Point-by-point inscription of first-order fiber Bragg grating for C-band applications

The influence of the fiber geometry on the point-by-point inscription of fiber Bragg gratings using a femtosecond laser is highlighted. Fiber Bragg gratings with high spectral quality and strong first-order Bragg resonances within the C-band are achieved by optimizing the inscription process. Large birefringence (1.2×10-4) and high degree of polarizationdependent index modulation are observed in these gratings. Potential applications of these gratings in resonators are further illustrated.

A circular Malmquist-type index for measuring productivity

This paper develops two new indices for measuring productivity in multi-input multi-output situations. One index enables the measure of productivity change of a unit over time while the second index makes it possible to compare two units on productivity at the same or different points in time. Productivity in a single input single output context is defined as the ratio of output to input. In multi-input multi-output contexts this ratio is not defined. Instead, one of the methods traditionally used is the Malmquist Index of productivity change over time. This is computed by reference to the distances of the input-output bundles of a production unit at two different points in time from the efficient boundaries corresponding to those two points in time. The indices developed in this paper depart form the use of two different reference boundaries and instead they use a single reference boundary which in a sense is the most efficient boundary observed over two or more successive time periods. We discuss the assumptions which make possible the definition of such a single reference boundary and proceed to develop the two Malmquist-type indices for measuring productivity. One key advantage of using a single reference boundary is that the resulting index values are circular. That is it is possible to use the index values of successive time periods to derive an index value of productivity change over a time period of any length covered by successive index values or vice versa. Further, the use of a single reference boundary makes it possible to construct an index for comparing the productivities of two units either at the same or at two different points in time. This was not possible with the traditional Malmquist Index. We decompose both new indices into components which isolate production unit from industry or comparator unit effects. The components themselves like the indices developed are also circular. The components of the indices drill down to reveal more clearly the performance of each unit over time relative either to itself or to other units. The indices developed and their components are aimed at managers of production units to enable them to diagnose the performance of their units with a view to guiding them to improved performance.

Productivity change in the water industry in England and Wales:application of the meta-Malmquist Index

This paper uses a meta-Malmquist index for measuring productivity change of the water industry in England and Wales and compares this to the traditional Malmquist index. The meta-Malmquist index computes productivity change with reference to a meta-frontier, it is computationally simpler and it is circular. The analysis covers all 22 UK water companies in existence in 2007, using data over the period 1993–2007. We focus on operating expenditure in line with assessments in this field, which treat operating and capital expenditure as lacking substitutability. We find important improvements in productivity between 1993 and 2005, most of which were due to frontier shifts rather than catch up to the frontier by companies. After 2005, the productivity shows a declining trend. We further use the meta-Malmquist index to compare the productivities of companies at the same and at different points in time. This shows some interesting results relating to the productivity of each company relative to that of other companies over time, and also how the performance of each company relative to itself over 1993–2007 has evolved. The paper is grounded in the broad theory of methods for measuring productivity change, and more specifically on the use of circular Malmquist indices for that purpose. In this context, the contribution of the paper is methodological and applied. From the methodology perspective, the paper demonstrates the use of circular meta-Malmquist indices in a comparative context not only across companies but also within company across time. This type of within-company assessment using Malmquist indices has not been applied extensively and to the authors’ knowledge not to the UK water industry. From the application perspective, the paper throws light on the performance of UK water companies and assesses the potential impact of regulation on their performance. In this context, it updates the relevant literature using more recent data.

800 nm WDM interrogation system for strain, temperature, and refractive index sensing based on tilted fiber Bragg grating

A low-cost high-resolution wavelength-division-multiplexing (WDM) interrogation system operating around 800 nm region with operational bandwidth up to 60 nm and resolution of 12.7 pm utilizing a tilted fiber Bragg grating (TFBG) and a CCDarray detector has been implemented. The system has been evaluated for interrogating fiber Bragg grating based strain, temperature sensors, giving sensitivities of 0.59 pm/µe and 5.6 pm/°C, which are in good agreement with previously reported values. Furthermore, the system has been utilized to detect the refractive index change of sample liquids, demonstrating a capability of measuring index change as small as 10¯5. In addition, the vectorial expression of phase match condition and fabrication of TFBG have been discussed.

Point-by-point inscription of first-order fiber Bragg grating for C-band applications

The influence of the fiber geometry on the point-by-point inscription of fiber Bragg gratings using a femtosecond laser is highlighted. Fiber Bragg gratings with high spectral quality and strong first-order Bragg resonances within the C-band are achieved by optimizing the inscription process. Large birefringence (1.2x10-4) and high degree of polarizationdependent index modulation are observed in these gratings. Potential applications of these gratings in resonators are further illustrated. © 2007 Optical Society of America.

Tilted fibre Bragg grating based 800nm WDM interrogation system for strain, temperature and refractive index sensing

We report the implementation of a low-cost high-resolution WDM interrogation system operating around 800nm region with bandwidth up to 60 nm and resolution of 13 pm by utilising a tilted fibre Bragg grating as an out-coupling device and a CCD-array detector. The system has been evaluated for interrogating fibre Bragg grating based strain, temperature sensors, giving sensitivities of 0.6 pm/µe and 5.6 pm/°C which are in good agreement with previously reported values. Furthermore, the system has been utilised to detect refractive index change of sample liquids, demonstrating a capability of measuring index change as small as 10-5.

Fiber laser incorporating an intracavity micro-channel for refractive index and temperature sensing

In this letter, we present a standard linear cavity fiber laser incorporating a microchannel for refractive index (RI) and temperature sensing. The microchannel of ~6µm width created by femtosecond laser aided chemical etching provides an access to the external liquid; therefore, the laser cavity loss changes with the liquids of different RIs. Thus, at a fixed pump power, the output laser power will vary with the change of RI in the microchannel. The results show that the proposed sensing system has a linear response to both the surrounding medium RI and temperature. The RI sensitivity of the laser system is on the order of 10-3, while the temperature sensitivity is about 0.02 C. Both sensitivities could be further enhanced by employing a more sensitive photodetector and using higher pump power.

Fibre laser using a microchannel based loss tuning element for refractive index sensing

We have proposed and demonstrated a fibre laser system using a microchannel as a cavity loss tuning element for surrounding medium refractive index (SRI) sensing. A ~6µm width microchannel was created by femtosecond (fs) laser inscription assisted chemical etching in the cavity fibre, which offers a direct access to the external liquids. When the SRI changes, the microchannel behaves as a loss tuning element, hence modulating the laser cavity loss and output power. The results indicate that the presented laser sensing system has a linear response to the SRI with a sensitivity in the order of 10-5. Using higher pump power and more sensitive photodetector, the SRI sensitivity could be further enhanced.

Tilted fibre Bragg grating based 800nm WDM interrogation system for strain, temperature and refractive index sensing

We report the implementation of a low-cost high-resolution WDM interrogation system operating around 800nm region with bandwidth up to 60 nm and resolution of 13 pm by utilising a tilted fibre Bragg grating as an out-coupling device and a CCD-array detector. The system has been evaluated for interrogating fibre Bragg grating based strain, temperature sensors, giving sensitivities of 0.6 pm/µe and 5.6 pm/°C which are in good agreement with previously reported values. Furthermore, the system has been utilised to detect refractive index change of sample liquids, demonstrating a capability of measuring index change as small as 10-5.

The Point of Continuity Property: Descriptive Complexity and Ordinal Index

∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142

Hybrid tilted fiber grating based refractive index and liquid level sensing system

We report a refractive index (RI) and liquid level sensing system based on a hybrid grating structure comprising of a 45° and an 81° tilted fiber gratings (TFGs) that have been inscribed into a single mode fiber in series. In this structure, the 45°-TFG is used as a polarizer to filter out the transverse electric (TE) component and enable the 81°-TFG operating at single polarization for RI and level sensing. The experiment results show a lower temperature cross-sensitivity, only about 7.33 pm/°C, and a higher RI sensitivity, being around 180 nm/RIU at RI=1.345 and 926 nm/RIU at RI=1.412 region, which are significantly improved in comparison with long period fiber gratings. The hybrid grating structure has also been applied as a liquid level sensor, showing 3.06 dB/mm linear peak ratio sensitivity.