A hollow-core photonic band-gap fiber with very high group birefringence is fabricated and characterized. Two independent methods, wavelength scanning and direct measurement of differential group delay (DGD), are used to obtain the group beatlength and group birefringence. The fiber illustrates a very high group birefringence of 0.025 at 1550 nm. The wavelength dependence of the group beatlength and group birefringence are also analyzed.
©2004 Optical Society of America
Fibers with high birefringence are of significant research interest as they are expected to find many applications in optical communication systems, devices and fiber sensors. In conventional polarization maintaining (PM) fibers, high fiber birefringence is achieved by introducing anisotropy in the geometry or stress in the fiber profile . Fibers such as PANDA  and bow-tie fiber  achieve high birefringence through stress members while fibers with an elliptical core  and side air holes  reach the high birefringence through asymmetry in core geometry. For highly birefringent fibers that use geometrical anisotropy the birefringence is influenced by the index contrast between the high index core and low index region .
In recent years, alternative approaches for achieving high birefringence have been explored in the area of photonic crystal fibers (PCFs) since they can have a much higher refractive index contrast than conventional fibers [7–12]. Highly birefringent index-guiding PCFs with holes of different diameters along two orthogonal fiber axes or with asymmetric core designs have been proposed [7–11]. Highly birefringent photonic bandgap fibers (PBGFs) with asymmetric air cores have also been suggested . Numerical analysis indicates that birefringence as high as 10-3 is possible for both types of fibers. Measured birefringence values resulting from index-guiding PCFs, which are in the range of 10-4 to 10-3, have confirmed the numerical predictions [7, 9, 10]. No experimental efforts in achieving high birefringence in PBGFs have been reported, although experimental study on a birefringent PBGF with beatlength as short as 4 mm around 850 nm has been conducted . The level of the birefringence in Ref. has not exceeded that of conventional polarization maintaining fibers.
In this paper, we report on a highly birefringent PBGF. Fiber group birefringence of 0.025 at 1550 nm is demonstrated. To the best of our knowledge, this is the first experimental demonstration of such high level of group birefringence in microstructured fibers. Our focus in this paper is the group birefringence. The birefringence mentioned in the literature can either be group birefringence (beatlength) or phase birefringence (beatlength). However, since the difference in value between the two is usually within 10–15%, a fiber with high group birefringence also has high phase birefringence.
2. The highly birefringent photonic bandgap fiber and its characterization
Figure 1 shows the scanning electron micrograph (SEM) image of the cross section of the PBGF. In contrast to previous hollow-core PBGFs, we have intentionally altered the core to increase the anisotropy of the fiber profile. As can be seen in Fig. 1 the core has an anisotropic shape with two-fold symmetry, which is directly linked to the birefringence of the fiber. The core has a long axis of 9.4 µm and a short axis of 8.1 µm with an aspect ratio of 1.16. The photonic crystal structure (referred to as cladding) surrounding the core has a pitch (hole-to-hole distance) of ~4 µm. There are 8 to 9 rows of air holes surrounding the core. The overall fiber diameter is 120 µm. The transmission spectrum of this fiber is shown in Figure 2. The photonic bandgap extends from 1200 to 1700 nm with a dip around 1380 nm. The loss of the fiber in the wavelength range from 1500 to 1625 nm is around 1.5 dB/m.
We employ two independent methods, wavelength scanning and direct measurement of differential group delay (DGD) to obtain the group beatlength of the fiber under test.
First, we describe the measurement of the fiber group birefringence using the wavelength scanning method [14, 15]. Such method has recently been used to measure the group birefringence of photonic crystal fiber and its dependence on wavelength . The experimental setup is shown in Fig. 3. A broadband ASE source with a spectrum span from 1500 to 1625 nm is used. Since the light from the ASE source is randomly polarized, a polarizer is used to polarize the light launched into the sample fiber. In our experiment, a single mode fiber, which has a core diameter of around 12 µm, is butt-coupled with the PBGF and the polarized light was launched through the center. Since the size of the single mode fiber is similar to that of the PBGF, the light is predominantly coupled into the core region of the PBGF, which ensures that primarily only the core mode is excited. After the light passes through the fiber under test, a polarizer is used to analyze it. Because the sample fiber is highly birefringent, the state of polarization incident on the second polarizer is highly wavelength dependent, resulting in a modulation in the spectrum observed in the optical spectrum analyzer (OSA). The spacing of the modulation Δλ is related to the group beatlength and fiber length. The group beatlength is measured through the following simple equation,
where λ̄ is the center wavelength between the two peaks and L is the length of the sample fiber. In  it is suggested that both polarizers be aligned at 45 degrees to the birefringent axis of the fiber under test, we find that the period of the modulated signal is not affected by the polarizer orientations. Therefore, in our measurements, little effort was made to align the polarizers except that we ensured that sufficient modulation be observed.
Fiber birefringence is further calculated by the use of the OSA spectrum. In Figure 4, we show the optical spectrum collected by the OSA. The original OSA trace is processed to remove the spectral background. This is achieved by taking the difference between the OSA traces with and without the fiber under test. As the spectral modulation is very dense, the fine structure cannot be clearly shown when the whole spectrum is displayed. We thus expand the wavelength scale in the vicinity of 1520 nm, and 1580 nm as shown in Figure 4(b) and (c). Using Eq. (1), we obtain the group beatlength of the fiber at 1520 nm and 1580 nm to be 0.052 mm, and 0.075 mm, respectively. The group birefringence B, the group index difference between the two polarization modes, is related to the group beatlength by a simple equation,
Using Eq. (2), we obtain the birefringence of the sample to be 0.029 and 0.02 at 1520 nm and 1580 nm, respectively. To our knowledge, this is the highest fiber birefringence ever reported in the literature. Despite of very high birefringence, higher order mode that can be excited due to slight misalignment at the light launch end can negatively affect the polarization maintaining capability of the fiber. This fiber does not preserve polarization as well as conventional polarization maintaining fibers without a careful alignment.
We also study the wavelength dependence of the group beatlength and group birefringence. As shown by Figs. 4(b) and (c), and the resulting birefringence information, both the group beatlength and group birefringence of the fiber are wavelength dependent. To be able to obtain such information across the entire spectral range, we perform a windowed Fourier transformation of the data to retrieve the dominant fringe frequency around each wavelength. In Fig. 5(a) we show the normalized frequency as a function of wavelength. Actual period is obtained the by dividing the data spacing by the normalized frequency. It is found that for most of the wavelength range of interest, the dominant fringe frequency follows a clear trend. The step structure is due to the finite sampling interval used for the Fourier transformation and is an artifact resulting from this type of data processing. From 1528 to 1550 nm, no clear fringe frequency is observed. We believe that this may be related to significant change in the photonic band-gap structure. We further obtain the group beatlength and group birefringence in the range of 1550 to 1625 nm, which is shown in Fig. 5(b). A linear fitting of the fiber birefringence as a function of wavelength is conducted. The resulting equation takes the form, B=0.02546-0.000125(λ-1550), where λ is the wavelength in units of nanometers. Using this equation, we are able to predict the birefringence at a given wavelength. For example, the birefringence at 1550 nm is 0.025. In addition, we obtain the dependence of group beatlength on wavelength using this equation, which is also shown in Fig. 5(b).
In addition to the wavelength scanning measurement, we also conducted a measurement of differential group delay (DGD)  on essentially the same piece of fiber. In this measurement, the fiber length is 520 mm. The fiber used in the wavelength scanning method is cut short so that OSA has sufficient resolution to observe the spectral modulation. The measurement was conducted on a commercial PMD bench (Profile PAT9000B) at wavelengths from 1570 to 1620 nm based on Jones Matrix Eigen-analysis . The DGD results are shown in Fig. 6(a). Although the data look slightly noisy, a clear trend is exhibited. The DGD (τ) is directly related to the group beatlength and group birefringence by the following equation ,
where L is the length of the fiber under test and c is the speed of light in vacuum. Using Eq. (3) we calculate the fiber birefringence as shown in Fig. 6(b). For comparison, we also show the birefringence obtained by fitting the wavelength scanning data. Good agreement is achieved between the two methods.
A highly birefringent hollow-core photonic bandgap fiber is characterized. The fiber group birefringence properties were measured by two independent methods: wavelength scanning, and direct measurement of differential group delay. The fiber group beatlength and group birefringence have subsequently been calculated. Good agreement between the two methods is achieved. It is found that the fiber has a group birefringence of 0.025 at the wavelength of 1550nm. We also obtain an empirical equation describing the group birefringence as a function of wavelength.
To our knowledge, this is the first experimental work intentionally realizing high group birefringence in a hollow-core photonic band-gap fiber. The reported group birefringence is higher than all previously reported microstructured fibers, and is one order of magnitude higher than that predicted in a theoretical calculation . Understanding the discrepancy between our experimental results and the theoretical predictions represents a significant theoretical challenge. Note that in a typical PBGF, the refractive index span of a photonic band gap is on the order of 0.02. We believe that understanding the detailed theoretical mechanism of such a high level of group birefringence in hollow-core photonic band-gap fiber is a subject worthy of future research. Further effort along this line has been initiated.
This work was funded in part by DARPA under contract MDA972-02-3-0004. We also would like to thank Dirk Müller for some preliminary measurements in early stage of the work.
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