Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fibre

Reported are experimental results from investigations of the sensing properties of long-period gratings (LPGs) recorded in two different geometries of photonic crystal fibre (PCF): a large-mode area PCF and an endlessly single mode PCF. The LPGs have been characterised for their sensitivity to temperature, bending, surrounding index and strain. The LPGs in both fibres have been found to have negligible temperature sensitivity whilst exhibiting useful strain sensitivities. Strong directional bend sensitivity is shown by one PCF whilst the other shows good non-directional bend sensitivity. The fibres exhibit differing sensitivities to surrounding refractive index.

Temperature-insensitive long period grating sensors in photonic crystal fibre

A long period grating has been fabricated in endlessly single-mode photonic crystal fibre using a spatially-periodic electric arc discharge. The sensing characteristics of the grating have been studied and it was found to possess an insensitivity to temperature, a bend sensitivity of 3.7 nm · m and a strain sensitivity of -2.0 pm/µe.

Nondestructive index profiling of long period gratings in photonic crystal fibres

A numerical model of a long period grating in photonic crystal fibre fabricated by an electric arc is proposed that allows for the spectral characterisation of the grating. In the combination with the suggested model of the photonic crystal and the experimentally recorded grating growth it is used to find the index change induced by the electric arc.

Multiple period resonances in long period gratings in photonic crystal fibres

In order to characterise long period gratings fabricated in endlessly single mode photonic crystal fibres with bulk cladding we perform eigenanalysis of guided modes supported by these fibres. Resonant coupling occurs only when the beating length equals the multiple grating periods. Experimentally obtained grating spectra and sensitivity are fully explained using modified phase matching condition.

Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors

A series of symmetric and asymmetric LPGs were inscribed in photonic crystal fibre by a low repetition rate femtosecond laser system. The asymmetric LPGs were found to be spectrally sensitive to bend orientation, with some of the attenuation bands producing both red and blue wavelength shifts, whilst the symmetric devices produced only a unidirectional wavelength shift. Both sets of devices displayed strong polarisation dependence.

Sensing properties of femtosecond laser-inscribed long period gratings in photonic crystal fiber

The use of near infrared, high intensity femtosecond laser pulses for the inscription of long period fiber gratings in photonic crystal fiber is reported. The formation of grating structures in photonic crystal fiber is complicated by the fiber structure that allows wave-guidance but that impairs and scatters the femtosecond inscription beam. The effects of symmetric and asymmetric femtosecond laser inscriptions are compared and the polarization characteristics of long period gratings and their responses to external perturbations are reported.

Characterisation of femtosecond laser inscribed long period gratings in photonic crystal fibre

The use of high intensity femtosecond laser sources for inscribing fibre gratings has attained significant interest. The principal advantage of high-energy pulses is their ability for grating inscription in any material type without preprocessing or special core doping - the inscription process is controlled multi-photon absorption, void generation and subsequent local refractive index changes. The formation of grating structures in photonics crystal fibre has proven difficult, as the presence of holes within the fibre that allow wave-guidance impair and scatter the femtosecond inscription beam. Here we report on the consistent manufacture of long period gratings in endlessly single mode microstructure fibre and on their characterisation to external perturbations. Long period gratings are currently the subject of considerable research interest due to their potential applications as filters and as sensing devices, responsive to strain, temperature, bending and refractive index. Compared to the more mature fibre Bragg grating sensors, LPGs have more complex spectra, usually with broader spectral features. On the other hand they are intrinsically sensitive to bending and refractive index. Perhaps more importantly, the fibre design and choice of grating period can have a considerable influence over the sensitivity to the various parameters, for example allowing the creation of a bend sensor with minimal temperature cross-sensitivity. This control is not possible with FBG sensors. Here we compare the effects of symmetric and asymmetric femtosecond laser inscription.

Annealing and spectral characteristics of femtosecond laser inscribed long period gratings written into a photonic crystal fibre

A series of LPGs with the same period was inscribed by femtosecond laser into photonic crystal fibre with various powers. All suffered post-fabrication spectral evolution at low temperatures, apparently related to inscription power.

Comparison between femtosecond laser and fusion-arc inscribed long period gratings in photonic crystal fibre

The use of high intensity femtosecond laser sources for inscribing fibre gratings has attained significant interest. The principal advantage of high-energy pulses is their ability for grating inscription in any material type without preprocessing or special core doping. In the field of fibre optical sensing LPGs written in photonic crystal fibre have a distinct advantage of low temperature sensitivity over gratings written in conventional fibre and thus minimal temperature cross-sensitivity. Previous studies have indicated that LPGs written by a point-by-point inscription scheme using a low repetition femtosecond laser exhibit post-fabrication evolution leading to temporal instabilities at room temperatures with respect to spectral location, strength and birefringence of the attenuation bands. These spectral instabilities of LPGs are studied in photonic crystal fibres (endlessly single mode microstructure fibre) to moderately high temperatures 100°C to 200°C and their performance compared to fusion-arc fabricated LPG. Initial results suggest that the fusion-arc fabricated LPG demonstrate less spectral instability for a given constant and moderate temperature, and are similar to the results obtained when inscribed in a standard single mode fibre.

The spectral characteristics of femtosecond laser inscribed long period grating bend sensors written into a photonic crystal fibre

A series of LPGs was inscribed in photonic crystal fibre by a low repetition femtosecond laser system. When subjected to bending they were found to be spectrally sensitive to bend orientation and displayed a strong polarisation dependence.

Multiple period resonances in long period gratings in photonic crystal fibres

In order to characterise long period gratings fabricated in endlessly single mode photonic crystal fibres with bulk cladding we perform eigenanalysis of guided modes supported by these fibres. Resonant coupling occurs only when the beating length equals the multiple grating periods. Experimentally obtained grating spectra and sensitivity are fully explained using modified phase matching condition. © Springer 2006.

Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fibre

Reported are experimental results from investigations of the sensing properties of long-period gratings (LPGs) recorded in two different geometries of photonic crystal fibre (PCF): a large-mode area PCF and an endlessly single mode PCF. The LPGs have been characterised for their sensitivity to temperature, bending, surrounding index and strain. The LPGs in both fibres have been found to have negligible temperature sensitivity whilst exhibiting useful strain sensitivities. Strong directional bend sensitivity is shown by one PCF whilst the other shows good non-directional bend sensitivity. The fibres exhibit differing sensitivities to surrounding refractive index. © 2005 Elsevier B.V. All rights reserved.

Nondestructive index profiling of long period gratings in photonic crystal fibres

A numerical model of a long period grating in photonic crystal fibre fabricated by an electric arc is proposed that allows for the spectral characterisation of the grating. In the combination with the suggested model of the photonic crystal and the experimentally recorded grating growth it is used to find the index change induced by the electric arc. © Springer Science+Business Media B.V. 2007.