fiber beam expansion

70 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. LT-5, NO. 1, JANUARY 1987

Optical Fiber Tapers-A Novel Approach to Self-Aligned Beam Expansion

and Single-Mode Hardware N. AMITAY, FELLOW, IEEE, H. M. PRESBY, F. V. DIMARCELLO, AND K. T. NELSON

Abstract-We investigate the performance characteristics of single- mode optical fiber tapers. These devices have a standard single-mode fiber geometry at one end and gradually increase in cross section so that the size of the core at the other end is comparable or greater to that of a multimode fiber. These tapers effectively expand the single- mode spot size and are envisioned as basic building blocks in a multi- tude of optical components.

Analytical and experimental studies, at X = 0.63 pm, show that the dominant mode is preserved while traveling through the taper, from either direction. The excess coupling loss between two tapers is less than 0.1 dB. The sensitivity of the excess loss to lateral and axial displacements for two coupled tapered sections is greatly reduced compared to that between two single-mode fibers. The sensitivity to angular displacement is increased but is within practical limits. For example, for an excess loss of 0.5 dB, the maximum allowed lateral displacement is 3.1 pm for taper coupling, while only 0.73 pm is allowed in the case of fiber coupling. An axial displacement of 291 pm for taper coupling produces 0.5 dB loss while a displacement of only 16.5 pm produces a 0.5 dB loss for fiber coupling. For the same loss, angular displacements of 0.42" for the tapers and 1.77" for the fiber are allowed.

I. INTRODUCTION

S INGLE-MODE fiber is rapidly becoming the medium of choice for lightwave communications systems car-

rying long distance terrestrial and submarine traffic as well as local distribution and local area networks traffic. Wide- spread and convenient utilization of single-mode fibers re- quires reliable and reasonably priced hardware such as low-loss backplane and field connectors, laser-fiber couplers, and directional couplers. The main drawback of single-mode fibers, which makes fabrication of these components difficult, is their small core size, on the order of 5-10 pm. All hardware constructed from and for these fibers, where two cores or light source and core have to be aligned, are inherently very sensitive to axial and transversal displacements as well as to tiny dust particles. These displacements can be induced mechanically or ther- mally, while the dust comes from just routine handling.

These problems can be greatly alleviated, if not theo- retically eliminated, by the introduction of beam expansion optics. In this approach, components which could

Manuscript received May 28, 1986; revised July 1, 1986. N. Amitay and H. M. Presby are with AT&T Bell Laboratories, Craw-

F. V. DiMarcello and K. T. Nelson are with AT&T Bell Laboratories,

IEEE Log Number 861 1061.

ford Hill Laboratory, Holmdel, NJ 07733.

Murray Hill, NJ 07974.

Fig. 1. Optical fiber tapers. (a) Single-mode fiber with a gradual taper, (b) two coupled optical tapers, (c) a practical optical fiber taper structure.

consist of spherical lenses [ 11, GRIN lenses [2], cylindrical lenses [3], and combinations thereof [4], are used to increase the single-mode spot size and thus reduce alignment sensitivities. These discrete elements, however, introduce problems of their own. They themselves require a critical and difficult alignment which must remain sta- ble, and in addition they possess aberrations which limit performance [5].

Another means of achieving beam expansion is by ta- pering-down a single-mode fiber through heating and stretching [6], [7]. With this technique the field is no longer tightly bound to the core making it sensitive to ex- ternal refractive index changes and mechanical damage. Special means are required to reduce these effects [7].

In this work we present a novel approach to beam-expansion optics which suffers none of the deficiencies of the previous approaches. We propose to gradually up-taper a single-mode fiber so as to enlarge the dimensions of its cross section, by about an order of magnitude at the end of the taper, Fig. l(a). These enlarged dimensions

0733-8724/87/0100-0070$01.00 O 1987 IEEE

AMITAY et al . : OPTICAL FIBER TAPERS-BEAM EXPANSION AND HARDWARE 71

1 .o

0.8

I E

3 0 0.6 a a

In

Y P 2 0.4

0.2

1 I 1 I 1 1 I 0 10 20 30 40 50 60

LENGTH [mm]

Fig. 2. Optical taper radius (expanded) versus length. Actual taper is shown in the insert.

allow us, in principle, to relax the tolerances of the axial (S) and lateral (D) displacements (Fig. l(b)) while coupling energy from A to B with very low excess loss. In this case the field of the dominant mode is tightly confined and guided by the core throughout the entire structure. Conversion of the fundamental mode to higher-order modes or radiation by the taper, which at the enlarged end can support multimode propagation, must be negligible if we are to maintain a very low excess coupling loss. We show that for a gradual taper this is indeed the case. This structure has the unique advantage of being self-aligning and as aberration-free as the fiber itself. The fiber pigtail will be permanently spliced to the end of the fiber to be coupled into or out of. The taper is envisioned as a basic building block for many hardware applications. The ulti- mate practical structure, Fig. l(c), may consist of a fiber pigtail, and a tapered section followed by a cylindrical section of the enlarged dimensions for simple mechanical mounting.

In this work we measure the sensitivity of the coupling loss of two tapered sections, as shown in Fig. 1 (b), to axial, lateral, and angular displacements by using tapers with fiber pigtails designed to be single moded at X = 0.63 pm. Lateral displacement tolerances can be relaxed manifold at the expense of angular tolerances which, however, still remain reasonable. Axial displacement tolerances can be relaxed by almost two orders of magnitude, thus relaxing the proximity requirements between the two sections. We find that the tapers can be coupled with very low excess loss-less than 0.1 dB.

We have also found that the Gaussian beam representation can accurately describe the various relationships between the fiber parameters, the excess coupling losses and displacements, thus permitting projections to tapers with different parameters and operating wavelengths.

In the subsequent sections we shall describe our experimental and theoretical studies.

11. THEORETICAL AND EXPERIMENTAL STUDIES If we are to accurately measure the excess coupling

losses, the various light losses due to cladding modes,

higher-order mode conversions, or geometric imperfec- tions should be easily spotted. We therefore decided to perform the experiments at X = 0.63 pm using a He-Ne laser as the light source. A photograph of a typical taper is shown at the top of Fig. 2. The tapers used in these studies were obtained by reducing preforms in the con- ventional fiber drawing procss. The curve in Fig. 2, is an expansion of the taper radius to more clearly show the smooth transition from fiber through taper which takes place over about 6 cm. The refractive index profile of the taper and fiber is shown in Fig. 3. The cladding is of the depressed index type and the core has a graded profile. The tapers had dimensions for the fiber pigtails of either 130-pm OD with 7.27-pm core diameter or 1 10-pm OD with 6.15-pm core diameter.

A. Modal Purity In this series of experiments we verified that no notice-

able amount of mode conversion takes place in the taper. The experimental setup is depicted in Fig. 4. The He-Ne laser is coupled via a lens into either the fiber pigtail or the aperture of the taper. We observe the transmitted light on the other side. The light coupling and mode of excitation of the fiber pigtail or the taper is adjusted with the x-y-z translating stage. The length of the pigtail is about 25 cm. In such a short length, the next higher-order mode, if excited, can still propagate without appreciable atten- uation, although it is nominally cut off. We have therefore chosen the larger core fiber to. demonstrate modal purity.

Fig. 5 shows the intensity of the transmitted light when the dominant mode was excited in either the pigtail or the taper. At the top of the figure we see the intensity versus radial displacement profile of the radiated field. As can be seen, the dominant mode can be excited at either end, and travel practically unperturbed through the taper, in either direction. The small variations on top of the intensity profile are due to the graininess of the ground glass and dis- appear if the screen is vibrated during the exposure. We thus conclude that the tapers are sufficiently gradual and uniform, that no significant asymmetries, which would

72 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. LT-5, NO. 1. JANUARY 1987

A

-- 0.002 a

I I 1 I I 1 I I I I I , I I

-1.0’ -0 .8 -0 .6 -0.4 -0 .2 I

1.0 NORMALIZED 0.2 0.4 0.6 0.8 I I

RADIUS

I\ _-

-

Fig. 3. Graded index fiber characteristics:

x - v - 2 GROUNDGLASS TRANSLATING

STAGE VIEWING SCREEN

x - y - z GROUND GLASS

VIEWING

(b)

Fig. 4. Modal punty experiments. (a) He-Ne laser coupled into the fiber, (b) laser coupled into the taper. Fiber pigtail length - 10”. Fiber OD 130-pm with 7.27-bm graded index core diameter. X = 0.63 pm.

(a) (b)

Fig. 5. Intensity of transmitted light under dominant mode excitation. (a) Fiber pigtail excited-transmission through the aperture of the taper, (b) aperture of taper excited-transmission through single-mode fiber aperture. Same fiber and taper parameters as in Fig. 4.

perturb the symmetry of the dominant mode, are intro- duced. Also, note that the intensity profiles can be well approximated by a Gaussian function of the transverse radial coordinate.

When we introduce coupling asymmetry at the input end, e.g., a lateral displacement relative to the center of the core and/or an angular displacement, the next higher- order mode is excited Fig. 6. Movement pf the translating stage in the x or y directions, away from‘the center of the fiber core, results in the transmitted fields of Fig. 6(b) or 6(c), respectively. As can be seen, once the next higher- order mode is excited, it stays pure and we thus conclude that the purity of the mode of excitation at the input end is preserved to a high degree throughout the optical tapers.

We also tried to excite the higher modes, shown in Fig. 6(b) and 6(c), in the taper with the smaller diameter fiber pigtail (110-pm OD with 6.15-pm core). Since the core is smaller, these modes are in deeper cutoff. We measured the maximum power carried by these modes to be less than - 30 dB relative to the power carried by the dominant mode.

B. Excess Coupling Loss-Analytical Studies

Here we study the excess coupling loss between two tapers and its dependence upon the various coupling pa- rameter, Fig. 7. The excess coupling loss is defined as the ratio between the output power Po (in the dominant mode) in the right hand fiber pigtail to the incident power Pi in the left hand fiber pigtail.

We adopt the Gaussian beam representation [6] for the dominant modes in the tapers. The excess coupling loss of the tapers will then be the coupling loss between two Gaussian beams with parameters determined by the tapers. As we shall see, this representation agrees very well with our experiments.

For two identical tapers (or Gaussian beams with identical waists) the coupling loss is given by [7]

4 Ts =

4 + (s/X)2/7r2(W0/X)4 ’

for axial displacement

TDI Ts I = exp I - (D/w0J2I >

for lateral displacement

AMITAY et al.: OPTICAL FIBER TAPERS-BEAM EXPANSION AND HARDWARE 73

(a) (b) (c)

Fig. 6. Intensity of transmitted light through the aperture of the taper. (a) Dominant mode-LP,, excitation, (b) LP,, excitatibn, (c) LPl0 excitation.

(c)

Fig. 7. Displacement parameters. (a) S-axial, (b) D-lateral, (c) &angular. Graded index profile X = 0.63 Fm.

for angular displacement (3)

where wot is the equivalent Gaussian beam waist of the aperture of the taper.

We can evaluate the equivalent beam waist radius wOr for a parabolic profile [6]

(4)

with n1 being the index at the center of the core, a the radius of the core, r the transverse radial coordinate, and A the relative index difference between the core and cladding

In our tapers, with a = 43.25 pm and A = 0.0025, we have

wot = 9.19 pm, wor/X = 14.53. (6)

For the fiber pigtail, with core diameter 6.15 pm, the beam radius wof was numerically evaluated from its measured profile and found to be

w O ~ = 2.175, w,/X = 3.44. ~ (7) So far we have calculated the equivalent waist size of

the taper output face but we do not know its location relative to that face. To obtain this value and estimate Ts as S -+ 0, equation (1) can be written as

1 1 + (27~/X)~(w~/2R)~

Ts = (8)

where w # wOr is half the beam diameter at the aperture and R is its radius of curvature. For these very gradual tapers, the phase fronts are practically spherical being perpendicular to the conical surface of the taper. We could thus estimate the radius of curvature from the taper geometry (Fig. 2) and find R = 1.3 cm. If we assume w = wOt in (8), T, = 0.99896, and from (1) we find that the equivalent beam waist is located about 11 pm behind the aperture, justifying the assumption of w = war. The above value of Ts corresponds to a minimum loss of less than 0.005 dB due to nonplanar wavefronts at the faces of these tapers. This value would be further reduced with the straight cylindrical geometry of Fig. l(c).

Substituting the beam waist values of the taper and fiber of (6) and (7) into (1)-(3), we can calculate the dependence of the excess losses upon the displacement parameters and compare the taper-to-taper and fiber-to-fiber excess losses. In Figs. 8(a) and 8(b) we note the reduced sensitivities of the taper-to-taper coupling losses to axial and lateral displacements, shown by the dashed curve, as compared to the fiber-to-fiber coupling losses shown by the solid curve. The lateral sensitivity is reduced bv a factor of 4.2 (the ratio of wor/wof). For example, 0.5-dB loss corresponds to a lateral displacement of 0.73 pm for the fiber while the corresponding value for the taper is 3.1 pm. We note w e r an order of magnitude improvement for axial displacements. The 0.5-dB loss point corresponds

74 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. LT-5, NO. 1, JANUARY 1985

z - 6 e L -7 d = 6.15pm

wo/x = 3.44 -

i GRADED INDEX x = 0.6328~111

L '0 I

= 86.5pm , 0 EXPERIMENT

wolx = 14.53 1 -11

-12 0.20 0.5 1.0 5.0 10.0 50.0 100.0

LATERAL DISPLACEMENT - D(pm)

(a)

I I I I I I I I I

-1 s I-- \o -.-&.-&. -

\ O

\ o \ \O

\ " I- \ " w - 7 - \O

0 EXPERIMENT z 0 - 6 - U v) z \ d = 86.5pm

- 8

- 9 - - \ 2 = 14.53

W

\ x -10

-11

- 12 I I I I I I l l I I I 1 1 1 1 I I I I I I 1 1 1

- \ - \

\

20 50 100 500 1000 5000 10000

(b) AXIAL DISPLACEMENT - SIX

= 0.6328pm - 2

- 3 -

-

i s - 4 - 3 3 - 5 s z - 6

-

- 0 F - 7 - a

- 8

-9

W EXPERIMENT I

- 0 EXPERIMENT II - -

-10 -

-11 -

- 12 I I I l l l l l I I I I I I I I I

0.02 0.1 0.5 1.0 ANGULAR DISPLACEMENT - 8 (DEGREES)

5.0 10.0

- (c)

Fig. 8. Calculated and measured optical fiber tapers insertion (Excess coupling) loss versus displacements. (a) Lateral, (b) axial, (c) angular. Graded index profile, h = 0.63 pm.

AMITAY et al.: OPTICAL FIBER TAPERS-BEAM EXPANSION AND HARDWARE 75

METER

(b)

Fig. 9. Experimental procedure for measuring the insertion loss of an optical fiber taper. (a) Establishing the power level reference, (b) Mea- surement of insertion loss.

Fig. 10. Experimental mounting of two optical fiber tapers.

to an axial displacement of 16.5 pm for fiber coupling and 291 pm for taper coupling. The price one pays for this decrease in translational sensitivity is an increase in angular sensitivity of the taper coupling relative to the fiber coupling, by a factor equal to the decrease in lateral sensitivity. This is shown in Fig. 8(c) where, again, the fiber is represented by the solid curve and the taper by the dashed one. The 0.5-dB loss point corresponds to an angular displacement of 1.77" for fiber coupling and 0.42" for taper coupling. Angular accuracies well below 0.42" can be easily achieved in practice.

C. Excess Coupling Loss-Measurements The experimental procedure is depicted in Fig. 9. Power

is launched into the fiber pigtail. The cladding modes are stripped and we measure the transmitted power which is carried by the dominant mode, Fig. 9(a). This measure- ment, with index matching, establishes the power refer-

ence level Pi. We now add the second taper and properly position and align both tapers. The tapers are held on electronically adjustable micropositioning stages. We index match the space between the tapers and measure the power transmitted from the fiber pigtail of the second taper Po in Fig. 9(b). The ratio P O P i is the excess coupling loss which was previously discussed. These experimental points are plotted by the circles in Fig. 8.

Fig. 10 shows the actual mounted tapers used in the experiment. Examining Fig. 8, we note the excellent agreement between the experimental and analytical results for the lateral and axial displacements. The results of two series of measurements are displayed in Fig. 8(c) for the angular displacement, showing good agreement. The angular and transverse measurements were made with the tapers close together.

The taper length and profile used in this work are not critical for preserving the guidance of the fundamental

76 JOL JRNAL OF LIGHTWAVE TECHNOLOGY, VOL. LT-5, NO. I , JANUARY 1987

mode with minimal loss. Analytical studies of step-index profiles for various taper geometries and lengths show low loss for tapers as short as 1 cm [ 111.

111. CONCLUSIONS In this work we have demonstrated the practicality of

optical fiber tapers as a basic building block for single- mode hardware. The tapers, which enlarge the dimension of the dominant mode beam, are self-aligning elements. When tapers are coupled to one another, the loss sensitivity to lateral and axial displacement is decreased manifold relative to fiber-to-fiber coupling. We have obtained a very good correlation between experimental and analytical results for the sensitivity of the excess loss of two coupled tapers to various displacements at X = 0.63 pm. The tapers are essentially lossless for close coupling. The increased angular displacement sensitivity is within practical limits.

was a Research Assistant in 1957, a Project Engineer in 1958, and an In- structor in 1959, all at Carnegie Institute of Technology. He served as a Consultant on electronic instrumentation for Magnetics, Inc., Butler, PA, from 1957 to 1958 and from 1960 to 1961. From 1960 to 1962, he was an Assistant Professor in the Department of Electrical Engineering, Carnegie Institute of Technology, and a part-time employee of the New Products Laboratories of Westinghouse Electric Corporation, Pittsburgh, PA. He joined the Bell Telephone Laboratories, Inc., Whippany, NJ, in 1962, where he conducted reserach in phased array radar and communication antennas, electromagnetic theory, and numerical methods and analysis. In recent years, he has been involved in studies of satellite communication antennas, digital radio communications and lightwave networks. At present, he is a distinguished member of the technical staff in the Local Com- munications Research Department at AT&T Bell Laboratories, Holmdel, NJ .

Dr. Amitay is a member of the International Scientific Radio Union.

*

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ing, coating and strengi

Frank V. DiMarcello was born in Hazleton, PA, on February 22, 1939. He received the B.S. degree in geochemistry from Pennsylvania State University, University Park, PA, in 1960, and the M.S. degree in ceramics from Rutgers University, New Brunswick, NJ, in 1966 with a thesis relating to the oxygen diffusion in sodium silicate glasses.

Since joining AT&T Bell Laboratories in 1960, he has worked on the preparation and property evaluation of ceramics and glasses for a variety of applications. He is currently involved in the draw-

th improvement of optical waveguides.

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fiber beam expansion

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