CA1069359A - Lens type optical equalizer for signal transmissions via multimode optical waveguides - Google Patents
Lens type optical equalizer for signal transmissions via multimode optical waveguidesInfo
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- CA1069359A CA1069359A CA273,270A CA273270A CA1069359A CA 1069359 A CA1069359 A CA 1069359A CA 273270 A CA273270 A CA 273270A CA 1069359 A CA1069359 A CA 1069359A
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B3/00—Simple or compound lenses
- G02B3/02—Simple or compound lenses with non-spherical faces
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
- G02B6/14—Mode converters
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- Optics & Photonics (AREA)
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- Optical Integrated Circuits (AREA)
Abstract
ABSTRACT OF THE DISCLOSURE
A lens type optical mode delay equalizer for multimode optical waveguides requires only two parallel lenses as equalizing elements, these lenses each having a cross section corresponding to that which would be formed by cutting away parts of two identical converging lenses by cuts parallel to their optical axes, and joining the remaining portions at the cuts. The parallel lenses are spaced between the ends of two lengths of waveguide in accos-dance with a relationship involving various parameters of the lenses and the separation and maximum angle of propagation of the wave-guide. Practical lens configurations may be toroidal or cushion-cuspidal for circular waveguides and bicylindrical or cuspidal for ribbon waveguides.
A lens type optical mode delay equalizer for multimode optical waveguides requires only two parallel lenses as equalizing elements, these lenses each having a cross section corresponding to that which would be formed by cutting away parts of two identical converging lenses by cuts parallel to their optical axes, and joining the remaining portions at the cuts. The parallel lenses are spaced between the ends of two lengths of waveguide in accos-dance with a relationship involving various parameters of the lenses and the separation and maximum angle of propagation of the wave-guide. Practical lens configurations may be toroidal or cushion-cuspidal for circular waveguides and bicylindrical or cuspidal for ribbon waveguides.
Description
10~;93S9 The present invention relates to signal transmission via optical waveguides of the multimode type, having a step refractive index profile, and, more particularly, it refers to a lens type optical equalizer able to equalize signals transmitted via such waveguidesO
It is known that a light signal enteræ an optical fibre waveguide as a plurality of rays at different angles to the wave-guide axis, which strike at different angles the wall of the core of the waveguide itself, where the refractive index changeæ abrupt-lyO At this wall the rays undergo refraction according to a wellknown physical law.
The various rays progressing along the fibre follow dif-ferent paths having different lengths: the axial ray will follow the shortest path, whilst the ray forming the maximum angle (the so called maximum guidance angle) with the axis of the fibre will follow the longest optical pathO The result of this difference in path length i8 a dispersion of the signalO
In fact, in any cross section of the waveguide at a certain distance from the generator, Lt is found that a signal generated as a theoretically instantaneous pulQe (Dirac function) presents a finite width, which increases with the distance of the point of examination from the generatorO
When long di~tances are concerned, this mode delay dis-persion of the sisnal is the main reason why, in this type of wave-guide, the transmissible bandwidth is considerably limited, since the maximum pulse repetition frequency must be chosen according to the degree of dispersion of the signals as they arrive at the receiver, in ordPr to avoid interference between successive signalsO
In order to compensate for this serious diæadvantage, devices called mode delay equaliæers have been proposedO
Firstly, equalizers of electronic type were proposed, but this type was soon rejected owing to difficulties of embodiment and maintenanceO
Then optical equalizers were studied, and various kinds have been proposed.
Generally these equalizers consist of lenses and/or cone~
refracting rays of incident light~ at various angles depending on their different angles of incidence, according to the well known laws of refractionO The common principle applied in equalizers of thiS type is that of converting rays parallel to the axis of the ~ptical wave guide (axial rays), into ray~ which form the maximum guidance angle with the axis of the optical waveguide, and vice versa, converting rays having the maximum guidance angle into axial rays, 80 compensating, through this exchange, for the difference in the optical path lengths of different transmission modesO :~
In UOSo Patent NoO 3,759,590 issued September 189 1973 to J.A. Arnaud proposes a system of three lenses: a biconvex lens positioned between two toroidal lenses, which together carry out the above described equalizationO The use of three lenses makes this type of equalizer rather complex and expensiveO
In another UOSo Patent NoO 3~832,o30, issued to DoCo Gloge, August 2~, 19~4~ proposes various equalization systems in which there i8 always present a central array of two cone-shaped len~es facing each other base to base, either accompanied or not by two plano-conuex lensesO However, these equalizers present a common basic disadvantage due to the presence of the cones: at their surface light rays are incident almost at grazing angle, thus giving rise to Fresnel losses which increase with increase of the iO~9359 angle between the incident ray and the perpendicular to the surface of the cone at the point of incidenceO
These and other disadvantages are overcome by the optical equalizer of the present invention, which, while it avoids the incidence of rays almost grazing the surface of the refractive medium, makes use of the minimum number of components, that i8 of two lenses only, thus obtaining a simpler and cheaper embodimentO
It is the main object of the present invention to provide an optical mode delay equalizer for optical telecommunication wave-guideQ of the multimode type and having a step refractive indexprofile, which is able to link two lengths of waveguide and com-prises a ~ystem of two identical lenses in parallel planes spaced along an axis common to both said lengths, each of said lenses having a form such that a longitudinal ~ection of the whole system shows them as having the same section as two converging lense~ of the same focal length, from each one of which a part has been cut away parallel to the optical axis, said cut lenqes being joined by the plane surface~ resulting from said cut; the minimum distance of said cut surfaces from the opposite vertex of each of the two lenses being at lea t equal to the distance of ~id common axis from the point of incidence on the len~ of that light ray leaving the adjacent length of waveguide at the maximu~ guidance angle;
the ratio of said minimum distance to the distance from said common axis of the optical axis of each cut lens being equal to the ratio of the separation of the parallel lense~ to the common focal length of the converging lensesO
These and other characteristics of the pre~ent invention will become clearer from the following description of two preferred embodiments thereof, taken in conjunction with the annexed drawings~ :
10~93S9 in which:
Yig. 1 is a block diagram illustrating the geometry of a fir~t embodiment of the invention;
Fig. 2 is a diagram illustrating the relation~hip of some parameters characteristic of the geometry of the system of Fig.l;
Fig. 3 is a perspective view of an equalizer according to the first embodiment of the invention, for use with circular optical fibres;
Fig. 4 is a perspective view of the equalizer according to the first embodiment of the invention, for use with thin ribbons;
Fig. 5 i~ a block diagram illustrating the geometry of a second embodiment of the invention;
Fig. 6 is a perspective view of the equalizer according ;~
to the second embodiment of the invention, for use with circular optical fibres;
Fig. 7 is a perspective view of the equalizer according to the second embodiment of the invention, for use with thin ribbons The invention may be realized in two embodiments, based on the same theoretical principle, but having slightly different geometries. They will hereinafter be described separately, for the 9 ake of clarity.
For each of the two embodiments, the theory related to the particular geometry will be discussed first; then two actual struc-tures will be disclosed, a first StructurQ for the case in which the optical guide is a circular multimode optical fibre, and a second structure for the case in which the optical guide is a thin ribbon exhibiting multimode behaviour along its width, and monomode 10f~9359 behaviour along its thic~nessO
With reference to FigO 1, referenc~ g and g' denote two lengths of optical waveguide conveying signals to be equalized, whose ends have as geometrical centres points P and P' respectively;
references 3-23 and 4-24 denote the sections of two parallel and îdentical converging lenses~
In this first embodiment of the invention, the particular shape of each said section results from the longitudinal section of a system formed of two equal converging lenses from each of 10 which has been removed, by a cut parallel to the optical axis, a portion which doe~ not comprise the optical axis, the cut converging lenses being then joined by the planes resulting from said cutso Reference 5 denotes the axis of the system formed by the lenses and the optical guides; said axis is an ideal line parallel to optical axe~ A and A' of the lense~, passing through geometric ~
centres Q and Q' of the lenses and through geometric centres P and r P' of the terminal sections of the guid~ and coinciding, inside the guides themselves, with their axesO
The following description refers throughout to the upper 20 halve~ 3, 4 of the ~ections of the lenses, as the same description applies to the lower parts 23,24, in mirror symmetryO
The optical axis A common to lenses 3 and 4 is at a dis-tance c from the axis 5 of the system; this distance c is in a certain ratio to the distance w of points R and R' from the axis 5, R and R' being the points of incidence on the lens of an optical ray at the maximum guidance angle; this distance may be the same, as in FigO l, as the total semiamplitude of the section of the lens, but it can also be less than this semiamplitude. The above ratio will be discussed further hereinafter.
106'9~59 Reference z denotes tlle axial ray of the guide g corres-ponding to a ray z' leaving lens 3, corresponding in turn to a ray z" entering guide g' at the maximum guidance angle eM. Reference r denotes a light ray leaving guide g at maximum guidance angle eM corresponding to a ray r' leaving lens 3, corresponding in turn to an axial ray r" entering the second guide g'O
Reference t denotes a ray leaving guide g at an angle e, passing through a focus F of lens 3, corresponding to a ray t' leaving the lens 3 parallel to the optical axis A, corresponding in turn to a ray t" passing through a focus G' of lens 4, and entering the guide g' at the same angle 0.
Reference m denotes a ray leaving guide g at any angle ::
e, which corresponds after successive refractions to rays m' and mn, the latter entering the guide g' at angle e~O
Reference P" denotes the intersection of the rays between ~:
the two lenses 3 and 4. Physically, point P" is the real Lmage of point P0 References F' and G denote the foci of the lens . .
portions 3 and 4 respectively, situated in the space between the lensesO References 0 and 0', S and S' denote the optical centreæ
of the longitudinal sections of the lens portionsO
Reference f denotes the focal length common to the portions of both lenses, reference d is the distance between the points Q
and Q', hereinafter referred to as the separation of the lenses;
reference s denotes the distance between the lenses and the guide lengths, that is the di~tances PQ and Q' P'0 It may be pointed out that this first embodiment of the invention is obtained by forming lenses 3-23 and 4-24 each of two lens portions which each comprise optical axes A and A', as the parts removed from the two converging lenses composing each one of lenses 3-23 and 4-24 do not comprise said optical axes.
~ 6 --....
, . . . , ~
10~93S9 The theoretical principle on which the present invention is based is expressed by the relation:
w = d (1) where w, c, d, f, are the distances hereinabove defined.
In this first embodiment, relation (1) is obtained as follows.
From the relationships, which can be geometrically deduced w=s tgeM
c = (s-f) tg e tg ~ = ltg eM
there can be derived w = 2s c ~-f from which w.f 12) s = c _ ~ 2 . r Moreover, it can be demonstrated that s s-f (3) From relationships (2) and ~3~ relationship (1) is easily obtained.
From the obvious condition that all the parameters must be positiveJ the following conditions are apparent:
w/c ~ 2 (4) s ~'f Inequality (4~ de~otes that the distance c between optical centres 0, O' of the lenses and points Q and Q' respectively, must bs less than the distance between optical centres O and O' and in-cidence points R, R' of the rays at the maximum guidance angleJ
r and r~O
Distances s and d defined by relations (2) and (1), as functions of the focal distance f and of ratio w/c, vary according to the curves shown in Fig. 2, where f forms the unit of measurefor the ordinates; the curve representing s is a branch of an equilateral hyperbola having as asymptote the stright lines w/c = 2 and s = f, whilst the representation of d is a straight line having an angular coefficient f which asymptotically approaches the point whose coordinates are (2, 2f)o Once condition (4) is satisfied, ratio w/c can have any valueO Unequivocally defined values for s and d will derive therefromO For instance, when w/c = 3, then s = 3f, d = 3f; when w/c = 4 then s = 2 f, d = 4f; when w/c = 5 then s = 5/3f, d = 5f.
Fig. 1 represents the case w/c = 8/3, for which s = 4f, d = 8/3f.
It is to be noted that when two lenses are specified having definite values of w, c and f, an equalizer for guides having any numerical aperture can be realized (provided that tgeM C w/f);
it will be enough to calculate the distanees between the optical elements s,d in accordance with given formulae; conversely, by giving the distances s,d between the elements, and the numerical aperture of the guide, it i8 possible to design an e~ualizer formed of two lensesJ provided the values of w,c and f of said lenses ~atisfy the preceding formulae.
In the case~ in which the optical waveguide i9 a multimode circular optical fibre, and in accordance with the principles already mentioned, two toroidal parallel lenses can be used, having as lon~itudinal sections the sections shown in FigO 1.
Schematically, such an equalizer is represented in Fig. 3, where H and H' denote the toroidal lenses. The geometry of the lenses depends both on the focal length and on the value chosen or ratio w/c; once having chosen this ratio in the mo~t suitable way, that is in the way that better satisfies the tachnological requirements both of construction o~ the lenses and of the sizeof the equalizer, the len~es will be placed at the separation d defined by relationship (1), and the ends of the fibre lengths g and g' will be fLxed at distances from the lenses, as defined by relationship t2). The whole assembly can be embedded into a block of transparent material (not shown in the figure) having a re-fractive index equal to that of the core of the fibreO
When the optical waveguide is a thin ribbon, of the type in which the multimode behaviour is present only along the width of the ribbon (that is its greatest cross-sectional dLmension)~
the beam of rays leaving the end of a length of the ribbon will be angularly dispersed only in the direction of said width.
In this case equalization will be necessary only in the direction of the angular dispersion of the rays, whilst in the orthogonal direction (that is the direction of the minLmUm dLmension of the ribbon) it will be enough to provide two parallel reflec$ing planes, spaced at a distance equal to said minimum dimension, that is in such a position as to form continuations othe cladding of the ribbonO
FigO 4 shows schematically the structure of an equalizer according to this first embodiment of the invention,suitable for thin ribbon waveguides. In this case, the lenses are two bicylin-drical lenses, having as longitudinal sections the section9 of Fig. lo In the drawing, references L and L' denote said bicylin-drical lense~, satisfying the laws stated in connection with Fig. 1, having a separation dJ with lengths of ribbon waveguide g and g' placed at distance s from the lenses~ References B and B' denote two parallel slabs of transparent material, for directing the 3o light rays in that dLmension in which dispersion does not occurO
_ g _ 10~i9~359 The two ends of the waveguides, the two lenses L and L' and guiding slabs B and ~' may be embedded into a block of trans-parent material - not shown in the figure - having a refractive index equal to that of the core of the optical waveguideO
The basic relationship (1) permits of a second embodLment of the invention, when the following requirements are fulfilled.
It is known from geometric optics that light ray~ coming from a source placed in the focal plane of a converging len~, but not on its optical axis, refract in the lens giving rise to a beam of outgoing rays all having the same direction, that is they are parallel rays. Vice versa, a beam of parallel rays, incident on a converging lens and making with the focal axis of the lens an angle which is not zero, refracts giving rise to a beam of rays all converging at a point lying in the focal plane of the lens at a certain distance from the optical axis.
With reference now to FigO 5, references g and g' denote two lengths of optical waveguide as in FigO 1, whose ends have as geometrical centres points P and P' respectively; references 13-33 and 14-34 denote the sections of two parallel converging lensesO
For this second embodiment of the invention, the particular shape of each of said sections re~ults from the longitudinal section of a ~ystem formed of two convergent lenses from each of which has been removed, by a cut parallel to the optical axis, a portion which comprises the optical axis, the remaining portions being then joined at the planes resulting from said cutso The height of the remaining portions, for instance of portion 13, is le~s than the distance of point R from the optical axis A of the lens. For the ~ake of clarity, an exact half of the lens is completed in the drawing by the partly broken line 10~9359 VRV'. The boundary CD of the portion of the lens actually used lieQ on the axis 5 of the system, which joins centres P,P' of the ends of two lengths of optical waveguide g and g', and which constitute a prolongation of the axes of the waveguides themselvesO
The same considerations are obviously valid for the second lens 14-34, which i8 placed at a distance d from the lens 13-33 and parallel thereto.
Reference f denotes the focal diætances of the two lenses, ~and 1~' denote the two focal planes external to the system of lenQesO The ends P and P' of the lengths of waveguide are in these focal planes.
A ray r at the maximum guidance angle eM of guide g, incident on the first lens 13, is refracted to become a ray r' which passes through lens 14 and emerges as ray r", on the axis of guide g'0 A ray z, on the axis of guidP g, is refracted in lens 13, giving rise to one of the rays z'; which in turn i8 incident on lens 14 and emerges as ray z" making the maxLmum guidance angle ~ with the axis of guide g'.
The inclination of the refracted rays emerging from the lens 13 i8 obviously the same as that of the straight line which joins point P to optical centre 0 of lens portion 13, which opti-cal centre is only virtual, as previously explained. Analogously, rays emerging from the portion of lens 33, will be parallel to the straight line (not ~hown in the drawing) which joins point P
to the virtual optical centre of the lens portion 33. In the drawing, a denotes the angle made by said strai~ht line and said emerging rays with the axis 5 of the ~ystemO
From the above it can be seen that a ray r leaving guide g at the maximum guidance angle, enters guide g' as an axial ray r"
_ 11 --.
10f~359 and, conver~ely, a ray z leaving guide g as an axial ray enters guide g' as a ray z" at the maximum guidance angle. The required equalization is therefore achievedO
The mathematical relation (1) existing between tha different parameters considered, iOe. the focal length f, the separation d of the lenses, the minimum height w of the portions of len~es 13,33;
14,34, and the distance c between each centre Q,Q' of the lenses and the corresponding virtual optical centers 0, 0' can be readily deduced, in this second embodiment of the invention, from the 0 geometry of the system. We have:
c = f tga w = d tga w = f tgeM (~) from which relation (1~ is obtained.
It is clear that relationships (1) and (5) are sufficient to define the whole geometry of this system. For instance, by ~pecifying the maxLmum guidance angle eM and the focal length f cf the lenses, relation (5) gives the minimum height w of the len~
portions 13,33, 14,34 which is necessary for ensuring that the light 20 beam leaving the guide, is preserved by the lenses; relation (1) gives the distance d between the lenses when ratio w/c ha~ been specified.
When the optical waveguide is a circular multimode optical fibre, the two lenses T, T have a cushion~cuspidal shape a~ shown schematically in Fig. 60 The axial section of these lenses is of course that shown in Fig. 5, When the optical waveguide is of the thin ribbon type in which multimodal behaviour is present only in the direction of the width of the ribbon, the beam of rays emerging from the guide will ~0~91359 be angularly dispersed only in the direction of said width, as already statedO In this case equalization will be necessary only in the direction of the angular dispersion, whilst in the orthogonal direction it will be sufficient to provide two reflecting parallel planes, spaced by the minimum dimension of the ribbon, that i9 30 -~
as to form extensions of the cladding of the ribbonsO
Fig. 7 shows schematically an exemplary embodiment of an equalizer in accordance with the above principles, suitable for thin ribbon waveguides~ In this case cuspidal lenses N,N' are formed by portions of cylindrical lensesO In the drawing, references B and B' denote two parallel planes of transparent material, for guiding the light ray~ in the dimension in which dispersion is absent.
In these embodiments also, the lenses and the parallel guide planes if used, may be embedded into a block of transparent material, not shown in the drawing, having a refractive index ~imilar to that of the core of the optical waveguideO
Modifications and variants may be made in the preferred embodiments of the invention here de~cribed, without departing from the scope of the appended claims. For instance, the lenses forming the ~ystem, instead of being biconvex as shown in the drawings, may have any other shape, for instance plano-convex; the invention may also be realized by using lenses having a refractive index less than that of the medium in which they are embedded, and their shape will then be for instance bi-concave or plano-concave in order to obtain the required convergent characteristics.
. . : : . . . :. .
,,, : ~ :: ., ;
It is known that a light signal enteræ an optical fibre waveguide as a plurality of rays at different angles to the wave-guide axis, which strike at different angles the wall of the core of the waveguide itself, where the refractive index changeæ abrupt-lyO At this wall the rays undergo refraction according to a wellknown physical law.
The various rays progressing along the fibre follow dif-ferent paths having different lengths: the axial ray will follow the shortest path, whilst the ray forming the maximum angle (the so called maximum guidance angle) with the axis of the fibre will follow the longest optical pathO The result of this difference in path length i8 a dispersion of the signalO
In fact, in any cross section of the waveguide at a certain distance from the generator, Lt is found that a signal generated as a theoretically instantaneous pulQe (Dirac function) presents a finite width, which increases with the distance of the point of examination from the generatorO
When long di~tances are concerned, this mode delay dis-persion of the sisnal is the main reason why, in this type of wave-guide, the transmissible bandwidth is considerably limited, since the maximum pulse repetition frequency must be chosen according to the degree of dispersion of the signals as they arrive at the receiver, in ordPr to avoid interference between successive signalsO
In order to compensate for this serious diæadvantage, devices called mode delay equaliæers have been proposedO
Firstly, equalizers of electronic type were proposed, but this type was soon rejected owing to difficulties of embodiment and maintenanceO
Then optical equalizers were studied, and various kinds have been proposed.
Generally these equalizers consist of lenses and/or cone~
refracting rays of incident light~ at various angles depending on their different angles of incidence, according to the well known laws of refractionO The common principle applied in equalizers of thiS type is that of converting rays parallel to the axis of the ~ptical wave guide (axial rays), into ray~ which form the maximum guidance angle with the axis of the optical waveguide, and vice versa, converting rays having the maximum guidance angle into axial rays, 80 compensating, through this exchange, for the difference in the optical path lengths of different transmission modesO :~
In UOSo Patent NoO 3,759,590 issued September 189 1973 to J.A. Arnaud proposes a system of three lenses: a biconvex lens positioned between two toroidal lenses, which together carry out the above described equalizationO The use of three lenses makes this type of equalizer rather complex and expensiveO
In another UOSo Patent NoO 3~832,o30, issued to DoCo Gloge, August 2~, 19~4~ proposes various equalization systems in which there i8 always present a central array of two cone-shaped len~es facing each other base to base, either accompanied or not by two plano-conuex lensesO However, these equalizers present a common basic disadvantage due to the presence of the cones: at their surface light rays are incident almost at grazing angle, thus giving rise to Fresnel losses which increase with increase of the iO~9359 angle between the incident ray and the perpendicular to the surface of the cone at the point of incidenceO
These and other disadvantages are overcome by the optical equalizer of the present invention, which, while it avoids the incidence of rays almost grazing the surface of the refractive medium, makes use of the minimum number of components, that i8 of two lenses only, thus obtaining a simpler and cheaper embodimentO
It is the main object of the present invention to provide an optical mode delay equalizer for optical telecommunication wave-guideQ of the multimode type and having a step refractive indexprofile, which is able to link two lengths of waveguide and com-prises a ~ystem of two identical lenses in parallel planes spaced along an axis common to both said lengths, each of said lenses having a form such that a longitudinal ~ection of the whole system shows them as having the same section as two converging lense~ of the same focal length, from each one of which a part has been cut away parallel to the optical axis, said cut lenqes being joined by the plane surface~ resulting from said cut; the minimum distance of said cut surfaces from the opposite vertex of each of the two lenses being at lea t equal to the distance of ~id common axis from the point of incidence on the len~ of that light ray leaving the adjacent length of waveguide at the maximu~ guidance angle;
the ratio of said minimum distance to the distance from said common axis of the optical axis of each cut lens being equal to the ratio of the separation of the parallel lense~ to the common focal length of the converging lensesO
These and other characteristics of the pre~ent invention will become clearer from the following description of two preferred embodiments thereof, taken in conjunction with the annexed drawings~ :
10~93S9 in which:
Yig. 1 is a block diagram illustrating the geometry of a fir~t embodiment of the invention;
Fig. 2 is a diagram illustrating the relation~hip of some parameters characteristic of the geometry of the system of Fig.l;
Fig. 3 is a perspective view of an equalizer according to the first embodiment of the invention, for use with circular optical fibres;
Fig. 4 is a perspective view of the equalizer according to the first embodiment of the invention, for use with thin ribbons;
Fig. 5 i~ a block diagram illustrating the geometry of a second embodiment of the invention;
Fig. 6 is a perspective view of the equalizer according ;~
to the second embodiment of the invention, for use with circular optical fibres;
Fig. 7 is a perspective view of the equalizer according to the second embodiment of the invention, for use with thin ribbons The invention may be realized in two embodiments, based on the same theoretical principle, but having slightly different geometries. They will hereinafter be described separately, for the 9 ake of clarity.
For each of the two embodiments, the theory related to the particular geometry will be discussed first; then two actual struc-tures will be disclosed, a first StructurQ for the case in which the optical guide is a circular multimode optical fibre, and a second structure for the case in which the optical guide is a thin ribbon exhibiting multimode behaviour along its width, and monomode 10f~9359 behaviour along its thic~nessO
With reference to FigO 1, referenc~ g and g' denote two lengths of optical waveguide conveying signals to be equalized, whose ends have as geometrical centres points P and P' respectively;
references 3-23 and 4-24 denote the sections of two parallel and îdentical converging lenses~
In this first embodiment of the invention, the particular shape of each said section results from the longitudinal section of a system formed of two equal converging lenses from each of 10 which has been removed, by a cut parallel to the optical axis, a portion which doe~ not comprise the optical axis, the cut converging lenses being then joined by the planes resulting from said cutso Reference 5 denotes the axis of the system formed by the lenses and the optical guides; said axis is an ideal line parallel to optical axe~ A and A' of the lense~, passing through geometric ~
centres Q and Q' of the lenses and through geometric centres P and r P' of the terminal sections of the guid~ and coinciding, inside the guides themselves, with their axesO
The following description refers throughout to the upper 20 halve~ 3, 4 of the ~ections of the lenses, as the same description applies to the lower parts 23,24, in mirror symmetryO
The optical axis A common to lenses 3 and 4 is at a dis-tance c from the axis 5 of the system; this distance c is in a certain ratio to the distance w of points R and R' from the axis 5, R and R' being the points of incidence on the lens of an optical ray at the maximum guidance angle; this distance may be the same, as in FigO l, as the total semiamplitude of the section of the lens, but it can also be less than this semiamplitude. The above ratio will be discussed further hereinafter.
106'9~59 Reference z denotes tlle axial ray of the guide g corres-ponding to a ray z' leaving lens 3, corresponding in turn to a ray z" entering guide g' at the maximum guidance angle eM. Reference r denotes a light ray leaving guide g at maximum guidance angle eM corresponding to a ray r' leaving lens 3, corresponding in turn to an axial ray r" entering the second guide g'O
Reference t denotes a ray leaving guide g at an angle e, passing through a focus F of lens 3, corresponding to a ray t' leaving the lens 3 parallel to the optical axis A, corresponding in turn to a ray t" passing through a focus G' of lens 4, and entering the guide g' at the same angle 0.
Reference m denotes a ray leaving guide g at any angle ::
e, which corresponds after successive refractions to rays m' and mn, the latter entering the guide g' at angle e~O
Reference P" denotes the intersection of the rays between ~:
the two lenses 3 and 4. Physically, point P" is the real Lmage of point P0 References F' and G denote the foci of the lens . .
portions 3 and 4 respectively, situated in the space between the lensesO References 0 and 0', S and S' denote the optical centreæ
of the longitudinal sections of the lens portionsO
Reference f denotes the focal length common to the portions of both lenses, reference d is the distance between the points Q
and Q', hereinafter referred to as the separation of the lenses;
reference s denotes the distance between the lenses and the guide lengths, that is the di~tances PQ and Q' P'0 It may be pointed out that this first embodiment of the invention is obtained by forming lenses 3-23 and 4-24 each of two lens portions which each comprise optical axes A and A', as the parts removed from the two converging lenses composing each one of lenses 3-23 and 4-24 do not comprise said optical axes.
~ 6 --....
, . . . , ~
10~93S9 The theoretical principle on which the present invention is based is expressed by the relation:
w = d (1) where w, c, d, f, are the distances hereinabove defined.
In this first embodiment, relation (1) is obtained as follows.
From the relationships, which can be geometrically deduced w=s tgeM
c = (s-f) tg e tg ~ = ltg eM
there can be derived w = 2s c ~-f from which w.f 12) s = c _ ~ 2 . r Moreover, it can be demonstrated that s s-f (3) From relationships (2) and ~3~ relationship (1) is easily obtained.
From the obvious condition that all the parameters must be positiveJ the following conditions are apparent:
w/c ~ 2 (4) s ~'f Inequality (4~ de~otes that the distance c between optical centres 0, O' of the lenses and points Q and Q' respectively, must bs less than the distance between optical centres O and O' and in-cidence points R, R' of the rays at the maximum guidance angleJ
r and r~O
Distances s and d defined by relations (2) and (1), as functions of the focal distance f and of ratio w/c, vary according to the curves shown in Fig. 2, where f forms the unit of measurefor the ordinates; the curve representing s is a branch of an equilateral hyperbola having as asymptote the stright lines w/c = 2 and s = f, whilst the representation of d is a straight line having an angular coefficient f which asymptotically approaches the point whose coordinates are (2, 2f)o Once condition (4) is satisfied, ratio w/c can have any valueO Unequivocally defined values for s and d will derive therefromO For instance, when w/c = 3, then s = 3f, d = 3f; when w/c = 4 then s = 2 f, d = 4f; when w/c = 5 then s = 5/3f, d = 5f.
Fig. 1 represents the case w/c = 8/3, for which s = 4f, d = 8/3f.
It is to be noted that when two lenses are specified having definite values of w, c and f, an equalizer for guides having any numerical aperture can be realized (provided that tgeM C w/f);
it will be enough to calculate the distanees between the optical elements s,d in accordance with given formulae; conversely, by giving the distances s,d between the elements, and the numerical aperture of the guide, it i8 possible to design an e~ualizer formed of two lensesJ provided the values of w,c and f of said lenses ~atisfy the preceding formulae.
In the case~ in which the optical waveguide i9 a multimode circular optical fibre, and in accordance with the principles already mentioned, two toroidal parallel lenses can be used, having as lon~itudinal sections the sections shown in FigO 1.
Schematically, such an equalizer is represented in Fig. 3, where H and H' denote the toroidal lenses. The geometry of the lenses depends both on the focal length and on the value chosen or ratio w/c; once having chosen this ratio in the mo~t suitable way, that is in the way that better satisfies the tachnological requirements both of construction o~ the lenses and of the sizeof the equalizer, the len~es will be placed at the separation d defined by relationship (1), and the ends of the fibre lengths g and g' will be fLxed at distances from the lenses, as defined by relationship t2). The whole assembly can be embedded into a block of transparent material (not shown in the figure) having a re-fractive index equal to that of the core of the fibreO
When the optical waveguide is a thin ribbon, of the type in which the multimode behaviour is present only along the width of the ribbon (that is its greatest cross-sectional dLmension)~
the beam of rays leaving the end of a length of the ribbon will be angularly dispersed only in the direction of said width.
In this case equalization will be necessary only in the direction of the angular dispersion of the rays, whilst in the orthogonal direction (that is the direction of the minLmUm dLmension of the ribbon) it will be enough to provide two parallel reflec$ing planes, spaced at a distance equal to said minimum dimension, that is in such a position as to form continuations othe cladding of the ribbonO
FigO 4 shows schematically the structure of an equalizer according to this first embodiment of the invention,suitable for thin ribbon waveguides. In this case, the lenses are two bicylin-drical lenses, having as longitudinal sections the section9 of Fig. lo In the drawing, references L and L' denote said bicylin-drical lense~, satisfying the laws stated in connection with Fig. 1, having a separation dJ with lengths of ribbon waveguide g and g' placed at distance s from the lenses~ References B and B' denote two parallel slabs of transparent material, for directing the 3o light rays in that dLmension in which dispersion does not occurO
_ g _ 10~i9~359 The two ends of the waveguides, the two lenses L and L' and guiding slabs B and ~' may be embedded into a block of trans-parent material - not shown in the figure - having a refractive index equal to that of the core of the optical waveguideO
The basic relationship (1) permits of a second embodLment of the invention, when the following requirements are fulfilled.
It is known from geometric optics that light ray~ coming from a source placed in the focal plane of a converging len~, but not on its optical axis, refract in the lens giving rise to a beam of outgoing rays all having the same direction, that is they are parallel rays. Vice versa, a beam of parallel rays, incident on a converging lens and making with the focal axis of the lens an angle which is not zero, refracts giving rise to a beam of rays all converging at a point lying in the focal plane of the lens at a certain distance from the optical axis.
With reference now to FigO 5, references g and g' denote two lengths of optical waveguide as in FigO 1, whose ends have as geometrical centres points P and P' respectively; references 13-33 and 14-34 denote the sections of two parallel converging lensesO
For this second embodiment of the invention, the particular shape of each of said sections re~ults from the longitudinal section of a ~ystem formed of two convergent lenses from each of which has been removed, by a cut parallel to the optical axis, a portion which comprises the optical axis, the remaining portions being then joined at the planes resulting from said cutso The height of the remaining portions, for instance of portion 13, is le~s than the distance of point R from the optical axis A of the lens. For the ~ake of clarity, an exact half of the lens is completed in the drawing by the partly broken line 10~9359 VRV'. The boundary CD of the portion of the lens actually used lieQ on the axis 5 of the system, which joins centres P,P' of the ends of two lengths of optical waveguide g and g', and which constitute a prolongation of the axes of the waveguides themselvesO
The same considerations are obviously valid for the second lens 14-34, which i8 placed at a distance d from the lens 13-33 and parallel thereto.
Reference f denotes the focal diætances of the two lenses, ~and 1~' denote the two focal planes external to the system of lenQesO The ends P and P' of the lengths of waveguide are in these focal planes.
A ray r at the maximum guidance angle eM of guide g, incident on the first lens 13, is refracted to become a ray r' which passes through lens 14 and emerges as ray r", on the axis of guide g'0 A ray z, on the axis of guidP g, is refracted in lens 13, giving rise to one of the rays z'; which in turn i8 incident on lens 14 and emerges as ray z" making the maxLmum guidance angle ~ with the axis of guide g'.
The inclination of the refracted rays emerging from the lens 13 i8 obviously the same as that of the straight line which joins point P to optical centre 0 of lens portion 13, which opti-cal centre is only virtual, as previously explained. Analogously, rays emerging from the portion of lens 33, will be parallel to the straight line (not ~hown in the drawing) which joins point P
to the virtual optical centre of the lens portion 33. In the drawing, a denotes the angle made by said strai~ht line and said emerging rays with the axis 5 of the ~ystemO
From the above it can be seen that a ray r leaving guide g at the maximum guidance angle, enters guide g' as an axial ray r"
_ 11 --.
10f~359 and, conver~ely, a ray z leaving guide g as an axial ray enters guide g' as a ray z" at the maximum guidance angle. The required equalization is therefore achievedO
The mathematical relation (1) existing between tha different parameters considered, iOe. the focal length f, the separation d of the lenses, the minimum height w of the portions of len~es 13,33;
14,34, and the distance c between each centre Q,Q' of the lenses and the corresponding virtual optical centers 0, 0' can be readily deduced, in this second embodiment of the invention, from the 0 geometry of the system. We have:
c = f tga w = d tga w = f tgeM (~) from which relation (1~ is obtained.
It is clear that relationships (1) and (5) are sufficient to define the whole geometry of this system. For instance, by ~pecifying the maxLmum guidance angle eM and the focal length f cf the lenses, relation (5) gives the minimum height w of the len~
portions 13,33, 14,34 which is necessary for ensuring that the light 20 beam leaving the guide, is preserved by the lenses; relation (1) gives the distance d between the lenses when ratio w/c ha~ been specified.
When the optical waveguide is a circular multimode optical fibre, the two lenses T, T have a cushion~cuspidal shape a~ shown schematically in Fig. 60 The axial section of these lenses is of course that shown in Fig. 5, When the optical waveguide is of the thin ribbon type in which multimodal behaviour is present only in the direction of the width of the ribbon, the beam of rays emerging from the guide will ~0~91359 be angularly dispersed only in the direction of said width, as already statedO In this case equalization will be necessary only in the direction of the angular dispersion, whilst in the orthogonal direction it will be sufficient to provide two reflecting parallel planes, spaced by the minimum dimension of the ribbon, that i9 30 -~
as to form extensions of the cladding of the ribbonsO
Fig. 7 shows schematically an exemplary embodiment of an equalizer in accordance with the above principles, suitable for thin ribbon waveguides~ In this case cuspidal lenses N,N' are formed by portions of cylindrical lensesO In the drawing, references B and B' denote two parallel planes of transparent material, for guiding the light ray~ in the dimension in which dispersion is absent.
In these embodiments also, the lenses and the parallel guide planes if used, may be embedded into a block of transparent material, not shown in the drawing, having a refractive index ~imilar to that of the core of the optical waveguideO
Modifications and variants may be made in the preferred embodiments of the invention here de~cribed, without departing from the scope of the appended claims. For instance, the lenses forming the ~ystem, instead of being biconvex as shown in the drawings, may have any other shape, for instance plano-convex; the invention may also be realized by using lenses having a refractive index less than that of the medium in which they are embedded, and their shape will then be for instance bi-concave or plano-concave in order to obtain the required convergent characteristics.
. . : : . . . :. .
,,, : ~ :: ., ;
Claims (7)
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. An optical mode delay equalizer for connecting two lengths of optical waveguide of the multimode type having a step refractive index profile, comprising a system of two identical lenses in parallel planes spaced along an axis common to said lengths, each of said lenses having a form such that a longitudinal section in a plane containing said common axis shows them as having the same section as two equal converging lens portions having respective optical axes parallel with, and spaced from, the common axis, each section being formed by cut-ting away a part from a complete lens along a cut parallel to the optical axis and being joined to the other lens portion at said cut; the minimum distance of said cut from the opposite vertex of each of the two lenses being at least equal to the distance of said common axis from the incidence point on the lens of that light ray leaving the adjacent waveguide lengths at the maximum guidance angle; the ratio of said minimum dis-tance to the distance from said common axis of the optical axis of each lens portion being equal to the ratio of the separation of the parallel lenses to the common focal length of the lens portions.
2. An optical equalizer according to Claim 1, wherein the longitudinal axial section of each of said lenses is that of two converging lens portions, formed from lenses from each one of which a part not comprising the optical axis has been re-moved by a cut parallel to the optical axis, said lens portion being joined at said cuts.
3. An optical equalizer according to Claim 1, wherein the longitudinal axial section of each of said lenses is that of two converging lens portions, formed from lenses from each of which ......................................................
a part comprising the optical axis has been removed away by a cut parallel to the optical axis, said lens portions being joined at said cuts.
a part comprising the optical axis has been removed away by a cut parallel to the optical axis, said lens portions being joined at said cuts.
4. An optical equalizer according to claim 1 or 2, wherein, for the equalization of signals transmitted by circular optical fibres, said lenses forming the system have the shape of toroidal lenses.
5. An optical equalizer according to claim 1 or 2, wherein, for the equalization of signals transmitted through optical thin ribbons, said lenses forming the system have the shape of bicylin-drical lenses.
6. An optical equalizer according to claim 1 or 3, wherein, for the equalization of signals transmitted by circular optical fibres, said lenses forming the system have the shape of cushion cuspidal lenses.
7. An optical equalizer according to claim 1 or 3, wherein, for the equalization of signals transmitted by optical thin ribbons, said lenses forming the system have the shape of cuspidal lenses formed of two cylindrical lens portions.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| IT6759676A IT1062820B (en) | 1976-03-12 | 1976-03-12 | Optical equaliser lens system - is for signal transmission through optical waveguides and has abruptly changing refractive index profile (NL 14.9.77) |
| IT6796076A IT1059487B (en) | 1976-04-22 | 1976-04-22 | Optical equaliser lens system - is for signal transmission through optical waveguides and has abruptly changing refractive index profile (NL 14.9.77) |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1069359A true CA1069359A (en) | 1980-01-08 |
Family
ID=26329800
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA273,270A Expired CA1069359A (en) | 1976-03-12 | 1977-03-07 | Lens type optical equalizer for signal transmissions via multimode optical waveguides |
Country Status (5)
| Country | Link |
|---|---|
| CA (1) | CA1069359A (en) |
| DE (1) | DE2710311C3 (en) |
| FR (1) | FR2344038A1 (en) |
| GB (1) | GB1575319A (en) |
| NL (1) | NL169788C (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE3024104C2 (en) * | 1980-06-27 | 1986-02-20 | Fa. Carl Zeiss, 7920 Heidenheim | Method of making an integrated micro-optic device for use with multimode optical fibers |
| DE4014796A1 (en) * | 1990-05-09 | 1991-11-14 | Rheydt Kabelwerk Ag | Linearising transfer characteristic function - processing signal by compensation circuit based on filtered components for electronic component or circuit |
| WO2018157126A1 (en) * | 2017-02-27 | 2018-08-30 | Rutgers, The State University Of New Jersey | Ultra-compact planar mode size converter with integrated aspherical semi-lens |
-
1977
- 1977-03-04 FR FR7706400A patent/FR2344038A1/en not_active Withdrawn
- 1977-03-07 CA CA273,270A patent/CA1069359A/en not_active Expired
- 1977-03-09 DE DE19772710311 patent/DE2710311C3/en not_active Expired
- 1977-03-10 NL NL7702591A patent/NL169788C/en not_active IP Right Cessation
- 1977-03-14 GB GB1065277A patent/GB1575319A/en not_active Expired
Also Published As
| Publication number | Publication date |
|---|---|
| DE2710311C3 (en) | 1979-11-22 |
| FR2344038A1 (en) | 1977-10-07 |
| GB1575319A (en) | 1980-09-17 |
| DE2710311A1 (en) | 1977-09-15 |
| NL169788B (en) | 1982-03-16 |
| NL169788C (en) | 1982-08-16 |
| DE2710311B2 (en) | 1979-04-05 |
| NL7702591A (en) | 1977-09-14 |
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