The design, microfabrication and testing of diffractive optical elements (DOE’s) with continuous relief used for fiber coupling are discussed in detail. DOE’s with diameters as small as 50 mm are fabricated by means of focused ion beam (FIB) technology. A focused Ga+ ion beam is used to mill a continuous relief microstructure at a 50 kV acceleration voltage. The optical performance of DOE’s made in this way was compared with that of DOE’s fabricated by other methods. The focusing performance of DOE’s fabricated with three and six annulus by FIB milling was investigated. Testing of the system which has a coupling efficiency of -1.25 dB (75%) shows that the design meets the application’s requirement for fiber coupling, and that DOE’s manufactured by our FIB technology are practicable. Compared with a conventional fiber coupling system that uses a plano - convex lens, our system has the advantages of simplicity, short focal length, low cost for the lens and high coupling efficiency.
©2000 Optical Society of America
It is well known that the fibers used in optical communications have the advantages of low loss, wide bandwidth, lightweight, small cross-section area, absence of electromagnetic effects, high reliability, and bendability. However, because of limitations on the curvature of traditional spherical lenses, a small numerical aperture (N.A.) must be used for the required coupling efficiency to be achieved [1–9]. The thickness of the lens will be larger as the curvature increases. Therefore we consider in this paper an integrated micro -diffractive/refractive lens. In comparison with the traditional lens, the integrated micro - diffractive/refractive lens has the following advantages.
1. It is thinner and lighter;
2. It affords increased designing freedom;
3. It has a larger NA value than a traditional refractive lens;
4. It has less stringent material requirements.
Design, microfabrication, and testing of the microlens are discussed in detail in what follows.
For our design, the light source is a diode laser with a wavelength of 635 nm. The integrated microlens structure is shown in Fig.1 with its planar side towards the laser emission surface. The laser beam consists of paraxial light passing through plano — convex diffractive - optical elements (DOE’s). It is assumed that a plane wave is incident upon the planar side of a lens and is focused. The curvature of a Gaussian beam is zero at the beam waist, and therefore spherical aberration is ignored. Because the beam is monochromatic and the system works at room temperature, neither achromaticity nor athermalization is considered.
The first diffractive order -1 is selected as the main diffractive order for the DOE’s. A micro - diffractive/refractive structure is integrated with the plano — convex DOE’s. The spatial frequency and the diffractive angle are determined by Equation (1) below. By combining a blazed grating equation with geometrical optics theory, one can derive an equation that describes the continuous relief of the microlens scan [Equation (2)] which ensures that each phase annulus has the same focal length f0. f0 is less than fD (the focal length of the DOE's) because it is the synthetic result obtained from diffraction and refraction on a continuous relief surface. Therefore we used the equations for a refractive aspheric lens to derive Equation (2); it is valid for high N.A.,i.e., high frequency lenses with a period size of 2λ:
where rm is the m - th zone radius of the DOE’s, λ is the designed wavelength, m is the number of annuli (m=1,2,3, S), and f is the designed focal length of the DOE’s..
where c and K are factors that determine the relief curvature. They can be calculated from the following formulas:
where r is the radius of the annulus (in mm), n is the refractive index of the lens, and S(r) is the sag in the continuous relief (in mm).
Based on Equations (1) and (2), the geometrical size for each annulus can be calculated with the microlens parameters f0, N.A. and feature sizes of 125mm, 0.2, and 4.5 mm respectively, with Schott BK7 glass as the lens materials (see Fig.2).
3. Measurement and testing
The most obvious advantages of micromanufacturing a microlens with continuous relief by micromaching with a focused ion beam (FIB) are that the relief can be milled directly upon the substrate, and that there is no need for conventional mask making, photolithography and pattern exchange [9–10]. The substrate can be made from any material. In addition, DOE’s with feature size as small as the wavelength of the light source can be realized by FIB technology.
The milling experiments are carried out on a Micrion 9500EX FIB machine with a liquid-gallium ion source, integrated with a scanning electron microscope (SEM), and an energy dispersion X-ray spectrometer (EDX) facility and gas assistant etching (GAE) functions. This machine uses a focused Ga + ion beam with an energy of 5~50 keV, a probe current of 4 pA~19.7 nA and beam limiting aperture size of 25 mm~350 mm. For the smallest beam currents, the beam can be focused to a 7nm diameter a full width at half maximum (FWHM). The milling process can be programmed with various ion doses for different relief depths. The process relief accuracy is affected by beam spot size and pixel overlap during the raster scan. Using a larger beam spot size and less pixel overlap will cause the relief accuracy to deteriorate.
For a default discrete step size of 0.5 mm, we use a 100 nm beam spot size and a 60% overlap. A comparison of effects of height error and lateral error on relief accuracy shows that those of the lateral error are prominent. Because of the line broadening effect caused by the wing of the ion beam’s Gaussian distributions, the actual milled linewidth is larger than the designed size (this is called line broadening). Therefore, the defined linewidth should be less than the designed linwidth. Its concrete value will depend on the chosen beam spot size, beam current density, and calibrated of ion dose.
A. Optical Performance
To compare the suitability of DOE’s with the same focal length and N.A. value and different annuli for use in fiber coupling, we manufactured DOE’s with three and six annuli with our FIB machine. Figures 3 and 4 are SEM micrographs of micro-DOE’s manufactured by the FIB milling with three and six annuli respectively. It can be seen that the pattern is neat and the relief surface is smooth. The profiles of the DOE’s are measured with a WYKO NT 2000 interferometer. Both profiles are symmetric. There is a rounding effect during the measurement because the 0.7 mm resolution of the WYKO NT 2000 interferometer is limited by the wavelength (~0.55 mm) of its light source and by the N.A. value of the objective lens (maximum 0.9). The result is that a micro - structure smaller than 0.7 mm cannot be measured; thus the bottoms and the apexes of the reliefs shown in Figures 3 (b) and 4 (b) are fitted with data measured by software and not with the real form. The widths and heights of the DOE’s reliefs shown in these two figures are real.
We measured beam profiles at the focal plane for both of the DOE’s with our BeamScope-P5 beam scanner to evaluate the focusing characteristics of the DOE’s, as shown in Fig.5. Two 10¥10 DOE’s arrays were conveniently used for the measurement because a single DOE’s is too small to be measured and would require a light — beam diameter as small as 65 mm. It can be seen from Fig.5 that the focused spot size for a DOE’s with six annuli is smaller than that for a DOE’s with three annuli. Because the quality of the collimating light beam is not ideal and because of the presence of stray light during the measurement, there are large differences in peak intensity. It can be seen that the outside 4 th to 6 th annuli cannot be ignored in DOE focusing, which still plays a dominant role in the coupling. The measured diffraction efficiencies for the DOE’s with three and six annuli are 88.5% and 91.8% respectively. In table1, the optical performance of the DOE’s fabricated by the FIB is compared with that of DOE’smanufactured by other methods.
Compared with other binary techniques and analog methods, FIB milling has the major advantages of potentially high efficiency and simple implementation: only one milling step is required which eliminates the pattern transfer error that occurs with conventional methods 10 to 18. We can improve efficiency further by increasing the number of annulii of the DOE’s. High efficiency is a goal of each new manufacturing technology. Although we have quoted efficiencies in comparing with the manufacturing methods, these numbers should be used with caution. Ideally, one should compare results for a specific design. However, not even an experiment that compares results for a specific design would be fair, as different technologies are best for different applications. In choosing the DOE’s generation technology, one must compare the capabilities and limitations of each method with the critical performance aspects of the application.
B. Coupling Efficiency
The characteristics of DOE’s with six annuli were tested with a laser diode with a power of 30 mW and a wavelength of 635 nm. The distance d (shown in Fig. 1) should be as small as possible; here we set it to 10 mm.
A single mode optical fiber with a core diameter of 10 mm was used for the testing. First we made coupling efficiency measurements with an integrating sphere to measure the total output power of the laser. We determined the power coupled to the fiber through the DOE’s by measuring the power at the output of the fiber using the same integrating sphere. A pinhole with diameter of 70 mm was used in front of the DOE’s to shadow the other surplus beam, and only a beam with a diameter of 70 mm could pass through the pinhole and illuminate the DOE’s fully. The distance between the fiber end facet and the photodetector was 10 mm. By fine adjustment of the working distance around the site of focal plane, we could obtain the maximum power. The measured coupling efficiency of the DOE’s system is -2.5dB. There is no need to consider cross talk at an interface of fibers because only a single fiber is used. The coupling loss comes mainly from spherical aberration of the lens caused by form error during the fabrication process and by beam divergence from the end of the fiber facet. We could further improve the efficiency by reducing the manufacturing error, decreasing misalignment error during the measurement of the coupling efficiency, and decreasing the thickness of the lens substrate to increase the beam energy incident onto the DOE’s.
Table2 compares our DOE’s coupling system with several conventional single-mode fiber coupling systems with plano - convex lenses. It can be seen that our system has the advantages of simple configuration, short focal length, low cost lens material, and high coupling efficiency.
On the basis of testing results described above we can conclude that the method of directly milling by a FIB upon a glass substrate for microfabrication of DOE’s with continuous relief is available and practical. The coupling efficiency requirements can be met by DOE’s with designed focal length f0, N.A., and feature size of 125 mm, 0.2, and 4.5 mm respectively, with efficiency of -2.5 dB (75%). Because DOE’s are used for our method requires no special lens materials. The measured coupling efficiency proves that the assumption of a plane wave incident upon the plane - side of the lens is permissible. This method is also suitable for manufacturing integrated microlenses, micro-cylindrical lenses, micro-elliptical lenses, et al.
This study was supported in part by the Funding for Strategic Research Program on Ultra-precision Engineering of the National Science & Technology Board, Singapore (NSTB) and by research funding (ARC 9/96) from Nanyang Technological University. The authors thank Ong Aik San, Lim Boon Hung and Kok Lay Koon for enthusiastically checking the manuscript, and Gao Yingjie for performing atomic force microscope measurements
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