Achromatic overclad fiber optic coupler

Abstract

An achromatic fiber optic coupler of the type wherein a plurality of single-mode optical fibers, each having a core and a cladding, are fused together along a portion of the lengths thereof to form a coupling region. The propagation constants of the fibers are preferably equal; however if the fiber claddings have different refractive indices, the lowest cladding refractive index is n₂. A matrix glass body of refractive index n₃ surrounds the coupling region, n₃ being lower than n₂ by such an amount that the value of Δ₂-3 is less than 0.125%, wherein Δ₂-3 equals (n₂²- n₃²)2n₂².

Description

BACKGROUND OF THE INVENTION

This invention relates to single-mode fiber optic couplers that are capable of effecting a relatively uniform coupling of light between fibers over a relatively broad band of wavelengths.

Fused fiber couplers have been formed by positioning a plurality of fibers in a side-by-side relationship along a suitable length thereof and fusing the claddings together to secure the fibers and reduce the spacings between the cores. Various coupler properties can be improved by inserting the fibers into a capillary tube prior to heating and stretching the fibers, thereby resulting in the formation of an "overclad coupler". To form an overclad coupler, the fibers are inserted into a tube, the tube is evacuated, and its midregion is heated and collapsed onto the fibers. The central portion of the midregion is thereafter drawn down to that diameter and coupling length which is necessary to obtain the desired coupling.

Identical optical fibers were heretofore used to make a standard coupler, the couplinq ratio of which is very wavelength dependent, i.e. if it exhibits 3 dB coupling at 1310 nm it cannot function as a 3 dB coupler at 1550 nm because of that wavelength dependence. A "standard coupler" might be characterized in terms of its power transfer characteristics in a window centered about 1310 nm, which is referred to as the rust window. For example, a standard coupler might exhibit a coupling ratio that does not vary more than about ±5% within a 60 nm window.

An "achromatic coupler" is one wherein the coupling ratio is less sensitive to wavelenqth than it is for a standard coupler. There is no widely accepted definition of an "achromatic coupler". The least stringent definition would merely require an achromatic coupler to exhibit better power transfer characteristics than the standard coupler in the first window. More realistically, the specification is tightened by requiring an achromatic coupler to perform much better than the standard coupler in that first window, or to require it to exhibit low power transfer slopes in two windows of specified widths. These windows might be specified, for example, as being 100 nm wide and centered around about 1310 nm and 1530 nm. These windows need not have the same width; their widths could be 80 nm and 60 nm, for example. An optimally performing achromatic coupler would be capable of exhibiting low values of coupled power slope over essentially the entire single-mode operating region. For silica-based optical fibers this operating region might be specified as being between 1260 nm and 1580 nm, for example.

In the following discussion, the relative refractive index difference Δ_a-b between two materials with refractive indices n_a and n_b is defined as

Δ_a-b =(n_a² -n_b²)/(2n_a²) (1)

For simplicity of expression, Δ is often expressed in percent, i.e. one hundred times Δ.

Heretofore, achromatic couplers were formed by employing fibers having different propagation constants for the fundamental mode in the coupling region, i.e. by using fibers of different diameter and/or fibers of different refractive index profile or by tapering or etching one of two identical fibers more than the other.

U.S. Pat. Nos. 5,011,251 and 5,044,716 teach overclad achromatic fiber optic couplers wherein the coupled fibers are surrounded by matrix glass having a refractive index n₃ that is lower than that of the fiber cladding material. The propagation constants of the coupler fibers are different since the fibers have different cladding refractive indices. The difference between the refractive index n₂ of the cladding of the first fiber and the refractive index n₂ ' of the cladding of the second fiber is such that the coupler exhibits very little change in coupling ratio with wavelength over a relatively wide band of wavelengths.

U.S. Pat. Nos. 5,011,251 and 5,044,716 characterize the tube refractive index n₃ by the symbol Δ₂-3, the value of which is obtained by substituting n₂ and n₃ for n_a and n_b in equation (1). Commercially available single-mode optical fibers usually have a value of n₂ that is equal to or near that of silica. If silica is employed as the base glass for the tube, a dopant is added thereto for the purpose of decreasing the tube refractive index n₃ to a value lower rinq ring fibers. Based on the teachings of U.S. Pat. No. 5,011,251, it is thought that a maximum Δβ of about 0.002 μm-1 might be useful in such a coupler. Such a Δβ value can be obtained by employing a central fiber having slightly different cladding refractive index than the ring fibers. The difference between the lowest refractive index n₂ and the highest fiber cladding refractive index n₂ ' should be sufficiently small that Δ_CLADS will preferably be less than 0.03%. The value of Δ_CLADS is obtained by substituting the cladding indices n₂ and n₂ ' for n_a and n_b of equation (1) and solving for Δ. In the event that the claddinqs of the fibers have slightly different refractive indices, the lowest refractive index n₂ is to be used for the purpose of calculating Δ₂-3.

The coupled mode theory can be generalized to the case of N fibers around 1 fiber (N>2) (see, for example, FIGS. 14 and 19-21). The coupling constant between any two fibers is defined as it was in the 2×2 case. The index structure in this case is too complicated to solve without further simplification or more complicated modeling. As a first approximation, the following case was considered: all fibers except for the two in question are replaced by overcladding index material. This then allows exact solution. If only nearest-neighbor coupling is considered (usually a good approximation), and it is assumed that power is input into the central fiber, then the power as a function of length in any one of the ring fibers is given by

P_j (z)=F² /N sin² (Cz/F)j=1, . . .,N (8)

where ##EQU3## β_o is the propagation constant of the central fiber; β₁ is the propagation constant of the ring fibers, all of which are assumed to be identical (the model can be extended to non-identical); C=N^1/2 C₀1 ; C₀1 is the coupling between central and each ring fiber (C₀1 =C₀2 =. . . =C_ON); and C₁2 is the coupling between adjacent ring fibers (C₁2 =C₂3 =. . . ).

The central fiber power, which is assumed to be 1 on input, is given by

P_o (Z)=1-F² sin² (Cz/F) (10)

The physical mechanism leading to improved achromaticity in an M×N coupler is identical to that leading to achromaticity improvements in a 2×2 coupler. Further, the improvements are similar for similar Δ₂-3 values, and the nonadiabatic mode coupling limitations are also thought to be similar. Thus, a similar range of Δ₂-3 values should give optimum functionality for M×N couplers as for 2×2 couplers.

There are a number of different approaches that can be taken to achieve the required very small values of Δ₂-3. One approach involves the use of a pure SiO₂ tube and optical fibers having chlorine doped claddings to provide them with a refractive index greater than that of the silica tube. This technique provides good control of refractive index of both tube and fiber cladding. Polarization variability was good. The major disadvantage of this combination of glasses was that it resulted in very little difference in viscosity between the tube and the fibers. This caused the fibers to deform and resulted in relatively high excess loss.

Commercially available single-mode optical fibers usually have a value of n₂ that is equal to or near that of silica. When this type of fiber is employed, the tube can be formed of silica doped with a small amount of B₂ O₃. (in the range of 0.15 wt. % to 1.0 wt. %) . The B₂ O₃ softens the tube glass relative to the fiber cladding glass, thereby resulting in the formation of couplers having low excess loss. If the tube is formed of SiO₂ doped with more than 2.0 wt. % B₂ O₃, the fibers can be clad with a glass comprising SiO₂ doped with a sufficient amount of fluorine to depress the cladding refractive index to the level necessary to provide a Δ₂-3 value less than 0.125%.

A further approach is to form the tube from a base glass doped with one or more refractive index-decreasing dopants such as B₂ O₃ and fluorine and one or more refractive index-increasing dopants such as GeO₂ and TiO₂. The combination of the two types of dopants provides a refractive index n₃ that results in the desired value of Δ₂-3. Employing tubes of relatively soft glass enhances to a certain extent the collapsing of the tube onto the fibers; the tube glass flows around the fibers without distorting their shape.

Tube O is preferably made by a vapor deposition technique sometimes referred to as the flame hydrolysis process (see U.S. patent application Ser. No. 07/809,697 filed Dec. 16, 1991). The tube could also be formed from melted glass or by a sol gel technique.

Tubes having radial changes in composition have also been employed to make achromatic couplers. The inner region of the tube adjacent the tube bore is formed of a composition that provides the desired value of Δ₂-3. The remainder of the tube can be formed of one or more regions having refractive indices that differ from the inner region. Reference is made to FIG. 6. For example, the inner region of the tube between the inner surface r_is and transition radius r_t can contain a small amount of B₂ O₃ within the range of 0.15 wt. % and 2.0 wt. % to provide a sufficiently low value of Δ₂-3 to provide the coupler with achromaticity. The outer tube region between r_t and the outer surface r_o may contain n higher concentration of B₂ O₃ than the inner region. The higher B₂ O₃ concentration results in a lower refractive index region, thereby better confining the optical power. Couplers having similar excess losses have been achieved using both substantially constant radial refractive index tubes and tubes having a step decrease in refractive index with radius.

Whereas the preferred manufacturing technique results in a coupler having optical fiber pigtails extending therefrom, the invention also applies to overclad couplers of the type wherein the fibers extend through the elongated matrix glass body but end flush with the body endface. Methods of making such a coupler are disclosed in U.S. Pat. Nos. 4,773,924 and 4,799,949. Briefly the method comprises inserting a plurality of optical fiber preform rods into a glass tube, heating and stretching the resultant preform to form a glass rod which is then severed into a plurality of units. Heat is applied to the central region of each unit, and the central region is stretched to form a tapered region as described herein.

EXAMPLE 1

A method of making a 1×2 achromatic fiber optic double window switch is illustrated in FIGS. 7-10. A glass capillary tube 10 having a 3.8 cm length, 2.8 mm outside diameter, and 265 μm longitudinal bore diameter was employed. Tube 10, which was formed by a flame hydrolysis process, had a refractive index gradient of the type shown in FIG. 6. The inner region between r_is and r_t consisted of silica doped with about 8.0 wt. % B₂ O₃ and 2.5 wt. % GeO₂. The outer region between r_t and r_o consisted of silica doped with about 8 wt. % B₂ O₃. The thickness of the inner region was 300 μm. The value of Δ₂-3 was measured optically to be 0.02%.

Coated fibers 17 and 18 comprised 125 μm diameter single-mode optical fibers 19 and 20 having a 250 μm diameter urethane acrylate coatings 21 and 22, respectively. Both fibers had an 8 μm diameter core of silica doped with 8.5 wt. % GeO₂. The cutoff wavelengths of the fibers are below the operating wavelength of the coupler. If, for example, the minimum operating wavelength is 1260 nm, the cutoff wavelengths of the fibers are selected to be between 1200 nm and 1250 nm. These fibers, which were standard telecommunication fibers, were made in accordance with the teachings of U.S. Patent No. 5,011,251.

A 6 cm long section of coating was removed from the end of a 1.5 meter length of coated fiber 18. An antireflection termination was formed on the end of fiber 18 by directing a flame at the center of the stripped region of fiber, while the end of the fiber was pulled and severed to form a tapered end. The tip of fiber 20 was heated by a burner flame to cause the glass to recede and form a rounded endface, the diameter of which was equal to or slightly smaller than the original uncoated fiber diameter. The resultant stripped end region was about 3.2 cm long.

Approximately 3.2 cm of coating was stripped from the central region of a 3 meter length of fiber 17. The uncoated sections of fibers 17 and 18 were wiped, and a small amount of ethyl alcohol was squirted into the tube to temporarily lubricate the fibers during the insertion process.

Coated fiber 17 was inserted through bore 11 until its uncoated portion was situated below tube end 15. The uncoated portion of coated fiber 18 was held adjacent the uncoated portion of coated fiber 17, and both were moved together toward tube end 14 until the coating end regions were interior to funnel 13. The uncoated portion of coated fiber 17 was then disposed intermediate end surfaces 14 and 15. End 25 of fiber 18 was located between midregion 27 and end 14 of tube 10. A small amount of UV-curable adhesive was applied to fibers 17 and 18 near end 15 to tack them to funnel 13 and to fiber 17 near end 14 to tack it to funnel 12. Preform 31 was then inserted through ring burner 34 (FIG. 8) and was clamped to draw chucks 32 and 33. The chucks were mounted on motor controlled stages 45 and 46. The fibers were threaded through the vacuum attachments 41 and 41', which were then attached to the ends of preform 31. Referring to FIG. 7, vacuum attachment 41 was slid over the end of tube 10, and collar 39 was tightened, thereby compressing O-ring 38 against the tube. Vacuum line 42 was connected to tube 40. One end of a length of thin rubber tubing 43 was attached to that end of vacuum attachment 41 opposite preform 31; the remaining end of the tubing extending within tube clamping means. Upper vacuum attachment 41' was similarly associated with line 42', tubing 43' and tube clamping means. The coated portions of the fibers extended from tubing 43 and 43'. Vacuum V was applied to coupler preform 31 by directing air pressure against tubing 43 and 43' as indicated by arrows 44, 44', thereby clamping the tubing against the fibers extending therethrough.

With a vacuum of 61 cm of mercury connected to the tube bore, ring burner 34 was ignited. Flames were generated by supplying gas and oxygen to the burner at rates of 0.45 slpm and 0.90 slpm, respectively. The flame from ring burner 34 heated tube 10 for about 12 seconds. Midregion 27 of the matrix glass collapsed onto fibers 19 and 20 as shown in FIG. 9.

After the tube cooled, the burner was reignited, the flow rates of both the gas and oxygen remaining the same. The flames heated the center of the collapsed region to the softening point of the materials thereof. After 8 to 10 seconds, the supply of oxygen to burner 34 was turned off. Stages 45 and 46 were pulled in opposite directions at a combined rate of 1.0 cm/sec to elongate tube 10 by 0.65 cm to form neckdown region 51 (FIG. 10), the length and diameter of which were sufficient to achieve the desired optical characteristics in a single stretching operation.

After the coupler cooled, the vacuum lines were removed, and drops 48 and 49 of adhesive were applied to ends 14 and 15 of the tube. The adhesive was cured by exposure to UV light, and the coupler was removed from the chucks.

The spectral insertion loss curves for a switch made in accordance with Example 1 are shown in FIG. 11. Curve P₂ represents the coupled power. The excess loss for that switch was 1.6 dB and 2.4 dB at 1290 nm and 1560 nm, respectively. The double peak in the coupling ratio curves of FIG. 11 characterizes the resultant device as an ideal double window switch coupler. Approximately 91% of the total power propagating in the two fibers 17 and 18 at end 15 is guided by optical fiber 18 at 1290 nm and approximately 99% of the power is guided by output fiber 18 1560 nm. Couplers made in accordance with Example 1 exhibited a median excess device loss of about 2 dB. The lowest measured excess loss was 1.4 dB.

EXAMPLE 2

A 1×8 achromatic splitter was made by a method similar to that described in Example 1 except for the following differences. A glass tube 55 (FIGS. 12 and 14) having a 3.8 cm length, 2.8 mm outside diameter, and 465 μm longitudinal bore diameter was employed; it was formed of silica doped with about 0.5 wt. % B₂ O₃, the composition being relatively uniform throughout its radius. The composition of tube 55 was determined by wet chemistry; Δ₂-3 was then extrapolated to be 0.022% at 1300 nm from a known relationship between refractive index and B₂ O₃ content.

Since only six optical fibers can fit around another fiber of equal diameter, a glass spacer tube must be placed around a central fiber to permit seven or more fibers to be equally spaced around the central one. A spacer tube having an outside diameter of 205 μm and an inside diameter of 130 μm can be used with eight optical fibers having an outside diameter of 125 μm. A length of coated spacer tube can be used as a tool for initially inserting the eight fibers around the surface of the tube bore. A length of spacer tube was provided with a urethane acrylate coating having an outside diameter of 450 μm. About 2.5 cm of coating was stripped from the end of a piece 56 of spacer tube. The uncoated end of the spacer tube was inserted a sufficient distance into end 64 of tube 55 to ensure that the end of coating 57 wa was located in bore 58 a short distance beyond funnel 59.

Nine 1.5 m long optical fibers were provided with 3.2 cm long stripped ends, the endfaces of which had antireflection terminations. Eight optical fibers 61 were inserted into bore 58 around spacer tube 56 until they contacted coating 57. The eight fibers were moved together toward end 64 of tube 55 until the fiber coatings 62 were in funnel 59. The coated spacer tube was then removed. The ends of a 32 mm long piece of spacer tube 72 were fire polished to round off any sharp edges. Spacer tube 72 was composed of SiO₂ doped with 0.5 wt. % B₂ O₃ throughout its radius. The uncoated end 70 of the ninth fiber 71 was inserted into spacer tube 72 (FIG. 13), and the resultant combination was inserted through funnel 65 and into the cavity at the center of the eight fibers 61 from which spacer tube 56 had been removed. The insertion step was continued until coating 73 reached the vicinity of the small diameter end of funnel 65. A fragmentary cross-sectional view of the resultant preform is shown in FIG. 14. A small amount of UV-curable adhesive was applied to hold the fibers in place.

Vacuum was applied to one end of the tube bore and several drops of ethyl alcohol were applied to the other end to wash out debris. After the preform was put in the chucks, a vacuum of 45.7 cm of mercury was connected to both ends of the tube bore, and the burner was ignited for a 1 second burn to evaporate the alcohol.

With gas and oxygen flowing to the burner at rates of 0.55 slpm and 1.10 slpm, respectively, the flame heated the tube for about 18 seconds to collapse the matrix glass onto the fibers. After the tube cooled, with flow rates of gas and oxygen remaining the same; the burner was reignited. The flame heated the central portion of the collapsed region, and after 10 seconds, the supply of oxygen to burner 34 was turned off. Stages 45 and 46 were pulled in opposite directions at a combined rate of 1.0 cm/sec until the central portion of midregion 27 was stretched 0.8 cm.

The spectral insertion loss curves for a specific 1×8 splitter made in accordance with Example 2 are shown in FIG. 15. The curves represent the power coupled to each of the eight ring fibers. The excess loss for that coupler was 1.9 dB and 1.7 dB at 1310 nm and 1550 nm, respectively. The insertion loss was less than 11.3 dB in each output leg of that coupler over a wavelength range greater than 320 nm

Couplers made in accordance with this example generally exhibited a minimum excess device loss of about 1.0 dB at 1430 nm. The lowest measured excess loss was 0.8 dB.

EXAMPLE 3

A 1×8 coupler was made by a method similar to that described in Example 2 (immediately above), except that the tube had a radial composition gradient. A 300 μm thick region at adjacent the bore (from r_is to r_t of FIG. 6) was composed of SiO₂ doped with 0.5 wt. % B₂ O₃. The value of Δ₂-3 was extrapolated to be 0.022% at 1300 nm. The remainder of the tube was composed of SiO₂ doped with 8.2 wt. % B₂ O₃. The spectral insertion loss curves are shown in FIG. 16. The excess loss for that coupler was 1.8 dB, 0.9 dB and 2.0 dB at 1310 nm, 1430 and 1550 nm, respectively. The insertion loss was less than 11.1 dB in each output leg of that coupler over a 300 nm range of wavelengths up to about 1565 nm.

EXAMPLE 4

A 1×6 coupler was made by a method similar to that described in Example 2, except for the following differences. A glass capillary tube having a 3.8 cm length, 2.8 mm outside diameter, and 380 μm longitudinal bore diameter was employed; it was formed of silica doped with 8.0 wt. % B₂ O₃ and 2.5 wt. % GeO₂, the composition being relatively uniform throughout its radius. The value of Δ₂-3 was 0.02% at 1300 nm. Since six ring fibers can be equally spaced around a central fiber of equal diameter, no spacer ring was used. The fiber insertion tool was merely a piece of 125 μm outside diameter optical fiber having a 350 μm diameter urethane acrylate coating; about 2.5 cm of coating was stripped from the end of the fiber. This "fiber" tool was used in the same manner as the "spacer tube" tool described in connection with FIG. 12 to insert the six fibers around the inner surface of the capillary tube. The tool was removed and was replaced by the central fiber. A vacuum of 45.7 cm of mercury was applied to the tube bore during the tube collapse step.

With gas and oxygen flowing to the burner at rates of 0.55 slpm and 1.1 slpm, respectively, the flame heated the tube for about 18 seconds to collapse it onto the fibers. After the tube cooled, with flow rates of gas and oxygen remaining the same; the burner was reignited. After the central portion of the collapsed region was heated for 10 seconds, the supply of oxygen to the burner was turned off. Stages 45 and 46 were pulled in opposite directions at a combined rate of 1.0 cm/sec until the central portion of midregion 27 was stretched 0.6 cm.

The spectral insertion loss curves are shown in FIG. 17. The minimum excess loss for that coupler was 0.54 dB at 1460 nm. The insertion loss was less than 9.1 dB in each output leg of that coupler from 1260 nm to 1580 nm and was less than 9.0 nm from 1285 nm to 1575 nm. The absolute slope was 0.0033 dB/nm [0.010%/nm] at 1310 nm and was 0.0043 dB/nm [0.013%/nm] at 1550 nm.

EXAMPLE 5

For comparison purposes, a 1×6 coupler was made by a method similar to that described in Example 4 except that the tube refractive index was such that Δ₂-3 was about 0.5%. Tube composition in the region adjacent the bore was SiO₂ doped with 2 wt. % B₂ O₃ and 2 wt. % F. The resultant coupler exhibited higher insertion loss (see FIG. 18) and the spectral insertion loss curves exhibited greater slope than the coupler of Example 4. Various fiber packing arrangements are illustrated in connection with the specific examples. The modifications discussed below in connection with FIGS. 19-21 can be used in the manufacture other kinds of 1×N couplers or splitters. In these figures, a small circle concentrically within a large circle represents a core in an optical fiber. A large circle having no smaller circle within it represents a "dummy" fiber having no core and a length that is slightly shorter than the tube. The composition of the dummy fiber is such that its refractive index is the same or about the same as that of the tube. The dummy fibers could be formed of the same material as the tube.

The fibers in a 1×3 splitter can be arranged as shown in FIG. 19. The coupler preform is stretched until all of the power couples from the central fiber to the three ring fibers at the wavelength or wavelengths of interest, depending on whether the device is to operate at one or two windows.

The arrangement of FIG. 19 would also be used in a 1×4 splitter if, after the stretching operation is completed, the same amount of power remains in the central fiber as is coupled to each of the three ring fibers.

The arrangement of FIG. 20 can similarly be used to make a 1×4 splitter (by stretching so that all of the power couples from the central fiber to the four ring fibers) or a 1×5 splitter if, after the stretching operation is completed, the same amount of power remains in the central fiber as is coupled to each of the four ring fibers.

In a similar manner, the fiber arrangement of FIG. 21 can be used to form a 1×6 or a 1×7 splitter.

It may be possible to apply the principles of the present invention to fused fiber couplers by first fusing and stretching a plurality of optical fibers and thereafter potting or immersing the coupling region in an optical medium of proper refractive index such as oil, epoxy or the like. A disadvantage of such a coupler may be a sensitivity of the refractive index of the optical medium to temperature.

Claims

1. A An achromatic coupler comprising

a body of matrix glass, and

a plurality of optical waveguide paths extending through said body, each of said paths comprising a core region surrounded by a cladding region of refractive index less than that of said core region, the lowest refractive index of the cladding regions of said paths being n₂,

at least a portion of one of said optical waveguide paths being disposed in close proximity to another of said paths to form a coupling region,

the refractive index of at least that region of said body adjacent said paths being n₃, where n₃ is lower than n₂ by such an amount that the value of Δ₂-3 is less than .[∅125% #x2205;07%, wherein Δ₂-3 equals (n₂² -n₃²)/2n₂².

2. A coupler in accordance with claim 1 wherein said waveguide paths comprise optical fibers.

3. A coupler in accordance with claim 2 wherein said matrix glass is a cylindrically-shaped body through which said fibers longitudinally extend, said body having first and second opposed ends and a midregion, the diameter of the central portion of said midregion and the diameters of said optical fibers in said central portion of said midregion being smaller than the diameters thereof at the ends of said body.

4. A An achromatic fiber optic coupler comprising

an elongated body of matrix glass, said body having first and second opposed ends and a midregion,

a plurality of optical fibers extending longitudinally through said body, each of said fibers comprising a core surrounded by a cladding of refractive index less than that of said core, the lowest refractive index of the claddings of said plurality of optical fibers being n₂,

the refractive index of at least that region of said body adjacent said fibers being n₃, where n₃ is lower than n₂ by such an amount that the value of Δ₂-3 is less than .[∅125% #x2205;07%, wherein Δ₂-3 equals (n₂² -n₃²)/2n₂²,

the diameter of the central portion of said midregion and the diameters of said optical fibers in said central portion of said midregion being smaller than the diameters thereof at the ends of said body, whereby a portion of the optical power propagating in one of said fibers couples to the other of said fibers.

5. A fiber optic coupler in accordance with claim 4 wherein M optical fibers extend from said first end of said body and N optical fibers extend from said second end of said body, wherein M≧1 and N≧2.

6. A fiber optic coupler in accordance with claim 4 wherein the cladding refractive index n₂ ' of at least one of said fibers is greater than n₂ by an amount such that Δ_clads is no greater than 0.03%, wherein Δ_clads is (n₂² -n₂

'²)/2n₂². 7. A fiber optic coupler in accordance with claim 4 wherein said matrix glass comprises SiO₂ doped with up to 2.8 wt. %

B₂ O₃. 8. A coupler in accordance with claim 4 wherein said

matrix glass is a cylindrically-shaped body. 9. A fiber coupler in accordance with claim 8 wherein M optical fibers extend from said first end of said body and N optical fibers extend from said second end of said

body, wherein M≧1 and N≧2. 10. A fiber optic coupler in accordance with claim 8, wherein the cladding refractive index n₂ ' of at least one of said fibers is greater than n₂ by an amount such that Δ_clads is no greater than 0.03%, wherein Δ_clads

is (n₂² -n₂^{'2)/2n₂2. 11. A fiber optic coupler in accordance with claim 8 wherein said matrix glass comprises}

SiO₂ doped with up to 2.8 wt. % B₂ O₃. 12. In an optical coupler of the type comprising at least two adjacent waveguide paths that are elongated and in close proximity to one another in a narrowed coupling region to induce coupling between said waveguide paths, each of said waveguide paths comprising a core region surrounded by a cladding region of refractive index less than that of said core region, the lowest refractive index of the cladding regions of said waveguides being n₂, said coupling region being surrounded by matrix material of refractive index n₃, the improvement wherein n₃ is lower than n₂ by such an amount that the value of Δ₂-3 is less than .[∅125% #x2205;045, wherein Δ₂-3 equals (n₂²

-n₃²)/2n₂². 13. A coupler in accordance with claim 12

wherein said waveguide paths comprise optical fibers. 14. A coupler in accordance with claim 13 wherein said matrix glass is an elongated body through which said fibers longitudinally extend, said body having a first and second opposed ends and a midregion, the diameter of the central portion of said midregion and the diameters of said optical fibers in said central portion of said midregion being smaller than the diameters thereof

at the ends of said body. 15. A coupler in accordance with claim 14

wherein said body is cylindrically-shaped. 16. A coupler in accordance with claim 1 wherein Δ₂-3 is less than 0.045%. 17. A coupler in accordance with claim 5 wherein Δ₂-3 is less than 0.045%. 18. A coupler comprising

a body of matrix glass, and

a plurality of optical fibers extending through said body, each of said optical fibers comprising a core surrounded by cladding layer of refractive index less than that of said core, the lowest refractive index of the cladding layers of said optical fibers being n₂,

at least a portion of one of said optical fibers being disposed in close proximity to another of said optical fibers to form a coupling region,

the refractive index of at least that region of said body adjacent said paths being n₃, where n₃ is lower than n₂ by such an amount that the value of Δ₂-3 is less than 0.045%, wherein Δ₂-3 equals (n₂² -n₃²)/2n₂². 19. An achromatic coupler comprising

a body of matrix glass, and

a plurality of optical fibers extending through said body, each of said fibers comprising a core surrounded by a cladding layer of refractive index less than that of said core, one of said fibers extending from both ends of said body and N fibers extending from only one end of said body, wherein N≧3,

said N fibers being equally spaced around said one fiber in a coupling region where a portion of each of said N fibers is disposed in close proximity to a portion of said one fiber,

the refractive index of the cladding layers of said N fibers being different from the refractive index of the cladding layer of said one fiber, the refractive index of the cladding layers of said N fibers being n₂ if the refractive index of the cladding layer of said one fiber is n₂ ' and the refractive index of the cladding layers of said N fibers being n₂ ' if the refractive index of the cladding layer of said one fiber is n₂, n₂ being lower than n₂ ',

the refractive index of at least that region of said body adjacent said paths being n₃, where n₃ is lower than n₂ by such an amount that the value of Δ₂-3 is less than 0.125%, wherein Δ₂-3 equals (n₂² -n₃²)/2₂². 20. An achromatic fiber optic coupler comprising

an elongated body of matrix glass, said body having first and second opposed ends and a midregion,

a plurality of optical fibers extending longitudinally through said body, each of said fibers comprising a core surrounded by a cladding of refractive index less than that of said core, the lowest refractive index of the claddings of said plurality of optical fibers being n₂,

the cladding refractive index n₂ ' of at least one of said fibers is greater than n₂ by an amount such that Δ_clads is no greater than 0.03%, wherein Δ_clads is (n₂² -n₂^'2)/2n₂2,

the refractive index of at least that region of said body adjacent said fibers being n₃, where n₃ is lower than n₂ by such an amount that the value of Δ₂-3 is less than 0.125%, wherein Δ₂-3 equals (n₂² -n₃²)/2n₂²,

the diameter of the central portion of said midregion and the diameters of said optical fibers in said central portion of said midregion being smaller than the diameters thereof at the ends of said body, whereby a portion of the optical power propagating in one of said fibers couples to the other of said fibers.