Asymmetrical prism for beam shaping of laserdiode stacks

Xiaodong Zeng, Changqing Cao, and Yuying An

A beam-shaping scheme for a laser diode stack to obtain a flattop output intensity profile is proposed. Theshaping element consists of an asymmetrical glass prism. The large divergence-angle compression in thedirection perpendicular to the junction plane and the small divergence-angle expansion in the paralleldirection are performed simultaneously by a single shaping element. The transformation characteristicsare presented, and the optimization performance is investigated based on the ray-tracing method.Analysis shows that a flattop intensity profile can be obtained. This beam-shaping system can befabricated easily and has a large alignment tolerance. © 2005 Optical Society of America

OCIS codes: 140.3300, 140.2020, 140.2010, 220.2740.

1. Introduction

In recent years, high-power laser diode (LD) arrayshave been widely used in practical applications, suchas pumping solid-state lasers, material processing,and medical uses. Depending on the output power, ahigh-power LD array could consist of 1 cm bars orstacked diode bars. A diode bar is usually composed of19 laser emitters spaced on 500 �m centers, whichamounts to a fill factor of 20%. The bars can bestacked to form a two-dimensional array. In almostall practical work, the output beam of a LD stackmust be shaped to meet the requirements of the ap-plication. Because of the shape and the waveguideproperties of their active areas, these LDs generatelarge divergence-angle beams with ellipticallyshaped mode profiles, the FWHM values of a LD are40° ���� and 10° ���� perpendicular and parallel to thejunction plane, respectively. Moreover, the typical ap-erture area of a LD stack is of the order of several cm2

(e.g., a LD bar has a 1 �m � 1 cm aperture), it is anextended source, and several tens of emitterssparsely fill the aperture of the device. These proper-ties of the optical field of a LD stack result in diffi-culties in many practical cases in which a uniformsquare beam spot is needed.

The low brightness and asymmetrical field distri-bution of a LD stack are the main stumbling blocks inapplications of high-power LD devices. To shape theoutput beam of a LD stack, several methods havebeen suggested.1–9 These methods can be divided intotwo classes: One is based on the imaging system, suchas a two-dimensional microlens array and two-dimensional phase gratings. In principle, these shap-ing systems can improve the beam quality quite well.However, fabrication of a two-dimensional microlensarray (or gratings) exactly matching the LD stack isusually difficult. In addition, because of the largedivergence angle, the microlens array must have ahigh numerical aperture; the effect of this shapingsystem depends strongly on the alignment of the mi-crolens array. Such a method can hardly maintainhigh performance over a wide temperature range,other environmental changes, and time. The otherclass of methods is based on a nonimaging system,e.g., the lens ducts proposed by Beach.5 To obtaingood shaping results, a set of precollimating cylindri-cal microlenses must be used. Obviously, the use ofprecollimating lenses leads to considerable complex-ity of the shaping system. In addition, a lens duct canhardly improve the brightness of a LD stack withouta precollimation lens; the beam divergence angle willbecome extremely large after being reflected severaltimes by the walls of the lens duct.

In some medical applications, such as skin diseasetreatment, simple and low-cost shaping optics of theLD stack to obtain a uniform beam spot with a rela-tively smaller divergence angle is needed. In this pa-per we propose a beam-shaping scheme for a LDstack to obtain a uniform beam spot. The transfor-

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

Received 17 February 2005; revised manuscript received 6 May2005; accepted 9 May 2005.

0003-6935/05/265408-07$15.00/0© 2005 Optical Society of America

5408 APPLIED OPTICS � Vol. 44, No. 26 � 10 September 2005

mation characteristics of the beam-shaping systemare presented, and the optimization performance isinvestigated based on the ray-tracing method; thedesign method is also given. This shaping systemconsists of an asymmetrical glass prism. The largedivergence angle �� of each emitter is compressedthrough total internal reflection by the canted planarsides of the prism, and the small divergence angle ��is expanded simultaneously; then the output beam isguided into a rectangular cross section. The advan-tages of the shaping optics proposed are a simplestructure, easy fabrication, large position tolerance,and high coupling efficiency. This shaping scheme isexpected to provide a useful shaping technique for theoutput light wave of a LD stack.

2. Theory Background

A LD stack can be regarded as an extended planarsource, and its beam divergence angle can be as highas 40°. The emitters sparsely fill the total aperture.The shaping optics we propose is constructed by theasymmetrical prism element shown in Fig. 1. Theinput end face is a rectangle; its length depends onthe length of the LD bar, and its width depends on thenumber of bars in the LD stack. The output end faceis also a rectangle; its side length is designed to meetthe requirements of the application. The LD stack isplaced in front of the input end face of the shapingelement.

A. Divergence Angle Transformation

Figure 2 shows cross-sectional views of the shapingsystem in the directions perpendicular and parallel tothe junction plane, and the beam shaping mechanismfor one emitter is illustrated. When a ray passesthrough the input end face of the shaping element, itwill be refracted by the boundary between the air andthe glass. According to Snell’s law, the refractive an-gle � can be evaluated as

sin � � n sin �, (1)

where n is the refractive index of the glass. In theperpendicular direction, the divergence angle of therefracted ray in the prism is compressed through to-tal internal reflection by the canted planar side of theprism. To the contrary, the divergence angle in theparallel direction is expanded by the canted planarside. It is not difficult to see from the geometry in Fig.

2 that �, the angle between the ray reflected by theoblique plane and the optical axis within the prism,can be expressed as

� � � � 2u, (2)

where � can be regarded as the divergence angle ofthe ray within the shaping element and u is the angleof the canted plane with respect to the optical axis.Equation (2) shows that if a ray enters the shapingelement from the air at an incident angle � withrespect to the optical axis, it will propagate within theelement at an angle � with respect to the optical axis.Equation (2) is valid for both the perpendicular andthe parallel directions. Obviously, the beam diver-gence angle is compressed when u 0 and expandedwhen u 0. The parameter u should be determinedso that the output beam divergence angles in the twodirections are nearly the same. For example, when�� � 40° and �� � 10°, we have u � 3.75° from therelationship 20 � 2u � 5 � 2u.

For the sake of simplicity, we consider beam trans-formation only in the fast-axis direction hereafter.The output rays of one emitter of the LD within theprism can be divided into three parts, G0, G1, and G2,as shown in Fig. 3. The critical angles �� and �� of theoutput rays of the LD are defined so that the rayswithin the interval ���, ��� can pass through theprism directly and the rays beyond the interval���, ��� can pass through the prism only after reflec-tion by the canted planar side of the prism. Accordingto the geometry in Fig. 3, the critical angles �� and ��

can be determined by use of the relations

tan �1 �H1 � x1

d , (3)Fig. 1. Diagram of the beam-shaping system.

Fig. 2. Cross-sectional view of the shaping system: (a) Divergencecompression in the perpendicular direction; (b) divergence expan-sion in the parallel direction.

10 September 2005 � Vol. 44, No. 26 � APPLIED OPTICS 5409

tan �� �x1 � x0

t , (4)

sin �� � n sin �1, (5)

tan �2 ��H0 � x2

d , (6)

tan �� �x1 � x0

t , (7)

sin �� � n sin �2, (8)

where x0 is the x coordinate of the emitter, t is thedistance of the emitter from the input end face of theprism, and d is the length of the prism. The compres-sion depends on the oblique angle u, which should bechosen so that the divergence angles in the two di-rections of the output beam of the shaping system arenearly the same as mentioned above.

B. Light Power Synthesis

This shaping method is a nonimaging procedure andcan be regarded as the light power synthesis. Figure4 shows the principle of the beam transformation of asingle emitter (a cross-sectional view). The outputintensity is the superposition of three parts: the lightpower transmitted through the prism directly �G0�,the light power reflected by the upper canted planarside of the prism �G1�, and the light power reflected by

the bottom canted planar side of the prism �G2�. It isassumed that the far-field intensity distribution ofone emitter in the direction perpendicular to the junc-tion plane is Iin���, and the output intensity of theshaping system is evaluated at a plane M with adistance s from the output end face of the prism.

Intensity Distribution I0�x� within Region G0. Fromthe geometry in Fig. 5, we can obtain the relationshipbetween the emitting angle � and the x coordinate atplane M that the ray with emitting angle � projectson:

x � x0 � (t � s)tan � �d sin �

�n2 � sin2 �. (9)

Then the intensity distribution I0�x� at plane M canbe obtained:

I0(x) � Iin(�), �� � � � ��. (10)

Intensity Distribution I1�x� within Region G1. Basedon the geometry in Fig. 6, we can obtain

x � x0 � t tan � �(H1 � x0 � T tan �)

tan � � tan u

� d tan � � s� W1 � W, (11)

I1(x) � Iin(�), � ��, (12)

Fig. 3. Geometry for evaluating the beam transformation.

Fig. 4. Principle of optical power synthesis.

Fig. 5. Geometry for evaluation of I0�x�.

Fig. 6. Geometry for evaluation of I1�x�.

5410 APPLIED OPTICS � Vol. 44, No. 26 � 10 September 2005

where

W � n2tan2 �

1 � tan2 �, (13)

� � � � 2u. (14)

Intensity Distribution I2�x� within Region G2. Sim-ilarly, based on the geometry in Fig. 7, we can obtain

x � x0 � t tan � �(H1 � x0 � T tan �)

tan � � tan u

� d tan � � s� W1 � W, (15)

I2(x) � I2(�), � ��. (16)

Then the intensity distribution of the emitter atplane M can be expressed as

I(x) � I0(�) � I1(�) � I2(�). (17)

The most common LD bar is 1 cm long and consistsof a monolithic chip with 19 emitters. When thesource is a LD stack of N bars, the total output in-tensity distribution of the LD stack at plane M can beexpressed as

I(x) � �i�1

N

�j�1

19

Iij(x), (18)

where �j�119 Iij�x� is the intensity distribution of the

ith bar.

3. Numerical Results

Generally, a 1 cm LD bar consists of 19 emitters1 �m � 100 �m in size and spaced on 500 �m cen-ters. Such a device can produce an output of 20 or40 W in cw mode. A number of 1 cm bars can bestacked to form two-dimensional arrays. For a com-mercial LD stack the bar spacings range from 0.5 to3.0 mm, depending on the thickness of the copperheat spreader onto which each bar is mounted. It isassumed that each emitter in the LD stack has iden-tical optical properties.

To design a shaping system quantitatively, an ac-curate expression for the far-field distribution of eachLD emitter is needed. All LDs have an active layer of�0.1 �m that is significantly narrower than thewavelength of the light emitted, so that only the fun-damental mode exists in the direction perpendicularto the junction plane. However, the far-field intensitydistribution of a high-power LD emitter usually ex-hibits a bi-peak structure in the direction parallel tothe junction plane. Theoretical and experimental re-search indicates that the far-field intensity of such anemitter can be described as10,11

I(x, y, z) � |A�|2z2

r4 � 2

2 � x22

��A�

A��2

exp��2(r sin �� � y)2

��2

� exp��2(r sin �� � y)2

��2 �, (19)

where

A� � �u0�

2i�p � �

q�; (20)

2 �p2

k2 r2; (21)

��2 �

4q�

k2 r2; (22)

sin �� � k��k; (23)

r � �x � y � z�1�2 is the distance from the emitter tothe observation point; p, q�, u0� are the source pa-rameters related to the waveguide structure; k� 2��� is the wave number; and �� are the propaga-tion parameters of the two decentered Gaussian func-tions. The intensity distribution of a practical devicehas some dependence on the driving current. How-ever, in the direction parallel to the junction plane,most practical devices have a bi-peak distribution ina wide range of the driving current above the thresh-old. In this case, Eq. (19) is a good description of thefar field of a high-power LD with a single emitter. Ifthe far field exhibits a single peak, Eq. (19) cannot beused.

In the x–z plane, Eq. (19) can be rewritten in a formrelating to the argument �x:

I(�x) � Cx

cos4 �x

z2 � 12

12 � sin2 �x

2

, (24)

where Cx is a constant, 12 � 2�r, sin �x � x�r, and

cos �x � z�r. In the y–z plane, Eq. (19) can be rewrit-ten asFig. 7. Geometry for evaluation of I2�x�.

10 September 2005 � Vol. 44, No. 26 � APPLIED OPTICS 5411

I(�y) � Cy

cos4 �y

z2 �A�

A��2

exp��2(sin �� � sin �y)

2

�1�2

� exp ��2(sin �� � sin �y)

2

�1�2 �, (25)

where Cy is a constant, �1� � ���r, �1� � ���r,sin �y � y�r, and cos �y � z�r.

As examples, numerical simulations were made fortwo cases: a two-bar LD stack and a five-bar LDstack. Suppose that the LD bar is composed of 19emitters spaced on 500 �m centers, each emitter hasan emitting area of 1 �m � 100 �m with a beamdivergence of 10° � 40°. The LD stack is placed at adistance of t � 0.5 mm from the input end face of theprism.

Shaping Element for a Two-Bar LD Stack. Thestructural parameters were optimized to obtain auniform beam spot. The parameters are calculated asfollows: The length of the prism is d � 40 mm, thewidth of the output end face is 2H1x � 14 mm and2H1y � 10 mm, the oblique angle in the x direction isux � 4° and in the y direction is uy � �4°, and thespacing between the two bars is 6 mm. On plane Mwith a distance of s � 1 mm from the output end faceof the prism, a flattop beam profile can be obtained asshown in Fig. 8. Within an area of 14 mm� 10 mm, the intensity fluctuation is less than 5.2%.

Shaping Element for a Five-Bar LD Stack. Figure 9shows the results of the numerical simulation for afive-bar LD stack. The spacing between the bars is1.0 mm. On plane M with a distance of s � 1 mmfrom the output end face of the prism, a flattop beamprofile is also obtained as shown in Fig. 9. Within anarea of 14 mm � 10 mm, the intensity fluctuation isless than 5.4%.

To examine the changes in the intensity profile

with respect to the z coordinate, we also computed theintensity fluctuation at a different z plane. Figure 10shows the maximum intensity fluctuation as a func-tion of the distance of the measurement plane withrespect to the prism output surface. If we define thedepth of field of the output light as the length withinwhich the intensity fluctuation is less than 10%, Fig.10 shows that the depth of field is about 5 mm.

Because the output light of the prism is the super-position of the output intensity of different emittersas well as the reflected light from the walls of theprism, the divergence angle of the output beam iscomplicated. At any point in the measurement plane,we can define the beam divergence angle as the max-imum angle of the rays passed through this point.The computed results show that the maximum beamdivergence angle is less than 7.8° and appropriately96% of the output power of the LD stack is enclosed in

Fig. 8. Numerical results of the output intensity distributions fora two-bar LD stack in the perpendicular and parallel directions.

Fig. 9. Numerical results of the output intensity distributions fora five-bar LD stack in the perpendicular and parallel directions.

Fig. 10. Maximum intensity fluctuation changes with the dis-tance of the measurement plane from the prism output surface.

5412 APPLIED OPTICS � Vol. 44, No. 26 � 10 September 2005

a region of 14 mm � 10 mm with a flattop beamprofile.

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�5 �m�; gain-guided LDs usually have 30–60 �m ofastigmatism. Strictly speaking, astigmatism may in-fluence coupling efficiency. In this paper laser astig-matism has not been taken into account, mainlybecause this problem is not serious. Both theoreticaland experimental examinations indicate that thebeam astigmatism can hardly influence the intensityfluctuation of the output beam and the coupling effi-ciency when the beam-shaping element presentedabove is used.

4. Experiment

To demonstrate the feasibility of the shaping method,a prism shaping element for a five-bar LD stack isdesigned and fabricated. This LD stack is composedof five bars spaced by 1.0 mm. Each bar produces anoutput of 20 W, and the beam divergence angles are43° and 10° in the directions perpendicular and par-allel to the junction plane, respectively. To obtain a10 mm � 15 mm uniform beam spot, the optimalparameters of the prism are calculated: d � 40 mm,2H1x � 14 mm, 2H1y � 10 mm, ux � 4.0°, and uy ��4.0°. The LD stack is placed at the front of the prismat a distance of t � 1 mm from the input end face. Themeasurement plane is at a distance of 2 mm from theprism output surface, and the measurement of theoutput intensity is performed by a scan of a 0.3 mmdiameter pinhole with a photodiode at this plane

along y � 0 and x � 0. Figure 11 indicates the inten-sity profile in the x and y directions. It is shown thatexperimental results agree well with the theoreticalprediction. Flattop intensity profiles were obtained,and the maximum intensity fluctuation in the twodirections is less than 6.7%. The light power couplingefficiency is as high as 89% without an antireflectioncoating on the end face of the prism. If the light beamis incident normally onto the input and output sur-faces, there could be losses of �4 � 4�%. However, thediode laser beam has a large divergence angle, so theactual losses should be greater than this value.

To indicate the changes in the output intensitywith the distance from the prism, we also measuredthe output intensity distribution at different dis-tances from the end face of the prism. Figure 12shows these intensity distributions. We can see thatthe intensity fluctuation changes strongly in the par-allel direction, and the flattop decreases with in-creased distance.

5. Conclusions

The beam-shaping system we have proposed for high-power LD stacks can be used to obtain a uniformbeam spot. The output beam divergence angles in theperpendicular and parallel directions are nearly thesame. If an antireflection coating is applied to the endface of the shaping element, the actual coupling effi-ciency can be increased. In addition, theoretical andexperimental examinations show that this shapingmechanism has a large position tolerance. The maindrawback of this shaping system is that the intensityfluctuation of the output beam will increase rapidlywith a changing z coordinate. If a large depth of fieldis needed in practice, this shaping system must beimproved or another shaping method must be consid-ered. Nevertheless, the performance of the shapingsystem proposed in this paper could meet the require-

Fig. 11. Experimental results of the output intensity distribu-tions for a five-bar LD stack in the perpendicular and paralleldirections.

Fig. 12. Intensity distribution at different distances from the endface of the prism.

10 September 2005 � Vol. 44, No. 26 � APPLIED OPTICS 5413

ments of medical uses such as skin disease treat-ment. With the wide use of high-power LDs, thismethod is expected to provide a useful beam-shapingtechnique for a LD stack for some practical cases.

This study was supported by the National NaturalScience Foundation of China (grant 60277004) and bythe Research Fund for the Doctoral Program ofHigher Education (grant 20020701011).

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