Abstract

We present a highly birefringent fiber with a core made of artificial anisotropic glass material. The fiber core is composed of interleaved subwavelength layers of two types of soft glasses ordered in a rectangular structure. A pair of thermally matched glasses, a low refractive index borosilicate glass and a high refractive index lead oxide glass, are used. The fiber has a unique flat profile of birefringence over one octave, weakly dependent on wavelength. The group birefringence and effective mode area were measured in a broadband range across the visible and the near infrared for the fundamental mode and were found to be equal 1.8 × 10−3 and 20 μm2, respectively. The group birefringence is uniquely flat over the wavelength range of 0.8-1.7 μm and the relative difference of birefringence is below 0.2 × 10−3. The measured dispersion shows also relatively flat characteristics varying from −60 ps/(nm × km) at 1150 nm to 20 ps/(nm × km) at 1690 nm with Zero Dispersion Wavelength at 1520 nm. We demonstrated an application of the fiber for polarization maintaining broadband supercontinuum generation in the range of 1210-1830 nm when pumped with a subpicosecond fiber-based laser at 1560 nm.

© 2016 Optical Society of America

1. Introduction

Polarization maintaining optical fibers are one of the key type of fibers with a wide range of areas of application from sensors through telecommunications to nonlinear optics [1–4]. Recently, applications of microstructured optical fibers (MOFs) for the development of highly birefringent fibers have become one of the most successful approaches to the development of this class of fibers [5]. Photonic crystal fibers are a very attractive class of fibers for various applications since their certain parameters such as dispersion, birefringence, modality and mode area can be widely engineered [6]. The flexibility of the design of MOFs offers various mechanisms to introduce two-fold symmetry in a fiber required to obtain birefringence in the medium.

Birefringent MOFs can exhibit much higher birefringence than their conventional counterparts such as the elliptical core, bow tie and panda types of optical fibers [7]. Two fold geometry in MOFs is obtained by modification of the photonic cladding properties, usually by altering the size of air holes [8,9], or core shaping with multiple defects [10,11]. Considerable attention has been paid to MOFs with elliptical holes arranged into the hexagonal or rectangular lattice, since this approach offers birefringence as high as B = 10−2 [12–14]. However, the practical parameters of these types of structures are limited by the available technology and their fabrication repeatability [15,16]. Birefringence in photonic crystal fibers (PCFs) with a regular lattice can also be obtained by infiltration of air holes with liquid crystals [17].

One of the features of highly birefringent (HB) MOFs is very high phase birefringence B dependence on wavelength, hence spectral characteristic of the phase birefringence can be described by power low function [5,8–13]. Typically, the phase birefringence changes by 100% over the wavelength range of 800-1550 nm. According to our knowledge, the only HB PCF which poses relatively flat characteristic of B on wavelength is a PCF with stress applying elements located outside of the microstructured cladding made in silica [18] or poly(methyl methacrylate) - PMMA fibers [19]. The relative change of phase birefringence in the spectral range of 800-1550 nm exceeded 25% [18]. Moreover, due to the fact that the core in such fibers is made of a single material e.g. pure silica surrounded by air holes [18] the ZDW strongly depends on the relative hole diameter (d/Λ) and is located in the spectral range of 1200-1300nm. MOFs with air holes benefit from low temperature sensitivity. Therefore they are good candidates for various mechanical sensors of strain, stress or pressure [20]. The replacement of air holes in the photonic cladding with all-solid inclusions was also widely studied [21]. Various two-fold geometries were tested for the development of highly birefringent photonic bandgap fibers [22] or single polarization fibers [23,24]. These type of birefringent fibers have also been used successfully as interferometric sensors for strain and temperature measurements [21].

In all of the above mentioned approaches, birefringence is obtained by means of a two fold symmetry in the photonic cladding or a non-circular shape of the core. An alternative all-solid glass approach was proposed by Wang et al. [25], where birefringence was induced by effective anisotropy in the subwavelength structure of the core, instead of the commonly used birefringence of the photonic cladding. The considered fiber consisted of 5 interleaved layers built of two commercial Schott glasses: SF6 (nd = 1.79) and LLF1 (nd = 1.54). This type of core structure was originally named as the ‘lamellar core’. A similar approach was used by Waddie at al. to present a concept of volumetric anisotropic materials [26]. In that case, another set of lead-silicate glass F2 and silicate glass NC21A was considered to build a structure with several interleaved glass layers. According to simulations, the anisotropic structure showed a similar birefringence of 2 × 10−3 in a broad wavelength range of 800-2000 nm. The same set of materials was numerically studied when used as a core of the fiber [27]. There, a complete electromagnetic (EM) design cycle and an optimization process of a highly birefringent fiber with an anisotropic core made of F2 and NC21A glasses was demonstrated. It was shown that appropriate tuning of a microstructured fiber with a lamellar core enables flattening birefringence over the spectral range of 600 nm (1100-1700 nm) with birefringence variation below ± 6%.

In this paper we present experimental verification of the introduced concept of an anisotropic core fiber with flat birefringence. For the first time to our knowledge, a fiber with an anisotropic nanostructured core with unique, flat birefringence characteristics is presented, where the relative change of the phase birefringence is lower than 11% for a wavelength range corresponding to over one octave. The fiber has also an optimized flat dispersion characteristic with a zero dispersion wavelength near 1.5 µm making it highly attractive for polarization-stable supercontinuum generation. Experimental results of SG are also presented.

2. Influence of subwavelength core structure on birefringent and dispersion properties of the fiber

It is well known that a periodic structure with a lattice constant similar to the incident wavelength diffracts light propagating orthogonally to the periodicity. However if the lattice constant is reduced significantly below the incident wavelength the light is no longer simply diffracted and experiences the periodic structure as a homogeneous material. This kind of the material can be defined with an effective refractive index described by an effective medium model, such as the Maxwell-Garnet theorem [28]. However the propagation constant will depend on the orientation of polarization of the incident beam with respect to the lattice direction. In this way an artificial anisotropic material can be developed [26].

Recently we have shown that fibers with such a 1D nanostructured core and a solid cladding can have a high and flat birefringence [27]. To study the influence of the internal core structure on the birefringence and dispersion, we have simulated a fiber with a 1D periodic structure composed of two glasses with high and low refractive indices (Fig. 1). As the low index glass we used the borosilicate glass labeled NC21A developed in-house at ITME (nd = 1.526) and as the high index glass we used the lead-silicate glass labeled F2 (nd = 1.620). We have previously shown that both glasses are well suited for fiber drawing and for joint thermal processing [29]. It is important to point out that although the refractive indices of both glasses vary with wavelength, their relative difference is almost constant (variation of ± 0.001) for a broadband range between 0.9 and 2.0 µm (Fig. 2(a)). Also both glasses have similar dispersion characteristics with a flattened part in the same range between 0.9 and 2.0 µm, as shown in Fig. 2(b). This indicates the possibility to use them as an efficient medium for supercontinuum generation. Details about the thermo-physical properties of both glasses are reported in [29, 30].

 figure: Fig. 1

Fig. 1 Schematic of a fiber with anisotropic core. Anisotropic core composed of interleaved high-index and low-index glass strips. The lattice constant Λ is smaller than wavelength.

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 figure: Fig. 2

Fig. 2 Material dispersion (a) and dispersion characteristics (b) of borosilicate glass NC21A and lead-silicate glass F2 and their relative difference.

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We assume that the core is composed of seven 1D high refractive index strips incorporated into a structure of low refractive index glass rods (Fig. 3(a)). In addition, we consider also that the central strip has a defect in the center, where the high index glass is replaced with the low index glass, as shown in Fig. 3(b). As we have previously shown in [27] this additional defect in the core structure favors flat birefringence characteristics.

 figure: Fig. 3

Fig. 3 A schematic of nanostructured core composed of 7 1D high refractive index strips (a). A central strip has a nano-defect in the center (b).

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We considered various lattice constants Λ of the 1D grating to study the influence of the inner core structure on the birefringence and mode dispersion. The simulations were performed using the finite difference method using the COMSOL Multiphysics programming environment. The effective refractive indices of the guided modes were calculated taking into account the material dispersion of the glass. These simulations show that the considered structures are capable of effectively guiding up to a few modes, depending on the lattice constant. However the large difference in attenuation and spatial mode distribution allows in practice excitation of only the fundamental mode. Based on the calculated refractive index properties, the phase birefringence B, defined as the difference between the propagation constants βx and βy of the two orthogonally polarized components (LP01x and LP01y for the fundamental mode / LP11x and LP11y for the second mode), is calculated according to the formula:

B=nxny=λ2π(βxβy).
Whilst the group birefringence G is defined as:
G=BλdBdλ.
The dispersion of the polarization components of the fundamental mode is given by:

Dx=λcd2nxdλ2,Dy=λcd2nydλ2.

For the considered range of lattice constants between 300 and 500 nm we observe relatively flat phase birefringence across one octave corresponding to the range of 1.0 and 2.0 µm wavelengths (Fig. 4(a)). The flattest birefringence is found for the large lattice constant of Λ = 500 nm which varies by ± 1 × 10−4 in the considered wavelength range. The flatness degrades when the lattice constant decreases. This results from the difference between the refractive indices of the glasses (Fig. 2(a)). The dispersion characteristic vary significantly and the zero dispersion wavelength can be shifted between 1460 nm and 2000 nm (Fig. 4(b)).

 figure: Fig. 4

Fig. 4 Calculated birefringence (a) for the fundamental mode and dispersion (b) of the polarized component of the fundamental mode for various lattice constants Λ between 300 and 500 nm. The polarization components Ex denotes direction of electric field vector along layers in the core (X axis), while Ey denotes direction of electric field vector perpendicular to layers in the core (Y axis).

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As we previously showed in [27] the introduction of a defect in the core may result in a flattened phase birefringence. We consider in this case the introduction of a defect into the central strip with a size of 2.35 × Λ. For the lattice constant of Λ = 0.5 µm, the core size is 3.25 × 6.00 µm with a defect in the central strip of 1.18 µm, while for the lattice constant of Λ = 0.45 µm, the core size is 2.96 × 5.40 µm with a defect in the central strip of 1.06 µm. For both fiber structures we have calculated phase and group birefringence assuming either presence or absence of the defect in the core (Fig. 5). If we consider the whole range of 0.6 – 2.0 µm the fibers with the defect have less flatness of birefringence than the ones without the defects. Relative difference of the phase birefringence for the structure with the lattice constant Λ = 0.45 µm for the fiber with a defect is ΔB0.6–2.0 = 0.68 × 10−3, while for the fiber without defect it is ΔB0.6–2.0 = 0.63 × 10−3. However the relative difference of phase birefringence is smaller for the structure with the defect, than for the structure without the defect within the near-infrared wavelengths of 1.4– 2.0 µm. The relative difference of the phase birefringence is ΔB1.4–2.0 = 0.18 × 10−3 for the structure with the core with the defect, while the relative difference of the phase birefringence ΔB1.4–2.0 = 0.19 × 10−3 is obtained for the structure with the core without the defect. We note that the difference in flatness is very small.

 figure: Fig. 5

Fig. 5 Calculated phase and group birefringence for fundamental mode of the fiber with anisotropic core for ideal core structure with period of Λ = 0.5 µm and Λ = 0.45 µm and filling factor f = 1. The solid line denotes result for the structure without the central defect, and the dashed line denotes results for the central defect in the core.

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The relative difference of group birefringence is also smaller for structures without the defect for both lattice constants. In the case of the lattice constant Λ = 0.45 µm the relative difference of group birefringence for the structure with the defect is ΔG0.6–2.0 = 1.59 × 10−3, while for the structure without the defect it is ΔG0.6–2.0 = 1.54 × 10−3.

Dispersion characteristics for both the considered structures, with and without the defect in the core, remains unchanged (Fig. 6). The ZDW is obtained for 1490 nm and 1518 nm for both X (slow) and Y (fast) polarization components of the fundamental mode. The flatness in the range ± 30 ps/(nm × km) is maintained within the range of 747 nm and 720 nm for both X and Y polarization components of the fundamental mode.

 figure: Fig. 6

Fig. 6 Calculated dispersion for polarization components of the fundamental mode in the fiber with anisotropic core for ideal core structure with period of Λ = 500 nm and filling factor f = 1. Blue line denotes result for the structure without central defect, and red line denotes results for the fiber with central defect in the core 1.175 µm long.. Total size of the rectangular core is 3.25 µm × 6.00 µm.

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3. Development of the anisotropic core fiber

A borosilicate glass labeled NC21A developed in-house at ITME and the F2 lead-silicate glass labeled (Schott [30]) are used for the PCF development. The NC21A 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 [29], and is well thermally matched to the F2 glass. The main physical properties of NC21A are: refractive index nd = 1.526, density ρ = 2.50 g/cm3, coefficient of thermal expansion α = 82 × 10−7 K−1 (20-300 °C), glass transition temperature Tg = 500 °C and softening point DSP = 530 °C. The transmission of the 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 rods (drawn at a fiber drawing tower) with an axis aspect ratio of 2:1 ordered in a rectangular lattice. The core of the fiber is formed with array of 10 × 12 rectangular rods made of NC21A and F2 glass as presented in Fig. 7. In the center of the subpreform we have replaced two rectangular rods of F2 with NC21A rods to create a nano-defect in the center of the structure. The assembled subpreform was fused in a furnace at a temperature slightly above the glass softening point (Fig. 7). Next, the subpreform was placed in a tube made of NC21A glass and drawn to form the final fiber (Fig. 8).

 figure: Fig. 7

Fig. 7 Subpreform of the anisotropic core of the fiber.

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 figure: Fig. 8

Fig. 8 SEM image of the birefringent fiber ZEB II/4 with nanostructured core a) cross section of the fiber, (b) rectangular nanostructured core.

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During the sub-preform and fiber drawing, we used a low-speed drawing process to ensure a homogenous heat distribution in the subpreform and a relatively low pulling temperature of 800 °C to minimize the diffusion between the glasses. Accurate control and adjustment of these drawing parameters is essential to obtaining a well defined all-solid structure and to preserving the alignment of rectangular elements in the nanostructured core, since the subpreform tends to spin and disorder the internal alignment. We have developed two series of fibers, labeled ZEBII/4 and ZEBII/6, with different scale and internal core structures. The geometrical parameters of the fibers are presented in Table 1. The shape of the glass components slightly varies from the original design and the core shape is trapezoidal instead of the ideally rectangular (Fig. 8(b)). This is due to the slight differences in the thermal characteristics of both glasses used in the drawing process. Since the F2 glass is slightly softer than NC21 glass, and hence the F2 rods were deformed during the drawing process. This is the result of too high preform temperature during fiber drawing and corresponds to a lower than optimal F2 glass viscosity. Under these conditions, small differences in the inner dimensions of the preform rods result in pressure differences and, consequently, an increase in the diameter of some of the rods. These imperfections may have an influence on the fiber birefringence, dispersion and modal properties with respect to the design. The small-scale distortions of the rectangular lattice of the core structure observed at the level of the subpreform (Fig. 7) have practically disappeared after the final drawing of the fiber (Fig. 8). However, these imperfections have resulted in lattice flatness distortion during the sub-preform drawing process (Fig. 7) and they cannot be further corrected during the final fiber drawing. The SEM images seem to be blurred (Fig. 8(b)) which results from glass diffusion and not the quality of the SEM images. This indicates that some diffusion between the glasses occurred and may also influence the final fiber properties. Diffusion phenomena were not taken into account during the design process.

Tables Icon

Table 1. Geometrical parameters of developed fibers

We have simulated the birefringence and dispersion for the ideal fibers with structure parameters based on the SEM images for both the considered fibers ZEBII/4 and ZEBII/6 (Figs. 9 and 10). We do not take into account the fabrication imperfections such as the glass diffusion and the trapezoidal shape of the core.

 figure: Fig. 9

Fig. 9 Calculated phase (a) and group (b) birefringence for fundamental mode of the fiber with ideal anisotropic core with geometrical parameters based on SEM images (ZEBII/4 and ZEBII/6) for structure with and whithout nanodefect in the core.

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 figure: Fig. 10

Fig. 10 Calculated dispersion for polarization components of the fundamental mode of the fiber with ideal anisotropic core with geometrical parameters based on SEM images (ZEBII/4 and ZEBII/6) for structure with and without nanodefect in the core.

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In addition we performed simulations for fibers based on the SEM images assuming that the central defect of the nanostructure is removed. We assumed that the central strip was continuous. With these simulations we can verify the influence of the central defect in the core on the fiber performance, in the case of the real, fabricated structure. The obtained results are in general similar to those predicted in the case of the ideal structures presented in Fig. 5. The simulation results confirmed that for the simulated range of 0.6-2.0 µm wavelengths the structure without the defect offers better flatness with respect to structure without the defect: for the ZEBII/4 fiber, the relative difference of the phase birefringence: ΔB0.6–2.0 = 0.38 × 10−3 (the core with defect), ΔB0.6–2.0 = 0.26 × 10−3 (the core without defect), for ZEBII/6 relative difference of phase birefringence: ΔB0.6–2.0 = 0.49 × 10−3 (the core with defect), ΔB0.6–2.0 = 0.37 × 10−3 (the core without defect) (Fig. 9(a)).

For the near-infrared range of 1.4 – 2.0 µm we obtained better flatness for the structure with the defect than for the one without the defect in the case of the ZEBII/4 fiber. This result is in good agreement with calculated results of an ideal structure with the lattice constant Λ = 0.45 µm, similar to ZEBII/4 (the lattice constant Λ = 0.44 µm) presented in Fig. 5. For the ZEBII/4 we obtained the relative difference of birefringence: ΔB1.4–2.0 = 0.01 × 10−3 (the core with defect), ΔB1.4–2.0 = 0.04 × 10−3 (the core without defect), while for ZEBII/6 we obtained the relative difference of phase birefringence: ΔB1.4–2.0 = 0.08 × 10−3 (the core with defect), ΔB1.4–2.0 = 0.06 × 10−3 (the core without defect). Differences are practically negligible (the flatness difference is 0.18%) and practically the same value of relative difference of birefringence is obtained. Therefore we can conclude that the introduction of the defect is neutral for the flatness and disadvantageous for the phase birefringence, since it reduces birefringence by 1.8% for the wavelength of 800 nm: B0.8 = 2.43 × 10−3 for the core without the defect and B0.8 = 2.43 × 10−3for the core with the defect. In the case of group birefringence we obtained results that are in general similar to those predicted for the case of the ideal structures presented in Fig. 5.

The relative difference of group birefringence is also smaller for structure without defect for both fiber structure ZEBII/4 and ZEBII/6 (Fig. 9(b)). In case of ZEBII/4 the relative difference of group birefringence fot the structure with defect is ΔG0.6–2.0 = 1.52 × 10−3, while for the structure without defect ΔG0.6–2.0 = 1.46 × 10−3. In case of ZEBII/6 the relative difference of group birefringence fot the structure with defect is ΔG0.6–2.0 = 1.41 × 10−3, while for the structure without defect ΔG0.6–2.0 = 1.21 × 10−3.

We note that the dispersion characteristics are very similar for both fibers ZEBII/4 and ZEBII/6 and their structures with presence or absence of the defect (Fig. 10). The dispersion characteristics are very flat and its slope is almost identical in all cases (variation below 5%). The relative difference of dispersion for all the considered fibers are below 135 ps/nm × km for the wavelength range 1.0-1.7 µm. The ZDW is obtained for 1511 nm and 1472 nm for ZEBII/4 with the presence and absence of the defect, respectively. In the case of ZEBII/6 the ZDW is obtained for 1542 nm and 1516 nm with presence and absence of the defect, respectively.

4. Characterization of anisotropic core fibers

4.1 Group birefringence

To verify the predicted properties of the fibers, we measured its group birefringence, dispersion and modal properties. We used the standard spectral interferometric method with crossed polarizers to determine the group birefringence [31]. The measurement setup is presented in Fig. 11.

 figure: Fig. 11

Fig. 11 Group birefringence measurement set-up.

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Polarized supercontinuum light is launched into the sample fiber with the first polarizer aligned such that both polarization modes are equally excited. At the output of the sample, an analyzer is oriented at the same azimuth with respect to the input polarizer. The output signal is registered using an optical spectrum analyzer (OSA) and monitored with a CCD camera. The CCD camera allows verification of the near-field distribution of the fiber output and ensures proper light coupling into the core of the PCF. The OSA records the modulation of the intensity as a function of wavelength, which results from the interference between the polarized components of the propagating mode. The maximum intensity occurs when

dΔφdλΔλ=±2π,
where Δφ is the phase shift corresponding to successive fringes in the output spectrum represented by their maxima and Δλ is the distance between successive fringes.

By changing the input coupling conditions, we can selectively excite the fundamental mode without excitation of the higher modes. The selected mode is verified by the CCD camera simultaneously imaging the output facet of the measured fiber during the spectrum measurements (Fig. 11). The registered interferograms are presented in Fig. 12 (fiber length L = 95 mm).

 figure: Fig. 12

Fig. 12 Registered interferograms for the fundamental mode of the anisotropic core fiber ZEBII/4. Fiber length L = 95 mm.

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Based on the interferogams we calculated the group birefringence for the sample fiber (Fig. 12) as:

|G|=λ02ΔλL,
where λ0 is the average wavelength between two successive fringes, and L is the length of the measured fiber. We obtained a group birefringence magnitude of G = 1.55 × 10−3 and G = 1.33 × 10−3 at 1550 nm for ZEBII/6 and ZEBII/4 fibers, respectively. The sign of G cannot be directly determined in our experiment; however, modeling results show a positive sign of G.

Simultaneously we have calculated the phase and group birefringence based on the SEM micrographs taking into account all geometrical imperfections of the core structure (Fig. 8) using Eqs. (1) and (2). The calculated phase and group birefringence are presented in Fig. 13(a) and 13(b), respectively. The measured group birefringence is also presented in Fig. 13(b). Experimentally we observed about 18% lower group birefringence at 1550 nm than the one predicted numerically in the case of ZEBII/6 fiber: G1550 = 1.35 × 10−3 (measurements), G1550 = 1.65 × 10−3 (simulations) and about 12% lower in case of ZEBII/4 fiber: G1550 = 1.61 × 10−3 (measurements) and G1550 = 1.82 × 10−3 (simulations), respectively.

 figure: Fig. 13

Fig. 13 Numerical simulation results of phase modal birefringence against the wavelength for the developed fiber based on SEM images (a). Experimental (points) and numerical simulation (lines) results of group modal birefringence spectral dependence (b).

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This is the result of glass diffusion in the real structure which was not taken into account during simulations. During fiber drawing process the glasses become soft and some component ions can penetrate into the other glass. As consequence a transition regions between the well defined glass strips appear and the contrast between the glass strips in the core decreases. As a result, the birefringence drops. This behavior was already reported in [25]. The size of the transition zone strongly depends on the fiber drawing conditions such as the temperature, polling rate and construction of the furnace itself. Usually it is limited to about 100-200 nm and in the case of all-solid photonic crystal fibers it can be neglected. However in the case of submicron strips, this influences the optical performance. The transition zone cannot be modeled straightforwardly for the multicomponent soft glasses as a simple glass mixture, since various metal oxide ions can migrate at different rate, depending on their molecular weights and concentration as we recently showed [32].

Decrease of the birefringence for both fibers is different, since not only the thickness of the strips are different (380 nm for ZEBII/6, and 440 nm for ZEBII/4 as shown in Tab.1) but also the drawing conditions are different. As a consequence the diffusion region will vary and it will have different influence on the contrast and the effective birefringence of both fibers. We can notice that the profile of measured data is different from the simulated result in terms of slope for the longer wavelengths. We suppose that this is the result of an interplay between the wavelength and the diffusion region. For longer wavelengths, the diffusion are has relatively smaller impact on the propagation constant of polarization components than in the case of the shorter wavelengths. The decrease of group birefringence for short wavelengths near 900 nm in the case of ZEBII/4 is related to the errors in the calculations of the fringes distance, taken from the interferogram due to the low contrast and the high density of fringes at short wavelengths and steep spectral characteristics of the probing supercontinuum source in this range (Fig. 12).

The experimental results also confirm the ultra-flat group birefringence profile. Variation of the group birefringence is below ± 0.12 × 10−3 over the whole measurement range between 900 and 1700 nm.

According to the numerical simulations of the actual fiber, the confinement losses of the higher order modes are about one order of magnitude larger than those observed for the fundamental mode. This observation is confirmed by the very low signal for the second mode when the system is realigned to excite the higher order modes. In practice even short lengths of the sample fiber can be treated as single mode above 1.5 μm. The fundamental mode has an effective mode area of 16.8 μm2 and 20.5 μm2 for ZEBII/6 and ZEBII/4 fibers, respectively. This relatively large mode area ensures efficient coupling with standard single mode fiber.

4.2 Fiber dispersion

Fiber dispersion was measured in the Mach-Zehnder interferometer (MZI) setup (Fig. 14(a)) [33]. Due to the relatively high attenuation of the fabricated fiber, a short sample with a length of 190 mm was measured. The supercontinuum used as a light source was coupled to a variable fiber attenuator using a multimode optical fiber (MMF), to ensure the appropriate signal level at the output of the input single mode optical fiber. Then the light was collimated using a microscope objective (MO1) and the beam was divided after the first beamsplitter cube (BS1). The reference arm (left-bottom) of our unbalanced MZI contained a variable neutral density filter (NDF) and three mirrors of which two (M3 and M4) were placed on the linear manual stage, allowing compensation of the optical path of the measurement arm (top-right). In this second arm, the beam was focused on to the measured fiber (FUT) with a microscope objective (MO2) and then output with MO3. The beam was directed on to the second beamsplitter (BS2) with mirror M1, where the signal from the two arms was merged and collected with spectrometers. At the output we used a variable aperture (Ap), which enabled the eliminating of the light propagating in the cladding of the fiber. The two spectrometers we used covered spectral ranges from 350 to 1000 nm and from 1000 to 1700 nm, respectively. As a result, the interference pattern in spectral domain was obtained, with the characteristic wide fringes at wavelengths for which the interferometer was compensated (Fig. 14(b)). Changing the length of the reference arm, we were able to measure the optical path difference between the measurement and reference arms over a wide spectral range, and then to determine the chromatic dispersion of the fiber. Finally we applied a five-term power series fit to the obtained data (ΔL(λ)) in order to calculate the spectral dependence of the chromatic dispersion using the formula:

 figure: Fig. 14

Fig. 14 The unbalanced Mach-Zehnder interferometer setup used for dispersion measurement (a), interference image (b).

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D=1cLdΔL(λ)dλ,

We have measured the dispersion characteristics for both polarization components of the fundamental modes for both considered fibers (ZEBII/6 and ZEBII/4) (see Fig. 15). The dispersion characteristics are very similar for both fibers and both polarizations. The ZDW is obtained near 1520 nm in all the cases. The dispersion characteristics is also relatively flat over the broadband range. Variation of dispersion in the range ± 30 ps/(nm × km) is obtained around the ZDW in the range between 1250 and 1700 nm. Both features, the position of the ZDW and the relatively flat dispersion characteristics, indicate the possibility for supercontinuum generation in this fiber with standard femtosecond fiber-based lasers.

 figure: Fig. 15

Fig. 15 Measurements of dispersion in the spectral range of 900-1700nm for fibers with anisotropic core ZEBII/4, and ZEBII/6 (a). Measured and calculated dispersion for birefringent fiber ZEBII/4 (b).

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We have also measured the attenuation of a 5.42 m long sample of the fiber using the standard cut-back technique. The broad spectrum of a supercontinuum source was coupled to the fiber and measured with an OSA. The measured attenuation of the fiber is below 4.5 dB/m, except for the 8.5 dB/m water peak at 1410 nm (see Fig. 16). The main contribution to the attenuation is the material losses of the both NC21A and F2 silicate glasses. Since the glasses attenuation in the range 500-1600 nm varies below 1%, we expect similar fiber attenuation for wavelengths in that range.

 figure: Fig. 16

Fig. 16 Attenuation measurement of anisotropic core fiber with F2/NC21A glasses.

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5. Supercontinuum generation in anisotropic core fibers

Fiber ZEBII/6 had a measured dispersion profile with longest the ZDW at 1530 nm, and was selected for a supercontinuum generation experiment. For supercontinuum generation we used a high-power, high-repetition rate fiber femtosecond system. The ZEBII/6 fiber was pumped with a fiber-based, chirped-pulse amplification laser, delivering pump pulses centered at 1560 nm and lasting about 400 fs, at a 40 MHz repetition rate, seeded by a nonlinear polarization rotation mode-locked oscillator [34]. The maximum average pump power incident on the fiber input facet was 1.5 W and the coupling efficiency was estimated at roughly 35%. The generated SC was collected with a multimode fiber and delivered to the OSA in order to provide the analysis in the range from 800 to 2400 nm.

The experimental spectrum was confirmed by numerical simulation, based on the scalar, statistical Generalized Nonlinear Schrödinger Equation [35]. The model accounted for the frequency dependence of both the fiber loss and its effective mode area. Numerical representation of the fiber loss was constructed as a flat 3 dB/m level with an OH¯ absorption band (5 dB/m), centered at 1400 nm and modeled with a Gaussian lineshape. The results are plotted in Fig. 17.

 figure: Fig. 17

Fig. 17 Measured and simulated supercontinuum spectra for the structure of ZEB/II-6 fiber.

Download Full Size | PPT Slide | PDF

Comparison of these experimental and numerical data sets indicates that the physical mechanisms leading to observed experimental broadening of spectrum cannot be reconstructed with a standard, scalar propagation model. While the numerical spectrum enables the clear identification of typical modulation instability (MI) and dispersive wave features at wavelengths red-shifted and blue-shifted from the pump, the experimental spectrum has more optical intensity in the central area of spectrum. In a recently demonstrated photonic crystal fiber, made of the same pair of glasses, part of pump light was guided without nonlinear conversion [36]. The unconverted part of pump was further shown to have a seeding effect on the nonlinear broadening, which stabilized its shot-to-shot fluctuations [37]. The anisotropic core structure theoretically supports propagation of different guided modes. The potential of pump-related seeding stabilization of spectral coherence, similar in principle to that reported in [36] would be an interesting feature of the fiber structures reported in this work and is the aim of our next study.

6. Conclusion

We have reported the development of a highly birefringent fiber with a core made of nanostructured artificially anisotropic dielectrics. Nanostructuring of the core allows the tuning of the properties of the fiber in similar way to microstructured fiber. New fiber characteristics that are difficult to achieve in microstructured fibers are possible with the new fiber geometries, due to proper material and internal core subwavelength structure choices. In particular the ultra-flat birefringence for more than an octave is predicted numerically for a lamellar structure of the core with the lattice constant in the range 0.4-0.5 μm. We have shown that for the fiber with a subwavelength lamellar structure with a lattice constant of 0.44 μm the phase birefringence of B = 2.43 × 10−3 at 800 nm can be achieved. Simultaneously, the relative difference of the phase birefringence is as low as ΔB0.6–2.0 = 0.26 × 10−3 (11%) for over one octave corresponding to the range of 0.6-2.0 µm wavelengths. If we consider the near-infrared range of 1.4-2.0 µm, the relative difference of the phase birefringence is as low as ΔB0.6–2.0 = 0.04 × 10−3 which corresponds to 1.7% of difference if the phase birefringence of B = 2.34 × 10−3 at 1550 nm is taken into account as reference. All-solid structures provide very good repeatability of the designed structure and replication at the preform to preform level. We have developed a highly birefringent fiber with an artificially anisotropic core and an ultraflat phase birefringence characteristics.

In addition, we have introduced an nano-defect in the regular 1D lattice in the core to further increase the flatness of birefringence in the near-infrared range of 1.4-2.0 µm wavelengths. However the obtained results show that for real structures the influence of the nano-defect in the core is insignificant for the considered wavelengths and also reduce the flatness in a broadband wavelength range. Moreover this nano-defect reduces the expected birefringence by 1.8%.

Experimentally we have achieved the group birefringence G = 1.55 × 10−3 at 1550 nm for a fiber with a subwavelength lamellar structure with a lattice constant of 0.38 μm. Variation of the group birefringence was below ± 0.12 × 10−3 in the measurement range between 900 and 1700 nm. The developed fibers have a flat dispersion characteristic with zero dispersion near 1.52 µm, which predisposes them for supercontinuum generation. A proof-of-concept experiment showed broadband infrared supercontinuum generation in the range of 1230 and 1840 nm when pumped with 12 nJ pulses of a 400 fs fiber laser.

Acknowledgments

This work was supported by the project TEAM/2012-9/1 operated within the Foundation for Polish Science Team Programme co-financed by the European Regional Development Fund, Operational Program Innovative Economy 2007-2013 and National Science Centre in Poland UMO-2012/06/M/ST2/00479.

References and links

1. J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986). [CrossRef]  

2. T. R. Wolinski, “Polarimetric optical fibers and sensors,” in Progress in Optics vol. XL, E. Wolf, ed. (North Holland, 2000).

3. D. Penninckx, N. Beck, J.-F. Gleyze, and L. Videau, “Signal Propagation Over Polarization-Maintaining Fibers: Problem and Solutions,” J. Lightwave Technol. 24(11), 4197–4207 (2006). [CrossRef]  

4. Z. Zhu and T. Brown, “Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,” Opt. Express 12(5), 791–796 (2004). [CrossRef]   [PubMed]  

5. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25(18), 1325–1327 (2000). [CrossRef]   [PubMed]  

6. F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer Netherlands, 2007).

7. O. Frazão, J. Santos, F. Araujo, and L. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008). [CrossRef]  

8. L. Wang and D. Yang, “Highly birefringent elliptical-hole rectangular-lattice photonic crystal fibers with modified air holes near the core,” Opt. Express 15(14), 8892–8897 (2007). [CrossRef]   [PubMed]  

9. T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010). [CrossRef]   [PubMed]  

10. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001). [CrossRef]  

11. S. E. Kim, B. H. Kim, C. G. Lee, S. Lee, K. Oh, and C. S. Kee, “Elliptical defected core photonic crystal fiber with high birefringence and negative flattened dispersion,” Opt. Express 20(2), 1385–1391 (2012). [CrossRef]   [PubMed]  

12. M. J. Steel and R. M. Osgood Jr., “Elliptical-hole photonic crystal fibers,” Opt. Lett. 26(4), 229–231 (2001). [CrossRef]   [PubMed]  

13. N. A. Issa, M. A. van Eijkelenborg, M. Fellew, F. Cox, G. Henry, and M. C. Large, “Fabrication and study of microstructured optical fibers with elliptical holes,” Opt. Lett. 29(12), 1336–1338 (2004). [CrossRef]   [PubMed]  

14. Y. Yue, G. Kai, Z. Wang, T. Sun, L. Jin, Y. Lu, C. Zhang, J. Liu, Y. Li, Y. Liu, S. Yuan, and X. Dong, “Highly birefringent elliptical-hole photonic crystal fiber with squeezed hexagonal lattice,” Opt. Lett. 32(5), 469–471 (2007). [CrossRef]   [PubMed]  

15. F. Beltrán-Mejía, G. Chesini, E. Silvestre, A. K. George, J. C. Knight, and C. M. Cordeiro, “Ultrahigh-birefringent squeezed lattice photonic crystal fiber with rotated elliptical air holes,” Opt. Lett. 35(4), 544–546 (2010). [CrossRef]   [PubMed]  

16. I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012). [CrossRef]  

17. S. Ertman, M. Tefelska, M. Chylowski, A. Rodriquez, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and T. R. Wolinski, “Index guiding photonic liquid crystal fibers for practical applications,” J. Lightwave Technol. 30(8), 1208–1214 (2012). [CrossRef]  

18. J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12(5), 956–960 (2004). [CrossRef]   [PubMed]  

19. P. Mergo, T. Martynkien, and W. Urbanczyk, “Polymer optical microstructured fiber with birefringence induced by stress-applying elements,” Opt. Lett. 39(10), 3018–3021 (2014). [CrossRef]   [PubMed]  

20. 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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009). [CrossRef]  

21. B. Gu, W. Yuan, A. P. Zhang, and O. Bang, “All-solid birefringent hybrid photonic crystal fiber based interferometric sensor for measurement of strain and temperature,” Proc. SPIE 8311, 831121 (2011). [CrossRef]  

22. R. Goto, S. D. Jackson, S. Fleming, B. T. Kuhlmey, B. J. Eggleton, and K. Himeno, “Birefringent all-solid hybrid microstructured fiber,” Opt. Express 16(23), 18752–18763 (2008). [CrossRef]   [PubMed]  

23. A. Cerqueira S Jr, D. G. Lona, I. de Oliveira, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband single-polarization guidance in hybrid photonic crystal fibers,” Opt. Lett. 36(2), 133–135 (2011). [CrossRef]   [PubMed]  

24. R. Goto, S. D. Jackson, and K. Takenaga, “Single-polarization operation in birefringent all-solid hybrid microstructured fiber with additional stress applying parts,” Opt. Lett. 34(20), 3119–3121 (2009). [CrossRef]   [PubMed]  

25. A. Wang, A. George, J. Liu, and J. Knight, “Highly birefringent lamellar core fiber,” Opt. Express 13(16), 5988–5993 (2005). [CrossRef]   [PubMed]  

26. A. J. Waddie, R. Buczynski, F. Hudelist, J. Nowosielski, D. Pysz, R. Stepien, and M. R. Taghizadeh, “Form birefringence in nanostructured micro-optical devices,” Opt. Mater. Express 1(7), 1251–1261 (2011). [CrossRef]  

27. M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015). [CrossRef]  

28. A. Sihvola, Electromagnetic Mixing Formulas and Applications (The Institution of Electrical Engineers, 1999).

29. J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015). [CrossRef]  

30. Schott Glass Catalogue, 2003.

31. M. G. Shlyagin, A. V. Khomenko, and D. Tentori, “Birefringence dispersion measurement in optical fibers by wavelength scanning,” Opt. Lett. 20(8), 869–871 (1995). [CrossRef]   [PubMed]  

32. J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015). [CrossRef]  

33. P. Hlubina, M. Szpulak, D. Ciprian, T. Martynkien, and W. Urbanczyk, “Measurement of the group dispersion of the fundamental mode of holey fiber by white-light spectral interferometry,” Opt. Express 15(18), 11073–11081 (2007). [CrossRef]   [PubMed]  

34. K. Krzempek, G. Sobon, P. Kaczmarek, and K. M. Abramski, “A sub-100 fs stretched-pulse 205 MHz repetition rate passively mode-locked Er-doped all-fiber laser,” Laser Phys. Lett. 10(10), 105103 (2013). [CrossRef]  

35. M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18(14), 14778–14787 (2010). [CrossRef]   [PubMed]  

36. M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014). [CrossRef]   [PubMed]  

37. M. Klimczak, G. Soboń, K. Abramski, and R. Buczyński, “Spectral coherence in all-normal dispersion supercontinuum in presence of Raman scattering and direct seeding from sub-picosecond pump,” Opt. Express 22(26), 31635–31645 (2014). [CrossRef]   [PubMed]  

References

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  1. J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
    [Crossref]
  2. T. R. Wolinski, “Polarimetric optical fibers and sensors,” in Progress in Optics vol. XL, E. Wolf, ed. (North Holland, 2000).
  3. D. Penninckx, N. Beck, J.-F. Gleyze, and L. Videau, “Signal Propagation Over Polarization-Maintaining Fibers: Problem and Solutions,” J. Lightwave Technol. 24(11), 4197–4207 (2006).
    [Crossref]
  4. Z. Zhu and T. Brown, “Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,” Opt. Express 12(5), 791–796 (2004).
    [Crossref] [PubMed]
  5. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25(18), 1325–1327 (2000).
    [Crossref] [PubMed]
  6. F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer Netherlands, 2007).
  7. O. Frazão, J. Santos, F. Araujo, and L. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
    [Crossref]
  8. L. Wang and D. Yang, “Highly birefringent elliptical-hole rectangular-lattice photonic crystal fibers with modified air holes near the core,” Opt. Express 15(14), 8892–8897 (2007).
    [Crossref] [PubMed]
  9. T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
    [Crossref] [PubMed]
  10. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
    [Crossref]
  11. S. E. Kim, B. H. Kim, C. G. Lee, S. Lee, K. Oh, and C. S. Kee, “Elliptical defected core photonic crystal fiber with high birefringence and negative flattened dispersion,” Opt. Express 20(2), 1385–1391 (2012).
    [Crossref] [PubMed]
  12. M. J. Steel and R. M. Osgood., “Elliptical-hole photonic crystal fibers,” Opt. Lett. 26(4), 229–231 (2001).
    [Crossref] [PubMed]
  13. N. A. Issa, M. A. van Eijkelenborg, M. Fellew, F. Cox, G. Henry, and M. C. Large, “Fabrication and study of microstructured optical fibers with elliptical holes,” Opt. Lett. 29(12), 1336–1338 (2004).
    [Crossref] [PubMed]
  14. Y. Yue, G. Kai, Z. Wang, T. Sun, L. Jin, Y. Lu, C. Zhang, J. Liu, Y. Li, Y. Liu, S. Yuan, and X. Dong, “Highly birefringent elliptical-hole photonic crystal fiber with squeezed hexagonal lattice,” Opt. Lett. 32(5), 469–471 (2007).
    [Crossref] [PubMed]
  15. F. Beltrán-Mejía, G. Chesini, E. Silvestre, A. K. George, J. C. Knight, and C. M. Cordeiro, “Ultrahigh-birefringent squeezed lattice photonic crystal fiber with rotated elliptical air holes,” Opt. Lett. 35(4), 544–546 (2010).
    [Crossref] [PubMed]
  16. I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012).
    [Crossref]
  17. S. Ertman, M. Tefelska, M. Chylowski, A. Rodriquez, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and T. R. Wolinski, “Index guiding photonic liquid crystal fibers for practical applications,” J. Lightwave Technol. 30(8), 1208–1214 (2012).
    [Crossref]
  18. J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12(5), 956–960 (2004).
    [Crossref] [PubMed]
  19. P. Mergo, T. Martynkien, and W. Urbanczyk, “Polymer optical microstructured fiber with birefringence induced by stress-applying elements,” Opt. Lett. 39(10), 3018–3021 (2014).
    [Crossref] [PubMed]
  20. 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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
    [Crossref]
  21. B. Gu, W. Yuan, A. P. Zhang, and O. Bang, “All-solid birefringent hybrid photonic crystal fiber based interferometric sensor for measurement of strain and temperature,” Proc. SPIE 8311, 831121 (2011).
    [Crossref]
  22. R. Goto, S. D. Jackson, S. Fleming, B. T. Kuhlmey, B. J. Eggleton, and K. Himeno, “Birefringent all-solid hybrid microstructured fiber,” Opt. Express 16(23), 18752–18763 (2008).
    [Crossref] [PubMed]
  23. A. Cerqueira S, D. G. Lona, I. de Oliveira, H. E. Hernandez-Figueroa, and H. L. Fragnito, “Broadband single-polarization guidance in hybrid photonic crystal fibers,” Opt. Lett. 36(2), 133–135 (2011).
    [Crossref] [PubMed]
  24. R. Goto, S. D. Jackson, and K. Takenaga, “Single-polarization operation in birefringent all-solid hybrid microstructured fiber with additional stress applying parts,” Opt. Lett. 34(20), 3119–3121 (2009).
    [Crossref] [PubMed]
  25. A. Wang, A. George, J. Liu, and J. Knight, “Highly birefringent lamellar core fiber,” Opt. Express 13(16), 5988–5993 (2005).
    [Crossref] [PubMed]
  26. A. J. Waddie, R. Buczynski, F. Hudelist, J. Nowosielski, D. Pysz, R. Stepien, and M. R. Taghizadeh, “Form birefringence in nanostructured micro-optical devices,” Opt. Mater. Express 1(7), 1251–1261 (2011).
    [Crossref]
  27. M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015).
    [Crossref]
  28. A. Sihvola, Electromagnetic Mixing Formulas and Applications (The Institution of Electrical Engineers, 1999).
  29. J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
    [Crossref]
  30. Schott Glass Catalogue, 2003.
  31. M. G. Shlyagin, A. V. Khomenko, and D. Tentori, “Birefringence dispersion measurement in optical fibers by wavelength scanning,” Opt. Lett. 20(8), 869–871 (1995).
    [Crossref] [PubMed]
  32. J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
    [Crossref]
  33. P. Hlubina, M. Szpulak, D. Ciprian, T. Martynkien, and W. Urbanczyk, “Measurement of the group dispersion of the fundamental mode of holey fiber by white-light spectral interferometry,” Opt. Express 15(18), 11073–11081 (2007).
    [Crossref] [PubMed]
  34. K. Krzempek, G. Sobon, P. Kaczmarek, and K. M. Abramski, “A sub-100 fs stretched-pulse 205 MHz repetition rate passively mode-locked Er-doped all-fiber laser,” Laser Phys. Lett. 10(10), 105103 (2013).
    [Crossref]
  35. M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18(14), 14778–14787 (2010).
    [Crossref] [PubMed]
  36. M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014).
    [Crossref] [PubMed]
  37. M. Klimczak, G. Soboń, K. Abramski, and R. Buczyński, “Spectral coherence in all-normal dispersion supercontinuum in presence of Raman scattering and direct seeding from sub-picosecond pump,” Opt. Express 22(26), 31635–31645 (2014).
    [Crossref] [PubMed]

2015 (3)

M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015).
[Crossref]

J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
[Crossref]

J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
[Crossref]

2014 (3)

2013 (1)

K. Krzempek, G. Sobon, P. Kaczmarek, and K. M. Abramski, “A sub-100 fs stretched-pulse 205 MHz repetition rate passively mode-locked Er-doped all-fiber laser,” Laser Phys. Lett. 10(10), 105103 (2013).
[Crossref]

2012 (3)

2011 (3)

2010 (3)

2009 (2)

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

R. Goto, S. D. Jackson, and K. Takenaga, “Single-polarization operation in birefringent all-solid hybrid microstructured fiber with additional stress applying parts,” Opt. Lett. 34(20), 3119–3121 (2009).
[Crossref] [PubMed]

2008 (2)

R. Goto, S. D. Jackson, S. Fleming, B. T. Kuhlmey, B. J. Eggleton, and K. Himeno, “Birefringent all-solid hybrid microstructured fiber,” Opt. Express 16(23), 18752–18763 (2008).
[Crossref] [PubMed]

O. Frazão, J. Santos, F. Araujo, and L. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
[Crossref]

2007 (3)

2006 (1)

2005 (1)

2004 (3)

2001 (2)

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

M. J. Steel and R. M. Osgood., “Elliptical-hole photonic crystal fibers,” Opt. Lett. 26(4), 229–231 (2001).
[Crossref] [PubMed]

2000 (1)

1995 (1)

1986 (1)

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Abramski, K.

Abramski, K. M.

K. Krzempek, G. Sobon, P. Kaczmarek, and K. M. Abramski, “A sub-100 fs stretched-pulse 205 MHz repetition rate passively mode-locked Er-doped all-fiber laser,” Laser Phys. Lett. 10(10), 105103 (2013).
[Crossref]

Anuszkiewicz, A.

T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
[Crossref] [PubMed]

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

Araujo, F.

O. Frazão, J. Santos, F. Araujo, and L. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
[Crossref]

Arriaga, J.

Bang, O.

B. Gu, W. Yuan, A. P. Zhang, and O. Bang, “All-solid birefringent hybrid photonic crystal fiber based interferometric sensor for measurement of strain and temperature,” Proc. SPIE 8311, 831121 (2011).
[Crossref]

Beck, N.

Beltrán-Mejía, F.

Berghmans, F.

T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
[Crossref] [PubMed]

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

Birks, T. A.

Bjarklew, A.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

Broeng, J.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

Brown, T.

Buczynski, R.

J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
[Crossref]

M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015).
[Crossref]

J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
[Crossref]

M. Klimczak, G. Soboń, K. Abramski, and R. Buczyński, “Spectral coherence in all-normal dispersion supercontinuum in presence of Raman scattering and direct seeding from sub-picosecond pump,” Opt. Express 22(26), 31635–31645 (2014).
[Crossref] [PubMed]

M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014).
[Crossref] [PubMed]

I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012).
[Crossref]

S. Ertman, M. Tefelska, M. Chylowski, A. Rodriquez, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and T. R. Wolinski, “Index guiding photonic liquid crystal fibers for practical applications,” J. Lightwave Technol. 30(8), 1208–1214 (2012).
[Crossref]

A. J. Waddie, R. Buczynski, F. Hudelist, J. Nowosielski, D. Pysz, R. Stepien, and M. R. Taghizadeh, “Form birefringence in nanostructured micro-optical devices,” Opt. Mater. Express 1(7), 1251–1261 (2011).
[Crossref]

Cerqueira S, A.

Chesini, G.

Chylowski, M.

Cimek, J.

J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
[Crossref]

Ciprian, D.

Cordeiro, C. M.

Cox, F.

Dabrowski, R.

de Oliveira, I.

Dong, X.

Eggleton, B. J.

Ertman, S.

Fellew, M.

Ferreira, L.

O. Frazão, J. Santos, F. Araujo, and L. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
[Crossref]

Fleming, S.

Folkenberg, J.

Fragnito, H. L.

Frazão, O.

O. Frazão, J. Santos, F. Araujo, and L. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
[Crossref]

Frosz, M. H.

Geernaert, T.

George, A.

George, A. K.

Gleyze, J.-F.

Golojuch, G.

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

Goto, R.

Gu, B.

B. Gu, W. Yuan, A. P. Zhang, and O. Bang, “All-solid birefringent hybrid photonic crystal fiber based interferometric sensor for measurement of strain and temperature,” Proc. SPIE 8311, 831121 (2011).
[Crossref]

Hansen, T. P.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

Heidt, A.

Henry, G.

Hernandez-Figueroa, H. E.

Himeno, K.

Hlubina, P.

Hudelist, F.

Issa, N. A.

Jackson, S. D.

Jakobsen, C.

Jensen, J. R.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

Jin, L.

Kaczmarek, P.

K. Krzempek, G. Sobon, P. Kaczmarek, and K. M. Abramski, “A sub-100 fs stretched-pulse 205 MHz repetition rate passively mode-locked Er-doped all-fiber laser,” Laser Phys. Lett. 10(10), 105103 (2013).
[Crossref]

Kai, G.

Karpisz, T.

M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015).
[Crossref]

Kee, C. S.

Khomenko, A. V.

Kim, B. H.

Kim, S. E.

Klimczak, M.

M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015).
[Crossref]

J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
[Crossref]

M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014).
[Crossref] [PubMed]

M. Klimczak, G. Soboń, K. Abramski, and R. Buczyński, “Spectral coherence in all-normal dispersion supercontinuum in presence of Raman scattering and direct seeding from sub-picosecond pump,” Opt. Express 22(26), 31635–31645 (2014).
[Crossref] [PubMed]

Klimek, J.

Knight, J.

Knight, J. C.

Knudsen, E.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

Krzempek, K.

K. Krzempek, G. Sobon, P. Kaczmarek, and K. M. Abramski, “A sub-100 fs stretched-pulse 205 MHz repetition rate passively mode-locked Er-doped all-fiber laser,” Laser Phys. Lett. 10(10), 105103 (2013).
[Crossref]

Kuhlmey, B. T.

Kujawa, I.

J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
[Crossref]

M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015).
[Crossref]

I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012).
[Crossref]

Large, M. C.

Lee, C. G.

Lee, S.

Li, Y.

Libori, S. E. B.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

Liu, J.

Liu, Y.

Lona, D. G.

Lu, Y.

Makara, M.

T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
[Crossref] [PubMed]

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

Mangan, B. J.

Martynkien, T.

J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
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P. Mergo, T. Martynkien, and W. Urbanczyk, “Polymer optical microstructured fiber with birefringence induced by stress-applying elements,” Opt. Lett. 39(10), 3018–3021 (2014).
[Crossref] [PubMed]

I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012).
[Crossref]

T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
[Crossref] [PubMed]

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

P. Hlubina, M. Szpulak, D. Ciprian, T. Martynkien, and W. Urbanczyk, “Measurement of the group dispersion of the fundamental mode of holey fiber by white-light spectral interferometry,” Opt. Express 15(18), 11073–11081 (2007).
[Crossref] [PubMed]

Mergo, P.

Mortensen, N.

Nasilowski, T.

T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
[Crossref] [PubMed]

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

Nielsen, M.

Noda, J.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Nowinowski-Kruszelnicki, E.

Nowosielski, J.

Oh, K.

Okamoto, K.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Olszewski, J.

T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
[Crossref] [PubMed]

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

Ortigosa-Blanch, A.

Osgood, R. M.

Penninckx, D.

Pniewski, J.

Poturaj, K.

Pysz, D.

J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
[Crossref]

J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
[Crossref]

M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014).
[Crossref] [PubMed]

S. Ertman, M. Tefelska, M. Chylowski, A. Rodriquez, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and T. R. Wolinski, “Index guiding photonic liquid crystal fibers for practical applications,” J. Lightwave Technol. 30(8), 1208–1214 (2012).
[Crossref]

I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012).
[Crossref]

A. J. Waddie, R. Buczynski, F. Hudelist, J. Nowosielski, D. Pysz, R. Stepien, and M. R. Taghizadeh, “Form birefringence in nanostructured micro-optical devices,” Opt. Mater. Express 1(7), 1251–1261 (2011).
[Crossref]

Radzewicz, C.

Rodriquez, A.

Russell, P. St. J.

Sadowski, M.

I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012).
[Crossref]

Salski, B.

M. Swat, B. Salski, T. Karpisz, G. Stepniewski, I. Kujawa, M. Klimczak, and R. Buczynski, “Numerical analysis of a highly birefringent microstructured fiber with an anisotropic core,” Opt. Quantum Electron. 47(1), 77–88 (2015).
[Crossref]

Santos, J.

O. Frazão, J. Santos, F. Araujo, and L. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
[Crossref]

Sasaki, Y.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Shlyagin, M. G.

Silvestre, E.

Simonsen, H.

J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12(5), 956–960 (2004).
[Crossref] [PubMed]

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklew, J. R. Jensen, and H. Simonsen, “Highly brefringent index-guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13(6), 588–590 (2001).
[Crossref]

Siwicki, B.

Skibinski, P.

Skorupski, K.

Sobon, G.

M. Klimczak, G. Soboń, K. Abramski, and R. Buczyński, “Spectral coherence in all-normal dispersion supercontinuum in presence of Raman scattering and direct seeding from sub-picosecond pump,” Opt. Express 22(26), 31635–31645 (2014).
[Crossref] [PubMed]

K. Krzempek, G. Sobon, P. Kaczmarek, and K. M. Abramski, “A sub-100 fs stretched-pulse 205 MHz repetition rate passively mode-locked Er-doped all-fiber laser,” Laser Phys. Lett. 10(10), 105103 (2013).
[Crossref]

Sonnenfeld, C.

Statkiewicz-Barabach, G.

T. Martynkien, G. Statkiewicz-Barabach, J. Olszewski, J. Wojcik, P. Mergo, T. Geernaert, C. Sonnenfeld, A. Anuszkiewicz, M. K. Szczurowski, K. Tarnowski, M. Makara, K. Skorupski, J. Klimek, K. Poturaj, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure,” Opt. Express 18(14), 15113–15121 (2010).
[Crossref] [PubMed]

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, and H. Thienpont, “Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature,” Appl. Phys. B 94(4), 635–640 (2009).
[Crossref]

Steel, M. J.

Stefaniuk, T.

Stepien, R.

J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
[Crossref]

J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015).
[Crossref]

M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014).
[Crossref] [PubMed]

I. Kujawa, R. Buczynski, T. Martynkien, M. Sadowski, D. Pysz, R. Stepien, A. J. Waddie, and M. R. Taghizadeh, “Multiple defect core photonic crystal fiber with high birefringence induced by squeezed lattice with elliptical holes in soft glass,” Opt. Fiber Technol. 18(4), 220–225 (2012).
[Crossref]

A. J. Waddie, R. Buczynski, F. Hudelist, J. Nowosielski, D. Pysz, R. Stepien, and M. R. Taghizadeh, “Form birefringence in nanostructured micro-optical devices,” Opt. Mater. Express 1(7), 1251–1261 (2011).
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Figures (17)

Fig. 1
Fig. 1 Schematic of a fiber with anisotropic core. Anisotropic core composed of interleaved high-index and low-index glass strips. The lattice constant Λ is smaller than wavelength.
Fig. 2
Fig. 2 Material dispersion (a) and dispersion characteristics (b) of borosilicate glass NC21A and lead-silicate glass F2 and their relative difference.
Fig. 3
Fig. 3 A schematic of nanostructured core composed of 7 1D high refractive index strips (a). A central strip has a nano-defect in the center (b).
Fig. 4
Fig. 4 Calculated birefringence (a) for the fundamental mode and dispersion (b) of the polarized component of the fundamental mode for various lattice constants Λ between 300 and 500 nm. The polarization components Ex denotes direction of electric field vector along layers in the core (X axis), while Ey denotes direction of electric field vector perpendicular to layers in the core (Y axis).
Fig. 5
Fig. 5 Calculated phase and group birefringence for fundamental mode of the fiber with anisotropic core for ideal core structure with period of Λ = 0.5 µm and Λ = 0.45 µm and filling factor f = 1. The solid line denotes result for the structure without the central defect, and the dashed line denotes results for the central defect in the core.
Fig. 6
Fig. 6 Calculated dispersion for polarization components of the fundamental mode in the fiber with anisotropic core for ideal core structure with period of Λ = 500 nm and filling factor f = 1. Blue line denotes result for the structure without central defect, and red line denotes results for the fiber with central defect in the core 1.175 µm long.. Total size of the rectangular core is 3.25 µm × 6.00 µm.
Fig. 7
Fig. 7 Subpreform of the anisotropic core of the fiber.
Fig. 8
Fig. 8 SEM image of the birefringent fiber ZEB II/4 with nanostructured core a) cross section of the fiber, (b) rectangular nanostructured core.
Fig. 9
Fig. 9 Calculated phase (a) and group (b) birefringence for fundamental mode of the fiber with ideal anisotropic core with geometrical parameters based on SEM images (ZEBII/4 and ZEBII/6) for structure with and whithout nanodefect in the core.
Fig. 10
Fig. 10 Calculated dispersion for polarization components of the fundamental mode of the fiber with ideal anisotropic core with geometrical parameters based on SEM images (ZEBII/4 and ZEBII/6) for structure with and without nanodefect in the core.
Fig. 11
Fig. 11 Group birefringence measurement set-up.
Fig. 12
Fig. 12 Registered interferograms for the fundamental mode of the anisotropic core fiber ZEBII/4. Fiber length L = 95 mm.
Fig. 13
Fig. 13 Numerical simulation results of phase modal birefringence against the wavelength for the developed fiber based on SEM images (a). Experimental (points) and numerical simulation (lines) results of group modal birefringence spectral dependence (b).
Fig. 14
Fig. 14 The unbalanced Mach-Zehnder interferometer setup used for dispersion measurement (a), interference image (b).
Fig. 15
Fig. 15 Measurements of dispersion in the spectral range of 900-1700nm for fibers with anisotropic core ZEBII/4, and ZEBII/6 (a). Measured and calculated dispersion for birefringent fiber ZEBII/4 (b).
Fig. 16
Fig. 16 Attenuation measurement of anisotropic core fiber with F2/NC21A glasses.
Fig. 17
Fig. 17 Measured and simulated supercontinuum spectra for the structure of ZEB/II-6 fiber.

Tables (1)

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Table 1 Geometrical parameters of developed fibers

Equations (6)

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B = n x n y = λ 2 π ( β x β y ) .
G = B λ d B d λ .
D x = λ c d 2 n x d λ 2 , D y = λ c d 2 n y d λ 2 .
d Δ φ d λ Δ λ = ± 2 π ,
| G | = λ 0 2 Δ λ L ,
D = 1 c L d Δ L ( λ ) d λ ,

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