Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency

We have applied the diffractive optics and digital holography technologies to the design and fabrication of fiber Bragg gratings (FBG). We studied the phase mask near field diffraction using the numerical simulation. Our new understanding on the phase mask has critical importance for fabrication of complex FBGs, such as the sampled grating DBR laser, multi-channel dispersion compensator, and phase-shift band-pass filters. In the design of the FBGs we introduced the phase-only sampling multi-channel FBGs using the Dammann diffractive grating, such that the maximum reflective index modulation required for <i>N</i> channels is only &#8730;<i>N</i> times of that for the single channel. We apply the discrete layer-peeling algorithm directly design the multi-channel FBGs, whose seed grating contains abrupt phase jumps in order to correct the channel distortions in the sampled multi-channel complex gratings. In addition, we introduced the iterative layer-peeling algorithm as a generic approach for the design of the FBGs. Our research provided a foundation of the advanced multichannel complex FBGs technology, which produces FBGs of very high channel count (45 channels and higher).

A fiber Bragg grating can be worked as reflector, it is constructed in a short section of optical fiber that reflects light of specific wavelength and allow to pass remaining wavelengths. This is possible by creating a periodic change in refractive index within the fiber core. The change in the modal index of fiber caused due to strain results in a Bragg wavelength. This work describes performance of Fiber Bragg Gratings as a strain sensor at 1550nm wavelength is considered for simulation, corresponding dynamic strain and wavelength shifts are analysed. This performance analysis is useful especially for intrusion detection system where environments are harsh. This sensor is compatible with data communication system and can be used for remote sensing.

Polymer optical fibers (POF) have received increased attention in recent years in the fields of data communication and sensing applications. The lower cost and higher flexibility are the main advantages of POF compared to silica fibers and make them interesting candidates for Fiber Bragg grating (FBG) sensor applications. FBG are convenient measurement devices for strain and temperature measurements, as they can be multiplexed within one fiber yielding a sensor array and the fiber can be embedded in structures. This work investigated the possibility of producing FBG in polymer fibers and their use as sensor units. It could be shown that using excimer laser irradiation at 308 nm, it is possible to write FBG in single-mode POF employing a standard phase mask, side writing technique. Index changes of up to 1.7 × 10-4 and reflectivies of up to 87% could be reached. The induced refractive index change due to pulsed UV irradiation was shown to be negative. The polymer material of the core (Polystyrene (PS) / Polymethyl methacrylate (PMMA)) was not sensitized prior to irradiation. During the grating formation an irradiation induced insertion loss of up to 11 dB/cm was observed. Excimer laser written FBG showed stability of over 9 months for approximately 40% of written FBG. Results of FBG writing using femto second laser irradiation showed FBG with reflectivities of up to 1.2 × 10-4, however these POFBG were not stable. The POFBG were characterized using optical low coherence reflectometry (OLCR) which enables to calculate the FBG location and length as well as the induced amplitude Δnac and mean refractive index change Δndc. Taking into account fiber and insertion losses, good agreement of these calculations and measurements were found. The results show that large variations of the induced index change result from irradiation. Local index change peaks of up to 4 times the mean value were observed, indicating inhomogeneity of the fiber material. Birefringence in the core of the POF (≈ 1.2 × 10-3) is up to a factor 3 higher than in the cladding which is due to the PS content within the core. The birefringence is due to inelastic strain and stress induced in the drawing process. Annealing, uniform irradiation and FBG writing using 308 nm excimer laser light induces a decrease of the absolute birefringence value. The changes upon irradiation are confined to the core of the fiber. Large variations in the initial and final birefringence before and after irradiation support the findings of the OLCR measurements indicating material inhomogeneities in the fiber. POFBG were found to be sensitive to relative humidity, temperature and strain. This is in contrast to glass fiber FBG which do not show humidity sensitivity. POFBG relative humidity sensitivity is non-linear with a change of up to 8 nm for a RH change of ≈ 100%. The non-linearity is introduced by a non-linear water sorption process. The POF grating response to temperature changes under dry conditions (1.5±1 % RH) is –10±0.5 pm/°C. The temperature response of the FBG submerged in water is –36±2 pm/°C due to an increased thermal expansion coefficient and a change in polarizability. Under ambient conditions the grating response to heating is typically ≈ –138 pm/°C, predominantly due to a change in POF swelling, i.e changes in relative humidity and POF water content. The diffusion coefficient of water in this POF at 23.5°C is 6.7 × 10-9cm2/s for sorption and 10 × 10-9cm2/s for desorption. Equilibrium of water content within the fiber and the surrounding air is typically reached after approximately one hour. Calculation showed that a reduction of the fiber diameter can increase this humidity sensitivity response time down to approximately 5 minutes for a fiber diameter of 25 µm.

Fiber Bragg gratings written using a phase-mask exhibit a complex refractive index pattern in the fiber core, as observed in differential interference contrast (DIC) microscopy. This results in dual periodicities along the fiber core and gratings at both the Bragg wavelength, twice the Bragg wavelength, and the harmonics of these. Features in grating spectra arise from one or both of these periodicities and spectra for twice the Bragg wavelength (or its odd harmonics) are very sensitive to the details of how the UV complex diffraction field of the phase mask becomes imprinted as refractive index changes in the fiber core.

We proposed and demonstrated a novel practical fiber Bragg grating (FBG) fabrication setup constructed with high performance linear stages, piezoelectric translation (PZT) stages, and a highly stable continuous wave laser. The FBG fabrication system enables writing of long FBGs by a continuous translate-and-write process and allows implementation of arbitrary chirp and apodization. A key innovation is that the local Bragg wavelength is controlled by a simple movement of the phase mask by a PZT in the direction perpendicular to its surface. The focus position of the two writing beams is not changed during the Bragg wavelength change, an intrinsic feature of the design, ensuring simplicity, robustness and stability. Apodization can be achieved by vibrating the phase mask in the direction parallel to its surface by a PZT. Phase steps can also be inserted in FBGs at any desired locations by stepping the same PZT. A long uniform FBG and a linearly chirped FBG are written to demonstrate the performance of the setup.

Wavelength independent chemical sensing using etched thermally regenerated FBG

Results are presented on the photosensitivity behavior of a phosphate glass optical fibre using 248nm, 500fs laser radiation. Bragg grating exposures performed using a double phase mask interferometer and peak intensities of 0.37TW/cm2, revealed that grating growth becomes non-monotonic in terms of average and modulated refractive index changes, resembling the Type IIA photosensitivity behavior. Average refractive index changes greater than 10−3 were measured after accumulated energy density doses of 6.5KJ/cm2. The Bragg gratings inscribed maintained significant part of their strength up to 377°C. Exposed and side-polished fibre samples were subjected to Knoop micro-hardness measurements for revealing that the irradiated glass undergoes significant volume dilation.

Due to the limitations of measurement equipment and the influence of factors such as the environment and target, measurement errors may occur during the data acquisition process of airborne LiDAR bathymetry (ALB). The refractive index of water is defined as the propagation ratio of the speed of light waves in a vacuum to that in water; this ratio influences not only the propagation speed of the laser pulse in water but also the propagation direction of the laser pulse entering water. Therefore, the influence of refractive index changes in water on the ALB errors needs to be analyzed. To this end, the principle of ALB is first briefly introduced. Then, the calculation method for the refractive index of water is described with Snell’s law and an empirical formula. Finally, the influence of refractive index changes on ALB errors is analyzed using the derived formula at the water–air interface and in the water column. The experimental results showed that in a constant elevation of 50 m for a bathymetric floor, the refractive index changes in water caused by temperature, salinity, and depth are less than 0.001. The maximum bathymetric error and maximum planimetric error caused by the refractive index changes at the water–air interface are 0.036 m and 0.015 m, respectively. The ALB errors caused by refractive index changes in the water column are relatively low, and the water column does not need to be layered to calculate the ALB errors. The influence of refractive index changes in water on the ALB error is minimal, accounting for only a small proportion of all bathymetric errors. Thus, it is necessary to determine whether the effect of the ALB error due to refractive index changes in water needs to be corrected based on the accuracy requirements of the data acquisition. This study and analysis can provide a reference basis for correcting ALB errors.

Amongst the most important and frequently used fibre devices, fibre Bragg and long-period gratings are conventionally fabricated by low-intensity (I < 107 W cm−2) UV quanta with an energy of about 5 eV, which coincides with the maximum of the absorption band of defects in germanosilicate glass (the usual material of a fibre core). Such a single-quantum photochemical technique produces refractive index changes in the fibre core and not in the fibre cladding. The use of single-quantum excitation with high-energy vacuum UV photons with 157 nm wavelength or two-quantum 193 nm excitation through the real intermediate state results in a higher excitation energy (7.9 and 12.8 eV, respectively) and significantly increases the efficiency of grating inscription. However, neither of these high-energy approaches is free of disadvantages: the 157 nm radiation is strongly absorbed by practically all optical materials and even by air; the application of the second approach is based on the existence of an intermediate state, i.e. presence of absorption at the irradiation wavelength. The new multi-photon high-excitation-energy approach to fibre grating fabrication is based on refractive index change modification by high-intensity (I ∼ 1011–1013 W cm−2) femtosecond UV, near-UV or IR laser radiation applied to fibre, which acquires a total excitation energy of about 8–12 eV via two-, three- or even five-photon (through the intermediate virtual state/states) absorption processes. Such a high value of excitation energy exceeds the band-gap energy values for both the fibre core and the cladding, which could result in asymmetric light energy deposition inside the fibre and even inside the fibre core. We will consider the advantages of this novel technique such as grating fabrication in fibres of any content, including photonic crystal ones; the writing of extremely stable gratings with erasing temperatures above 1000 °C; the point-by-point inscription of Bragg gratings, including non-uniform ‘chirped’ ones; the creation of fibre gratings with high polarization properties; etc.

Mach–Zehnder interferometer cascaded with FBG for simultaneous measurement of RI and temperature

Plane-by-plane fabrication of fiber Bragg gratings in optical fibers using short-pulse femtosecond IR laser is proposed and demonstrated. By incorporating a cylindrical lens in the fabrication setup, a plane of index modification can be directly inscribed in fiber core by a single laser pulse through the proposed method. This plane-by-plane method simplifies the grating inscription process and allows for the fabrication of complicated grating structures.

This study explores how hydrostatic pressure, temperature, incident light intensity, and structural parameters modulate optical absorption coefficients and refractive index changes in GaAs/Al0.3Ga0.7As spherical quantum dots under the screened cosine Kratzer potential. We use the Nikiforov-Uvarov method to solve the Schrödinger equation to determine the relevant wave functions and energy levels. And using iterative method and density matrix theory, we derived analytical expressions for the optical absorption coefficients and refractive index changes. The results of the numerical analyses demonstrate that both the structural parameters of the quantum dots and the external environmental factors significantly influence the optical absorption coefficients and refractive index changes, with varying degrees of impact. It is particularly noteworthy that these factors are extremely important for modulating the peak amplitude and resonance peak position of the optical absorption coefficients and refractive index changes, providing important theoretical basis for us to deeply understand and modulate the nonlinear optical properties of quantum dots.

Intersubband optical absorption coefficients and refractive index changes in modulation-doped asymmetric double quantum well

Theoretical and experimental study of refractive index sensors based on etched fiber Bragg gratings

To remove or reduce the cladding layer thickness of fiber Bragg grating, the refractive index changes in the surrounding environment will affect the fiber Bragg grating effective refractive index of the core, resulting in changes in the Bragg wavelength. Solution concentration changes will cause changes in refractive index of the solution. A new kind of solution concentration sensor is designed with the etched phase shifted fiber Bragg grating, and concentration sensing detection with four kinds of solutions is experimentally demonstrated. With resolution concentration increasing, the phase shifted label wavelength shifts to the red, and the sensor is more sensitive in the case of higher concentration.