Abstract

A new method for designing calculated holograms (diffractive optical elements) in form of a 4-levels relief is presented briefly. The calculation method is combined with earlier developed technological scheme based on 3D proximity correction, one step e-beam lithography and electroplating (for obtaining rigid stamp) to experimentally evaluate producing phase DOEs. Two demonstrators (passive splitter and generator of 3D scene) confirm reliability of the whole long set of design and technological steps.

Introduction

These elements have several names kinoforms, diffractive optical elements (DOE), calculated holograms. The main feature of the elements is a continuous relief of a working layer. The advantages of diffractive optical elements are well known [1-5]. The main one is their higher effectiveness in comparison to binary (Fresnel) elements. An electron beam lithography was suggested in 1987 [1,2] for direct producing simple DOEs such as microlenses. An optical lithography was used for DOE producing together with replication by castings or embossing from a Ni shim [3]. The possibility of several sequential e-beam exposures (or several masks usage in photolithography) for continuous relief producing was analyzed and demonstrated in [4,5].

A technology of micro/nanostucturing is based on one-step e-beam lithography with 3D proximity correction [6, 7]. It allows one to create structures in organic resists (on a substrate) of the predefined profile with vertical sizes in the range 50nm-5um and 50nm-1mm in the lateral direction. Metal replicas were created by electro-chemical deposition from the resist profile [7]. The replicas were used then as a stamp for fast transferring of relief in soft material (polymer). By this procedure lenses of high efficiency were fabricated [7]. Plasma-chemical and ion etching were used to transfer the resist profile into Si and glass directly.

But the lens is a relatively simple element which transfers a parallel beam into a focal point. As to the generation of more complicated images, the fundamental problem is transferring of a parallel (or any given) beam into an arbitrary image. The key point of the problem is the fact that an experimenter (a technologist) is able to control the phase (or amplitude) only. It is not clear up to now whether it is possible or not to create arbitrary images manipulating by phase alone.

The paper is devoted to an experimental evaluation of a new method for designing and creating an arbitrary image by DOE which comprises a four level hologram. The technological basis of the method is an electron beam lithography with nano/micro structuring. Experimental examples of DOE are presented.

DOE design (hologram synthesis)

A DOE design begins (Fig.1) with designing of an image (or even a 3D scene). The next procedure is calculating a field of a complex amplitude in the plane of the DOE (Fig. 2). It seems evident that if one is able to create an optical element by transferring an original wave front (for example a plane wave where the amplitude and phase are constant) into a wave with a calculated complex amplitude, the desirable image in the image plane

Fig. 2. With given image (scene) calculation of hologram means determination of a complex amplitude field in the plane of a hologram followed by calculation of an effective phase field in hologram plane

will be obtained owing to interference. But as was mentioned above, the possibilities to change simultaneously both the amplitude and phase we are restricted. Practically one can manipulate with a phase or with amplitude only. The technology [6,7] allows producing a given relief in a transparent material therefore we deal with the phase DOE.

We developed a method of calculating an effective phase field from the complex amplitude. The method produces the phase field in form of a 4-level phase hologram. Details of the method including estimation of effectiveness of a 4-level hologram will be presented elsewhere. Of importance here is that the effective phase field is directly related to the relief via the refraction index of a DOE material. The analysis of relieves and our experimental experience show that the relief has spatial features with sizes from 100nm to 10um. This was the reason why e-beam lithography (not a photolithography) was used for DOE producing. in [4,5].

DOE technology

The technology of DOE producing is described in [6,7]. The main advantage of the technology is the fact that only one e-beam exposure it used. This became possible after and due to the development of a special 3D proximity correction technique [6,7]. The possibility of the given relief creation was demonstrated by producing lenses with a continuous relief [6]. Further we developed additional technological steps to produce a rigid copy from the resist relief and to obtain copies of the relief from soft material [7]. We estimated the spatial resolution of the whole technological chain to be 50nm. This estimation was confirmed in [8] where resolution 25nm was achieved during imprinting in polymer (PMMA).

Fig.3e. An AFM image of a relief of a transparent polymer DOE after copying from the metal replica.

Fig.3f. An image corresponding to the 4-level DOE. image resulting from the 4-level hologram.

Fig4.a. A DOE with two different focal planes.

Fig.4b. An image formed DOE (hologram) on distance = 2mm.

Fig.4c. An image formed by DOE (hologram) on distance = 3mm

Two examples

The first example (Fig.3) comprises a passive splitter of a parallel laser beam into tens of distinct beamlets. Fig. 3a shows a designed image where the beamlets are arranged as some letters. An effective 4-level phase field is shown in the gray scale in Fig. 3b. The hologram of 200um by 200um was calculate for PMMA with refractive index n=1.49 and for a laser with wave length l=632.8nm. An elementary height step provides the 3.14../4 phase shift. Figure 3c demonstrates a 200um by 200um lithographic pattern consisting of about ten thousand domains with specific exposure times assigned as result of the 3D proximity correction implemented in the advanced version of PROXY. We used the SEM JSM-840 as the exposure tool together with PROXY-WRITER for lithographic data preparation and exposure control. After the exposure and development 4-level relief in resist was created. Electroplating with Cu was used to obtain a rigid copy (a stamp) of the resist relief. The expected 4-levels of the metal are clearly seen in Fig. 3d. Several tens of polymer copies were than obtained by imprinting in heated PMMA. A PMMA relief of a polymer copy obtained by AFM is shown in Fig. 3e. The last picture Fig. 3f presents a computer simulation of an image corresponding to the 4-level DOE. image resulting from the 4-level hologram.

Fig.3a. A designed (desirable) image.

Fig.3b. A phase distribution (4 levels) of phase DOE to produce image the of Fig.3a.

Fig.3c. Exposure time isolevels after correction

Fig.3d. A SEM image of a metal replica from resist relief (DOE) obtained by one step e-beam lithography and electroplating

The sizes of the beamlets and their relative intensities for the image generated by real 4-level phase hologram were very close to those predicted by simulation. This was demonstrated during the paper presentation at MNE'96.

The second example demonstrates the possibility to create not only image in the plane but 3D scene and comprises tens of focal spotlets concentrated in two distinct focal planes as shown in Fig. 4a. In this case a 200um by 200um hologram was created. Figure 4b and Fig 4c show the corresponding images in two focal planes. The sizes and relative intensities of the spotlets were consistent with the simulated picture.

Conclusion

A method for designing of calculated holograms (DOEs) in form of a 4-levels relief is presented briefly. The technological scheme based on 3D proximity correction, one step e-beam lithography and electroplating for obtaining rigid stamp for further producing cheap polymer copies of DOE is experimentally evaluated. Two demonstrators (passive splitter and generator of 3D scene) confirm the reliability of the whole long set of designing and technological steps.

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