This invention will be readily understood by the following description of certain embodiments, by way of example, in conjunction with the accompanying drawings, in which:
FIG. 1 is a diagrammatic illustration of a multimode step-index guide or fibre;
FIG. 2 is a curve illustrating wavelength variation of the group index for fused silica;
FIG. 3 is a curve illustrating ray angle variation of the group index for a step-index fibre;
FIGS. 4a and 4b illustrate the angular variation of the input spectrum required for dispersionless guide or fibre operation;
FIG. 5 illustrates diagrammatically the use of a grating to provide angular variation of the input spectrum;
FIG. 6 illustrates diagrammatically the positioning of a grating on an inclined fibre face.
In the following disclosure and description certain reference characters are used and these are listed with their corresponding relationship, as follows:
.lambda. = wavelength
.DELTA..lambda. = width of source spectrum
.phi. = mode angle or ray steepness (angle between ray and fibre axis)
n = core index of refraction
n-.DELTA.n = cladding index of refraction
N = group index = light speed in vacuum (C)/signal speed in fibre
Na = numerical aperture of fibre
The group index N decreases with increasing wavelength (.lambda.) and increases with the mode order or ray steepness, as expressed by the angle (.phi.) between the ray and the fibre axis. It is therefore arranged for the long wavelengths to be fed into large angles within the fibre and short wavelengths into small angles; the precise functional relationship is derived below. These opposing modal and material effects result in a substantially constant group index for all rays, and this concept is the heart of the invention. With all group velocities approximately equalized, the information capacity of the fibre would be then very high.
As a simplified analytical explanation, consider the step-index fibre of FIG. 1 which has a core 10 of refractive index n and a cladding 11 of index n - .DELTA.n (with the reasonable approximation .DELTA.n << n). The group index is:
where
is the core (lowest mode) group index. As schematically indicated in FIGS. 2 and 3, N increases with mode angle .phi. but N (and n) decreases with wavelength .lambda.. The maximum value of .phi. is related to the numerical aperture
Pulse spreading in a fibre of length L can then be specified by the time delay difference T = (L/C) .DELTA.N due to two causes. For a monochromatic source
is due to mode dispersion, whereas for a spectral width .DELTA..lambda.
is due to material dispersion. Numerically, for NA = 0.2 and .DELTA..lambda. = 40 nm, the time delays corresponding to .DELTA.N.sub.1 and .DELTA.N.sub.2 are respectively T.sub.1 = 67 ns/km and T.sub.2 = 3.4 ns/km, using the values of FIG. 2. The concept of the present invention reduces the net effect of mode and material dispersions by putting them in opposition.
The two dispersions will cancel if .lambda. is launched into .phi. = 0 with .lambda. + .DELTA..lambda. into .phi..sub.max such that .DELTA.N.sub.1 = .DELTA.N.sub.2, i.e. ##EQU2## (The same result is obtainable from (d/d.phi.) N(.lambda.,.phi.) = 0 at .phi. = 0). Numerically, Na .apprxeq. 0.066 for .DELTA..lambda. = 60 nm, a spectral full bandwidth which can be comfortable accommodated. For intermediate wavelengths, the angular distribution should satisfy ##EQU3## If this distribution, illustrated in FIGS. 4a and 4b, is maintained within the fibre, pulse spreading should be very small.
While the achievement of a close approximation to the above described desired distribution is somewhat difficult, any technique whereby longer emitted wavelengths are coupled to the higher order modes and the shorter emitted wavelengths coupled to the lower order modes will reduce the overall dispersion. Such techniques may utilize lenses, prisms, mirrors, gratings etc.
One approach is to utilize a device which will transform a collimated source beam incident upon it into a set of diverging beams with each propagating at a unique angle for each constituent wavelength. A diffraction grating can provide the required nagnitude of angular spreading.
In FIG. 5 a grating 12 is positioned opposite the end of the fibre core 10. If D is the grating spacing and m is the diffraction order, one can derive the equation ##EQU4## where for simplicity we have taken the rays 14 to be impinging normal to the plane of the grating 12. In the simpler variation of FIG. 6, the grating 12 may be laid upon an inclined fare 13 of the fibre core 10. Again with normal incidence, the inclination angle .beta. is chosen to satisfy
and equation (7) holds.
It should be noted that Equation (7) varies linearly with .sqroot..delta..lambda. as required in Equation (6). The diffraction grating approach can therefore only approximately cancel modal and material dispersions. Nevertheless, if one optimizes the grating parameters with respect to the fibre and source parameters via the relation ##EQU5## then the chromatic dispersion of Equation (4) is compensated to the extent of
numerically, again using the numbers of FIG. 2 and .DELTA..lambda. = 40 nm, Equation (9) gives
A high order m may be used to increase the grating period D and the grating may be blazed to concentrate light into that order. Suitable gratings are commercially available or else may be fabricated (interferometrically, for example) by methods well known in the optical art. By Equation (10), even this imperfect compensation reduces the chromatic dispersion to 4.3% of the 3.4 ns/km following Equation (4), i.e., to a residual value of 0.15 ns/km.
Other dispersive devices may be used. For integrated optical circuitry, source light travelling in a thin film waveguide encounters a variable pitch in-plane grating above or within the guiding layer which performs the angular dispersion (U.S. Pat. No. 3,817,498). A distributed feedback laser may be designed to angularly spread out its range of emitting wavelengths to be coupled into the fibre.