Laser to single-modefiber coupling in the laboratory

Ivan Ladany

All the information necessary to achieve reasonably efficient coupling of semiconductor lasers tosingle-mode fibers is collected from the literature, derived when necessary, and presented in mainly

tabular form. Formulas for determining the laser beam waist radius and the fiber-mode radius aregiven. Imaging relations connecting these values with the object and the image distances, includingthick-lens correction factors, are given for three types of lenses: ball, hemisphere, and gradedindex. Sources for these lenses are indicated, and a discussion is also given about ways of reducingfeedback effects and about the use of wedge-ended fibers.

A common need in many laboratories is the couplingof the output of a semiconductor laser into a single-mode fiber. While there are many papers that dealwith various aspects of this problem, there does notseem to be a convenient reference from which one canobtain all the information needed to accomplish thistask. The current paper has been written in anattempt to satisfy this need for the interested worker.

The coupling problem, in general, consists of align-ing the laser and the fiber, together with some opticalelement, in such a way as to obtain the maximumpower transfer between the two systems. Usuallythis step must be followed by a means of permanentlylocking these elements into a fixed position, but thecurrent paper does not address this issue, laboratoryor optical bench methods being those mainly consid-ered.

In principle,' the correct procedure can delivercoupling efficiencies approaching 100%. This re-sults if the laser mode and the fiber mode are made tohave the same form and to overlap in the same regionof space. In practice, achieving such high efficienciesis quite involved, requiring aberration-corrected andantireflection-coated lenses. Other difficulties ariseif the laser beam is strongly elliptic. The positiontaken in this paper is that most workers will besatisfied with lower efficiencies, of the order of 40% or50%. Such values are achievable in single-lens sys-tems, which possess a further advantage in that

The author is with Lockheed Engineering and Sciences Com-pany, Hampton, Virginia 23665-5225.

Received 14 January 1992.0003-6935/93/183233-04$06.00/0.c 1993 Optical Society of America.

Fresnel reflection losses are often tolerable, so thatantireflection coatings are not required. However,simple lenses cannot deal adequately with lasers withextremely elliptic beams, although the wedge configu-ration, which is discussed below, has been recentlyproposed as a solution to this problem. One prob-lem, laser astigmatism, is not addressed in this paper,mainly because currently popular lasers are of theindex-guided type, for which this problem is notserious; another problem that is not addressed is thedisplacement of the laser waist away from the laserfacet, because this can be compensated for by a slightadjustment away from the calculated optimum posi-tion. In any case, it is common procedure to usecalculations such as those described in this paper todetermine what optical element to use and where toposition it, and then to maximize coupling efficiencyby further small adjustments in positions.

The content of this paper is arranged in the follow-ing way: after a few words on laser beams, a table isprovided that permits the calculation of the laserbeam waist radius, in other words, the laser modesize. Next, a formula that can be used to obtain thefiber-mode size is displayed. The conversion of thelaser mode into a fiber mode is then handled by meansof a rearrangement of the formulas given by Kogel-nik2 and by Self,3 which yield the object and the imagedistances for a particular lens that carries out thisconversion. Before using these formulas it is neces-sary to decide on the lens type, and then look up thefocal length and the thick-lens correction terms inTable 2 and insert them into the equations. Thistable covers three types of optical element: thespherical ball lens, the hemispherical lens, and thegraded-index (GRIN) lens. Both ball lenses and

20 June 1993 / Vol. 32, No. 18 / APPLIED OPTICS 3233

GRIN lenses can be obtained commercially, but thehemispherical lens is usually fabricated in the labora-tory. A fabrication procedure is indicated, andsources are given for obtaining ball and GRIN lenses.Ways of reducing feedback are discussed, and aformula is derived for the design of wedged fiber endsthat are useful in reducing feedback and have re-cently been found effective in coupling elliptical beamsinto single-mode fibers.

Laser BeamsIn all that follows it is assumed that the laser emits aGaussian beam. From the knowledge of the beamangle it is possible to estimate the dimension of thelaser beam near the exit aperture of the laser, i.e.,near the laser facet. The laser beam angle is some-times specified by the manufacturer, but more oftenthan not it must be measured. For this purpose oneneeds a photodetector that is provided with an en-trance slit and some means of rotating the laser intwo perpendicular planes. The diameter of the beamnear the laser facet is taken to be the beam waist, i.e.,the minimum diameter of the laser beam. However,following common practice, formulas given below usethe waist radius rather than the diameter. Table 1may be helpful for use in converting each of threecommon beam angle definitions into the laser beamwaist radius.

The definition of waist radius in the table and inthe rest of this paper is based on the 1/e 2 value, andthe units are those used to express the wavelength.If the laser beam is not circular, one obtains two waistradii, one for each semi-axis of the ellipse. If thesevalues are not too different, one can proceed bycalculating their geometric mean (WaWb)'/ 2 and usingthis number in the formulas that require an entry forthe laser waist radius. A ratio of 3:1 is perhapsacceptable, but higher ratios make it difficult toobtain an adequate coupling efficiency without somemeans of circularization, such as by use of anamor-phic beam expanders or wedge-polished fibers, asdiscussed below.

The equation of Marcuse4 can be used to estimate thisspreading:

- = 0.65 + (1.619/V' 5 ) + (2.879/V 6 ),a (1)

where

2'rr 1/2V = - a(n 2

- n22) (2)

where n, is the core index and n2 is the cladding index.The fiber-mode radius can sometimes be obtaineddirectly from the manufacturer. One often findsthat wf/a 1.1.

Imaging FormulasAn unspecified optical element is defined by focallength f, an entry surface, an exit surface, and twoprincipal planes, as shown in Fig. 1. Desired objectdistance so, and image distance si are distances fromthe object to the entry surface and from the exitsurface to the image, respectively, as shown in thefigure, while A and A', the thick-lens correctionfactors, are distances between the entry surface andthe entry principal plane and the exit surface and theexit principal plane, respectively. We deal with thecase of a real object and a real image, so that allquantities are taken as positive. It can then beshown that

s = f - A + f[(Wl/wf) 2- (ZR/f) 2

]1/2,

S, = f- A + (Wf/W) 2 (So + A -f),

(3)

(4)

where ZR = 'rW 12 / X.

Before using these equations it is necessary tochoose one of three optical elements and consultTable 2 for the appropriate expressions for f, A, andA'.

Fiber-Mode RadiusThe mode propagating in the fiber can also be approx-imated by a Gaussian beam and described through amode radius Wf. This mode radius is slightly largerthan the single-mode fiber core radius a because ofthe spreading of the mode into the cladding region.

Comments

Ball Lens

A variety of materials are available from DeltronicsCrystal Industries5 in diameters ranging from 0.4 to 3

entry surface I I exit surface

Table 1. Beam Angle and Beam Waist Radius

Waist Radiuswl Near

Laser Facet,Definition of Beam in Same Units as

Angle (deg) X

Full width at half-maximum intensity 21.5 X/O(FWHM)

Half-width at 1/e times maximum intensity 12.9 /0Half-width at 1/e2 times maximum intensity 18.24 X/O

fiber

al planes

Fig. 1. Coupling geometry.

3234 APPLIED OPTICS / Vol. 32, No. 18 / 20 June 1993

Table 2. Imaging Formula Parameters

Type of Lens f A A'

Ball: radius R index n nR R R2(n - 1)

Hemispherical: radius R RR, indexn, convex n - 1 0 nside facing laser

GRIN: length 1, diame- b b I b Iter D, axial index no, 21 2tan- 2tan-

grade b 2n, sin

The refractive index of the lens may be approxi-mated by the index of the core, if the diameter issmall, or else by the index of the cladding material.

GRIN LensGrading parameter b is defined by the expression

n = n0 (l - 2r2 /b2 ).

Two other expressions are often used:

n = n.(1 - g2r2 /2)

mm. A list from one of its catalogs is given below: n = nj(i - Ar 2/2)

giving b = 2/g,

givingb = 2/1C.

MaterialSapphireYAGGGGCZYIGSi

Refractive Index at 0.80 pm1.751.8241.9532.1352.253.505

Some of these spheres need to be coated with anantireflection film since the two-surface Fresnel loss(for a flat surface) ranges from 15% to 62%. Antire-flection-coated ball lenses with diameters of 2, 3, and5 mm are available from Melles Griot6 with n = 1.83at 0.83 pm.

Hemispherical Lens

The most useful case arises when the lens is directlyattached to the fiber. One can then substitute si = 0into Eq. 4, which leads to

Rs= n - 1 -1 - ! (Wl/wf),

while substituting Eq. (5) into Eq. (3) yields

R (n -1)R (6)w - 1 ()2]1/2

In this case the lens diameter is restricted to aparticular value for a given index, and there is only asingle value for the laser to lens distance. Because ofpossible truncation at the output surface, the hemi-spherical lens on the end of the fiber gives the highestcoupling efficiency if the laser beam satisfies theinequality

O(FWM) < (21.5)(n - 1)wr or = 31. (7)

For larger angles there will be some mode mismatchloss.

A convenient way of making such a lens has beendescribed by Izadpanah and Reith.7 The fiber isetched in HF placed in a teflon beaker, with a thinlayer of oil floating on top of the HF. After the fiberis etched to the desired diameter, the lens is formedby heating in a fusion splicer.

Melles Griot6 carries a selection of these, and they canalso be obtained from the manufacturers, NSG Amer-ica, Inc.8 The standard version discussed here hasflat end faces. NSG also sells antireflection-coatedunits with curved input surfaces for aberration correc-tion.

Feedback and Elliptical Beams

Reflection back into the laser is undesirable as itaffects the laser wavelength, stability, and noise.For critical applications it will be necessary to useisolators, while for other applications one can useantireflection-coated optics. Of most importance isthe first surface facing the laser, and it is oftensufficient to make that spherical. An uncoated hemi-spherical lens with a 145-jim diameter, on the end ofa fiber, has been reported9 to display a reflectivity of10-5-10-6.

Yet another approach to reducing feedback fromthe first surface is to grind the end of the fiber into awedge. This can be done by pressing the freestand-ing end of the fiber into the disk of a lapping andpolishing machine, and then repeating the procedureafter rotating the fiber through 180°. Although thismethod has been proposed for coupling elliptic beamsinto multimode fibers,9"10 workers at NASA LangleyResearch Center" have obtained coupling efficienciesof 18% into wedged single-mode fibers. A remark-ably high value of 47% has been reported recently' 3

for a 560 (full width at 1/e) beam coupled into asingle-mode fiber through a 120° wedge. Publishedanalyses of wedge coupling into fibers10"12 are onlyapproximate in their applicability to single-modefibers as they are based on ray tracing. Anotherestimate for the desired wedge angle can be obtainedas follows:

The wedge is treated as a thick prism on the end ofthe fiber, as shown in Fig. 2, and one considers anincoming ray at the core to cladding boundary, whichis bent just enough to become parallel to the opticaxis. The distance from the prism to the ray origincan be considered the focal length, , of a section of alens approximated by the prism. Then

Wf

tan y(8)

20 June 1993 / Vol. 32, No. 18 / APPLIED OPTICS 3235

l .

Fig. 2. Approximation to the wedge.

It can also be deduced from Fig. 2 that

,y = sin-1(n sin at) - a. (9)

This is now used in the imaging formulas of Eqs. (3)and (4) as the focal length of a refracting elementattached to the fiber (however, thick-lens correctionfactors have been neglected). Letting si in Eq. (4)equal 0, substituting the resultant expression for s,,into Eq. (3), and substituting for from Eq. (8), oneobtains

tan y = (wl/ZR)[1 - (1/Wf) 2]'/ 2. (10)

This expression, together with Eq. (9), permits thecalculation of the wedge angle a (or 2 = 1800 - 2)for a given set of beam parameters, wavelength, andrefractive index of the fiber core. The case discussedin Ref. 12, and assuming a fiber-mode radius of 3 imand a core index of 1.5, yields 2 of 1000.

While wedge ends applied to single-mode fiberswere mainly considered as providing a trade-off be-tween reduced feedback and coupling efficiency, theresults given in Ref. 12 suggest that it may be possibleto have both respectable coupling efficiency for ellipti-cal beams and reduced feedback.

The support and assistance of H. Hendricks and T.Mack of NASA Langley Research Center is gratefullyacknowledged.

References1. H. Kogelnik, "Matching of optical modes," Bell Syst. Tech. J.

43,334-337 (1964).2. H. Kogelnik, "Imaging of optical mass-resonators with inter-

nal lenses," Bell Syst. Tech. J. 43, 455-494 (1965).3. S. A. Self, "Focusing of spherical Gaussian beams," Appl. Opt.

22,658-661 (1983).4. D. Marcuse, "Loss analysis of single-mode fiber splices," Bell

Syst. Tech. J. 56, 703-718 (1977).5. Deltronic Crystal Industries, Inc., 60 Harding Avenue, Dover,

N.J. 07801.6. Optics Guide 5, Melles Griot, 1770 Kettering Street, Irvine,

Calif. 92714.7. H. Izadpanah and L. A. Reith, "Microlens fabrication tech-

nique for an efficient laser/single mode fiber coupling" inOptoelectronic Materials, Devices, Packaging, and Intercon-nects T. E. Batchman, R. F. Carson, R. L. Gallawa, and H. J.Wojtunik, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 836,306-310 (1987).

8. NSG America, Inc., a subsidiary of Nippon Sheet Glass Co., 28Worlds Fair Drive, Somerset, N.J. 08873.

9. W. Bludau and R. Rossberg, "Characterization of laser-to-fibercoupling techniques by their optical feedback," Appl. Opt. 21,1933-1939 (1982).

10. I. Ladany and A. N. Dholakia, "Wedge coupling of lasers intomultimode fibers," Appl. Opt. 22, 960-961 (1983).

11. Terry Mack, NASA, Langley Research Center, Hampton, Va.23681 (personal communication).

12. V. Shah, L. Curtis, Richard S. Vodhanel, W. C. Young, andD. P. Bour, "Efficient power coupling from a 980-nm broad-area laser to a single-mode fiber using a wedge shaped fiberendface," in Optical Fiber Communication, Vol. 1 of 1990 OSATechnical Digest Series (Optical Society of America, Washing-ton, D.C., 1990), p. 199.

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