An elliptical core tellurite microstructured optical fiber with high birefringence was demonstrated and the chromatic dispersion of the two orthogonal modes in this fiber was experimentally characterized by a white light spectral interferometric technique over a wide spectral range. A series of spectral interferograms as a function of the optical path difference were recorded in the Mach-Zehnder interferometer. The birefringence dependence of the wavelength in the fiber was determined by interferograms. The measured and calculated dispersion matched well within the whole spectrum range under test.
© 2014 Optical Society of America
Polarization-maintaining elliptical core optical fibers have attracted considerable interest for a number of applications, including sensing of various physical quantities employing interferometric techniques [1, 2]. For these applications, it is important to know the dispersion of the group modal birefringence in the sample fiber. Several methods have been developed to measure the dispersion of optical fibers over a wide spectral range . Chromatic dispersion of long length optical fibers can be determined by two widely used methods: the time-of-flight method which measures relative temporal delays for pulses at different wavelengths, and the modulation phase shift technique which measures the phase delay of a modulated signal as a function of wavelength. White-light interferometer based on the use of a broadband source in combination with a standard Michelson or a Mach-Zehnder interferometer is considered as one of the best tools for dispersion characterization of short length optical fibers . This technique uses a series of the recorded spectral interferograms to resolve the equalization wavelengths at which the overall group optical path difference (OPD) is zero and finally to obtain the wavelength dependence of the intermodal group dispersion in the sample fiber.
Microstrured optical fiber (MOF) has an array of microscopic airholes running along its length. Compared with conventional fiber technology, the large index contrast and the two-dimensional nature of the microstructure greatly widen the range of waveguide parameters attainable. MOF can potentially be highly birefringent: The large index contrast facilitates high form birefringence, and the stack-and-draw fabrication process permits the formation of the required microstructure near the fiber core. Based on design flexibility and large refractive index contrast, various designs for achieving high birefringence are reported in case of MOF [5–7]. Non-silica MOFs using soft glasses such as tellurite and chalcogenide glasses have even larger refractive indices and nonlinearities, which make the high birefringence possible without special design for these kinds of fibers. But the nature of the soft glass has limited the complex structure of the tellurite fiber, making the fabrication of birefringent tellurite MOF difficult.
In this paper, we demonstrate for the first time to our best knowledge an elliptical core tellurite MOF with birefringence comparable with the commercial bow-tie or panda polarization-maintaining silica fiber. The technique of white-light spectral interferometry is extended to measure the dispersion of birefringence in this elliptical-core optical fiber over a wide spectral range. A series of the recorded spectral interferograms as a function of the OPD in a Michelson interferometer were recorded to obtain the wavelength dependence of group modal birefringence in this two orthogonal modes optical fiber. The measured and calculated dispersion of the fast axis and slow axis matched well within the whole spectrum range under test. Soliton generation along the fast axis and slow axis were performed by pumping close to zero dispersion wavelength (ZDW) in the normal dispersion region. The good fit of ZDW and soliton means that the polarization state of generated SC is well maintained along the polarization axis of the fiber.
2. Experimental method
The birefringence tellurite MOF we fabricated has an elliptical core surrounded by six ring holes. The composition of the tellurite glass was 76.5TeO2-6Bi2O3-11.5Li2O-6ZnO (mol%) [8, 9]. The preform was fabricated by the rod-in-tube and stacking method. Positive pressure was pumped into the holes in the fiber drawing process, the fabrication process was similar to reference  but with an elliptical core. Figure 1 shows the cross-section of MOF that was taken by microscope and scanning electron microscope (SEM). The core diameters are measured to be about 3.8 μm in the long axis and 2.5 μm in the short axis. The elliptical structure of the core makes the fiber birefringence and it could support two orthogonal modes, which can be referred as fast axis and slow axis.
Figure 2 shows the setup for measuring the chromatic dispersion of the MOF . It consists of two supercontinuum (SC) sources for measuring different wavelength ranges, a collimating lens, two IR fused silica plate beam splitters, a retroreflector fixed on a computer-controlled stepper motor, a microscope objective, two lens for fiber coupling, and two optical spectrum analyzers (OSAs) (Agilent 86142B, 600-1700 nm and Yokogawa AQ6375, 1200-2400 nm). In the test arm of the interferometer a combination of a microscope objective, a fiber sample under test and a collimating lens were inserted. While in the reference arm a retroreflector fixed on a computer-controlled stepper motor and two mirrors were used to compensate the optical path of the test arm. A polarization controller and a half-wave plate were used to adjust the polarization state of input beam to the axis of the fiber and enhance the interference of reference arm.
In order to obtain a high power and coherent light in a relatively wide wavelength range, especially in the near infrared range which covered most of the commercial available pump laser source, we developed an all-fiber high power broadband SC source using a highly nonlinear fiber (HNLF) with 10 dB bandwidth covered one octave from 1120 nm to 2245 nm . This home-made SC source and another commercial SC source (Fianium SC450, 450-1800nm), can be connected independently to the system to measure the chromatic dispersion of a sample fiber from the visible to mid-IR.
In the dispersion measurement system, the generated SC was split into two arms by the first beam-splitter. One beam was injected into the test arm of the Mach-Zehnder interferometer and coupled into the fiber under test. The other beam was injected into the reference arm in which the beam was reflected by the moving retroreflector and two mirrors. Both beams were combined by the second beam splitter. Then the combined beams were coupled into a single-mode fiber and recorded by the OSAs. With precise placement and alignment of the optical components in the test arm and the polarization state of the input beam, we can observe the interference fringes when the optical paths were exactly compensated for both arms. Interference fringes were recorded by the OSAs at different wavelengths by moving the positions of the stepper motor and the chromatic dispersion can be obtained by differentiating the measured positions to wavelengths of the interference fringes. The system was first tested for accuracy by a standard non-zero dispersion-shifted fiber (NZ-DSF) with a fiber length of 50 cm and compared with the result measured by the commercial optical dispersion analyzer (Agilent 86038A, 1440 nm-1640 nm) with a fiber length of 5 km. The dispersion profiles measured by the two systems were almost identical while our system had a very wide measurement range and only a very short fiber was needed.
3. Experimental results and discussion
A length of 33 cm long elliptical core tellurite MOF was selected and inserted into the test arm of the system. The unusual optical properties of the MOF cladding are accompanied by unique mechanical properties, making it difficult to measure the chromatic dispersion. According to the simulation of chromatic dispersion, this MOF is not single mode at 1.56 μm, but we could still excite primarily the fundamental mode using a 1.56 μm ASE source by adjusting the fiber couple condition. And then the input laser beam was changed to the SC sources to measure the chromatic dispersion in a very wide spectrum range. With precise placement and alignment of the optical components in both arms, we can observe the interference fringes when the optical paths were exactly compensated for both arms. In this elliptical core tellurite MOF, usually two fringes will appear first for the fast axis when the optical path compensation close to ZDW, the two fringes will move to the opposite directions while increasing the optical path of the reference arm. Then another two fringes will appear for the slow axis and move along with the optical path. Figure 3 shows the typical spectra for the four interference fringes recorded from OSA Yokogawa AQ6375. These interference fringes were recorded by the OSAs at different wavelengths by moving the positions of the stepper motor. A series of data points can be measured with optical path dependence on wavelength for this two-mode optical fiber. Figure 4 shows the data points recorded from interference fringes by moving the positions of the stepper motor. These data points were fitted with a polynomial by fourth order. Then the chromatic dispersion can be obtained by differentiating the optical path to wavelengths of the interference fringes as the fiber length was measured to be 33 cm.
The measured chromatic dispersion of the fast axis and slow axis are shown in Fig. 5. This fiber has a ZDW of 1606 nm at its fast axis and 1571 nm at slow axis. For comparison, the full-vectorial finite-difference method (FV-FDM) was used to simulate the chromatic dispersion and modal refractive indices of the two orthogonal modes. The simulations were performed based on material refractive index dispersion of the tellurite glass and cross-section image taken from SEM. The simulated results are shown in Fig. 6. The measured and calculated dispersion matched well within the whole spectrum range under test.
The strength of modal birefringence is defined by a dimensionless parameter 
For a given value of , the two modes exchange their power in a periodic fashion as they propagate inside the fiber with the period, which is defined as polarization beat length
Where and are the propagation constants of the two modes, and are the refractive index respectively, with shorter corresponding to stronger birefringence. Figure 7 shows the calculated modal refractive indices of two modes and the corresponding beat length. The beat length of this fiber is about 1.7 mm at wavelength of 1550 nm, with a of 9.2 . Although the nature of soft glass has limited the complex structure of the tellurite MOF, by making the fiber core elliptical in shape, the birefringence of this tellurite MOF becames comparable with the stress induced birefringence bow-tie or PANDA silica fiber (typical beat length is 2 mm). With an optimum design, even higher birefringence can potentially be made with tellurite MOF . This significant feature would be very useful in sensing technology using fiber birefringence.
To test the performance of the polarization-maintaining tellurite fiber, a section of MOF was pumped just on the left side of the ZDWs of the two modes with a polarized femtosecond mode-locked fiber laser centered at 1550 nm. A half-wave plate was inserted between the pump laser and fiber to adjust the polarization state of the input laser beam. A minimum power of 60 mW just beyond the threshold of SC generation was chosen to pump the fiber in normal dispersion region. The phenomena were the same with the SC generation pumped close to ZDW in normal dispersion region . Self phase modulation and Raman shift dominate the initial SC generation in the normal dispersion region. When the SC expends to longer wavelengths and hits the ZDW, the broadened pulse spectrum experiences opposite type of dispersion across the zero dispersion point. As discussed in reference , in the case of this fiber with a positive third-order dispersion (TOD), optical soliton will be formed by the red components of the pulse on the right side of ZDW in the anomalous dispersion region. However, a significant amount of pulse energy lies in the blue part falling in the normal dispersion domain. Figure 8 shows a clear soliton generation on the right side of ZDW when the polarization of the input pump beam was adjusted to the fast axis of the fiber. The starting position of soliton fits very well with the ZDW at 1606 nm. When the polarization was clockwise or anticlockwise rotated by 90 degree, which adjusted the polarization state to the slow axis of the fiber, the starting point of soliton became 1571 nm. Figure 9 shows the good fit of ZDW and the starting point of soliton in the slow axis. The good fit of ZDW and soliton means that the polarization state of the generated SC was well maintained along the slow axis of the fiber and precise measurement of chromatic dispersion were performed by our home-made system.
In conclusion, we demonstrate a highly birefringent tellurite MOF with elliptical core and the chromatic dispersion of two orthogonal modes in this fiber was precise measured by a white light spectral interferometric technique over a wide spectral range. Even without any stress induced birefringence design just making the fiber core elliptical in shape, the birefringence of this tellurite MOF is comparable with the standard commercial polarization-maintaining fiber. Soliton generation along the fast axis and slow axis were performed by pumping the fiber with femtosecond fiber laser close to ZDW in the normal dispersion region. The good fit of ZDW and soliton means that the polarization state of generated SC is well maintained along the axis of the fiber.
This research was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) under the Support Program for Forming Strategic Research Infrastructure (2011–2015).
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