Fabrication of mid-index contrast ring resonators with a well-defined gap is very challenging, while gapless rings suffer from substantial coupling losses. To avoid these issues, we propose a gapless design based on a step-like structuring of the bus/ring waveguides. As we show with numerical simulations, our design allows to spatially confine the modes to the steps formed on the bus/ring waveguides thus mitigating the coupling losses. Additionally, the step on the ring waveguide reduces the bending losses. Finally, we show how varying the heights and widths of the steps allows to tailor the transmittance and quality factor of the ring.
Performance of multimode interference couplers is constrained by the phase errors caused by the deviations of the modes propagation constants from the required quadratic dependence upon mode number. In this work, we show that by creating a rectangular grating on the top surface of the coupler with a spatial frequency matching the intensity distribution of the i-th order mode, it is possible to control the phase errors of all spatial modes up to the i-th order. The effect of the grating on the propagation constants of higher-order modes is studied using perturbation-based and strict vector calculus. The efficacy of the method was demonstrated using numerical examples of an MMI-based two-mode (TE0 and TE1) coupler in the 1.31 μm wavelength region and the singlemode (TE0) 1.31/1.55 μm wavelength splitter, both made of medium index contrast material (TiO2:SiO2).
Numerical modeling of many optical-fiber-based devices' operation requires an exact knowledge of fiber's parameters like core diameter and dopant, usually GeO2, concentration. While diameters are typically specified in the fiber's data sheet, material composition, including dopant in the core, is rarely available. We present a procedure utilizing a reverse engineering approach to find GeO2 concentration in single-mode step-index optical fiber. Our method consists of several stages. First, we measured the numerical aperture NA for several commercially available fibers employing a onedimensional far-field scan. The far-filed mode intensity was acquired by a Ge detector placed on a rotation stage with a stepper motor for fiber end-face positioned on the motor's axis of rotation. We calculated NA for the angular detector position when the light intensity reached 13.5%, 5%, and 1% of its maximum value. Then, taking the corresponding values of core and cladding diameters and using the Sellmeier formula for pure (cladding) and GeO2 doped (core) silica glass, we found the concentration of GeO2 numerically matching calculated NA to the experimental data. We found that dopant concentration equals 9.0, 18.0, 34.0, 34.5, and 39.8 mol% for the fibers, respectively, 980-HP, UHNA1, UHNA3, UHNA4 and UHNA7 produced by Coherent. To verify the correctness of our method, we performed this procedure for several fibers with a known level of GeO2 concentration in the core fabricated by the Laboratory of Optical Fiber Technology, Maria Curie-Sklodowska University. The results of this simulation coincide with expectations with great accuracy.
We proposed a simple method of reducing bend-related loss and inter-mode crosstalk in two-mode ridge waveguide by step-like thickness structuring of bent section. It is already known that the effect of bend can be compensated by linear variation of the waveguide thickness or effective index, however, fabrication of such waveguides requires complicated technologies, which limits mass applications of such structures. We show that the two-step like structuring of the ridge waveguide thickness is sufficient to significantly reduce pure bending loss, bend-related inter-mode crosstalk and excess loss at the interface between straight and bent waveguides sections. Based on the rigorous numerical simulation conducted using transformation optics formalism, we determined the thickness change required to compensate for bend-induced effects and confirmed effectiveness of the proposed approach.
We present a novel method for determining a spectral phase derivative from a single spectral interferogram obtained by using a white-light interferometry technique, which is further used for calculation of chromatic dispersion profile. The method is based on direct calculations of a second derivative of the registered spectral intensity at extremal points. We explain theoretical background of the method, discuss its limitations and evaluate an accuracy by numerical simulations. Additionally, we validate the proposed method in dispersion measurements of the BK7 glass plate and the SMF-28 fiber.
Theoretical studies on Stokes polarimeter made of one twisted nematic crystal (TNLC) and one linear polarizer were carried out. Approaching the description of the TNLC theoretically, a model of Stokes polarimeter was created and its behavior was investigated in a numerical way. The minimization criterion of the condition number of the matrix describing the setup’s behavior was applied leading to the conclusion concerning the extension of the introduced by TNLC phase difference range up to 4π.
The intermodal sensitivity of a two-mode birefringent holey fiber to strain, temperature and hydrostatic pressure is measured in the spectral domain. In an experimental setup comprising a broadband source, a polarizer, a twomode birefringent holey fiber under a variable physical parameter, an analyzer and a compact spectrometer, the spectral interferograms are resolved. These are characterized by the equalization wavelength at which spectral interference fringes have the largest period due to the zero group optical path difference between the fundamental, the LP01 mode and the higher-order, the LP11 mode. The spectral interferograms are processed to retrieve the phase as a function of the wavelength. From the retrieved phase functions corresponding to different values of the physical parameter, the intermodal sensitivity as a function of wavelength is obtained. Using this approach, the intermodal sensitivity to strain, temperature and hydrostatic pressure is measured for two orthogonal (x and y) polarizations.
Polarimetric sensitivity of a birefringent holey fiber to strain, temperature and hydrostatic pressure is measured in the spectral domain. In an experimental setup comprising a broadband source, a polarizer, a birefringent holey fiber under a variable physical parameter, a birefringent delay line, an analyzer and a compact spectrometer, the spectral interferograms are resolved. These are characterized by the equalization wavelength at which spectral interference fringes have the largest period due to the zero overall group modal birefringence. The spectral interferograms are processed to retrieve the phase as a function of the wavelength. From the retrieved phase functions corresponding to different values of the physical parameter, the polarimetric sensitivity as a function of wavelength is obtained. Using this approach, the polarimetric sensitivity to strain, temperature and hydrostatic pressure is measured.
The spectral dependence of the polarimetric sensitivity of a birefringent side-hole fiber to temperature and hydrostatic pressure was measured using a simple experimental setup comprising a broadband source, a polarizer, a birefringent fiber under test, a birefringent delay line, an analyzer and a compact spectrometer. The spectral interferograms, characterized by the equalization wavelength at which spectral interference fringes have the highest visibility (the largest period) due to the zero overall group birefringence, were processed to retrieve the phase as a function of wavelength. First, from the retrieved phase functions corresponding to different temperatures of the fiber under test, the spectral polarimetric sensitivity to temperature was obtained. Second, from the retrieved phase functions corresponding to different hydrostatic pressures in a chamber with the fiber under test, the spectral polarimetric sensitivity to hydrostatic pressure was obtained.
In this paper, the strain sensitivity of a two-mode birefringent holey fiber is measured in the spectral domain. In a
simple experimental setup comprising a broadband source, a polarizer, a two-mode birefringent holey fiber under
varied elongations, an analyzer and a compact spectrometer, the spectral interferograms are resolved. These are
characterized by a specific wavelength, the equalization wavelength, at which spectral interference fringes have the
highest visibility (the largest period) due to the zero group optical path difference between the fundamental, the
LP01 mode and the higher-order, the LP11 mode. The spectral interferograms with the equalization wavelength
are processed by a new method to retrieve the phase as a function of the wavelength. From the retrieved phase
functions corresponding to different elongations of a two-mode birefringent holey fiber under test, the spectral
strain sensitivity is obtained. Using this approach, the intermodal spectral strain sensitivity was measured for
two orthogonal (x and y) polarizations.
We report on sensing characteristics of the rocking filter fabricated in specially designed microstructured fiber with
enhanced sensitivity to hydrostatic pressure. The filter shows a very high sensitivity to pressure ranging from 16.2 to
32.2 nm/MPa, depending on the resonance order. Extremely low cross-sensitivity between pressure and temperature
27÷66×103 K/MPa has also been recorded and therefore the rocking filter can be used for pressure measurements with
mbar resolution with no need for temperature compensation.
Microstructured optical fibers (MOFs) have been widely studied owing to their potential for obtaining novel
transmission, nonlinear and sensing characteristics. Sensing applications of MOFs cover various types of devices for
measurements of different physical and specific chemical compounds in gases and liquids employing evanescent field
techniques. Such fibers can also be used as active and passive elements in fiber-optic polarimetric and interferometric
sensors. We present an in-line fiber modal interferometer fabricated in boron-doped highly birefringent microstructured
fiber. The boron-doped region located in the middle of the core decreases the effective index of the fundamental mode
and facilitates coupling between the fundamental and the first order mode. The coupling regions have the form of fiber
narrowings fabricated using CO2 laser and are distant by a few millimeters. The spectral intensity at the sensor output is
modulated only by intermodal interference produced by a short piece of fiber between the two coupling points.
Moreover, as the fiber is highly birefringence, each pair of polarization modes produces its own intermodal fringes,
which results in the contrast modulation of the overall interference signal observed at the fiber output, and provides an
additional degree of freedom to measure simultaneously a pair of measurands.
The combination of the functionalities of Fiber Bragg Gratings (FBGs) and Photonic Crystal Fibers (PCFs) has unveiled
new potential for FBG based sensors. The fabrication of FBGs in PCFs has been reported in literature. However, using
dedicated PCFs to improve the sensitivity of FBG-based sensors has received only limited attention. In this report we
therefore show how to eliminate some of the drawbacks of FBGs in conventional step-index fibers for sensor
applications by exploiting the design flexibility of PCFs. The added value of PCFs stems from the ability to design an
optical fiber in which an FBG acts as a sensor with a selective sensitivity, e.g. a sensor that is sensitive to strain but not
to temperature. For this purpose we use a PCF with a birefringence on the order of 10-3, which is one order of magnitude
larger than for conventional birefringent fibers. The two FBG reflection peaks are therefore significantly separated from
each other, e.g. 2 nm, which makes these FBGs suited for sensing purposes since both peaks can be unambiguously and
accurately identified. As a conclusion we summarize the advantages and disadvantages of our approach to design and
fabricate selective FBG-based sensors.
We demonstrate that bending loss in large mode area photonic crystal fiber (LMA PCF) reveals a strong dependence of
the amplitude and location of the loss peaks on the bend radius and on the fiber angular orientation. To do so we
measured bending induced loss in LMA PCF as a function of wavelength in a broad spectral range (800-1500 nm) for
different bend radii and for different angular orientations of the fiber with respect to the bending plane. The oscillations
of bending loss with the bend radius and orientation are particularly well pronounced when the radiative component of
the fundamental mode is reflected from the flat boundary of the holey cladding. We also show the good agreement
between our measurement results and earlier simulations relying on a finite element method with perfectly matched
layers and equivalent index model.
We review exceptional properties of the photonic crystal fibres enabling sensing applications of this new class of fibres.
First, the sensing capabilities of highly birefringent index guided fibres are discussed. This includes dispersion
characteristics of phase and group modal birefringence in different fibre structures, and sensitivity of these parameters to
hydrostatic pressures and temperature. We demonstrate that index guided and photonic bandgap holey fibres of specific
construction can be used as wide-band fibre-optic polarizer. We also show that combining of geometrical and stress
effects makes it possible to design the holey fibres with either zero phase or group modal birefringence at virtually any
given wavelength. Finally, different designs and performance of PCFs suitable for gas sensing are overviewed.
We numerically analyzed the polarization effects in birefringent all-solid photonic bandgap fiber with different index
contrast between matrix and circular inclusions. The birefringence in the analyzed fibers is induced by elliptical shape of
the core composed of double defect in the hexagonal lattice of high index inclusions. Our simulations were fully
vectorial and based on a plane wave method and finite element method. We determined location of photonic bandgaps,
spectral dependence of phase and group modal birefringence, and confinement loss characteristics for different
polarization modes in three analyzed structures.
We investigated theoretically and experimentally the wavelength dependences of phase and group modal birefringence
for the fundamental (E11) and the higher order mode (E31) supported by index guiding highly birefringent photonic
crystal fiber. The birefringence in the investigated structure was induced by asymmetrical cladding consisting of one row
of cladding holes with a diameter lower than the other cladding holes. The numerical simulations carried out with use of
the full-vector finite elements method show that the birefringence of the E31 mode can be about 30% higher than of the
fundamental mode. Additionally, we measured the modal birefringence of the both modes using scanning wavelength
method. A comparatively good agreement between the calculation and experimental results was obtained confirming the validity of the theoretical analysis.
Microstructured fibers (MOF), also called photonic crystal fibers (PCF), constitute a class of optical fibers, which
has a large potential for number of novel applications either in the telecom or in the sensing domain. However, some of
the applications require the use of specialty fibers with a doped core. We have made a preliminary exploration of PCF
with doped regions and with inscribed Bragg gratings. The extensive study of the fiber cross-section structure in respect
to possibilities of writing the Bragg gratings and the sensitivities of PCF Bragg gratings was our main concern.
Selective measurement of strain without temperature compensation is achieved with fiber Bragg grating (FBG) in
highly birefringent (HB) PCF, since such grating is characterized by two reflection bands corresponding to the two
polarization modes generated due to the fiber birefringence. The measurement range of such FBG in HB fiber sensor
depends on how strong is the separation of the polarization modes, which is expressed as phase birefringence.
In next step, we have modeled, designed and fabricated specialty PCF with Ge doped core in such way that after
writing the Bragg grating into the fiber we have obtained a sensors exhibiting low sensitivity to any temperature drifts.
Traditional optical fiber sensors are not able to make such a distinction between stress and temperatures and require
complex temperature compensation mechanisms.
Paper presents technology manufacturing and basics parameters of photosensitive high birefringent photonic crystal fiber made from high silica glasses. It was especially elaborated for Bragg gratings inscriptions. Common photonic optical fibers have cores made from nondoped silica glasses. Therefore Bragg gratings inscriptions are difficult or impossible. In photosensitive photonic optical fibers cores are made from germanium doped silica glasses. In presented fiber core glass was made with MCVD method. Technology of manufacturing of high birefringent photonic crystal fibers are analogous to technology of manufacturing of common low birefringent holey fibers.
Fast, frequent, accurate and reliable measurements of physical factors such as temperature, stress or strain play a key role when it comes to ensuring the smooth operation of processes in many domestic, commercial and industrial constructions or devices. For example, most fabrication devices and production process rely on temperature and stress measurements to operate; and most large buildings depend on a series of temperature sensors to control the heating or cooling to maintain the temperature.
Photonic crystal fibres (PCF), constitute a class of optical fibres, which has a large potential for number of novel applications either in the telecom or in the sensing domain. Analysis of sensing characteristics of different photonic crystal fibre structures, including effective index and mode field distribution, photonic bandgap, chromatic dispersion, phase and group modal birefringence, confinement and bending losses, sensitivity to temperature, hydrostatic pressure, and other physical parameters are revealed.
The benefits of PCF allow fabrication of different types of specialty microstructured fibres such as endlessly single mode, double clad, germanium or rare earth doped, highly birefringent, and many other microstructured fibres as sensor components. The developed characterization techniques of specialty microstructured fibres are reviewed as well. Finally, the new microstructured fibres and fibre component for sensing applications which were designed, fabricated and characterized will be presented. One of the demonstrated components is the effective Bragg grating written in highly birefringent and single mode photonic crystal fibre.
We report on experimental studies of polarimetric sensitivity to temperature and hydrostatic pressure in two highly birefringent index guided photonic crystal fibers. Our results confirm earlier theoretical predictions indicating that polarimetric sensitivity to temperature in highly birefringent PCF with specific constriction can be very low. Proper choice of constructional parameters of the PCF can lead to complete temperature desensitization. On the other hand, relatively high polarimetric sensitivity to hydrostatic pressure in the analyzed structures make them good candidates for applications as active elements in hydrostatic pressure sensors.
We proposed and theoretically analyzed birefringent holey fibers of new construction. The birefringence in these fibers is induced by a highly asymmetrical cladding, which is composed of only two rows of large holes separated by one row of small holes The fiber cores have the form of single defects made of pure silica or containing GeO2 doped circular inclusion The geometries of both fibers were preliminarily optimized in order to assure minimum number of structural elements, while keeping the confinement losses of the fundamental mode below 1 dB/km. We used an edge finite element method to calculate the spectral dependence of the confinement losses and the phase birefringence. Due to small number of the cladding holes, the proposed fiber construction with GeO2 doped inclusion in the core region may be especially useful for inscription the Bragg gratings.
We report on research towards application of birefringent photonic crystal fibers as active and passive elements of fiber optic sensors for measurements of different physical parameters. Using experimental and theoretical methods, the sensing characteristics of different photonic structures are studied, including spectral behavior of phase and group modal birefringence, polarization dependent losses, sensitivity to temperature and hydrostatic pressure.
We numerically analyzed the polarization properties of two birefringent photonic bandgap holey fibers with different geometries. Our calculation method is fully vectorial and uses a hybrid edge/nodal finite element approach with PML absorbing boundary conditions. In both structures, we determined the spectral dependence of the phase modal birefringence and the spectral dependence of the losses for the fundamental modes of orthogonal polarizations. Our results show that the dependence of losses upon mode polarization is so high that both structures can be used as fiber polarizers.
We present a numerical investigation of fundamental and higher order modes propagating in doped core birefringent holey fiber. The conditions for the co-existence of two competing light guiding mechanisms, their consequences on the mode propagation and the potentialities for Bragg grating applications with this are discussed.
We measured and calculated the spectral dependence of the polarimetric sensitivity to temperature (dB/dT) in a photonic crystal holey fiber. The birefringence in this fiber is induced by the elliptical shape of the core, which consists of a triple defect in the hexagonal structure. Comparison of the temperature sensitivity measured for the bare fiber and for the fiber with polymer coating shows that the stress induced by the thermal expansion of the polymer contributes significantly to the overall temperature response. Measurements carried out for the bare fiber demonstrate that the temperature sensitivity has a positive sign and strongly increases vs. wavelength. Additionally, we present the results of calculations of the spectral dependence of dB/dT obtained using a finite element method. The calculated and measured values of dB/dT show relatively good agreement.
We analysed spectral dependence of modal birefrincence and susceptibility to temperature and to strain in two birefringent photonic bandgap fibers. The birefringence in these fibers is induced by the elliptical shape of either the core or the cladding holes. We show that in one of the fibres, the sensitivity to temperature nad to strain reaches zero in the center of the photonic bandgap. Our calculation method is fully vectorial and based on a hybrid edge/nodal finite element approach.
A construction of the polarizing holey fiber was optimized in order to assure maximum single polarization bandwidth. We demonstrated that the polarization bandwidth of the holey fiber can be increased up to 480 nanometers by properly choosing the fiber constructional parameters. A single-polarization operation in the analyzed structure was achieved by introducing a pair of air holes adjacent to the fiber core and having diameters greater than the cladding holes. Similarly to traditional polarizing fibers, the operation principle of the analyzed holey fiber is related to the difference in cut-off wavelengths of the two orthogonally polarized fundamental modes.
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