CA1072790A - Full optical equalizer for transmission of signals via multimode optical wave guides - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE

An optical equalizer is provided which connects two segments of a multimode optical waveguide in such a manner that the path length of all rays passing through the guide can be equalized regardless of their guidance angle. The equalizer comprises two identical lenses, or equivalent structure, the lenses having a variable focal length which varies according to the distance r from the axis of the system according to the relation where s is the distance between each lens, and the adjacent waveguide segment, d is the separation of the lenses and ?M
is the maximum guidance angle of the waveguide segments.

Description

æ~J~
The pxesent invention relates to the transmission of signals via multimode optical waveguides having a step rafractive index profile, and more particularly it refers to an optical equalizer, able fully to e~ualize siynals transmitted by such waveguides.
It is known that a light signal ~ntexing an optical waveguide ma~ be considered as a plurality of ray~ forming different angles with the waveguide axis, and striking at different angle~
the wall of the core of the waveguide itself. At this wall the refractive index profile changes abruptly, and the rays are reflected according to well known phy~ical laws.
The various rays progressing along a fibre waveguide follow different path~ having different len~ths; the axial ray will ~ollow the shoxte~t path, and the rays at the max~mum guidance angle will follow the longest optical paths. Between these two extremes, intermeaiate rays forming intermediate angles with the waveguide axis obviously occur, these rays following paths of ,' , length intermediate between that of the axial ray and that of the rays at the maximum guidance angle.
The result of such differences in path leng~h is a broadening of the pulse signals used in digital data transmission.
~ In fact in any cross section of the fibre, at a certaîn distance ;~; from the generator, it is found that a signal generated as a `~ theoretically instantaneous pulse (~irac function~ presents a finite width increasing with the distance of the section from the generator~
When long distances are involved, this broadening , . . .
of the siynal is the main reason why, with this type of waveguide, the usable bandwidthis considerably limited, as tha maximum repetition rate of the pulses has to be corxelated to the width ~ Z'~q30 of the signals as they arrive at the receiver, in order to avoid interference between consecutive signals, In order to overcome this serious disadvantage, devices called equalizers have been propose~d.
A first type of equalizer is electronic~ and acts upon the received signal. In this type o~ equaliz~r, rays received at different angles to the waveguide axis, are electroni~ally detected in separate zones, and passed through suitabl2 delay llnes, having delay periods varying according to said angles. In theory, such an equalizer can reduce by 90% the broadening of the signal.
This kind o equ~lizer is no longer used as it was very difficult to put into practice. The latest equalizers are of the optical type, and consist of converging lenses of different shape~, refracting the light rays pas~ing therethrough at different angles according $o the well known laws o~ refraction. The common principle applied in equali~ers of this type is that rays at a -~ zero angle to the axis of the optical guide ~axial rays), are converted into rays at a maximum guida~ce an~le relati~e to khe axis of an optical waveguide, and vice versa, rays at the maximum ~ .
guidance angle being convert~d into axial rays~ thus compensating, by this exchangeD for differences in optical path lengths. These equalizers have the common characteristic of equa7 izing only those rays covexing the longest and shortest paths, that is axial ray5 and rays at the Tnaximum guidance angle; the intermediate rays ;~ are not taken into account ana as a consequence are not fully equalized. The most outstanding consequence of this partial equaliza~ion is that the bxoadening of the received ~ulse is only reduced by 75O/o of that which would have occurred without equalization;
this reduction can be sufficient when the transmission invol~ed ~ 9~

is not over ve~y long distances, or when the bandwidth of the original transmission is not very great; otherwise the broadening of the received signal is still a serious problem These and other disadvantages can be overcome by the op~ical equalizer of the present invention, which can achieve a total equalization, that is it equalize~ all rays whatever their angle relative to the axis of a segment of wavcguide.
Another feature of the present invention is that, starting from one theoretical principle, it can be embodied in different way~, according to the characteristic.s of ~he transmission line to be compensated and of the technology available.
A further feature of the inven~ion i9 ~hat i~ utilizes at most two refracting bodies, thus ensuring a minimum energy loss due to the refl~ctions alway~ associated with refraction phenomena.
It is the main objec~ of the present invention to . provide a full optical equalizer for multimode op~ical tele-communications waveguide~ with a step refracki~e index profile, ~ which equalizer is adaptad to connect two guide ~egment~ and comprises .~. an optical system consisting of, or equivalent to two identical ~ 20 refractive lenses, coaxial with each other and said waveguide segments and placed in two parallel planes ~erpendicular to th~
~ axis of the system, ~he lenses having a focal length which vaxies ;~ ``` according to the distance from the axis oE the system as a unction - of the distance of each of the ~wo lenses from the adjacent waveguide segments, of the distance between the lenses, and of the maximum guidance angle of the two segments of waveguide, this function being defined by a mathematical relationship~
These and other characteristics of the present invention will become clearer from the following description of some preferred embodiments thereof, given by way of example and not in a limiting sense, tak~n in conjunction with the annexed drawings, in w~ich:
- Fig. 1 is a diagram generically illu~trating the optical paths of the rays through an equalizer in accordance with khe invention;
- Fig. 2 represents the contour of lenses forming a total equalizer in accordance with the invention:
- Fig. 3 is a diagram showing the path~ of the light rays in ca~e of a lens having the contour of curve A of Fig, 2;
- Fig. 4 is a diagram showing the paths of the light rays in case of a lens having the contour of curve B of Fig. 2;
- Fig. 5 is a diagram showing a cross section of a system of len~es of an equalizer employing lenses whose cross section is the curYe A of Fig. 2;
- Fig. 6 is a diagram showing a cross section of a system of lenses ; of an equali~er employing lenses whose cross section is the curve : B of Fig, 2 - Fig. 7 is a diagram showing a cross section of a system of - lenses of an equalizer which is a modification of that of Fig. S, - Fig. 8 is a diagram showing a cross section of a system of lenses of an equalizer which is a modification of that of FigO 6;
-- Fig. 9 is a diagram showing a cross section of an equalizer using a refractive bo~y having a graded refractive index pr~-file.
The structure and the mode of operation of an equalizer in accordance with the present invention will become clearer from a study of the theory underlying the in~ention, ~rom which the contours shown in Fig. 2 are obtained. This theory will be now br.iefly described, with reference to FigO 1.
It has been stated ("Optical Equalizer for Multimode Optical Fibres" by P. Di Vita, R. Vannucci, paper presented at the ~ XIII Rassegna Elettronica ~ucleare ed Aerospaziale", ~ome, March 18-28, 1976) that by denoting by ~ ~Fig. 1) the angle formed by a ~eneric ray emerging from a first segment o waveguide g the axis of the system, that is the axis ~ommon to the two segm~nts of waveguide g and g' and to the lenses It and L' forming the equalizer;
by denoting by ~' the angle formed with said axis by the ray a"
emerging from the sec~nd len3 L' and corresponding to said ray a by denoting by ~M the maximum guidance angle o~ the waveguid~, a perfect equalization of the optical path of the rays i~ obtained when the relation:
: sec ~ ~ sec ~ sec ~ M (1) is satisfied~
Dsnoting by w the portion of len5 L subtended ~y the ray b at maximum guida~ce angle and by s ths distanca from the terminal point P of the waveguide g from lens ~7 we o~tain the elementary relation w = s t~ ~ M (2) Since, in order to convey much infonmation, low : guidance angle fibre~ are genexally used in telecommunication~, that is to say, ~ M is very low, then ~ 1 rad (3 Condition ~3) allows use of the well known rel~tion sec ~

which converts relation (1) into ~ 2 + ~ 2 ~ ~ M (4) and relation (2) into:
w ~~ s ~ M from which w ~ s is obtained~

9~

Moreover, denoting by r the portion of lens L sub-tended by the generic ray a and by r' the portion o lens L' subtended by the corresponding ray a", and assuming that the second segment of waveguide g' is at the same distance s from the second lens L', then clearly:
r = s tg ~ , that is r ~ s ~ ' r' - s tg that is r' -~ s ~ O
If f(r) denotes the variation of the focal length of the lenses as a function of the quantity r, it can be demonstrated that, in order to implement the relation (4) ~y a qystem of two identical refracting lense3 coaxial with the two segments of fibre, spaced by a distance d, the variable focal length must satisfy the relation 1 f(r) s d ~ 1 ~ J s ~ u 1~ (5) where the variation range of r is obviously 0 ~ r < w.
~:~ It should be noted that, with variabla focus lenses satisfyin~ relation (53 taken with sign ~ before the radical sign, the light rays beha~e as illustrated in Figure 3.
In this Figure it can be seen that rays incident on ~he first lens and belonging for instance to the upper half plane with respect to the common axis of the system, are refracted giving rise to rays, pairs of which interse~t between the two lenses.
With variable focus lenses satisfying relation (5) taken with sign -- before the radical sign, the light ray~ behave as illustrated in Fig. 4 from which it may be seen that rays incident on the first lens and belonging for instance to the upper half plane with respect to the common axis of the system, are refracted giving rise to rays which do not intersect between the two lenses.

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Relation (5) allows the contour of the lenses forminy the equalizer to be obtained, once the type o~ lens one intend~ to use, that is plano-convex, symmetr.ical biconvex, or asymmetrical biconvex, i5 determined.
Technological reasonsi relating to the ease of manu-facture of the lenses, suggest use of plano-convex len~es.
In this case, the law de~ining the contour z (r) of the convex face of the len~, whose refractive index is denoted by n, i~ obtained from formula (5).
The following law may be obtained math~matically:

:' z(r) = ~ 1 t2s 2d - 2d (r ~ I ( s ~M ) -r +
(5 ~M)2 arc3in ( r ~ ~ const~ (6) Formula (6) provide~ two profiles, one corresponding to ~ :
`-. a + si~n between the second and the third terms within the square bxackets~ the other one coxresponding to a - sign.
.~ These signs correspond exactly to the ~ and - signs :: of formula (5~ and, accoxding to the chos~n sign, len~e~ causing light rays to progress along paths shown in Fig. 3 ( ~ sign and 4 ( - sign ) are obtained.
A graphic representation of fo~mula (6) is shown in Fig. 2, where A denotes the profile obtained from formula ~6~
taken with a ~ sign, and B denotes the profile obtained from ormula (6) taXen with a - sign.
The curves A and B of Fig~ 2 are drawn relative to one of the semiplanes into which the sy3tem is divided by its axis (Fig. 1).
~he yeneral th~ory given above gives rise to various practical embodiments.
~ first embodiment employs two plano-convex lenses placed in two parallel planes perpendicular to the axis o~ the system, and has a cross section as shown in Fig. 5. The two lenses are de-noted by R and ~'; they each have a plane surface VPV' and a convex surface VOV' where profile V0 is identical to pro~ile OV'v and : corresponds exactly to curve A of E~ig. 2.
The whole equalizer operate~ in accordance with tha : aiagram of Fig. 3 where the lines L and L' represent len~es having the cross section ~hown in Fig. 5; light ray~ will pro~ress alony . the path~ denoted in Fig. 3.
: When the optical waveguide is a ~ircular fibre, th~
two len~es R and R' (Fig. 5) are symmetrical in space with respect to the axis oP (which is the common axis of khe sy~tem), so they will have a semi pseudo-toroidal shape, the plane surface of the lens being circular.
When the optical waveguide is a thin ribbon, in which the multi-mode propagation of light rays takes place only in the direction of the larger aimension of the ribbon, the tw~
lenses ~ and ~' will be symme~rical in space with respect to a plane passing through the axis OP and perpendicular to the plane of the drawing.
It transpires that for lenses having a plano-p~eudo-: bicylindrical shape, the ribbon will be placed with its larger dimension, that is in the direction of multimode propagation, orthognnal to the plane of symmetry, i~e, to the generatrices of the pseudo-cylinders. The plane surface of the lens will then be a rectangle~
In a second embodiment two plano-convex lenses are ~,7,~9~

again situated in two plane~ parallel and perp~ndicular ~o the axis of the systemO but have the cross section shown in Fig. 6.
The two lenses are denoted by H and H', and have a flat sur*ace CEC' and a convex surface CDC', where the profile CD is the same as profi.le DC' and exactly corresponds to the curve B o~ Fig. 2.
From the operating pcint of view, this equaliæer corresponds to the diagram of Fig. 4, where the lines ~ ana L' are replaced by the lenses H and H' of Fig. 6, and the light rays .
will progress along the paths sh~wn in Fig. 4.

Where the optical waveguide is a circular fibre, the ; two lenses H an~ H' ~Fig. 6) are symmetrical in space with respect to the axi~ DE (which is the common axi~ of the sys~em), and so ~` have a plano - cuspidal shape.

Where the optical waveguide is a thin ribbon, the two , ~' lenses H and H ' will be symmetrical in space with respect to a plane passing through axis DE and perpendicular to the plane of the drawing. Using len~es having a plano-pseudo-eylindrical shape, with a cross se~tion as shown in Fig. 6, the ribbon will be placed with its larger dimension, in which multimode propagation oc~urs, orthogonally with respect to the generatrices of the pseudo-cylinders, Another embodiment of the invention uses Fresnel lenses 9 whose profile is interrupted by a plurality of groo~es~ In this case, relation (6) allows the shape of th~ profile Z' (r) to be presented by the m-th groove to be derived. If a number M of groovesO increasing according to the perfection of equa~ization required is selected for the Fresnel lens, the following relation is obtained:
Z' Ir) = z(r) ~ Z (M w) (7) .
.

~ '7_~

.,here the variability field r for each groove is:

m 1 w ~ r ~ m w Function Z in (7) is obviously the same function z as in relation (6) which includes the double sign ~ and - , and is used to determine the shape of the Fre~nel lenses. Consider-: ing the ~ sign in relation (6), and thus in relation (7), the Fresnel lens has a toothed profile simulating curve A of Fig. 2;
considering the - sign in relation (6) and thu~ in relation ~7), the Fre~nel lens has a toothed profile simulating curve B of Fig, 2 By taking due account of what is stated above about th~ choice o a sy~tem of two converging, parallel, plano-convex lanses having their axi~ common with the axi~ of ths optical wave-guides, i~ is easy to derive ~he lens sy~tem~ whose cro~s seckions are sche~atically repre~ented in Figures 7 and 8. Fig. 7 shows Fresnel lenses having profiles simulating curve A of Fig. 2, and Fig. 8 shows Fresnel l~nses having profiles simulating curve B o Fig. 2. The paths of the light rays will correspond, as far as the pair of lenses shown in Fig. 7 is ¢oncerned, to the diagram o~ Fig. 3 and, as far as the pair of lenses of Fig. 8 is concer~ed, to the diagram of Fig. 4.
When the optical waveguide is a circular fibre, the two lenses K and :K' ~Fig. 7) or X and X' (Fig. 83 are symm~trical in space with respect to axis FG or ~Q respectively, so they have a shape analogous to the embod.iment shown in Fig. 5 in the case of the lenses of Fig. 7, and analogous to the embodiment of Fiy. 6 in the case of the lenses of Fig. 8; but the surface will ba formed by concentric rings and each ring will have a profile as given by relation (7).
: When the optical waveguide is a thin ribbon, the 1~)'7Z'-~9(~ .

wo lenses K and K' or X and X' will be symmetrical in space with respect to a plane passing through the axis FG (or NQ) and perpendicular to the plane of the dxawingO
Thus the lenses have a shape similar to the embodiment shown in FigO 5 (or in ~ig. 6), and the ribbon is again placed with its larger dimension orthogonal to the generatrices of the pseudo-cylinders; the surface of th~e lenses will have rectanyular straight grooves, and each yroove will have a profile as given by relation (7).
- The principles of the invention can be practically ;j embodied by use of holographic techniques.
More precisely, the bodies shown in Figures 3 and 4 by the lines L and ~', can be~ instead of lenses as in the previous cases, two holographic elements, on`which the profile3 of lenses of Fig. 5 and 6 respectively, are recorded as holograms~
In act, as known, a hologram acting as a lens may - be recorded by means of a lens. So the difficulties of embodiment - of the lenses just described may be overcome by making use o~
"holographic records". Holograms so recorded have the same effect on incident light rays as the lenses 5 and 6, and so for this type of embodiment also the previous considerations applying to the cases of circular fibres and thin ribbons remain valid. A suitable reproduction of the holograms will be adequate.
~ owever~ such holograms cause some losses, so they can replace the lenses previously suggested only when the available energy in the fibxe is such as to permit such losses.
Finally, the principles of the invention may be applied by using a graded-refractive-index transparent body.
It is known that recent techniques for production of : ~ "~ ; - 11 -:~V'~ 90 optical fibr~s permit the manufactura of cylindrical tran~parent bodies ~small bars or wire~) having a graded xefractive index profile, which varies in the direction of the cylinder radius.
More particularly, the so-called CVD (Chemical Vapour Deposition) technique has been developed, which allows cylindrical bodies to be obtained whose refractive-index ~ariance is a continuou~ function of the radius of the body itself. A cylinder having a refrartive index which varies in the direction of the radius according to any esired law can be obtained by this techni~ue.
By the same technique, transparen~ ribbons can also be made, having a graded-refractive index which varies along one of the Carte~ian axes of the cross section, for instance the axis of the larger dimension, while it remains constant on the second axis.
So a body of such a kind, either cylindrical or ribbon~
shaped, will be called hereinater a "graded index body"; its length will be determined by the condition that all the rays emerging from an end of a first se~ment of waveguide g ~Fig, 1) are conveyed, at the output of said graded index body, to the end of a second segment of waveguide g'~
It has been theoretically proposed and experiment~lly verified, that, for a system of lenses having specified optical characteristics, it is always possihle to realize a graded-inaex body able to modify incident light rays in the same manner as said system of le:nses.
In the present case, the system of lenses to be simulated, for instance that shown in Fig. 5~ is known, with formula (6~ re~ulating the convex profile z(r) of the lenses as func-tion of their mutual separation d, of the distance s of the lenses from the ends of the optical waveguides, and o~ the maximum guidance angle a M o the waveguides themselves~
: Thus it is possible to obtain by mathematical processing, a function n(r) determining the variation of the : refractive index inside the body, so as to make it e~uivalent to the above-mentioned system o~ lenses.
In this embodiment, the equalizer has the same external geometry whether the refractive index n~r) i~ o~tained from formula (6) taken with the sign ~ between the second and 10 third term inside square brackets, or n~r) i5 obtained from the same form~la taken with th~ sign - in th.i~ position.
Thi~ type o~ equalizer is schematically represented in Fig. 9, where S is the cro~s section of the graded-index body.
T'ne ~ifference batwePn the ~wo cases will ob~iou~ly consist in the law of variation of the refractive index of body S, according to whether the equivalent o the system shown in Fig~ 5 is wanted, or the system shown in Fig. 6.
Wh2n the optical waveguide i5 a circular fibre, the body S is a right cylindex having minimum radius w (Fig. 1) who~e length is de~ermined by the above-mentioned con~itions.
When the optical waveguide is a thin ribbon, ~ody S
is a right parallelepiped having a rectangular cross section, :. whose refractive :index varies in the direction of th~ larger dimension of its section (side y in Fig. 9) and remains constant in the orthogonal direction in the plane o~ the section~ For the other geometric d:imensions, the above considerations concerning cylindrical body S are 5'till valid.
The practical realization o an optical equalizer according to the present invention, whatever the realization may be 1~ 30 among those mentioned above, r~uires some common features.
The optical system and the terminals of the optical waveguide, should be embedded into a block of transparent material (not shown in the drawing) having the same refractive index as the core of the optical waveguide.
Moreover, when the equalizer is built for thin-ribbon waveguides, and equalization is thu~ required in one direction only, two reflecting slabs parallel to the plane o multimode propa~ation are needed. Such slabs are spaced by the thickness of the ribbon~ in such a position as to prolong, in effect, the cladding of the ribbon itself. Their longitudinal section parallel to the axis of the sy~tem is denoted by T in Figure g.
Modifications and variations can be made to the above described embodiments of the invention. For examp}e, the - lenses forming ~he syste~ may have a refractive index less than that of the medium in which they are embedded; in this case they sho~ld have a plano-concave shape, and their curved profiles will correspond again to one of the two relations given by (6~. If other form~
of lenses derived from formula (5) are used, it will be sufficient to derive from this form~la suitable profile~ for both symmetri~al and asymmetrical bi-concave lenses.

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Claims (11)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A full optical equalizer for connecting two segments of a multimode optical telecommunications waveguide with step refractive index profile, comprising an optical system consisting of or equivalent to two identical lenses coaxial with each other and said waveguide segments and placed in two parallel planes perpendicular to the axis of the system, the lenses having a focal length f(r) which varies according to the distance r from the axis of the system as a function of the distance s of each of the two lenses from the adjacent waveguide segments, of the distance d between the lenses, and of the maximum guidance angle ?M of the two waveguide segments, the function f(r) being defined for low guidance angle waveguides by the relation

2. A full optical equalizer according to claim 1, comprising an optical system formed by two identical converging plano-convex lenses each having a cross section consisting of two symmetrical profiles with respect to the axis of the lens, the convex face of each lens being defined by profiles obtained as a graphic representation of a mathematical function z(r) representing the profile required to obtain a lens exhibiting said function f(r).

3. A full optical equalizer according to claim 1, comprising an optical system formed by two identical plano-convex Fresnel lenses having a plurality of grooves; each lens having a section consisting of two symmetrical shapes with respect to the xis of the lens and having a face delimited by a plurality of grooves whose profiles are obtained as graphical representations of a function Z'(r) representing the profile required to obtain a lens exhibiting the function f(r).

4. A full optical equalizer according to claim 1, comprising two identical holographic elements recorded in such a way as to simulate said lenses.

5. A full optical equalizer according to claim 1, comprising a transparent body having a refractive graded index n(r) varying with the distance from the axis of the body, the size of said body being determined by the condition that all the rays leaving the first segment of waveguide are directed at the output from said body into the second segment of waveguide; the value of the refractive index of said body being obtained for each distance r from the axis of the body, through a mathematical function n(r) derived from said function f(r).

6. A full optical equalizer according to claim 2, wherein the optical waveguide is a circular fibre, and said converging plano-convex lenses are symmetrical in space with respect to the axis so that the plane surface of each lens has a circular shape.

7. A full optical equalizer according to claim 2, wherein the optical waveguide is a thin ribbon, and said converging plano-convex lenses are symmetrical in space with respect to a plane passing through their axis and perpendicular to the direction of the larger dimension of the cross section of said ribbon, so giving the plane surface of the lens a rectangular shape.

8. A full optical equalizer according to claim 5, wherein the optical waveguide is a circular fibre, and the trans-parent body having a graded refractive index is a cylinder whose refractive index varies radially.

9. A full optical equalizer according to claim 5, wherein the optical waveguide is a thin ribbon, and the transparent body having a graded refractive index is a right parallelepiped having a rectangular cross section, in which the larger dimension of said cross section has the same direction as the larger dimension of the cross section of said ribbon, and in which the refractive index varies along the direction of larger dimension.

10. A full optical equalizer according to claim 1, wherein said system of lenses has two identical refractive biconvex lenses, coaxial with each other and the segments of the optical waveguide.

11. A full optical equalizer according to claim 1, wherein said system of lenses has two identical refractive biconcave lenses, having a refractive index inferior to that of the surrounding medium, and coaxial with each other and to said guide segments.