Coupling light from a laser diode into a multimodefiber

Xiaodong Zeng and Yuying An

A parabolalike fiber end to couple the light from a high-power laser diode into a multimode fiber ispresented. The formula for the coupling efficiency of such a system is given, and numerical evaluationshows that the theoretical coupling efficiency can be as high as 92% without an antireflection coating onthe fiber’s end face. This beam-shaping system can be fabricated easily and has a large alignmenttolerance. © 2003 Optical Society of America

OCIS codes: 060.1810, 140.3300, 350.3950, 140.2020.

1. Introduction

Many applications require shot-distance fiber-opticdelivery of laser diode �LD� output power to a work-place. Separate optical fibers are also combined inbundles of various configurations. These bundlesaccumulate radiation from an array of individualLD sources and are used for end pumping of solid-state lasers. The key technique is to couple effi-ciently the output light from a LD emitter into amultimode fiber. In this paper we restrict our dis-cussion to the coupling of a single-emitter LD to amultimode fiber.

Several methods to improve the coupling effi-ciency between a LD and a fiber are in use.1–3

These methods can be divided into two types. Thefirst type is direct micromachining of the end of thefiber up to a special form. In general the specialform is a continuous curve; it can improve the nu-merical aperture of the fiber. However, fabricationof a fiber end is difficult. The second type is cou-pling of LD light corrected by an additional cylin-drical microlens into the flat end face of the fiber.For example, Yoda et al. proposed using a wedge-shaped coupling element4 for single-mode coupling.Obviously, the use of additional optical elementsleads to considerable complexity of the device.And such a method can hardly maintain precise

The authors are with the School of Technical Physics, XidianUniversity, Xian 710071, China. X. Zeng’s e-mail address isxdzeng@xidian.edu.cn.

Received 9 October 2002; revised manuscript received 27 March2003.

0003-6935�03�224427-04$15.00�0© 2003 Optical Society of America

alignment over a wide temperature range, otherenvironmental changes, and time.

Two main factors influence the coupling efficiencyof LD light into multimode fiber. First, the ellipticalwave spot of the LD mismatches the circular modefield of the fiber. Further, the large divergence an-gle of the LD perpendicular to the junction planemismatches the acceptance angle of the fiber.

The emitter size of a typical LD is approximately 1�m � 100 �m, and the divergence angles �FWHMvalues� of the LD are 10° and 40° perpendicular andparallel, respectively, to the junction plane. Nor-mally the acceptance angle of the multimode fiber is�20°; the divergence angle of the LD parallel to thejunction plane is less than the acceptance angle of thefiber. Therefore, the light can easily be coupled intothe fiber in this direction, provided that the spot sizeof the LD and the mode spot are the same. However,a large divergence angle of a LD perpendicular to thejunction plane strongly mismatches the acceptanceangle of the fiber. The divergence-angle mismatchis the most important factor that influences couplingefficiency. A novel coupling method that uses a pa-rabolalike fiber end is proposed in this paper. Thecoupling efficiency is evaluated, and the structuralparameters are discussed.

2. Beam-Shaping Optics

Although the emitter of the LD is an extended sourcein the direction parallel to the junction plane, theemitter’s size cannot influence the coupling efficiencybecause of the small divergence angle in this direc-tion, as discussed above. This means that the beamspot-size match always holds and that the angularmatch also holds automatically because the diver-

1 August 2003 � Vol. 42, No. 22 � APPLIED OPTICS 4427

gence angle of the laser beam is less than the criticalangle for total internal reflection in the fiber.

In the direction perpendicular to the junctionplane the emitter size is typically less than 1 �m; itis much less than the core diameter of the fiber��130 �m�, which indicates that the beam spot-sizematch can also hold. Therefore the emitter can beregarded as a point source. The most importantthing is to compress the divergence angle of the LDefficiently, such that it is less than the acceptanceangle of the fiber.

It is known that a parallel beam can be produced byuse of a parabolic mirror if a small light source isplaced at the focus of the parabolic mirror. A fiberend is polished into a parabolic curve. This curveboundary can be regarded as a two-dimensional par-abolic mirror owing to total internal reflection. TheLD is placed at the geometrical focus of the paraboliccurve, as shown in Fig. 1. Then high coupling effi-ciency can be obtained.

However, the LD is not in the fiber medium; thereis a boundary between the air and the fiber. In thiscase the propagation of light is much different fromthat of the parabolic mirror in air. Because of theexistence of the fiber end face it seems that rays thatcross through the fiber end face come from differentpoints; i.e. the result is astigmatism �Fig. 2�, where �is the incident angle. Therefore the light from a LDplaced at geometrical focus F �Fig. 2� will be reflectedby the parabolic curve, not as a parallel beam withinthe fiber. This astigmatism does not seriously influ-ence coupling, provided that the angles between thereflected rays and the optical axis are less than theacceptance angle of the fiber.

In practice, it is difficult to polish a continuouscurve in a fiber end. Therefore two segments of astraight line instead of a parabolic curve have been

used to form a beam-shaping system, as shown in Fig.3. That is, two planes at different oblique angles arepolished at the fiber end. The position of the inter-section point of the two straight lines can be opti-mized through evaluation of the maximum couplingefficiency. Two factors must be taken into account:First, to prevent large reflective loss by the end facein an off-axis region, the geometrical focus should notbe too close to the end face of the fiber. Second, thecore diameter of the fiber should be larger than thesize of the emitter parallel to the junction of the LD.For example, if the emitter size is 100 �m, the fibercore diameter could be 130 �m.

Figure 4 shows how the divergence angle is com-pressed by the beam-shaping optics. For conve-nience, only one oblique plane is plotted in Fig. 4. Itis not difficult to see from this geometry that theangle between the beam refracted by the obliqueplane and the fiber axis within the fiber can be ex-pressed as

� � �� � 2, (1)

where �� is the refractive angle of the fiber end face inthe fiber and is the angle of the oblique plane pol-ished with respect to the fiber axis. Because therefractive index of the fiber is �1.5, incident angle �is always greater than refractive angle ��, fromSnell’s law.

Equation �1� shows that if a light ray enters a fibercore from air at an incident angle � with respect tothe fiber axis, it will propagate within the fiber at anangle � with respect to the fiber axis. Then totalinternal reflection can occur, provided that propaga-

Fig. 1. Schematic of a parabolic fiber end to improve the numer-ical aperture of a fiber.

Fig. 2. Astigmatism owing to the existence of the fiber end face.

Fig. 3. Diagram of the parabolalike fiber end.

Fig. 4. Diagram of divergence-angle compression.

4428 APPLIED OPTICS � Vol. 42, No. 22 � 1 August 2003

tion angle � is chosen such that it satisfies the fol-lowing condition:

� �

2� sin�1 n2

n1, (2)

where n2 is the refractive index of the fiber cladding.The discussion above indicates that the equivalentnumerical aperture of the fiber is improved. In Figs.1–4 the fiber cladding is not shown; this cannot in-fluence the results obtained above, because the fibercladding above the oblique plane has been polishedaway. All the rays reflected by the oblique planepassing along the fiber will strike the core–claddinginterface at such an angle that the rays are totallyinternally reflected after each reflection; i.e., thesemodes are guided modes.

3. Coupling Efficiency

A LD has a large divergence angle perpendicular tothe junction plane. The off-axis optical model of thefar-field distribution should be used. A far field heremeans that the distance from the source to the ob-servation point is much greater than the wavelengthas well as the size of the source. In considering theLD in the direction perpendicular to the junctionplane, in most practical cases the far-field conditionholds, provided that the distance between the sourceand the observation point is not less than 100 �m.In our case the optical field is treated in the fiber, andthe observation point is significantly greater than 100�m. We assume here that the fiber end face cannotinfluence the propagation of the laser beam, exceptthat the propagation direction can vary owing to re-fraction of the glass surface. The far-field intensitydistribution perpendicular to the junction plane canbe expressed as5

I� x, 0, z� � � A�21z2 � �2

�2 � x2�2

, (3)

where �2 p2z2��k2 � p2�, A and p are parametersrelated to the waveguide structure, and k 2�� isthe wave number. Substituting x�z tan � into Eq.�3�, we obtain

I��, z� �� A�2

z2 � �12

�12 � tan ��

2

, (4)

where �12 p2��k2 � p2�. Then the coupling effi-

ciency can be described as

� �

���1

�1

I��� R���T���d� � 2 ��1

�2

I��� R���T���d�

���2

�2

I���d�

,

(5)

where T��� is the transmissivity of the fiber endface, which can obtained by use of Fresnel’s for-mula. R��� is the reflectivity of the oblique plane,

which can also be obtained by use of Fresnel’s for-mula. The limits of the integral in the numeratorcan be determined according to the position of theintersection point of the two straight lines as well asthe criterion that the angle of the reflected raysfrom the optical axis be less than the acceptanceangle of the fiber.

Astigmatism is an inherent property of the outputbeam of a LD. The wave front emerging from the LDis cylindrical. The beam waist perpendicular to thejunction plane is located at the output facet of the LD,but the waist parallel to the junction plane is dis-placed a distance � behind the facet. � is the astig-matism parameter of a LD. Index-guided LDstypically exhibit a small amount of astigmatism �2–5�m�; gain-guided LDs usually have 30–60 �m ofastigmatism. Strictly speaking, astigmatism mayinfluence coupling efficiency. In this paper laserastigmatism has not been taken into account, mainlybecause currently popular LDs are of the index-guided type, for which this problems is not serious.Both theoretical and experimental examinations in-dicate that beam astigmatism can hardly influencethe coupling efficiency between LD and multimodefibers when the beam-shaping optics presented aboveare used. This can be easily understood: Theastigmatism is equivalent to moving the LD a dis-tance � from the fiber end in the direction parallel tothe junction plane. Because the laser beam has asmall divergence angle in this direction, the spot sizeof the laser beam cannot vary significantly. For ex-ample, assume that the distance of the LD facet fromthe fiber end is 20 �m. Then the 100-�m astigma-tism can lead to only a 2-�m variation of the spot sizeat the fiber end face. Computed results show thatthe maximum coupling efficiency can be as high as92% without an antireflection coating on the end faceof the fiber.

4. Conclusions

By use of a parabolalike shaping system the couplingperformance of a LD and a multimode fiber can besignificantly improved. If an antireflection coatingis applied to the fiber end face, the coupling efficiencycan be increased. Theoretical examination hasshown that this coupling mechanism also has a largeposition tolerance; this means that the coupling sys-tem is not sensitive to vibration or to environmentaltemperature.

This study is supported by Ministry of Education ofChina and the National Natural Science Foundationof China �grant 60277004�.

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3. S. B. Sevastianov, S. M. Vatnik, and A. P. Mayorov, “Shaping ofthe end of a multimode optical fiber for efficient coupling lightfrom a laser diode,” Appl. Opt. 38, 77–85 �1999�.

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