The "glowing"optical fibre designs and parameters

The "glowing" optical fibre designs and parameters

Janis Spigulis, Daumants Pfafrods*, Maris Stafeckis*, and Wanda Jelinska-Platace

University of Latvia, Raina Blvd. 19, Riga, LV-1586, Latvia

*ANDA OPTEC Ltd., P.O. Box 326, Livani, LV-5316, Latvia

ABSTRACT

Side-emittive optical fibre designs and main parameters have been studied. A simplified model to describe emission of the "glowing" fibre is developed. Basic expressions for the emission parameters as functions of the input radiation intensity, distance along the fibre axis and scattering efficiency longitudinal distribution are given for several design modifications. The model assumptions have been checked experimentally by testing silica core side-glowing optical fibre samples.

Keywords: specialty optical fibres, linear illumination/irradiation sources.

1. INTRODUCTION

Optical fibres originally are supposed to transmit the introduced light energy with minimum losses to their distal ends which emit like semi-point light sources. However, optical fibres can also serve as linear or semi-linear light sources, if special efforts are undertaken to stimulate the core-transmitted light leakage through the fibre side surface. Several methods can be used to provide such side-glowing effect, including multiple microbending of the fibre axis ¹, mixing extra scattering or fluorescent additives into the fibre core or cladding material ^2,3, creating assymetries in the fibre core/cladding geometry ⁴, increasing the refractive index of the fibre cladding material above that of the core material ⁵, etc.

Simple model describing quantitatively the optical fibre side-emission is presented and discussed here. The model has been checked experimentally by testing the "glowing" optical fibre samples with pure silica core covered by plastic clad with scattering additives ^2,6. The fibre side-emission parameters have been measured and compared with the calculated ones, and several application aspects have been discussed.

2. THE MODEL REPRESENTATION

A correct description of light propagation in “glowing” optical fibre should take into account all channels of photon transport and losses, including transmission, absorption and scattering in fibre core, cladding and external coating materials, as well as reverse scatterings and luminescence. Proposing that side-scattering in this kind of fibre is much stronger than absorption and other losses, only core-transmission and side-scattering can be regarded as two dominant light transport channels (no matter which type of the “glowing” fibre is it). Consequently, the basic assumptions of our simplified physical model can be formulated as follows:

1. Side scattering is the only considerable mechanism causing the losses of the fibre core-transmitted radiation.

2. All initially scattered photons are penetrating the fibre cylindrical side surface without losses, and subsequently emitted isotropically into the surrounding space.

The radiation intensityI_TX which is transmitted through a short fibre core fragment of length Dx (Fig. 1) then can be expressed as

I_TX = I₀ exp (- k Dx) (1),

where I₀ is the input radiation intensity, and k is the side-scattering efficiency coefficient. The side-glowing intensity emitted from this fibre fragment at any direction per steradian in this case is

I_S= (4 p)^-1 I₀ [1 - exp (- k Dx)] (2).

Several design modifications of the glowing fibres will be regarded from this point in the next paragraphs.

2.1. Fibres with fixed side-scattering efficiency.

First let us concentrate on constantly scattering optical fibres (CSOF), whose side-scattering efficiency coefficient k is kept constant along the whole fibre length. This fibre can be represented as a sequence of numerous identical fragments like that shown on Fig. 1. Following (2), the side-glowing intensity as a function of the actual fibre length x can be expressed as:

I_S (x) = A exp (- k x) (3),

where the constant A, proposing Dx to be the fibre length unit (Dx = 1), is

A = (4 p)^-1 I₀ (exp k - 1) (4).

The comparision of (1) and (3) leads to conclusion that for CSOF both the core-transmitted and side-emitted radiation intensities are decaying exponentially as fibre length functions with the same rate constant k. This is illustrated at Fig. 2 for three fixed k-values.

Such inevitable decay causes some practical problems, since many real applications of “glowing” fibres (e. g. for linear decorative illumination) require uniform side-glowing intensity, or at least very limited variations of this intensity along particular fibre length. Therefore our model considerations can appear useful to increase the uniformity of the side-glowing intensity for several CSOF design versions.

2.1.1. Single light source version: optimum k-value for the given fibre length and glowing uniformity limit.

The simpliest fibre illumination version is to couple one end of it with appropriate light source, e. g. laser. If the fibre length and desired side-glowing uniformity are given, the optimum k-value of CSOF can be easily found using the expression (3). For example, let us suppose that the required uniformity interval for a 10 m long glowing distance lies within 20 % interval of the initial side-glowing intensity. To find the optimum k-value, one should solve the equation for the lower intensity limit (80 %): exp (-10 k) = 0.8, which gives k = - (ln 0.8) : 10 = 0.023 m^-1.

This design version, however, is not highly efficient from the point of input radiation conversion into the side-glowing: in relatively uniformly-glowing CSOFs most of the introduced light energy passes through the fibre distal ends instead of being scattered via the side surface. For instance, only 20 % of the input intensity will be emitted by the whole fibre side surface in the above regarded situation. Generally speaking, high side-glowing uniformity of a single-light-souce-coupled CSOF is always accopanied by low light conversion efficiency and considerable radiant energy losses.

2.1.2. Use of two light sources at each end of the fibre.

Attachment of light sources at both fibre ends may look somewhat more complicated technically, but this version

provides more uniform and more intense side-glowing if compared with the above regarded case. In frame of the present model, side emissions initiated by both sources are to be summarized. Let us assume that the intensities of radiation coupled into the fibre core at each end of the fibre are equal (say I_o), and the length of the given fibre fragment is L. Then the total side-emission intensity at fixed spatial direction as a fibre length function is

I_S2 (x) = A{ exp(- k x) + exp[- k (L - x)]} (5),

where A is given by (4).

The calculated I_S2 (x) distribution (5) along a 100 m fibre fragment with fixed k-value (0.01 m^-1) is presented on Fig. 3. One must note that when using real light sources, the intensity levels launched into optical fibre from both ends can differ substantially, even if identical light sources are used. It depends mainly on coupling efficiency and must be chequed experimentally. Other radiation parameters, e. g. light colour or time modulation frequency, can be different for each of the terminal sources, as well.

2.1.3. Use of a reflector at the distal end of fibre.

Mounting of an integrated reflector, e. g. a miniature plane mirror, on the distal end of CSOF can also efficiently increase the light output and uniformity of the side-emitted intensity. If the distal reflectivity R and the fibre length L are known, the side-emission intensity at each actual distance x from the input end can be calculated (3):

I_SR (x) = A {exp(- k x) + R exp[- k (2L - x)]} (6),

where A is defined by (4). For illustration, the calculated I_SR (x) distribution curves for 50 m long glowing-fibre fragment with 100 % reflective mirror are presented on Fig. 4.

For practical applications of (6) one must note that the real R-value strongly depends on the technology how the mirror is attached to the fibre end and how good is the end surface quality. Therefore, even if the mirror reflectivity is known, an experimental determination of the R-value after the mirror attachment procedure would be recommended.

2.2. Fibres with distributed side-scattering efficiency.

Non-uniform distribution of the k-value along the fibre length can appear useful for two main applications:

(i) to provide "bursts" of side-emission at specific limited fibre locations - e. g. close to the fibre distal end for laser therapy (PDT), regularly or randomly spread "glowing points" for decorative illumination, etc.;

(ii) to provide uniform side-glowing intensity along the whole length of the fiber.

Designs adjusted for the first application ⁶ are based on substantial increase of agents responsible for side-scattering at the respective fibre locations. As for the second application, some interesting features can be studied in frame of our simplified model.

Uniformity of side-glowing intensity along the whole fibre length means that all neighbouring fibre fragments like the one of Fig. 1, each with its own k-value, is side-emiting the same intensity I_S. Following (2), it can be expressed as:

I_S = (4 p)^-1 I₀ [1 - exp(- k_iDx)] = (4 p)^-1 I₀ [1 - exp(- k_i+1 Dx)] (7),

where i is an arbitrary fibre fragment number. Considering that each fibre fragment is of unit length (Dx = 1), a simple condition for the k-values of neighbouring fibre fragments follows after conversions:

k_i+1 = - ln (2 - exp k_i) (8).

The scattering efficiency distribution function k (x) calculated accordingly to (8) is presented on Fig. 5. It is rapidly increasing with the fibre actual length x, therefore the core-transmitted intensity decreases faster if compared with that of the CSOF design. The calculations of I_T(x) in this case resulted as linear response (Fig. 6). This figure also illustrates how different the functions I_S(x) and I_T(x) are for uniformly glowing fibres with distributed k-values, in contrary to the previously regarded CSOF design.

As for the light conversion efficiency in uniformly glowing fibres of this design, figures around 80 % might be achievable. The 100 % conversion looks doubtful due to very steep increase of the k-value with fibre length (Fig. 5). A certain technological limit of increasing the scattering efficiency in fibre will always take place; however, 5-fold increase of k-value (which seems realistic) provides 80 % light conversion efficiency - much higher than that in the CSOF case. As for the uniformly glowing length, it is generally determined by choise of the initial k-value of the fibre. For instance, following Fig. 6, at k₀ = 0.01 m^-1 around 80 % of the introduced radiation intensity is to be "pumped out" via the fibre side surface by passing the distance of 80 m. Since the dimensions given on both axis at Fig. 5 are mutually invertable, the same concerns also to 8 m long glowing distance in fibre with k₀= 0.1 m^-1, or to 0.8 m long fibre with k₀= 1.0 m^-1.

3. EXPERIMENTAL

3.1. The experimental set-up.

Block diagram of the experimental set-up is presented on Fig. 7. A stabilized He-Ne laser beam was focused by lens L into the silica core of a “glowing” fibre sample GFS, which was fixed on adjustable holder H. Both distal end radiation and side-emission at various distances from the fibre input end have been detected simultaneously by silicon photodiodes PD1 and PD2, respectively. The distal end emission signal from PD1 was registered by a digital voltmeter V. The side-emission initiated photoelectric signals from PD2 entered the amplitude-to-digital converter ADC and further were directly stored in the IBM/PC memory. The side-glowing detector PD2 had large (12 mm in diameter) photosensitive area and was hidden inside a dark chamber C; it was closely contacting the fibre side surface during the measurements.

Total optical attenuation of the fibre samples was also measured by means of PD1 using the conventional “cut-off “

Fig. 7. Block diagram of the experimental set-up.

method. Besides, radiation losses caused by external mechanical pressure applied perpendicularly to the “glowing” fibreaxis have been investigated by loading the crossing point of single fibre loop placed between two horizontal plates.

The CSOF-type fibre samples of length around 30 m, with silica core diameters of 200, 400, 600 and 800 microns and various side-scattering efficiencies have been studied; they all were manufactured in ANDA OPTEC Ltd. (Latvia) by a patented ² technology.

3.2. Results of the measurements.

The side-glowing intensity decrease with fibre length measured in this experiment confirmed the expected exponential character of the decay function (3) for all studied samples. The corresponding k-values obtained that way fitted satisfactory with those measured by the “cut-off” method. For illustration, the measured side-glowing intensity dependences on actual fibre length for two samples with equal core diameter 400 microns and different scattering efficiencies are presented on Fig. 8. The dashed lines represent calculated intensity decays if the respective k-values obtained from the “cut-off” measurements are used. In both cases the solid and dashed line slopes determined by the k-value fit within the 10 % interval of measurement accuracy. As for the determined numerical k-values for other samples, they ranged between 0.02 m^-1 and 0.13 m^-1 in this experiment. Certain correlation between the side-scattering efficiency and scatterer concentration in the “glowing” fibre cladding has been observed.

Rather unexpected, significantly higher sensitivity to external mechanical pressure was observed for the "glowing" optical fibres of our design if compared to the conventionally designed PCS fibres of the same dimensions. For the case of 400 micron core diameter (k = 0.029 m^-1) this is illustrated on Fig. 9. Attention must be paid to the fact that the same relative intensity drop with increasing mechanical load took place at both distal end- and side-radiations. The side glowing intensity changes were clearly seen visually if someone stepped on the fibre sample laying on the floor.

Fig. 8. Typical side-glowing intensity decay with the

fibre length (in semilogarithmic scale).

Fig. 9. Radiation losses in conventional (PCS) and glowing

(GF) optical fibres as the mechanical load function.

4. SUMMARY

The recently developed flexible “glowing” optical fibres have good potential for future applications in several areas, including:

- decorative linear illumination for interiors, shows, Christmas trees, etc.,

- framing of large objects like buildings, towers and bridges,

- emergency light guidance for tunnells, corridors, stairs, etc.,

- safe underwater illumination and framing,

- luminous signs and high-power laser demonstrations,

- infrared security control and surveillance,

- local phototherapy for treatment of tumors, infant Hyperbilirubinemia and skin diseases,

- single-fibre laser Doppler blood flowmetry,

- linear “cold light” illumination for biomedical applications.

Successful fibre designs for the above applications would be possible only taking into account the main parameters and limiting factors of this specific kind of fibre. To the knowledge of authors, no physical models of “glowing” fibres have been discussed in literature before. The simplified model presented in this work can be useful for better understanding of the light transport mechanism in “glowing” optical fibres and for quantitative characterization of their basic properties and quality. It gives also new knowledge how to achieve better uniformity of the side-glowing intensity.

The obtained model expressions were in general agreement with the experimental results when using fibre samples designed by the original ANDA OPTEC Ltd. technology. Even more, an unexpectedly high pressure sensitivity of the “glowing” fibres was observed, so opening possibility to apply them in sensor technology, e. g. for optical undercarpet security surveillance systems. Obviously, more detailed future studies will lead to new interesting results on this item.

5. ACKNOWLEDGEMENTS

Authors highly appreciate the financial support received from Latvian Ministry of Education and Science (Grant No. 95-61) and from Latvian Science Council (Grant No. BO755), as well as the technical support provided by J. Lazdins.

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