Ideal microlenses for laser to fiber coupling - IEEE Xplore

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Ideal Microlenses for Laser to Fiber Coupling. Christopher A. Edwards, Herman M. Presby, and Corrado Dragone. Abstract-We report the design and fabrication ...
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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11, NO. 2, FEBRUARY 1993

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Ideal Microlenses for Laser to Fiber Coupling Christopher A. Edwards, Herman M. Presby, and Corrado Dragone

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Abstract-We report the design and fabrication of ideal microlenses for semiconductor laser to fi-ber coupling. Properly coated for reflections, lenses of the new design can theoretically collect 100% of the radiated energy of a modal-symmetric laser source. The crucial feature is its hyperbolic shape. Microlenses fabricated directly on the end of the fiber by laser micromachining have demonstrated up to 90% coupling efficiency. This performance represents a major advance in microlens technology when compared to currently fabricated hemispherical microlenses which are at best 55% efficient. A theoretical comparison of the two lens shapes illuminates the advantages of the hyperbolic profile. The ability to couple all of the light from a semiconductor laser into a fiber has far-reaching implications for all optical communication systems.

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I. INTRODUCTION

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FFICIENT coupling between the laser source and fiber is essential for optimal performance in optical communications systems. Compared with butt coupling, efficiency is improved either by the use of a microlens on the end of the fiber [1]-[6] to match the modes of the laser and fiber or by bulk optics. Microlenses are more commonly used because of ease of fabrication and packaging. Microlenses are generally fabricated by tapering the fiber down to a point and melting the end. The resultant lenses are hemispherical in shape and consistently demonstrate imperfect coupling, collecting typically less than 50% (-3 dB), and at best 55% (-2.5 dB) of the available laser radiation. We have designed and fabricated optimal microlenses for laser to fiber coupling which have achieved 90% (-0.45 dB) coupling [7]. For an ideal laser, with symmetric modal output, and an anti-reflection coating on the microlens coupling efficiency theoretically approaches 100%. The technique for fabricating micromachined fiber lenses has already been reported [8]. In this paper we derive the optimal microlens profile using ray tracing techniques. This shape turns out to be a hyperboloid of revolution. The subsequent calculations show that uncoated lenses, limited solely by reflections, suffer only 0.22 dB loss when coupling to a typical laser with a symmetric Gaussian mode. We also discuss the method that has produced ideal, hyperbolic microlenses. These lenses demonstrate near optimal performance. The implications for improved system perforManuscript received February 27, 1992; revised August 28, 1992. C. A. Edwards was with AT&T Bell Laboratories, Crawford Hill Laboratory, Holmdel, NJ 07733. He is now with MIT, Department of Earth, Atmospheric and Planetary Sciences. H. M. Presby and C. Dragone are with AT&T Bell Laboratories, Crawford Hill Laboratory, Holmdel, NJ 07733. IEEE Log Number 9205547.

Fig. 1. Idealization of laser to fiber coupling. The laser, having beam waist W O , is separated a distance d from a fiber having a guided mode radius W I .

mance are varied and far-reaching, covering almost every area where fibers are coupled to lasers or amplifiers. We begin our analysis by examining the fundamental limitations on the efficiency of hemispherical microlenses [5], [9]-[17]. We take into account various sources of loss and calculate coupling efficiency as a function of lens radius for a variety of laser parameters. The resulting analysis reveals that maximum coupling efficiency for typical systems is limited to about 56% (-2.5 dB), in good agreement with reported results. 11. ANALYSIS

Consider the coupling arrangement of Fig. 1showing a laser separated a distance d from the lensed fiber. The l/e amplitude radius of the field is referred to as the mode radius, w . We denote WO to be the minimum mode radius of the laser, and w1 to be the guided mode radius of the fiber. As it propagates from the front facet of the laser, the mode of the laser widens; we call this expanded mode radius w2. The following assumes ideal, circularly symmetric, Gaussian field distributions for both the source and the fiber. A. Coupling Eficiency

We approximate the incident field on the lens surface in Fig. 1 by a spherical wave with wavefront centered at Q and amplitude distribution $9 = e-P2Iw;, where p = is the radial coordinate. The radius of curvature, R2 of the incident wavefront is the distance from Q, and from [18]

d

m

At the lens surface, the field is in part reflected, in part transmitted with transmission coefficient, t. Therefore, the

0733-8724/93$03.OO 0 1993 IEEE

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coupling efficiency 71 giving the efficiency of power transfer to the fiber mode can be written in the form

l p 1 $ 2 t e x P [ i F L ]PdPj2 (2)

71=

jp:pdP.p P d P where

$1

= e--P2Iw: and the phase factor

B. Efficiency of Hemispherical MicrolenslLaser System In order to calculate the efficiency 71, it is convenient to reverse the sense of transmission in Fig. 1. This will not affect the coupling efficiency, because of reciprocity, and it will not change the form of (2). However, since the incident wave becomes a plane wave incident from the right, the calculation of t will be simplified. We first calculate t, which is determined by the angle of incidence 8;, specified by dz tan 8; = = dP

exp ].fi[ is caused by the differencein phase bemeen the incident field and the fiber mode. For the incident field, the phase distribution on the lens surface is determined by the optical distance of a surface point P from the center Q. Therefore, since the fiber mode has uniform phase distribution, the difference between the two phase distributions causes a path length error,

P

J7g7-p’

First notice that t is zero, because of total internal reflection, radius for p exceeding the pc

=

n2RL

711

(9)

corresponding to the critical angle BC, specified by 712

sin 8, = nl where z ( p ) is the axial coordinate of P, and nl , n2 are the refracting indexes. For small values of p, expanding L in powers of p and neglecting terms of order 24,we obtain the well known relation for the phase error [19]

This truncating radius p2 defines the aperture within which coupling is permitted. Thus, for a fiber where n l = 1.46, less than 50% of the cross-sectional area of the lens can collect and transmit light. Refraction at the lens surface distorts both the amplitude and the polarization of the incident wave. To determine this (4) distortion, assume that the incident wave is polarized in the x-direction. Then for each incident ray, the field can be deThis relates L to the focal length f which for a hemispherical composed in two components, respectively polarized parallel lens is specified by the lens axial curvature ~ / R L and orthogonal to the plane of incidence. Their amplitudes are $1 cos 4 and $1 sin 4, where 4 is the azimuthal angle specified by the plane of incidence. By multiplying the two components (5) by the appropriate transmission coefficients tll ,t l , given by According to (2), the efficiency neglecting aberrations and reflections is maximized by choosing the separation d so that w2 = w1 and letting and

f = R2 so that L

N

0. If, for instance, we find that WO

= l p m and

then we obtain d z 11.8pm, f

2

w1

$1k

is transformed into

= 5pm

12.3pm, i.e.,

RL N 5.7pm.

(7)

However, the lens aberrations and reflections will, in fact, cause the optimum values of d and f to differ from the above values. Furthermore, a lens having this radius is not very efficient. The main reason for this poor performance is that efficient coupling requires both this small lens radius and a large aperture, which are incompatible for hemispherical microlenses. Both of these issues are discussed in the next section.

The second term represents an orthogonal mode which due to its 4 dependence will not be accepted by the device. Only the first component, the one with circular symmetry, contributes to t, giving

We can proceed to calculate r / , which can be written as a product of two efficiencies 71 = TJCJ2

(15)

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0

-1

dld,

U

w

-3

-4

.70

6

10

8

R,

-5 6

10

8

RL

12

12

14

(w)

14

(rm)

Fig. 3.

Fig. 2. Coupling efficiencies of a laser to hemispherical microlens. T is the lens transmittivity and shows the coupling loss between the apertured fiber and laser modes. q, Q', and qn are the total coupling efficiencies assuming R2 = f, neglecting phase error L , and optimizing separation distance d, respectively.

Separation distance shift d/do as a function of lens radius.

0

-2

h ) .

where the lens transmittivity T is caused by t ,

.f

-4

E w -6

-8

and C is the coupling coefficient between the refracted wave

11, = texp[z(27r/A)L]$l and

$2.

The calculated behavior of the two efficiencies T and IC(' as functions of RL is shown in Fig. 2. Transmission loss T, which for large RL approaches reflection loss at a planar interface, increases with decreasing lens aperture. IC1', which increases with RL due to the mismatch between w1 and w2, is also large for small RL. This loss demonstrates the severe penalty paid when coupling a pure Gaussian beam with one that is strongly apertured. The product of the two efficiencies, shown by the curve labeled Q in Fig. 2, has a broad maximum of -2.7 dB for a radius RL N 8.5 pm. Note that this value of the lens radius is larger than 5.7 pm, as calculated previously by setting w1 = w2. Also plotted in Fig. 2 is the efficiency Q', calculated neglecting the phase error L. The difference between Q and 7' is not large, showing that the phase error is relatively small over the lens aperture defined by the critical radius p c . So far we assumed the separation distance d as required by (5). As mentioned in Section 11-A, coupling can be improved by optimizing d. Using (2), one can determine the optimum d for maximum coupling. Although the shift in d is typically less than 70%, as shown in Fig. 3, the effect is noteworthy. The , plotted in Fig. 2, is calculated by including efficiency Q ~ also the phase error L and optimizing d. Thus coupling between a hemispherical microlens and laser is improved by optimizing the separation distance, but even so the maximum coupling is small (-2.4 dB for RL = 8.8pm). The above analysis can be extended to reveal Q,,, as a function of RL for different mode ratios wo/wl, and these

-10 4

6

8

10

12

14

16

18

20

22

RLIA

Fig. 4. Total coupling efficiency Q,,, for laser to hemispherical microlens for different lasedfiber mode ratios as functions of the normalized lens radius.

curves are shown in Fig. 4. As one might expect coupling approaches unity as the mode ratio increases. Interesting to note is the consistently large optimum value of RL for small mode ratios, showing the strong beam truncation effect for small RL. The above calculations are in good agreement with the measured losses of commercial lenses, typically with RL N 10 pm. A photograph of a commercially fabricated, hemispherical microlens is shown in Fig. 5. The lens contour is very nearly spherical, with a radius of curvature of approximately 10 pm. Although this lens suffers little truncation loss, its performance is limited by IC['. It is possible to directly measure T by comparing power transmission through an initially lensed and then cleaved fiber using a large area detector. The reflection loss at a planar interface is easily calculated to be 0.15 dB. Including this loss in the ratio of the two power measurements gives T. Measurements of several fibers with microlenses fabricated by the chemical etch and melt method [13] agree well with the plot of T shown in Fig. 2. However, a microlens taper can also be produced by heating a narrow portion of the fiber and then pulling apart the fiber [9], [11], [16]. Microlenses produced by this heat and draw technique were found to have significantly

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EDWARDS et al.: IDEAL MICROLENSES FOR LASER TO FIBER COUPLING

1

.5

0

llf

-.5

-1

-.5

-1

0

.5

I

1I f

Fig. 5. Photograph of actual hemispherical microlens. Approximate radius of curvature is 10 pm.

microlens to match mode of laser in units n o n a l Fig. 6. Ideal.. hvoerbolic ,. ized to the focal distance. 'Tko off-axial rays are shown converging at the distant focus of the hyperbola beyond intersection of the asymptotes.

U

0,

a

111. IDEAL MICROLENS DERIVATION AND ANALYSIS The above analysis suggests that hemispherical microlenses, regardless of their fabrication technique, are not ideally suited to collect all the available radiation emanating from a laser source, with an inherent coupling loss of typically 2.5 dB. We now derive and investigate the model microlens for this purpose. From (3), by requiring zero phase error (i.e., L = 0) and solving for z ( p ) we obtain the hyperbolic profile [20]

s

-

-6 -

.6

.a

1

1.2

1.4

1.6

1.8

2

wo (urn) Fig. 7. Total coupling efficiency of a laser to its matching hyperbolic microlens, as a function of laser mode radius, WO. Fiber mode radius, w1 = 5 pm, and X = 1.3 pm. The asymptotic approach to loss at a planar interface is shown.

nonsymmetric source, we may simply add the coupling loss for any x - y anisotropy. In general, this additional loss is where small; for example, a mode ratio w,/wv = 0.8 results in a 2 coupling loss of about 0.2 dB [6]. In practice, the incident a2 = (A) R: and b2 = ( e ) R g (18) wave is afflicted by aberrations. Furthermore, the hyperbolic 721 722 nl 722 illustrated in Fig. 6. This ideal profile exactly transforms profile has a finite angular aperture. the incident spherical wave into a plane wave, according to geometric optics. Using this profile, the optimum design parameters d, f that maximize the efficiency are obtained from defined by the asymptotes of the hyperbola and, therefore, (1) and (5) by requiring w1 = w2. The optimum efficiency it can not intercept the entire power radiated by the laser. using AR coating, will then approach unity. Qpically, however, the above losses are found to be small, Without coating, by calculating 17 as in the previous section, less than a few tenths of dB. In particular, the acceptance we can show from (2) that the lens transmittivity T will not cone of the hyperbolic lens for n1 = 1.46 and 722 = 1.0 has be less than -0.22 dB for wOIw1 > 0.2, as shown in Fig. 7. an aperture of 93O, large enough not to be a factor for most We remark that the above calculation predicting unity semiconductor laser sources. efficiency for an ideal lens contains several approximations. We have assumed that the incident wave is exactly a spherical IV. HYPERBOLIC LENSFABRICATION wave, that it produces on the lens surface the Gaussian

+

+

distribution $12, and that its polarization exactly matches the polarization of the fiber mode. To extend this analysis to a

We have shown that the hyperbolic microlens design is far superior for coupling to typical semiconductor lasers than are

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using a standard technique [6]. Nearly all of the hyperbolic microlenses fabricated show better than 2.5 dB coupling loss, and several have achieved less than 0.5 dB loss. These values are for uncoated lenses and no feedback control on the fabrication process. With better control, reproducible fabrication of lenses with greater than 90% (=0.45 dB) coupling should be possible.

V. CONCLUSION

Fig. 8. Photograph of a laser micromachined, hyperbolic microlens.

-15

-10

-5

0

5

10

15

MICRONS

Fig. 9. Contour of a laser micromachined, hyperbolic microlens with an ideal hyperbola.

hemispherical microlenses, by as much as several decibels. However, formation of an aspheric shape is nontrivial even in macroscopic optical components. Microscopic lenses such as these must have submicron precision in order to fully realize the coupling enhancement. Recently a powerful fiber lensing technique, laser micromachining, that offers the control necessary to fabricate these hyperbolically shaped microlenses was reported [8]. In this new process a spinning fiber is moved in a narrowly focussed CO2 laser beam, which ablates the silica fiber much like a machinists tool removes material from a metal rod. Hyperbolic microlenses have been fabricated by the laser micromachining technique under computer control. One is shown in Fig. 8. A lens profile, along with an ideal hyperbola, is shown in Fig. 9. As can be seen, the microlens is well approximated by a hyperbola near the core of the fiber. Several dozen microlenses have been evaluated by measuring coupling efficiency to different semiconductor lasers

We have investigated the relative merits of hemispherical versus hyperbolic microlenses for use coupling to semiconductor lasers in optical communication systems. Hemispherical microlenses are commonly used worldwide, and typically show poor coupling performance (c 2.5 dB). We showed that this high loss results from a combination of four effects: fiber truncation, mode-mismatch, spherical aberration, and Fresnel reflections. Understanding the fundamental limitations of these standard microlenses, we examined the microlens coupling and derived the lens shape for optimal collection of laser radiation. We showed that uncoated, ideal, hyperbolic microlenses typically exhibit 0.22 dB coupling loss due only to reflections. Furthermore, we have used a new technique, laser micromachining, to implement this design and manufacture these aspheric microlenses. Uncoated, laser micromachined lenses achieve up to 90% (-0.45 dB) coupling efficiency. Efficient coupling of semiconductor lasers to optical fiber has been a problem of general concern since the advent of optical fiber communications. With the development of the hyperbolic microlenses, considerable system improvement in nearly all communications systems can be realized. This applies not only when coupling to semiconductor lasers, but also to semiconductor amplifiers and to pump sources for fiber amplifiers as well.

REFERENCES H. Ghafoori-Shiraz and T. Asano, “Microlens for coupling a semiconductor laser to a single-mode fiber,” Opt. Lett., vol. 11, pp. 537-539, 1986. H. Ghafoori-Shiraz, “Experimental investigation on coupling efficiency between semiconductor laser diodes and single-mode fibres by an etching technique,” Optical and Quantum Electron., vol. 20, pp. 493-500, 1988. M. Saruwatari and K. Nawata, “Semiconductor laser to single-mode fiber coupler,” Appl. Opt., vol. 18, pp. 1847-1856, 1979. W. Bludau and R. H. Rossberg, “Low-loss laser-to-fiber coupling with negligible optical feedback,” J. Lightwave Technol., vol. LT-3, pp. 294-302, 1985. L. G. Cohen and M. V. Schneider, “Microlenses for coupling junction lasers to optical fibers,” Appl. Opt., vol. 13, pp. 89-94, 1974. G. Eisenstein and D. Vitello, “Chemically etched conical microlenses for coupling single-mode lasers into single-mode fibers,” Appl. Opt., vol. 21, pp. 3470-3474. H. M. Presby, “Near 100% efficient fiber microlenses,” OFC ’92 (San Jose, CA), Postdeadline Paper PD24, pp. 408-411, 1992. H. M. Presby, A. F. Benner, and C. A. Edwards, “Laser micromachining of efficient fiber microlenses,” Appl. Opt., vol. 29, no. 18, pp. 2692-2695, 1990. B. Hillerich and J. Guttmann, “Deterioration of taper lens performance due to taper asymmetry,” J . Lightwave Technol., vol. 7, pp. 9%104, 1989. K. S. Lee and F. S. Barnes, “Microlenses on the end of single-mode optical fibers for laser applications,” Appl. Opt., vol. 24, pp. 3134-3139, 1989.

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[ll] B. Hillerich, “Shape analysis and coupling loss of microlenses on singlemode fiber tips,” Appl. Opt., vol. 27, pp. 3102-3106, 1988. [12] K. S . Lee, “Focusing characteristics of a truncated and aberrated Gaussian beam through a hemispherical microlens,” Appl. Opt., vol. 25, pp. 3671-3676, 1986. [13] S. Sh. Gol’dshtein et al., “Matching of injection lasers to single-mode fiber waveguides,” Sov. J. Quantum Electron., vol. 18, pp. 521-525, 1988. [14] W. B. Joyce and B. C. DeLoach, “Alignment-tolerant optical-fiber tips for laser transmitters,” J. Lightwave Technol., vol. LT-3, pp. 755-757, 1985. [15] J. Yamada, Y. Murakami, J. Sakai, and T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” J. Quantum Electron., vol. QE-16, pp. 1067-1072, 1980. [16] H. Kuwahara, M. Sasaki, and N. Tokyo, “Efficient coupling from semiconductor lasers into single-mode fibers with tapered hemispherical ends,”Appl. Opt, vol. 19, pp. 2578-2583, 1980. [17] Y. Murakami, J. Yamada, J. Sakai, and T. Kimura, “Microlens tipped on a single-mode fibre end for InGaAsP laser coupling improvement,” Electron. Lett., vol. 16, pp. 321-322, 1980. [18] H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt., vol. 5 , pp. 1550-1567, 1966. 1191 M. Born and E. Wolf, Principles ofOptics, 6th ed. Oxford: Pergamon Press, 1959. [20] R. K. Luneburg, Mathematical Theory ofoprics. Berkeley, CA, University of California Press, 1966.

Christopher A. Edwards, received the B.S. degree from Haverford College, Haverford, PA, in 1988, graduating with honors in physics. He became a member of the Phi Beta Kappa Society in 1987, and of the Sigma Xi Society in 1988, having conducted undergraduate research in nonlinear fluid dynamics. Since joining AT&T Bell Laboratories, Holmdel, NJ in 1988, he has pursued experimental work on fiber micro-lenses and other passive photonic components. His current interests lie in the design and application of planar waveguide devices.

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Herman M. Pmsby, received the B.A. and Ph.D. degrees in physics from Yeshiva University in 1962 and 1966, respectively. He was a research scientist at Columbia University from 1966 to 1968, where he worked on electromagnetic shock wave and optical techniques for plasma diagnostics. From 1968 to 1972 he was an assistant professor of physics at the Belfer Graduate School of Science of Yeshsiva University doing research on high-energy plasmas and laser systems. He joined AT&T Bell Laboratories in 1972 where he is a Distinguished Member of the Technical Staff engaged in research relating to photonic networks and components. He has published over 100 papers and holds some 40 patents in this field. Dr. Presby is a fellow of the Optical Society of America.

Corrado Dragone (SM’84) received the Laurea in electrical engineering from Padua University, Italy, in 1961 and the Libera Docenza from the Minister0 della Pubblica Istruzione, Italy, in 1968. Since joining Bell Laboratories in 1961, he has been engaged in expenmental and theoretical work on microwave antennas, frequency converters, and solid-state power sources. In 1974 and 1975, he taught a course on antennas and propagation at Padua University. He has authored over 40 articles, holds over 20 patents, and is currently concerned with problems involving electromagnetic wave propagation, microwave antennas for terrestrial radio systems, integrated optics, and optical interaction in solids.