CA1117334A

CA1117334A - Gradient index optical waveguide

Info

Publication number: CA1117334A
Application number: CA000308482A
Authority: CA
Inventors: Suresh T. Gulati; George W. Scherer
Original assignee: Corning Glass Works
Current assignee: Corning Glass Works
Priority date: 1977-09-29
Filing date: 1978-07-31
Publication date: 1982-02-02
Also published as: BR7805597A; GB2004863B; NL174137C; NL174137B; NL7809849A; IT7828261A0; GB2004863A; AT388725B; FR2404864B1; FR2404864A1; ATA701778A; DE2841909A1; DE2841909B2; JPS6216904U; JPS5464134A; IT1099618B

Abstract

ABSTRACT OF THE DISCLOSURE

In the method of making a preform for a high numerical aperture gradient index optical waveguide, the concentration of two dopant constituents is changed during fabrication. Concentration of the first dopant, GeO2 is changed radially as the perform is built up in order to produce the desired radial refractive index gradient. the concentration of the second dopant, B2O3 is changed radially to compensate for the radial change * in thermal expansion coefficient caused by the varying GeO2 concentration. B2O3 is added to the cladding layer to make the thermal expansion coefficient of the cladding equal to or greater than the composite thermal expansion coefficient of the core. The magnitude of residual tension at the inner surface caused by thermal expansion gradients is reduced and premature cracking of the perform is eliminated.

Description

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Background Of The Invention ~. .
This invention relates to optical waveguides and more particularly to a method of making a high numerical aperture gradient index waveguide.
Waveguides used in optical communication systems are herein referred to as "optical waveguides," and are normally constructed from a transparent dielectric material, such as glass or plastic.
Gradient l~ndex optical waveguides have a radially varying composition and consequently a radially varying re~ract~ve index. These waveguides focus light propagated axially along them. This focusing effect is descri~ed as a high numerical aperture~ U. S. Patents 3,823,995, Carpenter and 3,826,560, Schultz, describe techni~ues for making gradient index optical waveguides.
The aforementioned Schultz patent describes a flame hydrolysis technique (now considered to be oxidation) for making a glass preform ~herein the concentration of a dopant added to a glass forming silicon compound is changed as the ~0 preform is built~up radially. Changing concentration of the dopant changes the refractive index in the desired manner.
Optical waveguldes having high numerical aperture values tapproximately 0.2Q or more~ have a sharp ra~ial composition gradient wh;ch causes stress in the waveguide.
These stresses arise from the variation in the thermal expansion coefficient introduced by the radial variation in composition. Also, in outside vapor phase oxidation processes, such as that described in the aforementioned ,.. ~ ' ~

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.

Schultz patent, removal of the starting member from the preform results in a small hole at the center. Residual tension in the waveguide has its highest value at the surface of this hole. All of these stresses cause fracture and failure when the preform i5 sintered into an optical waveguide preform and cooled. It is desirable to reduce these stresses.

Summary Of The Invention .
In accordance with this invention, stress is considerably reduced in a gradient index optical waveguide by radially controlling the concentration of the composition forming the waveguide.
In carrying out the invention, the concentration of one or more dopants is changed rildially as the preform is ; 15 built-up to produce a radially vary:ing index of refraction and the concentration of another dopan~, B2O3, is changed radially to compensate for the radial change in thermal expansion coefficient caused by the change in concentra-tion of the first constituent~
Further in accordance with the invention, a constituent having substantially no effect on the index of refraction is added to the cladding glass of an optical waveguide to increase the thermal expansion coefficient of the cladding so that it is approximately equal to the composite thermal expansion coeffifrient of the core of the waveguide. f It is an object of the present invention to - minimize the residual tension at the inner surace of an optical waveguidc preform.

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It is another object of the present invention to control the composition of an optical waveguide so that the inner part of the waveguide preform is placed under compression when it cools.
- Thus the present invention provides the method of making an optical waveguide having a radial gradient index of refraction comprising: forming a glass tubular member having at least two constituents; radially changing the concentration of a first of said constituents while forming to produce a radially varying index of refraction, and radially changing the concentration of a second of said constituents while forming to compensate for the radial change in thermal expansion coefficient caused by the change in concentration of said first constituent.
In a preferred aspect the present invention provides the method of making an optical wavegu:ide having a radial gradient index of refraction in the core thereof comprising:
forming a glass tubular member having at least two constituents, a first of said const1tuents being a dopant which produces glass having decreasing refractive index and thermal expansion . -~
coefficient with decreasing concentration, a second of said constituents being a dopant producing increasing thermal expansion coefficient with increasing concentration; radially .
changing the concentration of said first of said constituents while forming to produce a radially varying index of refraction;
radially changing the concentration of said second of said constituents radially while forming to maintain the thermal expansion coefficient substantially constant throughout said radial gradient of said tubular member; coating said tubular member with a layer of cladding glass having an index of ~,, i ~733~

of refraction less than that of said core; and adding to the composition of said cladding layer a constituent producing substantially no increase in the index of refraction and which increases the thermal expansion coefficient of said cladding to approximately the composite thermal expansion coefficient of said core so that residual stresses in said core caused-by a different expansion coefficient cladding become compressive.
In one aspect such a method is provided wherein the step of forming a glass tubular member is performed by outside vapor phase oxidation including the steps of: providing a substantially cylindrical starting member; rotating said member about the longitudinal axis thereof; entraining in a gaseous medium predetermined amounts of each of said constituents in vapor form; oxidizing said vapors in a flame to form a soot having a specified composition; and applying ~ -said soot to the exterior peripheral surface of said member;
and wherein the steps of radially changing the concentration of said constituents includes: varying the amount of vapor entrained in said gaseous medium of at least two of said constituents to radially change the concentrations of said first and said second constituents. Preferably said first constitu-ent is a dopant which produces glass having decreasing refractive index and thermal expansion coefficient with decreasing concentration, and wherein said second constituent is a dopant producing increasing thermal expansion coefficient and substantially no increase in index of refraction with increasing concentration.
In another aspect the invention provides such a method wherein said tubular member forms a core having a composite thermal expansion coefficient and further comprising coating said tubular member with a layer of cladding glass - 4(a) -~9L733~

having an index of refraction less than that of said core; and adding to the composition of said cladding layer a constituent producing substantially no increase in the index of refraction and which increases the thermal expansion coefficient of said cl-adding to approximately the composite thermal expansion coefficient of said core. Preferably said composite thermal-coefficient of expansion is given by: ~s = 1 (o~ + ~O) where ~s is said composite thermal expansion coefficient, ~i is the thermal expansion coefficient at the inner radius of said tubular member and ~ is the thermal expansion coefficient at the outer radius of said tubular member.
In another aspect the invention provides such a method of maki.ng an optical waveguide having a parabolic radial gradient index of refraction comprising: forming a glass tubular core member having at least two constituents; radially changing the concentration of one of said constituents to produce a parabolic radially varying index of refraction, and radially changing the concentration of another o~ said constitu-ents to compensate for the radial change in thermal expansion coefficient caused by the change in concentration of said first constituent.
In another embodiment the invention provides an optical waveguide having a radial graded index of refraction, said optical waveguide being formed from a glass tubular member having at least two constituents, the concentration of a first of said constituents varying radially to produce said radial graded index of refraction, the concentration of a second of said constituents varying radially to compensate for the radial change in thermal expansion coefficient caused by the change in concentration of said first constituent.

,~
- 4(b) -,. . ..

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In still a further embodiment the invention provides `
an optical waveguide comprising: a glass core; a coating of cladding glass on said core; said cladding glass being formed with a composition including a constituent having substantially no-effect on the index of refraction and which increases the thermal expansion coefficient of said cladding to approximately the composite thermal expansion coefficient of said core.
Description Of The Drawings Fig. 1 depicts the process of making an optical waveguide preform in accordance with this invention;
Fig. 2 shows the radial variation of axial stress in an optical waveguide preform;
Fig. 3 shows the variation of circumferential stress with radial coordinate in an optical waveguide preform;
Fig. 4 shows the distribution of axial and circumferential stresses in an optical waveguide preform; and Fig. 5 shows axial stress as a function of expansion coefficient o~ the cladding.
Description Of The Pr~ferred Embodiment Referring to Fig. 1, a layer 10 of glass is applied to a substantially cylindrical glass starting member or bait rod ll by means of outside vapor phase oxidation burner 12. ~-Fuel gas and oxygen or air are supplied to burner 12 from a source not shown by a suitable means such as pipe 13. This mixture is burned to produce flame 14 which is emitted from the burner.
Containers 15, 16 and 17 hold quantities of liquid constituents 18, 19 and 20 respectively which will ultimately form layer 10. A suitable gaseous medium, such as oxygen or the like, is supplied to the containers and - 4(c) -, - -;

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bubbled through the liquids by means of tubes 21, 22 and 23. The gaseous medium or carrier gas is supplied from a suitable source, not shown, in predetermined quantities and at predetermined pressures. The flow of carrier gas which is bubbled through liquid constituent 18 in container 15 is regulated by valve 24, the flow rate of this carrier gas being indicated by gauge ~5.
Similarly, the flows of carrier gas bubbled through liquid constituents l9 and 20 in containers 16 and 17 are regulated b~ valves 26 and 27 with the flow rates oE these gases being indicated by gauges 28 and 29.
The liquid constituents in the containers are maintained at the desired temperatures by heaters.
As the carrier gas is bubbled through the heated liquid constituents, vapors of this liquid become entrained in the carrier gas and are exhausted by means of tube or pipe 30. The carrier gas vapor mixture is fed to outside vapor phase oxidation burner 12 and is injected into flame 14 wherein the gas vapox mixture is oxidized to form a glass soot. The soot leaves 1ame 14 in a stream which is directed toward starting member ll. Starting member ll is both rotated and translated as indicated by the arrows adjacent the supporting end of the starting member so that a uniform deposition of soot is applied to the starting member.
Of course, it will be understood that a plurality of burners, in a row or radially displaced, can be provided adjacent the starting member so that a longitudinally uniform soot layer can be produced without ~he need for translating the starting member. In such an embodiment, starting mcmber ll would only have to be rotated.

`'`'' ~ 3~a Containers 15 17 contain a glass forming compound a~d at least two dopants. As an example, container 15 contains SiC14, container 16 contains GeC14 and container iZ7 contains BC13. The valves 24 and 26 are controlled in the manne-r described, for example, i~ the aforementioned ~chultz patent to produce a preform which has a parabolic gr~dient index of reraction. Simultaneously, valvs 27 is controlled to introduce a varying concentration of the ;~
, second dopant into the flame oxidation ~tream. In the ;o example under consideration, the concentration of GeO2, çontrolled by valve 26, is decreased as the layer 10 builds ~p radially. This has the effect of producing a parabolically ~ecreasing radial index of refraction in the layer 10.
~imultaneously, the concentration of B;203, controlled by valve 27, is increased. B203 has substantially no effect on the index of refraction. (Actually B203 lowers the index o refraction very slightly with incre~sing concentration).
B203 has the ffect of i~creasing the thermal expansion coefficient with increasing concentration. Thereforer ~y !0 changing the concentration of B203 radially, compensation can be made or the radial change in thermal expansion coeffi cient which would otherwise be caused by the decrease in concentration of the GeO~. By adjusting the germanium and ~oric oxide dopant variations in the preform, th~ residual `5 tension at the inner surface can be minimized.
The foregoing process is commonly referred to as out-side vapor phase oxidatio~ (OVPO). After the gradient index ;;
preform is laid down, a cladding layer is applied to the preform.

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Application of the cladding layer is also commonly earried out by OVPO or flame oxidation as depicted in ~' Fig. 1. In order to further reduce residual tension in the preform or eliminate it altogether, the concentrations of the constituents forming the cladding composition are adjusted. The amount of boric oxide added to the eladding layer is controlled by valve 27 so that the thermal expan-sion coefficient of the eladding is slightly higher than the composite expansion coefficient of the gradient core at the set point. In this mannex, residual stresses in the core due to a higher expansion eladding become eompressive and nullify any tension at the inner surface which was previously present due to parabolie expansion variation of the core. The clad_ing itself would then experience a slight tension but since the surEace quality of cladding is superior, it can withstand a slight tension without eausing failure of the preform. Furthermore, the value of this tension in the cladding can be kept at a safe level by adjusting the boric oxide content.
The manner in which the concentrations of the constituents are changed to eliminate stress will be apparent from the following analysis and examples.
The thermal-elastic properties of the gradient eore are related to the composition profile in the follow-ing manner:

~ 9.'733 s ~ 1 X ~ ~-, Y - ~3 XY + ~ x2 ~ ~ y2 L~
: s o l X ~ T2 Y ~ T3 XY ~ T4 x2 ~ T5 y2 (:21 . 0 1 X ~ E2 Y ~ E3 XY ~ E4 x2 + E5 y2 (3) - In the above equations ~s is the expansion coefficient at the ~ setting temperature, Ts is the setting temperature, E is ;'~ the elastic modulus at room temperature and X and Y axe weight percents of two different oxides which vary parabolically with the xadial position:
.;
`','''`, 10 X Xo Xl d2 _ a2 Y yO 1 d2 _ a2 ~. and in which a is the radius of the hole in the preform and d ,, is the outer radius of the gradient core.
~:~. Substitutions of eqns. (4) and (5) in eqns. (1) through : (3)\along with the neglect of mixed and second order terms results in the parabolic variation oi- thermal expansion coeffi-, cient, setting temperature and elasti.c modulus with the radial : coordinate r:
~ 2 2 - 20 as (r) = ~1 ~ (ai ~ aO~ ( d2 a2~ (6) ~ .

Ts (r) = Ti ~ (Ti ~ To) (d2 a2) ~ E (r~ = ~i ~ (Ei Eo) (d2 a2) (8) ;

: 30 L73;;3~
`~. .
In these equations, the subscripts i and o denote the property value at r = a and r = d respectively.
For the purposes of analysis of residual stress, it is convenient to integrate equations (6) through (83 over the gradient core to obtain an average value of the property. Pro-ceeding in this manner and denoting the average propexty value ^~ with a bar, we obtain the following remarkably simple expressions:
.. .

s 2 i o) (9) ~; 10 Ts = 2 (Ti + o (10) :: .
E = 1 (Ei + Eo) (11) ;~ Treating the gradient core as a hollow circular ;~ cylinder with an average setting temperature of Ts and an ` average elastic modulus and Poisson~s ratio of E and v, the residual stresses in the circumferential and axial directions which are the largest stresses, upon cooling from the setting temperature to room temperature are given by:

(l_~R T5~ [( 2 2) l~ ~S rdr ~ Ira aS rdr - ~sr2~(12) E (TR-TS) ~(d2 2) a a5 r dr ~ as~ (13) where TR denotes room temperature. The foregoing is explained in more detail in Timoshenko, S. P.; "Theory of Elasticity,"
Second Ed.; McGraw Hill, New York (1951).
Substitution of equations (6) into equations (12) and (13), followed by integration, results in the d0sired expressions for residual stresses due to parabolic variation of the thermal expansion coefficient in the gradient core:
; 30 , .

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, .
o) (T~-TR~ ~(r -a 1 (.r ~d~) ~ r~; (14]
(1 v~ (~d -a ~ 4 r (r~ = - i o S R) ¦ (d2 + a ) - r2 1 (15) (l-v) ~d -a ) .~ It is interesting to note that .,, ,: ,,.

~6 (a) = ~z (a) - i ( S TR) (16)

2 ( l-V !

` 10 aA (d) = ~ (d) = i ( S TR) (17) 7~'-'.' ; i.e., the circumferential and axial stresses are equal both :; at the surface of the hole and at the outer surface of the gradient core. This is a direct consequence of the parabolic variation of the expension coeffic.ient. Also observe that equations (16) and (17) give the maximum values of l:ensile and compressive .,` stresses respectively in the gradient core.
The stress analysis of the gradient index core surroundea by a cladding of constant composition is obtained by linear superposition of the foregoing solution and the addition- ~
al stresses caused by cladding glass of constant composition~ ~' Denote the cladding properties by ~c~ Tc and Ec and its outer radius by e. We treat the preform (without the cladding) as a core whose average properties are ~s' Ts and E and are given by equations (9) through (11). Also assume that the Poisson's ratios of core and cladding glasses are equal and are denoted by v. Then the circumferential and axial stresses, which are the largest stresses, introduced upon cooling of the preform to room temperature are given by:

~, .. _ 2 ; ~E~ ~C-~R) ( ~s~~c~ a,2~ ~
tr)=--- 2- ~ 2 ¦ (18) l-2v + ~ ~ m~ (1-2v ~ a2 ~ ¦
, ~ core ! ~ c( C TR) (~s ~c) (1 + d2 ~ m~ a2) ~z2 d 2 - (19) (l+~m) [1-2v + e2 + m~ (1-2v + a2)~

and ~.
. _ 2 Ec (TC-TR) (~s ~c) x2 1 (20) r e2 2 ~ I
:Ll-2v + 2 + m~ (1-2v + a2 ~ ~cladding . I

a = _ c ( C TR) (~s ~c) (1 ~ 2 + m~ a2 ) ¦ (21) z - _. ... 2 I
(l+~m) [1-2v + e2 + m~ 2v + a2)~ J
where . m = E /E
. and e2 _ d2 ~` 20 d' - aG
The foregoin~ is explained in~more detail in Rawson, H,; "The Theory of Stresses in Two-Component Glass-to-Me~al Tube Seals,"
J. Sci. Instr., Vol. 26 (1949). It should be noted that the axial stress is independent of radial coordinate r whereas the circumferential stress is not. The radial stress in the core is tensile and its magnitude is of the order of circum-ferential stress; the axial stress is the largest stress. Thus the core is in the state of triaxial tension except at the inner surface of the hole where the radial stress vanishes~

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The net s~re~ses in the core are given by the sum of equations (14~ and ~18~ and equations (15~ and ~191.
Similarly the net stresses in the cladding are given by the sum of equations (14) and (20) and equations (15~ and (21~. It follows immediately from equations (18~ through (21) that by adjusting the composition of the cladding glass, its expansion coefficient ~c can be made either larger or smaller than ~s " so that the additional stresses given by equations (18) and (19) can offset those given by equations (14) and (15). The net result, of course, would be a low-stress preform with little or no danger of spontaneous failure.
The above is illustrated by two examples. First, consider a gradient core whose average properties are ~s ~ 14.4 x 10 /C

Ts 805C

E ~ 8.4 x 106 psi `: :
= 0.2 Figures 2 and 3 show the variation of axial and cir-cumferential (equations 14 and 15) stresses with r for preforms -with the above core and three different cladding compositions.
As the expansion difference (ai ~ aO) and the setting temperature Ts decrease, the maximum values of axial and circumferential stresses at the surface of the hole also decrease. This is an ` effective technique to minimize the stress level.

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; As a second example consider a gradient preform with cladding of constant composition. The average properties ~ of core and cladding are assumed as:
... ~ _ 7 . ~ , ' ' . ' . , ~;
-~ 5 - Ts ~ 795C

~C ~ E ~ 9.6 ~ ~0 psi . v _,. 0.1~ ...
^, .
C ~ 3 X 10 . . . Tc~~ 92~C
~ , . . . .
lQ The axial and circumferential stresses as given by eqns.
14, 15 and 18 through 21 are plotted as a function of r in Fig. 4. The agreement between the solution given here (solid line~ and that given by inite element analysis (dotted line) is extremely good. The large magnitude of axial tension at the surface of the hole should be note~ Such a high tension may cause failure of the preform due to the presence of flaws at the surface of the hole. Since ac < ~s~ ~he effect of cladding is extremely harmful inso~ar as residual stresses are concerned. We may reduce the high level of core tension 2Q by increasing ac through appropriate composition adjustments.
Figure 5 shows the dependence of axial tension at the surface of the hole on the expansion coeficient of the cladding. It is clear that the core tension can be reduced drastically by modest changes in the expansion coefficient of the cladding.
Likewise, the axial stress in the cladding can be kept very low. Also, if the composition modifications reduce the ; setting temperature oE the cladding, the stresses will decre~lse correspondingly.

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~n example of a preform which was successfully prepared in accordance with this invention is one containing 25% GeO2 and 2% B203 at the bait rod surface and 0% GeO~ and 16% B~03 at the outside diameter. The concentrati~ns of these oxides were varied parabolically. The preforms were examined undex polarized light to obtain a measure of residual tension.
The axial tension at the bait surface was measured to be 2430 psi. Similar-~13~ the clrcumferential stress was measured (using a disc cut from the preform) to be 3900 psi. In the past, high NA preforms had residual tension > 9000 psio This shows that composition changes reduce the harmful tensile stresses, and make the high NA preform more likely to survive the consolidation and acid-etching processes.
Optical waveguides were drawn from the exemplary preform and drew very well despite wide variation of viscosity due to composition profile. The measured N~ (90~) ~; values were 0.194 and 0.191.
: In the preceding example, both GeO2 and B203 were varied parabolically. It is also possible to vary the concentra-tion of GeO2 parabolically and to vary the concentration of B203 in a manner which maintains the thermal expansion co-efficient constant throughout the preform. The radial change ~ in concentration of GeO2, denoted G(r), is chosen to suit optical - re~uirements. Then, the radial change in concentration of B203, denoted B(r) is such that the expansion coefficient is constant. It is known that the thermal expansion coefficient is related to the concentration of the t~; components by the following: ~ ' .
. ~ .

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aO + al B + a2 G + a3B2 ~ a4G2 (22) ; where B is the concentration of B203, G is the coneentration of GeO2 and the constants aO, al ... a4 ean be determined . empirically.
Assume a radial parabolie ehange in eoncentration of GeO2 which is given by ; G(r) - Go [1 (r/re) ] (23) where Go is the peak GeO2 eoncentration and a is the profile parameter, typically about 2.2.
Then, the radial variation in eoncentration of B203 is given by:

) al ~ [al 4a3 (aO + a2G~r) ~ a4 G2(r) - X )] (24) 2a3 ;.
where XO is the thermal expansion eoeficient throughout the blank.
The foregoing technique of minimizing undesirable residual tension at ~he surfaee of the hole by adjusting the dopants' concentration is ec~ally applicable to the preform manufaetured by the inside proeess described in Keck and Schultz U. S. patent 3,711,262. In particular, if the preform obtained by the inside process has a hole at the center ater sintering and consolidation, the advantages deseribed above regarding the outside process preform are e~ually applicable to the inside process preform.
Chemical vapor c'eposition processes can also be used.
While a particular embodiment o the invention has been shown and described, various modifications are within the true splrit and scope of the invention. The appended claims are intended to cover all such modifications.
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Claims

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. The method of making an optical waveguide having a radial gradient index of refraction comprising:
forming a glass tubular member having at least two constituents;
radially changing the concentration of a first of said constituents while forming to produce a radially varying index of refraction, and radially changing the concentration of a second of said constituents while forming to compensate for the radial change in thermal expansion coefficient caused by the change in concentration of said first constituent.

2. The method recited in claim 1 wherein the step of forming a glass tubular member is performed by outside vapor phase oxidation including the steps of:
providing a substantially cylindrical starting member;
rotating said member about the longitudinal axis thereof;
entraining in a gaseous medium predetermined amounts of each of said constituents in vapor form;
oxidizing said vapors in a flame to form a soot having a specified composition; and applying said soot to the exterior peripheral surface of said member; and wherein the steps of radially changing the concentration of said constituents includes:
varying the amount of vapor entrained in said gaseous medium of at least two of said constituents to radially change the concentrations of said first and said second constituents.

3. The method recited in claim 2 wherein said first constituent is a dopant which produces glass having decreasing refractive index and thermal expansion coefficient with decreasing concentration, and wherein said second constituent is a dopant producing increasing thermal expansion coefficient and substantially no increase in index of refrac-tion with increasing concentration.

4. The method recited in claim 3 wherein said first constituent is GeO2.

5. The method recited in claim 1 wherein said second constituent is B2O3.

6. The method recited in claim 1 wherein said tubular member forms a core having a composite thermal expansion coefficient and further comprising coating said tubular member with a layer of cladding glass having an index of refraction less than that of said core; and adding to the composition of said cladding layer a constituent producing substantially no increase in the index of refraction and which increases the thermal expansion coefficient of said cladding to approximately the composite thermal expansion coefficient of said core.

7, The method recited in claim 6 wherein the constituent added to the composition of said cladding layer is B2O3.

8. The method recited in claim 6 wherein said composite thermal coefficient of expansion is given by:

?s = ? (.alpha.i + .alpha.o) where ?s is said composite thermal expansion coefficient, .alpha.i is the thermal expansion coefficient at the inner radius of said tubular member and .alpha.o is the thermal expansion coefficient at the outer radius of said tubular member.

9. The method of making an optical waveguide having a parabolic radial gradient index of refraction comprising:
forming a glass tubular core member having at least two constituents;
radially changing the concentration of one of said constituents to produce a parabolic radially varying index of refraction, and radially changing the concentration of another of said constituents to compensate for the radial change in thermal expansion coefficient caused by the change in concentration of said first constituent.

10. The method recited in claim 1 wherein the concentrations of said first and second constituents are changed parabolically.

11. The method recited in claim 1 wherein the concentration of said one of said constituents is changed para-bolically and the concentration of the other of said constituents is changed radially to maintain the thermal expansion coefficient constant throughout said glass tubular member.

12. The method of making an optical waveguide having a radial gradient index of refraction in the core thereof comprising:
forming a glass tubular member having at least two constituents, a first of said constituents being a dopant which produces glass having decreasing refractive index and thermal expansion coefficient with decreasing concentration, a second of said constituents being a dopant producing increasing thermal expansion coefficient with increasing concentration;
radially changing the concentration of said first of said constituents while forming to produce a radially varying index of refraction;
radially changing the concentration of said second of said constituents radially while forming to maintain the thermal expansion coefficient substantially constant throughout said radial gradient of said tubular member;
coating said tubular member with a layer of cladding glass having an index of refraction less than that of said core; and adding to the composition of said cladding layer a constituent producing substantially no increase in the index of refraction and which increases the thermal expansion coefficient of said cladding to approximately the composite thermal expansion coefficient of said core so that residual stresses in said core caused by a different expansion coefficient cladding become compressive.