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ARTICLE IN PRESSG ModelJLEO-54345; No. of Pages 4

Optik xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Optik

jo ur nal homepage: www.elsev ier .de / i j leo

ptimum design of aspheric collimation lenses for optical antennaystem

uajun Yang ∗, Ping Jiang, Wensen He, Shasha Kechool of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China

r t i c l e i n f o

rticle history:eceived 9 July 2013ccepted 3 January 2014

a b s t r a c t

Three kinds of aspheric collimation lenses for optical antenna have been design by optimization. Theaspheric cylinder collimation lenses with aspheric surfaces (such as elliptic, hyperbolic and parabolicmarginal profiles) have been researched for the semiconductor laser beam with the characteristic of dot

vailable online xxx

eywords:spheric collimation lensesptimum designptical antenna

emitting source. Based on genetic algorithm and the optimization toolbox of MTLAB, the divergence anglehas been optimized. The collimation divergence angle is less than 115 �rad has been measured by laserbeam analyzer. This optimum design laser beam collimation lenses as a pre-collimation system can beused for optical antenna system. And it can be widely used in modern space laser communication.

© 2014 Elsevier GmbH. All rights reserved.

pace laser communication

. Introduction

Because of several unique characteristics, such as smallimension, low cost, high input-to-output conversion efficiency,igh-speed, and direct modulation, semiconductor are considereddvantageously used as a light source in space laser communi-ations [1,2]. There are two major application areas for spaceaser communications [3,4]. One is space communication for longistance (more than 100 km) and the other is infrared wireless com-unication for short distance (up to several kilometers) on ground.The main shortcoming of semiconductor is the astigmatic beams

ith elliptically shaped mode profiles due to the shape and theaveguide properties of their active areas [5]. For high-precision

pplications such as space laser communication, optical inter-onnections and high power fiber coupling, nonastigamtic andpherical laser beams are desirable [6]. Therefore, collimation tech-ology is important to deal with the different divergence propertyf laser beam space laser communication system possesses a tinyeam divergence of the laser beam [7], and its optical systems mustave the function of acquisition, tracking and pointing (ATP).

Especially for the long distance space laser communication, theaser beam divergence angles are need to be collimated both in

Please cite this article in press as: H. Yang, et al., Optimum design of asJ. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.

eridional plane (i.e., fast axis direction) and in sagittal plane (i.e.,low direction). In general, the divergence angles ˛x, ˛y are differ-nt, which is shown in Fig. 1.

∗ Corresponding author.E-mail address: yanghj@uestc.edu.cn (H. Yang).

ttp://dx.doi.org/10.1016/j.ijleo.2014.01.065030-4026/© 2014 Elsevier GmbH. All rights reserved.

Optical design of laser beam shaping system has evolved con-siderably from the early work of Frieden and Kreuzer during the1960’s to the contemporary work of many summarized in Refs.[8–11]. Frieden computed the shaping of an aspherical refractingsurface that would re-collimate the output beam parallel to theoptical axis and also to the input beam. Keuzer imposed the con-stant optical path length condition for all rays passing throughthe beam shaping optics to control phase variation of the outputbeam. Unfortunately, optical design and fabrication technologieswere generally not adequate until recently.

Optical design of beam shaping systems can be achieved usingeither physical or geometrical optics [8,9]. Based on the researchedrules [10,11], we will discuss collimation lenses by geometricaloptical principle. And consider the real manufacture, the cross sec-tion margin curves for aspheric lenses, such as ellipse, hyperbolaand parabola cylinder lenses have been discussed in this paper.

2. Optical antenna structure

Optical antenna, such as reflective telescopes can be widely usedin the fields of laser communications and remote sensing technol-ogy [3,4,12].

The optical antenna is the most important component of thelaser communication, and the pre-collimation technology (colli-mation lenses design) is a key for optical antenna system.

pheric collimation lenses for optical antenna system, Optik - Int.065

We design optical antenna system structure is shown in Fig. 2.It includes collimation lenses system and Cassegrain telescope sys-tem. The Cassegrain system consists of two reflecting surfaces,i.e., a concave parabolic primary mirror and a convex hyperbolic

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2 H. Yang et al. / Optik xxx (2014) xxx–xxx

y

x

z

x

y

Fast axis

Slow axis

f

Fig. 1. Laser beam emission character for semiconductor.

sll

tlotog

3

t(sa˛

stcm

Fig. 2. Optical antenna (includes collimation lenses).

econdary mirror. Each part (A, B, C, D) has been listed in the fol-owing Figure. In this paper, we will mainly research the collimationenses for the optical antenna system.

For a laser transmitter, the magnification of the telescope serveso decrease the divergence of the beam, thus making it spread outess. This kind of optical telescope can get much higher gain thanther kinds. By this optical antenna, the laser light beam is transmit-ed in space. At last, the acquisition/tracking laser beam is focusednto a CCD camera sensor which tracks the spot and drives theimbals system.

. Theoretical analysis for collimation lenses

In optical communication system, we choose a semiconduc-or with wavelength 860 nm. It possesses an emitting source area1 �m × 3 �m) laser beam character. The divergence angles of thisemiconductor are asymmetric between in fast axis and in slowxis direction. It possesses the maximum divergence half angle forxmax = 14◦, ˛ymax = 9◦, respectively.

A cylinder lenses collimation system with marginal profiles,uch as ellipse, parabola or hyperbola have been designed, respec-

Please cite this article in press as: H. Yang, et al., Optimum design of aJ. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.

ively. It is shown in Fig. 3. The first cylinder lenses are used toollimation the fast axis direction, and the second is used to colli-ation the slow axis direction.

Fig. 3. Collimation lenses system.

Fig. 4. Elliptical cylinder lenses collimation system.

3.1. Design for ellipse cylinder lenses collimation

The laser source emits beam from point P2 for fast axis direc-tion, and P1 for slow axis direction. First, we design an asphericcylinder lenses to collimation the divergence laser beam for merid-ional plane (i.e., fast axis direction). And then, the same theoreticalanalysis can be suitable for sagittal plane (i.e., slow direction).

The cylinder margin profiles is design as ellipse form to colli-mate the fast axis divergence laser beam, it is shown in Fig. 4 formeridional plane. Based on geometrical optics theory, we can tracethe light rays such as P2M, MN, NT.

The ellipse equation can be described as

z2

a2+ x2

b2= 1 (1)

Let

e = b

a(2)

(It can be optimum design in simulation program). Especially, ife = 1, it can be degenerated to the circle situation.

We can obtain the straight line equation for PM:

x = (z − a + d)tan ̌ + l sin ̨ (3)

Please pay attention to the tangential line NQ of point N is per-pendicular to the normal line of N point for the curve, so we canobtain

tan � = a2

b2

xN

zN(4)

By the formulas (1), (2), (4), we have

zN = a√1 + e2 tan �

(5)

By the formulas (2), (3), (4), we have

zN = l tan ̨ + (d − a)tan ˇ

e2 tan � − tan ˇ(6)

Therefore

l tan ̨ + (d − a)tan ˇ

e2 tan � − tan ˇ= a√

1 + e2 tan �(7)

By Eq. (7), we can obtain

tan � = −a2 tan ̌ ±√

(a tan ˇ)2 − (p2 − a2)[p2 − a2 tan2 ˇ]p2 − e2a2

(8)

where we have let p = l tan ̨ + (d − a)tan ˇ.

spheric collimation lenses for optical antenna system, Optik - Int.065

According to the physical meaning, i.e., real situation, we canselection the plus or minus sign.

By the refraction law, we can obtain the refraction angle ̌ is thefunction of ˛. i.e., ̌ = arcsin[(sin ˛)/n]. And � = arcsin[n sin(� − ˇ)].

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Table 1Structure of the elliptic collimation lenses.

(K9) a1 b1 d1 a2 b2 d2 l2

1.516 22.60 14.70 5.50 35.60 23.14 8.00 11.30

ti

ϕ

ϕ

l

M{

tw

aeldpfn

3

sS

3

x

x

Fig. 5. Parabola cylinder lenses collimation system.

Therefore, the refraction angle � can be described as the func-ion of collimation lenses structure parameters a, b, d, l, n and thencident angle ˛.

For any incident angle, we can obtain the collimation exit angle.

= � − � = � − arcsin[n sin(� − ˇ)] (9)

The same simulation methods can be used to the second cylinderenses for the light beam of slow axis direction in sagittal plane.

Based on genetic algorithm and the optimization toolbox ofATLAB, take the divergence angle as optimum aim, i.e.

min ϕ(a1, b1, d1, a2, b2, d2, l1, l2)

subject to : (d1 + l2 + d2 ≤ 25)(10)

In order to make the collimation system minimum, we set thewo cylinder lenses collimation system length less than 25 mm, soe make constraint satisfaction as d1 + l2 + d2 ≤ 25.

We simulate the collimation angle versus with the incidencengle and the elliptical structures. The optimum structure param-ters of the elliptical collimation system are listed in Table 1. Theength units are millimeter, and the subscript 1 is for the first cylin-er lenses, subscript 2 is for the second cylinder lenses, and thearameters meaning are shown in Fig. 2. Considering the pricesactor, all of the collimation lenses material are selected as K9,

= 1.516.

.2. Design for hyperbola cylinder lenses collimation

Now, we assume the marginal profile is hyperbola, the analy-is method for the hyperbola cylinder collimation is the same asection 3.1, it is just for the Eq. (1) should be changed into

z2

a2− x2

b2= 1 (11)

.3. Parabola cylinder collimation lenses collimation

We assume the coordinate zero point O, shown in Fig. 5In this coordinate system, the parabola can be represented by

2 = −2p(z − d) (12)

Please cite this article in press as: H. Yang, et al., Optimum design of asJ. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.

The straight line MN can be described as

= (z − d)tan ̌ + l tan ̨ (13)

Fig. 6. The collimation divergence angle versus incident angle.

In order to collimation the refraction rays by the similar deduce,the parameter p of parabola can be obtained by

p = 2(l tan ̨ + d tan ˇ)

tan2 � tan ̌ + 2 tan �(14)

By it we can obtain that the refraction angle � is the function ofstructure parameters l, d, p and the incident angle.

The same as Section 3.1, based on genetic algorithm and theoptimization tool box of MATLAB, We can simulate the collimationangle versus with the incidence angle and the parabola structures.

4. Optimum simulation and experiment

4.1. Optimum simulation

Based on the theory analysis in Section 3, we have simulatedthe circular, elliptic, hyperbolic and parabolic cylinder lenses col-limation lenses. The optimum collimation divergence angle versusincident angle for fast and slow axes are shown in Fig. 6(a) and (b),respectively.

The optimum simulation results indicate that the collimationdivergence angle for elliptical cylinder lenses is the less, and thenis the circle situation (It is a special situation of ellipse), an thenis the hyperbola cylinder lenses situation. However, the parabolacylinder lenses divergence angle is the most. We conclude that theelliptical cylinder lenses possess the best collimation effect.

So we have researched mainly for elliptical cylinder lenses.

4.2. Experiment measurement

pheric collimation lenses for optical antenna system, Optik - Int.065

We have synthetically considered all kinds of simulation anal-yses for aspheric cylinder lenses system and real fabricationsituation, and price factors. We have fabricated the elliptical cylin-der collimation lenses.

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4 H. Yang et al. / Optik xx

pcbo

h

r

ϕ

ϕ

1s

5

s

[

Fig. 7. Three-dimensional distributions for focus spot.

According to the laser beam distant field focus measure princi-le, we selected a lens with a focus distance 250 cm to focus theollimation beam, and measure the radius of focus point. By laseream analyzer, we can obtain the three-dimensional distributionsf focus spot, it is shown in Fig. 7.

According to the measure method of distant field focus spot, weave measured the mean radii:

x0 = 286.23 �m, ry0 = 281.41 �m (15)

Therefore, we obtain the fast axis divergence angle

x = rx0

f= 286.23 × 10−6

250 × 10−2= 0.11492 (mrad) ≈ 115 �rad (16)

And for slow axis divergence angle

y = ry0

f= 281.41 × 10−6

250 × 10−2= 0.11256(mrad) ≈ 113�rad (17)

Measure results indicate that the divergence angle is less than15 �rad (both for fast and slow axis). Experimental test resultshowed that it could achieve a good collimation effect.

Please cite this article in press as: H. Yang, et al., Optimum design of aJ. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.

. Conclusions

The aspheric cylinder lenses collimation system with asphericurfaces have been researched for the semiconductor laser beam

[

[

PRESSx (2014) xxx–xxx

with the characteristic of dot emitting source. The aspheric surfacesinclude elliptic, hyperbolic and parabolic marginal profiles. Basedon genetic algorithm and the optimization toolbox of MTLAB, thedivergence angle has been optimized. With laser beam analyzer,the collimation divergence angle is measured less than 115 �rad.

This optimum design laser beam collimation lenses as a pre-collimation can be used for optical antenna system. And it can bewidely used in modern space laser communication.

Acknowledgments

This work is supported by the National Natural Science Foun-dation of China under Grant No. 61271167. And it is supported byCulture funded of Sichuan Province academic leaders.

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