Simple diffraction structures having the form of a regular grid of pillars can generate a significant range of hues in white light transmission due to color-dependent diffraction into higher orders. We present the fabrication of such submicrometer scale structures by three dimensional laser two-photon photolithography, results of their optical properties measurements and compare the latter with numerical simulations.
©2013 Optical Society of America
Optical transmission color filters find numerous applications both in experimental sciences as well as in everyday life devices. The physical processes behind wavelength-dependent transmission can be divided into three broad categories. The first one uses selective absorption in molecules (dyes) or metal or semiconductor (quantum dots) nanoparticles, typically embedded in a transparent host material – glass or polymer. Another concept is to use interference of the waves reflected from interfaces separating transparent materials of different refractive indices in a sub-wavelength, multilayer stack. Thin film coating technology, in particular developed for dielectric (for applications in UV, VIS and NIR) and semiconductor (IR) materials, provides spectacular results in terms of color selectivity and contrast. While multilayer filters can also handle high incident powers, the fabrication process remains complex and has limited flexibility for patterning surfaces with different coatings on a small scale. The third approach to wavelength-dependent transmission relies on diffraction from microstructured surfaces that act like amplitude and/or phase diffraction gratings or, more generally, holograms. By selecting the pattern topography and the grating material(s), the diffraction into higher orders can be tuned, providing selective light transmission.
As early as in the late 1970s Knop [1,2] extensively studied the line phase gratings for their potential use as color transmission filters. Theoretical and experimental results showed that diffraction gratings with a rectangular profile [1–3], when used in transmission, can cover a significant range of transmission profiles (filter hues).
With the development of sub-micrometer fabrication techniques (chiefly planar photolithography), a number of concepts for color filters based on one-dimensional [4,5] as well as two-dimensional (2D) [6,7] periodic subwavelength diffraction structures have been demonstrated [4–14]. Silicon is the most popular material [4–7], and the metalized structures [8–14] offer reliable reproducibility. In particular, regular as well as patterned arrays of silicon  or InAs  nanopillars have been demonstrated as reflective color filters in the visible. With the pillar diameter between 70 and 350 nm the reflection spectra can be tuned and vivid colors are obtained . Metal-coated linear gratings fabricated with electron beam lithography combined with two-photon laser writing were also used as color filters in reflection .
In this paper we report on the design and fabrication of a two dimensional submicrometer scale diffraction structures by two-photon photopolymerization of a liquid resin. By designing the structure topography, the wavelength-dependent diffraction into higher orders can be tuned thus resulting in the desired light transmission profiles.
2. Structure fabrication
Among the fabrication techniques offering submicrometer resolution, the two-photon 3D photolithography, also known as direct laser writing (DLW), is one of the few with full free-form capability . Scanning a focused beam of femtosecond laser pulses within the volume of a light-sensitive photoresist (resin) is used to build arbitrary shapes line by line via two-photon absorption of light that initiates a chain of reactions leading to alteration of the physio-chemical properties (ultimately, in a negative-type process, the solidification) of the material. The structures described throughout this paper were made with a commercial DLW workstation and a negative liquid resin (Photonic Professional and IPL respectively, from Nanoscribe GmbH). The details of the setup and the process can be found in .
The 2D transmission phase gratings are made of a collection of microcolumns (pillars) with a given height h, set at constant intervals d on a square x-y grid (Fig. 1(a)). The pillars are fabricated on a 170 μm thick glass microscope coverslip. They are made of solid polymer resin having the index of refraction around 1.5 in the visible range of the spectrum (the exact dispersion curve has been measured on a separate sample). From the SEM images of several fallen columns their exact dimensions have been determined (Fig. 1(b)). Each of the microcolumns is written with a single line along the z-axis and as such has the average diameter (s) of 455 ± 10 nm, determined by the lateral resolution of the lithography setup. The top of the column is roughly hemi-ellipsoidal with the major radius (r) equal 340 ± 20 nm. In the following numerical simulations the shape was approximated with a hemi-ellipsoid-topped cylinder and we have verified that using the exact shape (conical column body) has little effect on light propagation in the structure and the resulting spectral transmission characteristics.
3. Results and discussion
Figure 2 presents the white light transmission micrograph of a series of the transmission pillar-type phase gratings (each having the area of approximately 40 x 40 μm2) with the (measured) column height and the column separation varied between 1.0 and 2.4 μm and 1.0-1.3 μm, respectively. The picture was taken with a 20x, 0.45 NA microscope objective (S Plan Fluor, Nikon) and an unpolarized tungsten halogen lamp used as the light source. The imperfections (spots) are mainly due to dust particles in the air and/or the solvent (resin developer) impurities.
A significant range of hues is available, covering the visible range. It is also possible to make low transmission structures (integrated transmittance over the visible range below 30%) – an important feature for integrated photonics applications. We have verified that the transmitted colors do not change if the structures are tilted by around 10° from the normal incidence. From a series of measurements with linearly polarized light source, we have concluded that, within the spectral measurements accuracy, there is no dependence of the polarized light transmission on the polarization direction.
To quantify the optical properties of the structures, the transmission spectra have been measured with the same microscope objective and a grating spectrometer (USB4000, OceanOptics) – three of these are plotted in Fig. 3(a), corresponding to the red, green and blue filters.
The characteristic dimensions of our structures, being of the order of a micron, place them between the classical (wave) and the sub-wavelength optics. The optical properties of the structures can be understood, in the first approximation, within the Fresnel diffraction picture: the light transmitted through the grating can be divided into two parts – one propagating in the columns and the other in the surrounding medium (air). For each part, the standard diffraction grating equation, responsible for the angular distribution of the transmitted radiation, holds. The two contributions can, however, interfere with each other and the result of this interference (constructive or destructive) depends on the phase difference between them. The latter is, in turn, directly related to the optical path difference between light propagating in the solid resin and in the air and determines the positions of the minima and maxima in the transmitted spectrum. The interference contrast (i.e. the minima depths), on the other hand, depends on the ratio of the two contributing field amplitudes and is related to the pillar diameter and spacing (filling ratio). Closer inspection of Fig. 2 reveals that indeed the resulting colors depend strongly on the pillar height (phase) and to a lesser extent on the pillar separation (interference contrast). Measured diffraction patterns (up to the first order) are plotted in Fig. 4 for the red, green and blue filters to confirm this qualitative understanding. The diffraction efficiency varies with wavelength for each structure and these variations directly determine the transmission spectra. The hues measured for all the fabricated structures are also plotted on the CIE-1931 chromaticity diagram in Fig. 5(a).
The next approximation is based on the full light propagation model that has been implemented using the finite-difference time-domain (FDTD) method (FDTD Solutions, Lumerical) and the results for the three filters are presented in Fig. 3(b). The filter topography was simulated on a 5 × 5 square grid of the top-rounded columns (see Fig. 1(b)), surrounded by perfectly matched layer (PML) walls, with broadband (400-800 nm) plane-wave light source, located 2 μm below. The energy flux was recorded 20 μm above the structure, this height being large enough to allow the diffracted light leave the simulation region.
Finally, to demonstrate the ability of the presented technology to produce patterned color filters, we have fabricated a series of pillar structures with different spectral characteristics side by side – compare Fig. 5(b).
We have demonstrated color transmission filters fabricated by direct laser writing, covering a broad range of hues in the visible range of the optical spectrum. By adjusting the grating topography, selective diffraction into higher orders can be achieved. Initial experiments with the last unexplored degree of freedom – the pillar diameter – have proved that the color range can be thus increased even further.
Color filtering with pillar type gratings has also limitations, resulting from the filtering mechanism – rejecting higher diffraction orders – itself, namely the numerical apertures of the optical devices using the filters must be properly chosen.
At the same time, the presented phase diffraction gratings offer several potential advantages compared to other technologies:
- 2. they can provide high resolution spatial patterning,
- 3. low transmission masks can be fabricated in the same process,
- 4. they can be made compatible with other microfabrication techniques used in the optoelectronics technology, resulting in a straightforward integration into a range of optical devices.
This work has been generously supported by the National Science Center (Poland) within the DEC-2012/05/E/ST3/03281 grant funds. Partial support by ERDF within the POIG.02.01.00-14-122/09-00 is also acknowledged.
References and links
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