Thick refractive beam shaping elements applied to

Thick refractive beam shaping elements applied to laser diodes

Matthias Cumme, Holger Hartung, Lars Wittig, E. - Bernhard Kley Friedrich-Schiller-University Jena, Institute of Applied Physics, Max-Wien-Platz 1, 07749 Jena, Germany, Tel. +49 3641 657642, Fax +49 3641 657680, e-mail: [email protected]

ABSTRACT In many laser diode applications, it is necessary to make a beam shaping or beam transformation. One example is the collimation, but often we wish to achieve additional properties like special shapes of the beam. Such beams can be designed with high efficiency and signal quality by means of refractive beam shaping elements. Frequently, we have to vary the beam propagation parameters significantly to fulfil the beam shaping task. If we want to use refractive beam shaping elements, the design results in an element with a large profile depth. A well suited fabrication method for refractive beam shaping elements is the gray tone lithography, however, it is limited by the achievable depth of profile. This means that design and fabrication methods should be taken into account to achieve the advantages of refractive elements. On the one hand, we have to improve fabrication technique for enlarging the producible profile depth. On the other hand, we have to use all of the design freedoms to reduce the profile depth. We will present results of the design and fabrication of a refractive beam shaping element with a profile depth up to 60µm to transform a laser diode beam into a line intensity distribution. Keywords: Micro optics, gray tone lithography, refractive beam shaping elements.

1. INTRODUCTION Optical wave transformations like beam deflection, beam splitting, and beam shaping have found rapidly growing applications in many technical fields. For example in material processing, information processing, medical technique, and measuring technique we often find applications where we have to transform an incoming optical wave into a wave with a required intensity distribution and propagation property. Micro optical elements like lens arrays, gratings, diffractive and refractive beam shaping elements can produce such transformations. In special beam shaping applications, a very high conversion efficiency and signal quality is needed. In such cases we prefer refractive beam shaping elements because of their excellent optical properties [1]. A disadvantage of refractive elements is, that their profile depth depends on the beam diameter and the deflection angle, that we need to achive the desired intensity

Lithographic and Micromachining Techniques for Optical Component Fabrication, Ernst-Bernhard Kley, Hans Peter Herzig, Editors, Proceedings of SPIE Vol. 4440 (2001) © 2001 SPIE · 0277-786X/01/$15.00

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distribution. It is easy to see, that the profile depth of a refractive beam shaping element increases when the angular spectrum or the beam diameter are increased [2]. This means, that in cases of strong changes of an incoming optical wave, the design results in an element with a large profile depth. For the fabrication of refractive beam shaping elements, we usually employ gray tone lithography [3, 4] which is a suitable technology to produce continuous three dimensional profiles. One of the limitations of this technology is, that when the profile depth is increased, the profile error increases proportionally. That leads to higher aberrations and surface roughness. Apart from the difficulty to fabricate deep profiles with high accuracy and quality we meet another problem: large profile depths combining large angles of profiles and non paraxial incident waves may lead to spherical aberrations. In this case it is necessary to use special design methods that consider these effects [5]. In addition to the mentioned difficulties, in fabrication of thick photo resist profiles, effects like the formation of bubbles in the resist layer and the take off of the resist layer from the substrate may occur. As a summary, we can note, that in design and fabrication of “thick refractive elements” we can meet with following problems: -

the use of thin element approximation is not appropriate, effects of refraction at the element surface have to be considered to avoid spherical aberrations

-

high surface roughness leads to strong intensity fluctuations of the shaped beam

-

aberrations of the produced intensity distribution from the desired distribution occur, caused by profile aberrations

-

special treatment of photo-resist should be made to avoid bubble formation and the take off of the resist layer

2. BASIC CONSIDERATIONS Considering of difficulties mentioned above, we have to answer the question, if and how it is possible to use known advantages of refractive elements if large profile depths are needed. In the present work, we want to present a special beam shaping task for an application in safety engineering, in which beam shaping elements with profile depths up to 60µm are used. We will show the design and fabrication process as well as discuss the reachable accuracy of the transformed signal. The optical setup is shown in Figure 1a. A wave coming from a laser diode has to be transformed into a line of constant 1.0

signal

signal slow axis

slow axis fast axis

fast axis Normalized intensity

0.8

beam shaping element

slow axis

collimation

transformation

0.6

0.4

0.2

illumination wave 0

fast axis

-500

0

500

Distance from optical axis [µm]

a)

b)

Figure 1: a) Optical setup of the present beam shaping task. b) Line scans along the fast axis and the slow axis of the laser diode beam at the element plane.

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intensity with a very high efficiency. An essential demand on the shown beam shaping setup is, to realize this transformation with one element only to avoid alignment problems. This means, that combination of beam shaping elements with lenses for reducing the profile depth is not possible. Parameters of the used laser diode beam were determined by measuring an intensity of line scans along the fast and the slow axis at several distances from the laser diode. Figure 1b shows the line scans as well as fitted Gaussian functions at the element plane. The correspondence between the fit and the measurement along the slow axis is very good. The fast axis shows some aberrations. The distance between the waist of the laser diode beam and the beam shaping element, that determines the beam diameter, was chosen in order to minimize the profile depth of the element. Resolution limit given by the diffraction and the alignment conditions was considered. The following beam shaping parameters were used: Beam shaping parameters illumination wave wavelength : beam diameter (1/e²) :

distance from waist :

670 nm 1140 µm (fast axis) 320 µm (slow axis) 0.31 (fast axis) 0.11 (slow axis) 1.2 mm

distance from element : line width (1/e²) : line length :

140 mm 0.7 mm 100 mm

numerical aperture :

signal

3. DESIGN OF THE ELEMENT As shown in Figure 1a, we can separate the beam shaping job into two tasks: in direction of slow axis we have to concentrate the intensity of the incoming wave, while in direction of fast axis we have to redistribute the intensity. This

b)

all dim ensions in µm

a)

c)

Figure 2 : a) Surface profile of a designed beam shaping element, cut at a profile height of 41µm. b) Assumed way of light rays through the element using the Thin Element Approximation (TEA), c) by using the Local Plane Interface Approximation (LPIA).


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means, that in direction of slow axis we have to apply a cylindrical lens. In direction of fast axis we have to apply a beam shaping element, that transforms a Gaussian into a top hat intensity distribution. Beam shaping elements of this kind can be calculated analytically using design methods of geometrical optics, if the desired intensity distribution is a super-gaussian distribution of order n [6]. In this work, we calculated a beam shaping element using a super gaussian intensity distribution with n=20. The combination of both phases (cylindrical and beam shaping phase) and its unwrapping led to the surface profile shown in figure 2a, that was cut at a profile height of 41 µm. Lateral dimensions of the presented element are 1.3mm (fast axis) and 0.5mm (slow axis) to collect more then 99% of the incident light. As mentioned above, to fabricate thick refractive profiles, we have to consider effects that are caused by refraction of the incident wave at the element surface. The simplest way to describe the phase change of a wave which propagates through an optical element is to use the Thin Element Approximation (TEA) [7]. By using TEA we assume, that the phase change ϕ(x,y) depends on the element height h(x,y) only and it takes place in an infinite thin plane. This means, that if we would split an incident wave into several rays, they would propagate straight through the element, the phase change at every point of exit will be ϕ[h(x,y)] (see figure 2b). TEA also leads to the easy calculation of the element profile for a given phase ϕ(x,y). The resulting element height h(x,y) is calculated by

h( x, y ) =

ϕ ( x, y ) λ ⋅ n −1 2π

with λ is the wavelength and n is the refractive index of the element. For the validity of TEA we have to guarantee a few essential conditions. For example, the following relation has to be fulfilled if we use TEA to describe gratings: xmin ⋅ n ≥ a ⋅ λ

where xmin is the minimum feature size and a is a factor. At a=14, the maximum error of the simulated optical function is less than 5% [8]. This rule can be translated into a limit to the maximum rim angle αmax that can be accepted to use refractive structures. The maximum rim angle of the profile shown in Figure 2a has a value of 17 degree, however, in our case (nElement=1.62, λ=670nm) αmax has to be less than 10 degree. This means, that an approximation by TEA does not allow us for an acceptable accuracy in case of the shown beam shaping task. To check this fact, we calculated an optical effect of the designed element using the Local Plane Interface Approximation (LPIA) described in [5]. With LPIA, we were able to calculate the phase function of an optical element under consideration of the refraction of the incident wave, its deflection and the resulting optical path (see Figure 2c). After calculating the phase and amplitude distribution behind the element

Figure 3: Simulated intensity distribution of the signal using LPIA.

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using LPIA, we simulated the wave propagation to the signal plane. We used the spectrum of plane waves representation [9] as propagation operator because of the non-paraxial character of the beam shaping task. The calculated intensity distribution is shown in Figure 3. Fortunately, at changing distance between the element and the laser diode, we were able to “adjust” the shaped intensity distribution so much that quality of signal was still good. Because of this opportunity we decided to fabricate the calculated element without any correction, based on the result of LPIA.

4. FABRICATION OF THE ELEMENT

The fabrication of the designed beam shaping element was done using gray tone lithography [3]. To apply this technology, we used a special kind of glass, which can be darken at electron beam exposure. This means, that we can control its lateral transmission, that depends on the locally applied electron dose. Using this glass as a mask in a photolithographic process gives an opportunity to control the locally applied light dose and correspondingly, the local dissolution rate of the exposed photo resist during its development. After development, we get a three dimensional resist profile that depends on the electron dose applied to the photo mask blank. Figure 4a shows the correlation between an electron dose applied to the mask and resulting height of the resist profile using different initial film thicknesses. We used HEBS-glass (high energy beam sensitive glass, Canyon Materials Inc.) as a mask blank and AZ 4562photo resist. initial film thickness

40

45µm 30µm

20

Relative profile height [µm]

70µm

60 profile height [µm]

24

20 R1 = 790 µm R2 = 723 µm

base area of element

16

18µm

0

0

400

800

electron dose [µC/cm²]

1200

12

R1 -100

R2 0

100

Distance from optical axis [µm]

Figure 4: a) Correlation between electron dose exposed on the mask and the resulting resist profile height using different initial film thicknesses. b) Measured profiles along the direction of slow axis of a fabricated element that cross the top (R1) and the saddle point (R2).

The fabrication of resist profiles with a sag of more then 30µm requires a very thorough tempering process to remove the solvent from the resist layer completely to avoid formation of bubbles during UV-exposure and development. We found, that not only the tempering duration and temperature, but also the tempering regime (duration of heat up and heat down) is of great importance. In addition, because of a poor adhesion of thick resist to the substrate it was necessary to coat the substrate with a primer. As mentioned above, an error of the profile of elements that were fabricated using gray tone lithography is a relative error; its maximum depends on the profile depth. Using gray tone lithography, a profile error of 1-2% is reachable, in special cases it can go down to 0.2%. The profile error can be splitted into profile aberration and profile roughness.


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Profile aberrations are caused primarily by effects of the UV-exposure and development of the photo resist. For the exposure of thick resist layers, especially if the feature size of the structures is smaller than the film thickness, diffraction effects may be of concern. In case of the considered beam shaping task, these effects are not significant. Nevertheless, we have to consider another problem: because of the fact, that the development occurs in both vertical direction and horizontal direction, different results can be found for equal desired profiles designed using various sags. For example, this effect leads to radius variation of the cylindrical profile that we apply to focus the slow axis (see section 3). Measured profiles along the slow axis direction of a fabricated element at the top (R1) and the saddle point (R2) are shown in Figure 4b. The measurement was done using a confocal microscope. The measured curves were normalized in order to have the same maximum value. It is noticeable, that the lens profile crossing the saddle point has a smaller radius compare to the profile crossing the top. By fitting square functions on the measured profiles, we calculated, that the profile radii differ by a value of 9.2%. The fitted profiles stretch over a region, where the amplitude of the illuminating beam comprise more then 5% of the maximum amplitude. To find the profile aberration of the fabricated element, the measured surface profile was converted into the resulting phase profile. The designed phase was subtracted from this phase profile; the difference over of left part of the element is shown 2.0π

R1

R2

b)

2.0π

1.6π

1.6π

1.2π

1.2π

0.8π

c)

0.8π

0.4π

a)

0π

0.4π

d)

0π

Figure 5: a) Phase difference of the left part of the fabricated element, calculated from the measured surface profile. b) Measurement of the realized intensity distribution. c) Line-scan of the distribution shown in b). d) Phase difference after correction of the element.

in Figure 5a by using the mod(2π)−representation. The dashed lines represent the profile scans (see Figure 4b). The maximum phase aberration that is shown in figure 5a was measured to be about 2.3π. Additionally, in the presented distribution, two areas can be seen that provide lens function. Figure 5b shows the measured intensity distribution, produced by the fabricated element. The end of the measured distribution, which looks like an eye of a needle, is caused by the lenslike phase aberrations of the element. A line-scan of the measured distribution is shown in figure 5c. It is easy to see, that the quality of the signal is unacceptable. We have found out how to improve it. One opportunity to produce thick profiles with a better accuracy is to use a pre-form technique [10]. However, due to a higher complexity of this technique and the difficulty to apply it to the special profile we need, we decided to apply gray tone lithography using iterations in the fabrication process. Therefore the measured, uncorrected profile of the fabricated element was used to calculate a correlation between the exposed electron dose and the profile height, which was adapted to the special profile shape we need. The profile aberration is shown in Figure 5d for an element fabricated using the correction, represented by the resulting phase difference. After the correction, the maximum phase aberration did not exceed 0.8π over the entire region, where the amplitude of the illuminating wave was higher than 5% of the maximum amplitude. As mentioned above, not only the profile aberrations, but also the profile roughness impacts the signal quality. The profile roughness is caused by an effect of the electron beam writing [11] and by inhomogenities in the photo resist film. Figure 6a

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shows the surface of the corrected element with a periodic structure, caused by electron beam writing effects; figure 6b shows a line scan of the same part. Such periodic structures lead to periodic intensity modulation that can be seen in the center of intensity line scan, see figure 5c.

a)

c)

b)

Figure 6: a) Surface of a fabricated element which shows a profile roughness caused by effects of electron beam writing. b) Line scan of structure shown in 6a. c) Profile roughness after smoothing. Applying a special melting process, we were able to smooth the surface. Therefore, the fabricated element was tempered in such a way, that only the surface was melted in order to preserve the global resist structure. Applying this technology, we were able to decrease the surface roughness from 40nm rms to 2nm rms within the measured area (see Figure 6c).

5. RESULTS An element was fabricated using the corrected correlation between electron dose and resulting profile depth (see section 4). It was applied in the beam shaping setup. The produced intensity distribution was measured using a CCD-camera, see figure 7a. An improvement, compared to the distribution shown in figure 5b, can be seen. However, endpoints of the line show significant widening. A possible reason to the widening is, that the diameter of the laser diode beam is too large in direction of fast axis. This leads to diffraction effects at the border of the element. Figure 7b shows the intensity distribution of the unshaped beam at the same distance from the laser diode as the measured line. The intensity profile of the measured

a)

b)

c)

d)

Figure 7: a) Resulting intensity distribution using a profile correction. b) Intensity distribution of the unshaped beam at the same plane. c) Scan of the line intensity before smoothing of the profile. d) Scan of the intensity after smoothing of the element profile.

line is shown in figure 7c. Points of the curve represent maximum intensity at every cross section perpendicular to the line. The profile shows the same intensity modulations as the center of the line scan in figure 5c which is caused by the surface roughness of the element. The rms-value of the line intensity was 6.8%, the peak to valley deviation was measured to be 30%. After smoothing the surface profile (see section 4), the homogeneity of the transformed intensity distribution was


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improved, see figure 7d. The rms was measured to be 3.3%, the peak to valley deviation was 13%. The conversion efficiency was measured to be better than 90%. Frequently, for a better stability of the elements, a profile transfer into other materials is necessary. One possibility of transferring micro-optical elements with large profile depths is the UV-embossing [12]. Because of the difference between the refractive indices of photo resist and the UV-curing polymer used for the embossing, a correction of the profile height is necessary. To address this demand and to improve the conversion efficiency, an element with a maximum profile depth of 60µm was fabricated. Figure 8a shows an SEM-photograph of the transferred profile ( UV-embossing was done by Fraunhofer Institut für Angewandte Optik & Feinwerktechnik, Jena ). Figure 8b shows the resulting intensity distribution and figure 8c shows its scan. The rms-value of the produced intensity profile was measured to be 8%, the maximum deviation was 30%.

a)

b)

c)

Figure 8: a) SEM-photograph of a beam shaping element with a profile depth of 60µm, transferred into UV-curing polymer. b) Produced intensity distribution using a beam shaping element that was transferred into UV-curing polymer. c) Intensity profile along the line shown in Figure 8b.

CONCLUSIONS

In the presented paper, an applicability of refractive elements to transform laser diode beams was demonstrated. In special beam shaping tasks, for example, in case of the demonstrated line beam shaper, the design requires an element with a large profile height. It was shown, that in order to design and fabricate such “thick elements”, we have to consider some essential factors to use advantages of refractive elements such as high efficiency and good signal quality. Using -

special baking process before the UV-exposure,

-

iteration step for profile correction and

-

smoothing process after development of the profile

we were able to fabricate elements with profile depths up to 60µm. The transformed intensity distributions have shown a homogeneity with an rms-value up to 3.3% and a peak to valley aberration of 13%. The measured conversion efficiency was more than 90%.

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ACKNOWLEDGEMENT

The authors would like to thank Mr. P. Dannberg* for carrying out the UV-molding, Mrs. A. Duparre* and Mr. J. Steinert* for the surface measurement of the fabricated elements with a confocal microscope. We also would like to thank Mr. H. Schmidt, Mrs. W. Gräf and Mr. D. Schelle for the co-operation in fabrication and investigation of several samples. *Fraunhofer Institut für Angewandte Optik & Feinwerktechnik, Jena

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[2]

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[3]

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[6]

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[8]

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[9]

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[11]

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