 and fy = 0.55 (Fig. 6). The average measured ellipticity of the air holes is about g = 1.275. The core of the fiber is rectangular with dimensions 4.1 6.5 lm. 4. Characterization and modeling of developed fibers We used the standard spectral interferometric method with crossed polarizers to determine the group birefringence. The measurement setup is presented in Fig. 7.
Polarized supercontinuum light is launched into the sample fiber. The first polarizer is aligned such that both polarization modes are equally excited. At the output of our sample, an analyser is oriented at 90° with respect to the input polarizer. The output signal is registered using a spectrum analyser and monitored with a CCD camera. The CCD camera allows the verification of the near field distribution of the fiber output and ensures proper light coupling into the core of the PCF. The spectrum analyser records the modulation of the intensity as a function of wavelength which results from the interference between the polarized components of the propagating mode. Maximum intensity occurs when
dD/ Dk ¼ 2p dk
ð3Þ
where D/ is the phase shift corresponding to successive fringes in the output spectrum represented by their maxima and Dk is the distance between successive fringes. By changing the input coupling conditions, we can selectively excite the fundamental and second modes. The selected mode is verified with a CCD camera simultaneously imaging the output facet of the measured fiber during the spectrum measurements (Fig. 7). The registered interferograms are presented in Fig. 8 (fiber length L = 0.5 m). The decrease of output signal we observe above 1.4 lm is related to the water absorption peak in the fiber (phenomena observed for both modes), but the further decrease of
Fig. 7. Group birefringence measurement set-up.
Fig. 8. Registered interferograms for fundamental (a) and higher mode (b). Fiber length L = 0.5 m.
phase B and group G birefringence
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
phase B and group G birefringence
224
wavelength [µm]
wavelength [µm]
(a)
(b)
Fig. 9. Experimental (points) and numerical simulation (lines) results of phase and group modal birefringence vs. wavelength for developed fiber based SEM photos (a) and based on estimated idealized fiber structures (b). Both the fundamental mode (black) and higher order mode (red) results are shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
intensity above 1.5 lm is related to the increasing losses for longer wavelengths above the sensitivity of the spectrometer. Based on the interferogams we calculated the group birefringence for the sample fiber (Fig. 9) as:
where k is the average wavelength between two successive fringes and L is the length of the measured fiber. We have obtained a group birefringence magnitude of G = 2 104 at 1550 nm. The sign of G cannot be directly determined in our experiment; however, the modeling results show a negative sign for G. Simultaneously we have calculated the phase and group birefringence based on the SEM micrographs (Fig. 6a) using Eqs. (1) and (2). The calculated values presented in Fig. 9a are in very good agreement with the measured group and phase birefringence values. To estimate an influence of imperfection in fiber development on the output characteristics we have calculated the group and
phase birefringence of a perfect structure based on the calculated average values of the hole dimensions and lattice pitch (Fig. 9b). The developed and idealized structures based on the drawn fiber are shown in Fig. 10. The experimental results match perfectly the numerical simulations for the drawn fiber based SEM photos (a) and those based on the estimated idealized fiber structures. This implies that imperfections introduced during the fiber manufacturing process have a minimal effect on the fiber birefringence and shows a good tolerance to fabrication errors of the designed fiber structure. According to the numerical simulations of the actual fiber, the confinement losses of the higher modes are about one order of magnitude greater than those observed for the fundamental mode (Fig. 11). This observation is confirmed by the very low signal for the second mode above 1.5 lm. In practice even short lengths of the sample fiber can be treated as single mode above 1.5 lm. The fundamental mode has an effective mode area of 20 lm2. This relatively large mode area ensures efficient coupling with standard single mode fiber.
Fig. 10. A SEM photo based (solid ellipses) and idealized rectangular lattice (empty ellipses) structures of the developed fiber.
Fig. 11. Calculated confinement losses vs. wavelength for fundamental (thin lines) and higher order mode (thick lines).
jGj ¼
k2 DkL
ð4Þ
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
5. Conclusion We have reported the development of a highly birefringent PCF with elliptical air holes and squeezed lattice cladding with a large mode area of 20 lm2. The large core is created by multiple defects of the photonic structures and allows the guiding of two propagating modes. The birefringence of both modes has been measured and shown to be in good agreement with numerical simulations. The phase birefringence of the fundamental mode is on the order of 104, due to the low air filling factor, and the group birefringence G = 2 104 at 1550 nm. These PCFs are well suited to applications in optical fiber directional transverse strain sensors where their rectangular cross-section allows the avoidance of twisting during mounting and provides straightforward orientation of the polarization axes with respect to the direction of applied force.
Acknowledgments This work was supported in part by Polish Ministry of Science of Science and Higher Education Research Grant NN515244737 and by an internal scientific grant of ITME.
References [1] T. Martynkien, M. Szpulak, W. Urbanczyk, Modeling and measurement of temperature sensitivity in birefringent photonic crystal holey fibers, Appl. Opt. 44 (2005) 7780–7788. [2] O. Frazao, J. Santos, F. Araujo, L. Ferreira, Optical sensing with photonic crystal fibers, Laser Photon. Rev. 2 (2008) 449–459. [3] A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, C. De Angelis, Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber, Opt. Express 14 (2006) 397–404. [4] D. Mogilevtsev, J. Broeng, S.E. Barkou, A. Bjarklev, Design of polarizationpreserving photonic crystal fibres with elliptical poresJ, Opt. A: Pure Appl. Opt. 3 (2001) S141–S143. [5] T. Martynkien, M. Szpulak, G. Statkiewicz, G. Golojuch, J. Olszewski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, et al., Measurements of sensitivity to hydrostatic pressure and temperature in highly birefringent photonic crystal fibers, Opt. Quant. Electron. 39 (2007) 481–489. [6] T. Martynkien, A. Anuszkiewicz, G. Statkiewicz-Barabach, J. Olszewski, G. Golojuch, M. Szczurowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, H. Thienpont, Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature, Appl. Phys. B 94 (2009) 635– 640.
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[7] C. Wu, J. Li, X. Feng, B.-O. Guan, H.-Y. Tam, Side-hole photonic crystal fiber with ultrahigh polarimetric pressure sensitivity, J. Lightw. Technol. 29 (2011) 943– 948. [8] M.J. Steel, R.M. Osgood Jr., Elliptical-hole photonic crystal fibers, Opt. Lett. 26 (2001) 229–231. [9] Y. Yue, G. Kai, Z. Wang, T. Sun, L. Jin, Y. Lu, C. Zhang, J. Liu, Y. Li, Y. Liu, S. Yuan, X. Dong, Highly birefringent elliptical-hole photonic crystal fiber with squeezed hexagonal lattice, Opt. Lett. 32 (2007) 469–471. [10] P. Szarniak, R. Buczynski, D. Pysz, I. Kujawa, M. Franczyk, R. Stepien Highly birefringent photonic crystal fibers with elliptical holes, in: Proc. SPIE 5950, 2005, 59501L. [11] N. Issa, M. van Eijkelenborg, M. Fellew, F. Cox, G. Henry, M. Large, Fabrication and study of microstructured optical fibers with elliptical holes, Opt. Lett. 29 (2004) 1336–1338. [12] R. Buczynski, I. Kujawa, D. Pysz, T. Martynkien, F. Berghmans, H. Thienpont, R. Stepien, Highly birefringent soft glass rectangular photonic crystal fibers with elliptical holes, Appl. Phys. B 99 (2010) 13–17. [13] F. Beltrán-Mejía, G. Chesini, E. Silvestre, A.K. George, J.C. Knight, C.M. Cordeiro, Ultrahigh-birefringent squeezed lattice photonic crystal fiber with rotated elliptical air holes, Opt. Lett. 35 (2010) 544–546. [14] A.M. Vengsarkar, W.C. Michie, L. Jaankovic, B. Culshaw, R.O. Claus, Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature, J. Lightw. Technol. 12 (1994) 170–177. [15] J.N. Blake, S.Y. Huang, B.Y. Kim, H.J. Shaw, Strain effects on highly elliptical core two-mode fibers, Opt. Lett. 12 (1987) 732–734. [16] K.A. Murphy, M.S. Miller, A.M. Vengsarkar, R.O. Claus, Elliptical-core two-mode optical-fiber sensor implementation methods, J. Lightw. Technol. 8 (1990) 1688–1696. [17] B.Y. Kim, J.N. Blake, H.E. Engan, H.J. Shaw, All-fiber acousto-optic frequency shifter, Opt. Lett. 11 (1986) 389–391. [18] B.Y. Kim, J.N. Blake, S.Y. Huang, H.J. Shaw, Use of highly elliptical core fibers for two-mode fiber devices, Opt. Lett. 12 (1987) 729–731. [19] W. Jin, Z. Wang, J. Ju, Two-mode photonic crystal fibers, Opt. Express 13 (2005) 2082–2088. [20] J. Ju, W. Jin, M.S. Demokan, Two-mode operation in highly birefringent photonic crystal fiber, IEEE Photon. Technol. Lett. 16 (2004) 2471–2474. [21] O. Frazao, C. Jesus, J.M. Baptista, J.L. Santos, P. Roy, Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber, IEEE Photon. Technol. Lett. 21 (2009) 1277–1279. [22] K.S. Hong, H.C. Park, B.Y. Kim, I.K. Hwang, W. Jin, J. Ju, D.I. Yeom, 1000 nm tunable acousto-optic filter based on photonic crystal fiber, Appl. Phys. Lett. 92 (2008) 031110. [23] J. Ju, Z. Wang, W. Jin, M.S. Demokan, Temperature sensitivity of a two-mode photonic crystal fiber interferometric sensor, IEEE Photon. Technol. Lett. 18 (2006) 2168–2170. [24] Comsol Multiphysics 3.4 User’s Guide, Modeling Guide and Model Library, Comsol AB, 2007. [25] D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, D. Velic, Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers, Appl. Phys. B: Lasers Optics 93 (2008) 531–538. [26] R. Buczynski, D. Pysz, R. Stepien, A.J. Waddie, I. Kujawa, R. Kasztelanic, M. Franczyk, M.R. Taghizadeh, Supercontinuum generation in photonic crystal fibers with nanoporous core made of soft glass, Laser Phys. Lett. 8 (2011) 443– 448.
Contents lists available at SciVerse ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass Ireneusz Kujawa a, Ryszard Buczynski a,b,⇑, Tadeusz Martynkien c, Marek Sadowski c, Dariusz Pysz a, Ryszard Stepien a, Andrew Waddie d, Mohammad R. Taghizadeh d a
Glass Laboratory, Institute of Electronic Materials Technology, Wolczynska 133, 01-919, Warsaw, Poland Faculty of Physics, University of Warsaw, Pasteura 7, 02-093 Warsaw, Poland Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland d School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK b c
a r t i c l e
i n f o
Article history: Received 1 December 2011 Revised 8 March 2012 Available online 26 June 2012 Keywords: Photonic crystal fibers Birefringent fibers Fiber sensors Soft glass
a b s t r a c t We present a dual mode, large core highly birefringent photonic crystal fiber with a photonic cladding composed of elliptical holes ordered in a rectangular lattice. The fiber is made of borosilicate glass and has a regular set of elliptical holes with an aspect ratio of 1.27 and a filling factor near 0.5. The group birefringence (G) and effective mode area were measured at 1550 nm for the fundamental mode and were found to equal 2 104 and 20 lm2 respectively. We discuss the influence of structural parameters including the ellipticity of the air holes and the aspect ratio of the rectangular lattice on the birefringence and on the fundamental and second modes of the fiber. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction The development of highly birefringent fibers remains one of the most promising applications of photonic crystal fibers (PCFs). It is well known that photonic crystal fibers (PCFs) can exhibit much higher birefringence values than their conventional counter parts such as bow tie and panda type optical fibers. Since the birefringence in PCFs results from the asymmetric distribution of the refractive index in the fiber cross-section, not form stress induced phenomena, they are highly sensitive to temperature variations [1] and, therefore, good candidates for various mechanical sensors such as strain, stress or pressure [2]. There are several methods proposed to break symmetry and achieve the asymmetric distribution of the field in PCFs including elliptical cores [3], small air holes in the core [4], varied sizes of circular holes in the cladding [5,6] and adding large air holes outside the cladding [7]. A lot of interest has also been focused on PCFs with elliptical holes in a hexagonal or rectangular lattice [8,9]. This solution offers extremely high birefringence, however the practical development of these types of structure suffers from a number of technological difficulties [10]. A successful demonstration of a polymer PCF with elliptical holes made from polymethyl methacrylate (PMMA) using an extrusion method was reported by Issa ⇑ Corresponding author at: Faculty of Physics, University of Warsaw, Pasteura 7, 02-093 Warsaw, Poland. Fax: +48 22 5546822. E-mail address: [email protected] (R. Buczynski). 1068-5200/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yofte.2012.04.004
et al. [11]. This polymer PCF exhibited a birefringence on the order of 104 at 850 nm. Recently two groups reported the successful development of PCFs with elliptical holes using soft [12] and silica glasses [13]. In most of work to date, the major focus has been on the realization of the maximum birefringence that it is possible to obtain in the photonic structures. As a result, the proposed structures posses a very small core and high coupling losses are expected. On the other hand, large mode fibers offer a likely route to single mode performance and high birefringence. Several groups have reported the use of step-index two-mode highly birefringent fibers as a good candidate for multi-parameter sensors for the simultaneous measurement of strain and temperature [14], the very sensitive measurement of strain or temperature individually [15,16] or the measurement of the acousto-optic frequency shift [17]. The two mode highly birefringent fiber can work as an interferometer using two spatial modes as the two interferometer arms – in this configuration the group delay is similar, while the difference in the phase delays is large [18]. The use of a photonic crystal fiber allows the development of two-mode fibers for a wide wavelength range [19]. Two mode photonic crystal fibers have been successfully used as inteferometric strain sensors at wavelengths from 650 nm to 1300 nm [20], as an interferometric torsion sensor [21], a tunable acousto-optic filter from 700 to 1700 nm [22] and as a temperature sensor [23]. In this paper we present a large core fiber design with elliptical holes on a rectangular lattice in the cladding. In order to increase
221
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
the mode area, the core is created by omitting the 4 central holes in the structures.
2. Influence of hole ellipticity on fiber properties The total birefringence of the squeezed lattice fibers is a combination of the birefringence induced by the rectangular lattice and the birefringence induced by the ellipticity of the air holes in the cladding. To study the influence of hole ellipticity, we have simulated a test structure with a rectangular lattice and various hole shapes with a constant minor axis diameter of 0.88 lm and major axis lengths between 0.88 lm and 1.2 lm (Fig. 1). We assume that the photonic crystal fiber is composed of four rings of air holes ordered in a rectangular lattice with lattice constants of Kx = 2.6 lm and Ky = 1.6 lm. The core of the fiber is formed by omitting the four central holes in the structure. In the simulations we consider the fundamental as well as second guided modes. The simulations were performed using the finite element method in Comsol 3.4 [24]. The effective refractive indices of the guided modes were calculated taking into account the material dispersion of the glass. Uniaxial perfectly matched layer (UPML) boundary conditions were used to determine the confinement loss of the selected guided modes in the fibers. These simulations show that the
Fig. 1. The scheme of core and first two rings in photonic cladding in the photonic crystal fiber with rectangular lattice and various shapes of air-holes from circular with the diameter of 0.88 lm (dotted line) to elliptical with the diameter of major and minor axis of 1.2 lm and 0.88 lm, respectively (solid line).
×10-4
considered structures are capable of effectively guiding up to 2 modes. Based on the calculated refractive index properties, the phase birefringence B, defined as the difference between the propagation constants bx and by of the two orthogonally polarized components (LPx01 and LPy01 for the fundamental mode/LPx11 and LPy11 for the second mode), is calculated according to the formula:
B ¼ nx ny ¼
k ðb by Þ 2p x
ð1Þ
Whilst the group birefringence G is defined as:
G¼Bk
dB dk
ð2Þ
We observe that the ellipticity of the air holes has consequences for the birefringence ratio between the first and second modes. For circular holes (e = 1), the birefringence of the second mode LP11 is higher than that of the fundamental mode LP01 – independent of the hole diameter. In addition, the observed change in the birefringence with increasing ellipticity of the air holes is different for the fundamental and second modes. The phase birefringence of the
Fig. 3. Phase birefringence vs. ellipticity of air-holes for fundamental LP11 (a) and higher mode LP11 (b) for a wavelength of 1200 nm.
×10-4
e=1 e=1.15 e=1.2 e=1.25 e=1.3 e=1.35
Fig. 2. Calculated phase (B) and group (G) birefringence for fundamental LP01 and second mode LP11 of the PCF structures with various shape of air-holes: e denotes aspect ration between fast and slow axis of elliptical holes. Rectangular lattice has lattice constant of Kx = 1.25 lm and Ky = 2.25 lm.
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
Loss [dB/m]
222
LP11y
LP11x
e=1.2 e=1.25 LP01
e=1.3
x
wavelength [µm]
LP01y
wavelength [µm]
Fig. 4. Calculated confinement loses of guided fundamental (thin lines) and second (thick lines) modes in PCFs with different aspect ratio of elliptical holes e = 1.2, 1.25 and 1.3. Material loses are not taken into account.
fundamental mode (LP01) increases with ellipticity, (Fig. 2a) whereas the phase birefringence of the second mode (LP11) decreases with ellipticity (Fig. 2b). Based on those simulations we can determine a target ellipticity of the air-holes, where the birefringence of both the fundamental and second modes are equal for a particular wavelength of illumination (Fig. 3). This property has important consequences for the characterization of the fiber and the determination of the measurement mode, since the confinement losses of the LP11 modes are one order of magnitude higher than for the fundamental mode (Fig. 4).
3. Development of large core birefringent PCF with elliptical airholes A borosilicate glass (NC-21A) is used for the PCF development. This multi-component glass, synthesized in-house at ITME, has an oxide composition by weight of 55.0% SiO2, 1.0% Al2O3, 26.0% B2O3, 3.0% Li2O, 9.5% Na2O, 5.5% K2O and 0.8% As2O3. This glass is well suited for the development of complex fiber structures with the stack and draw technology due to its very good rheological properties [12,25,26]. The main physical properties of NC21A are: refractive index nD = 1.533, density q = 2.50 g/cm3, coefficient of thermal expansion a20-300 = 82 107 K1, glass transition temperature Tg = 500 °C and softening point DTM = 530 °C. The transmission of NC-21A glass is limited to the range 380–2700 nm with a relatively high attenuation of 4 dB/m.
For the preform assembly, we used rectangular cross-section glass capillaries (Fig. 5c) with an axis aspect ratio of 0.33 and linear filling factors of fx = 0.90 and fy = 0.75 ordered in a rectangular lattice. The rectangular capillaries are drawn by a fiber drawing tower to a size of 2 by 4 mm. As a preform for these capillaries, a rectangular tube built from two L-shaped glass profiles fused in a furnace at a temperature slightly above the glass softening point was used. It is well known that the lattice geometry used at the PCF preform stage influences the shape of the air-holes formed during the fiber drawing process (Fig. 5). Choosing a rectangular lattice at the preform stage therefore results in elliptical air-holes during drawing of the subpreform rods. The core of the fiber is formed with four rectangular rods and surrounded by four concentric rings of elliptical rods. During sub-preform and fiber drawing, we use a low-speed drawing process to ensure a homogenous heat distribution in the subpreform and a relatively low pulling temperature of 730 °C to preserve the ellipticity of the air holes. The drawing process, performed on a fiber drawing tower, uses a feeding speed of 1.5 mm/ min and a pulling speed of 0.6 m/min. Accurate control and adjustment of these drawing parameters is essential to obtaining elliptical holes, since the subpreform air-holes tend to become circular. For our final fiber we chose a rectangular cross-section which allows easy identification of the main axis and simplifies the orientation and avoids twisting of the fiber during measurement. The fabricated fibers have lattice constants of Kx = 2.6 lm and Ky = 1.6 lm for main axes X and Y respectively (Fig. 6). The size of the elliptical holes varies slightly depending on the location in the structure
Fig. 5. Subpreform of large core birefringent PCF with rectangular air-holes – general view (a), core area (b) and rectangular-like microcapillary – the preform component (c).
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
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Fig. 6. SEM photograph of PCF with elliptical air-holes in the cladding (a) rectangular cross-section of the fiber, (b) photonic cladding, and (c) rectangular core.
(Fig. 6c). This is due to too high a preform temperature during fiber drawing corresponding to too low a glass viscosity. Under these conditions, small differences in the inner dimensions of the preform capillaries result in pressure differences and, consequently, an increase in the diameter of some of the holes. Most of the enlarged holes are located in the outside of the ring structure which correlates well with the temperature gradient in the structural preform during drawing. These imperfections don’t significantly degrade the fiber birefringence, attenuation or modal properties. The distortion of the rectangular lattice results form some irregularities of rectangular-like capillaries obtained during individual capillary drawing process (Fig. 5c) These imperfections resulted in lattice shifts during sub-preform drawing process (Fig. 5b) and it couldn’t be further corrected during final fiber drawing process. The holes have minor and major axes of dx = 1.12 lm and dy = 0.88 lm, respectively, yielding linear filling factors of fx = 0.43 and fy = 0.55 (Fig. 6). The average measured ellipticity of the air holes is about g = 1.275. The core of the fiber is rectangular with dimensions 4.1 6.5 lm. 4. Characterization and modeling of developed fibers We used the standard spectral interferometric method with crossed polarizers to determine the group birefringence. The measurement setup is presented in Fig. 7.
Polarized supercontinuum light is launched into the sample fiber. The first polarizer is aligned such that both polarization modes are equally excited. At the output of our sample, an analyser is oriented at 90° with respect to the input polarizer. The output signal is registered using a spectrum analyser and monitored with a CCD camera. The CCD camera allows the verification of the near field distribution of the fiber output and ensures proper light coupling into the core of the PCF. The spectrum analyser records the modulation of the intensity as a function of wavelength which results from the interference between the polarized components of the propagating mode. Maximum intensity occurs when
dD/ Dk ¼ 2p dk
ð3Þ
where D/ is the phase shift corresponding to successive fringes in the output spectrum represented by their maxima and Dk is the distance between successive fringes. By changing the input coupling conditions, we can selectively excite the fundamental and second modes. The selected mode is verified with a CCD camera simultaneously imaging the output facet of the measured fiber during the spectrum measurements (Fig. 7). The registered interferograms are presented in Fig. 8 (fiber length L = 0.5 m). The decrease of output signal we observe above 1.4 lm is related to the water absorption peak in the fiber (phenomena observed for both modes), but the further decrease of
Fig. 7. Group birefringence measurement set-up.
Fig. 8. Registered interferograms for fundamental (a) and higher mode (b). Fiber length L = 0.5 m.
phase B and group G birefringence
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
phase B and group G birefringence
224
wavelength [µm]
wavelength [µm]
(a)
(b)
Fig. 9. Experimental (points) and numerical simulation (lines) results of phase and group modal birefringence vs. wavelength for developed fiber based SEM photos (a) and based on estimated idealized fiber structures (b). Both the fundamental mode (black) and higher order mode (red) results are shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
intensity above 1.5 lm is related to the increasing losses for longer wavelengths above the sensitivity of the spectrometer. Based on the interferogams we calculated the group birefringence for the sample fiber (Fig. 9) as:
where k is the average wavelength between two successive fringes and L is the length of the measured fiber. We have obtained a group birefringence magnitude of G = 2 104 at 1550 nm. The sign of G cannot be directly determined in our experiment; however, the modeling results show a negative sign for G. Simultaneously we have calculated the phase and group birefringence based on the SEM micrographs (Fig. 6a) using Eqs. (1) and (2). The calculated values presented in Fig. 9a are in very good agreement with the measured group and phase birefringence values. To estimate an influence of imperfection in fiber development on the output characteristics we have calculated the group and
phase birefringence of a perfect structure based on the calculated average values of the hole dimensions and lattice pitch (Fig. 9b). The developed and idealized structures based on the drawn fiber are shown in Fig. 10. The experimental results match perfectly the numerical simulations for the drawn fiber based SEM photos (a) and those based on the estimated idealized fiber structures. This implies that imperfections introduced during the fiber manufacturing process have a minimal effect on the fiber birefringence and shows a good tolerance to fabrication errors of the designed fiber structure. According to the numerical simulations of the actual fiber, the confinement losses of the higher modes are about one order of magnitude greater than those observed for the fundamental mode (Fig. 11). This observation is confirmed by the very low signal for the second mode above 1.5 lm. In practice even short lengths of the sample fiber can be treated as single mode above 1.5 lm. The fundamental mode has an effective mode area of 20 lm2. This relatively large mode area ensures efficient coupling with standard single mode fiber.
Fig. 10. A SEM photo based (solid ellipses) and idealized rectangular lattice (empty ellipses) structures of the developed fiber.
Fig. 11. Calculated confinement losses vs. wavelength for fundamental (thin lines) and higher order mode (thick lines).
jGj ¼
k2 DkL
ð4Þ
I. Kujawa et al. / Optical Fiber Technology 18 (2012) 220–225
5. Conclusion We have reported the development of a highly birefringent PCF with elliptical air holes and squeezed lattice cladding with a large mode area of 20 lm2. The large core is created by multiple defects of the photonic structures and allows the guiding of two propagating modes. The birefringence of both modes has been measured and shown to be in good agreement with numerical simulations. The phase birefringence of the fundamental mode is on the order of 104, due to the low air filling factor, and the group birefringence G = 2 104 at 1550 nm. These PCFs are well suited to applications in optical fiber directional transverse strain sensors where their rectangular cross-section allows the avoidance of twisting during mounting and provides straightforward orientation of the polarization axes with respect to the direction of applied force.
Acknowledgments This work was supported in part by Polish Ministry of Science of Science and Higher Education Research Grant NN515244737 and by an internal scientific grant of ITME.
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