JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. I, NO. 1, JANUARY 1989 99

Deterioration of Taper Lens Performance due to Taper Asymmetry

BERND HILLERICH AND JOACHIM GUTTMANN

Abstract-The influence of rotationally asymmetrical, i.e., bent drawn fiber tapers on the coupling performance of taper lenses used for laser diode or LED to single-mode fiber coupling is investigated. It is found by experiments that the lateral offset of the taper tip with respect to the fiber axis should be below =6 p, if a significant in- crease in coupling loss is to be avoided. The experimental results are interpreted by numerical simulations applying the beam propagation method.

I. INTRODUCTION APER lenses, i.e., drawn-tapered fiber ends with a T molten lens on their tip [ l ] are widely used as a cou-

pling scheme for single-mode fibers. Their advantages are:

a) high coupling efficiency of 40 to 75 percent for laser

b) rather low optical feedback [4], [5], c) low production cost, and d) small dimensions which allow very compact trans-

The influence of the tapered region of the fiber on the coupling properties of the taper lens has not been fully clarified. Several authors prefer shorter tapers with lengths up to LT = 350 pm, because the yield of good tapers is higher than with longer tapers [3], or because longer ta- pers result in non-Gaussian far-field strong excitation of radiation modes and thus lower coupling efficiency [6]. Other authors obtained best coupling results with very short tapers (LT = 200 pm) 171.

In [6] it has been mentioned that drawn tapers should be rotationally symmetrical. Up to now, however, the in- fluence of taper asymmetries has not been examined quan- titatively. In this paper this influence is investigated. It will be shown that only very small deviations from rota- tional symmetry are allowed, if severe distortions of the field propagating in the taper, which result in a higher coupling loss, are to be avoided. These experimental find- ings are interpreted by simulations of the propagation of the fiber mode in the tapered fiber, applying the “beam propagation method” (BPM), which is widely used to analyze and design integrated-optical components [ 81-

diodes [2], [3],

mitter modules.

[ W .

Manuscript received June 3, 1987; revised October 20, 1987. This work was partially supported by the technological program of the Federal Min- istry of Research and Technology, F.R.G.

The authors are with AEG Aktiengesellschaft, Research Center Ulm, D-7900 Ulm, West Germany.

IEEE Log Number 8822067.

11. ANALYSIS OF BEAM PROPAGATION IN THE TAPER The taper lenses investigated here were made of

matched-cladding single-mode fibers using a computer controlled drawing apparatus. The drawing- and lens- melting-process is similar to those described in [2], [5]. Fig. 1 shows a microphoto of a typical taper lens. Due to a differential-interference contrast (DIC) technique, gra- dients of refractive-index are transformed into variations of gray level. The core-cladding interface is clearly vis- ible in the tapered region, and the core-cladding ratio re- mains constant. Obviously during the drawing process of the taper no significant diffusion of the doping material of the fiber core (i.e., Ge02) occurs. Only at the lensed tip the core is no longer discernible.

The propagation of the fiber mode in the taper is sim- ulated by a two-dimensional beam propagation method (BPM). This method is based on the scalar wave equation in the paraxial approximation (e.g., see [8]-[lo]) and has found widespread applications in integrated optics. For a given field distribution E ( x , G) the field E ( x , zo + 6z) follows from

= F-’[l?(k,, zo) exp { -jk, Sz)]

~ X P { - ~ ( N ( x , G) - ~ , ) b SZ} + o(az3) (1)

where I??( k,, zo) = F [ E ( x , zo)] denotes the Fourier trans- form of E ( x , zo). F -’ is the inverse Fourier transform.

N ( x , z ) and Nz denote the local and the substrate re- fractive index, respectively. k, and k, are related by

k, = m, with b = 2a/Xo. (2)

By iterative application of (1) the propagation of an ar- bitrary input field distribution through the indices distri- bution N ( x , z ) can be computed. For the application con- sidered here, an iteration step size 6z = 10 pm is sufficiently small. Three-dimensional structures like the fiber taper ought to be analyzed by a three-dimensional BPM, which, however, would require extensive computer time [SI. But by using an effective-index method proposed by Chiang [ l l ] , the circular step-index fiber is trans- formed into an equivalent slab waveguide which extends infinitely into the y-direction.

For a fiber with core index N1, cladding index N2, and

0733-8724/89/0100-09$01 .OO O 1989 IEEE

HILLERICH AND GUTTMANN: DETERIORATION OF TAPER LENS PERFORMANCE

TABLE I CALCULATED FIBLD RADIUS AT THE END OF TAPERS WITH DIFFERENT

LENGTHS ~~

taper length L, tpml [field radius wn C p m l

200

300

400

600

800

5.4

6.5

6.8

7.8

8 .5

decreasing to 1.8 pm is shortened and the zone with a ( 2 ) < 1.8 pm is as long as with the taper of 800-pm length (Fig. 2(b)). The field at the tip is similar to that taper.

The calculated field radii w, of tapers with LT = 800 pm agree rather well with measured values of similar ta- pers [12]. For tapers with LT = 400 pm, where the field radius w,, was evaluated from the relation between lens focal length f and field spot size wF in the waist of the beam, focused by the lens [13]:

W n w F (6) 2 -1/2 t:

w,, = WF(1 + ( W W ) ) where the focal lengthfis calculated from the lens radius R L using the thin lens formula:

f = RLl(N2 - 1) . (7) For a number of taper lenses with different focal lengths w, 5: 6 to 6.5 pm was found, which agrees with w, = 6.8 pm in Table I.

Generally the phase front of the field at the taper end is slightly curved. As it is shown in Fig. 3, the phase at the 1 /e-points of field amplitude lags by = 0.7 rad with re- spect to the maximum amplitude. However, this curva- ture can be compensated by slightly increasing the dis- tance between source and lens (typically on the order of 1 to 2 pm) and hence has no significant influence on the coupling efficiency.

If the lens molten on the taper tip is nearly hemispher- ical, and the lens radius RL is larger than the field radius w,, diffraction and spherical aberrations have little influ- ence on the imaging properties of the lens [ 141. Therefore the lens can be considered as a Fourier transformer (see, e.g., [15]), and the far-field distribution of the beam, which is focused by the lens, corresponds to its field dis- tribution just before passing the lens, i.e., at the taper tip, apart from a scale factor. For numerous taper lenses with lengths LT = 260-450 pm, with taper shapes similar to (3, the lens radii R L = 8 to 20 pm, the far-field intensity distribution was measured by an IR-TV camera, while ra- diation of a laser diode was launched into the far end of the fiber. If the taper is straight, the far field is well ap- proximated by a Gaussian profile, except for the some- what slower fall off with increasing angle. Fig. 4 shows a typical example of a measured far field. Deviations from a Gaussian far field are found for very small lens radii ( RL = 6 to 7 pm), presumably because the field width is larger than the lens radius.

2- 3 8 8 p

2- 8 W p . ...... .. ... . . . .

: .-

101

+PI12

0

-PI12 U.

+PI12

a

-PI12

Fig. 3. Calculated field distribution at the tip of the tapers of Fig. 2. Solid line: amplitude; dotted line: phase.

FAR-FIELD ANGLE CDEGI

@)

Fig. 4. Measured far fields of taper lens with L, = 300 pm. (a) Two- dimensional intensity distribution ( RL = 11 am). (b) Sectional view of (a) parallel to the x-axis. Dotted line: Gaussian approximation.

~ ~ ~ ~ ~ ~ - - - ~ ~ ~ ~ ~ ---. ________________^

----____-- Inrleecl. i t has been f w n d by other authors that with long tapers (e.g., I d [ = 400--8@J pn) the far field de-

usualiy. near and far fietds are non-(3nti tlierc observation!, are attributable to exteiision of the field at r h r tip beyond the lens radius, or to rotatio~zally asq~n- metricat tapers wliich wiIl be discussed in the f ~ ~ 1 1 ~ ~ ~ ~ 1 ~ i g aection . e -

z -..________ viates significantly from a Gaussian proflie [6] , or that. --------""".-

IV. A + _ _ c

If the lateral pasitrrons o f the fiber chucks in the t;ipe~ drawing machine are not exact13 aligned, due IC) a lateral tiffset e, of the clamped fiber, a taper lctis is made. the \ ertex ot U hich rhaws a lateral riffset with respect to the fiber axi\,. 'This process i b skctdml in F i g . 5

In circler to analyx the irif'luence of taper asymmetry 01) the c c~up 1 II ig perti, nn ai ice ~ ziircnt~o nal I j a s p rnetrica l ta- per tenser, Miere produced with varied chuck cifrwt values e, The fiber IX positioned in the chncks hy v-grcxwes. After carefully alrgnrng the lateral chuck position thc oiY- bet c', is rneasured by a position transducer. The taper iength ainouiitr to l,T = 300 pin: the lens radii Rf are bctucen I O and 12 prn. llrc r e d t i n p lens otTwt value:, e ? Rere evaluated from rnicrcqhtcis. Fig. 6 &nws rhe relation between chuck o%et and leiis ofhet h r a number of taper\ Tht. interrelation Ixmveen chuck oflset e< and len.; offset e7. is approx~matelj linear De; rutions froin tin . eanty are due to lriiirted accuracy o f the evalrratron of er from rrucrophotoh and due to cknrarice o f the tiber tri the chucks.

The couplisp efficiency was measured using ail In- GansP-T)C-PBH-laser dlrtde with far-field U idth\ ~ L ~ W H ~ ) of 28" ( I p-11) and 36" as well as an edge-liQht-emtttIng-diodc (FLED). as light s c ~ c c \ 'The ELED i i a lnGah\V-! -gnro;e i tc l ice 101 w t h near-tield

and far tiekt widths (FWCihl) of 76' ( 1: p-n f and 7.2': ( i p-n 1. 'The wavelength of tmrh sources i s near X ::: 1.3 i".lKl.

Fcrr xtraight taper\ the coupling efficiency mounts to -4-9 percent (L-DI and 4 percent t EL-ED). rrspectr~cly The results Ri th as3 nunetrical tapers arc' suiiiniariied 111 Fig. 7 . Mirth j n c r e r h g offset the cixqhig Iosi increzses drast- mi l l> . Even m a l l Icns ottwt vdlues. e.g , e l > (1 pni grve rise t o a q n i h c a n t ndditional couplrng loss C Y . H hich I> o n a atatistrcal tmsls - - a j ~ p " l a t e l y t h ~ sainc both f~ the LD and the EL,ED. For larger ofyicts. dighl sample- to-sample ~ariations in taper shape rewh iri mrte scatter-

Vrsually, i.e . hy ~nspectirm Ni th a r~iicroscttpc. it IC rsthcr difticult to detect slight raper ar! rnnietries which

._/

i p-n

H i d h (FWHM) ot 10 pm { I p-n) and 0 8 p.111 { A. I>-n ,I

irlg of the toss valucs.

" C

25 i-2s

(a)

Fig. 9. Far-field intensity distributions of asymmetrical taper lenses with different lens offsets. (a) er = 6 pm, (b) e , = 9 pm.

coupling loss (Fig. 9(b): e T = 9 pm, aLD = 1.1 dB). Obviously the asymmetry of a taper lens can be very sen- sitively checked by a far-field measurement. ~

We have analyzed the propagation of the fiber mode in an asymmetrical taper by BPM-simulations. We assume that the position X, of fiber core center in the taper does not shift abruptly, but in a smoothly bent fashion accord- ing to

~ ( z ) = ~ T ( Z / L ~ ~ ’ * . (8) In Fig. 10(a) the evolution of field amplitude for a bent taper with length L T = 300 pm and offset eT = 10 pm is presented. The field distribution becomes asymmetrical and widens considerably. Fig. 10(b) shows amplitude and phase front at the tip. The phase front is tilted ( =4”) which causes an angular offset of the far field. Parts of the field that exceed the taper contour and hence partly leave the taper before the lens, interfere with the main radiation lobe which causes the ripples in the far field of asymmetrical tapers.

The mechanism of coupling loss increase is illustrated in Fig. 11. Here the field propagation from the taper tip via the taper (length L T = 300 pm) into the single mode fiber is simulated by BPM. The starting field is a Gaussian far field of a laser diode with 32” FWHM, transformed by a lens with radius RL = 11 pm. The hatched portions are truncated by the lens due to its limited aperture [5 ] . In the straight taper (Fig. ll(a)) a stationary field distri- bution (corresponding to the fiber mode) appears for z > 500 pm. But with the asymmetrical taper ( e T = 10 pm, see Fig. 1 l(b)) weakly attenuated “leaky” modes are ex- cited. A stable fiber mode appears not before z > 4000 pm. The coupling efficiency is calculated according to

where wn and wr are 1 /e-field radii of the fiber mode and

48

E 3 A I x

-48

z- 388 1.

1 tPxn I . . I -

HILLERICH AND GUTTMANN: DETERIORATION OF TAPER LENS PERFORMANCE 103

- starting field (here wL = 9 pm), respectively. Eo and E L coupling efficiency.

Fig. 10. (a) Field,propagation in a bent taper (Lr = 300 pm, er = 10 pm) calculated by BPM. Broken lines: Effective-index profile; dashed-dotted lines: taper contour. (b) Field distribution at the taper tip.

E 88 168 248 328 488 488 568

48

E Y

El n

I x

-4E 326 488 488 568 2 -> Cpm)

Fig. 1 1 . Field propagation from the taper tip into the single mode fiber (taper length: 300 pm). (a) Straight taper. (b) Asymmetrical taper ( e r = 10 pm). Phase-ftont curvatue (defocusing of the LD position) and tilt (lateral offset of the LD) of the starting field are chosen to maximize the

a r t the pcak ainplitudes ot srlttiunary fiber niade and star-t- irig field, reqxctively. The calculated coiipling effrcicncy arnountcr to 43 pcrccnt (\traight taper) and is reduced h.c, a = 1 . I JR t o 33 percent for t he usyinetrical taper. Thcse values art: siinilar to mcawrcnients

The calculated curlie of the addirronal cvuplirig io>c in Fig 7 IS obtained b y ~ P ~ l ~ c a l w ~ ~ u r i ~ ~ i ~ ~ in the just de- scr-ibcd waq,