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Abstract
In this paper, we present a manual for the preparation of fully functional woodpile structures with partial photonic band gap (PBG) for applications in the visible (VIS) spectral range using an attractive polymer IP-Dip that is novel in photonic applications. In an experimental preparation of polymer-based woodpile structures using the IP-Dip polymer with partial PBG in VIS spectral range, a single-step laser lithography technique based on direct laser writing (DLW) was used. The woodpile structure preparation is based on a complex theoretical analysis of dispersion diagrams for the woodpile structure with fcc symmetry and IP-Dip polymer. We found partial PBGs in the Γ - X direction and dependence of PBG on the filling factor. Using a conventional DLW lithography system, we prepared a series of low-periodic woodpile structures with PBG in NIR and VIS spectral range attacking the yellow-green spectral range, which can be easily applied on different photonic components.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photonic crystals (PhCs) represent natural and artificial periodic structures with periodically modulated dielectric constant (refractive index) and the period of modulation is in the order of the wavelength of propagated electromagnetic wave. The selection of dielectric materials with sufficient refractive index contrast, the symmetry and the period of PhC structure are crucial for achieving good photonic properties. If the specific conditions are fulfilled, it opens up a photonic band gap (PBG), which prevents propagation of some wavelengths of light. The propagation of electromagnetic waves with frequency range inside the PBG interval is forbidden due to the depletion of the density of states [1,2].
Significant results have been achieved using one-dimensional (1D) and two-dimensional (2D) PhCs, even though they lose the confinement of light in the third dimension. The well-known Bragg gratings, representing 1D optical filters [3], were successfully used in many communication and sensing applications [4–6]. Very interesting results bring slab micro- and nanocavities and waveguides prepared in 2D PhC structures, although these structures prevent propagation of only in-plane wave vectors [7,8].
In recent years, a great attention is focused on three-dimensional (3D) PhC structures thanks to their complete PBG in all directions and thanks to the establishing of 3D technologies. Many 3D PhC structures show complete 3D PBG due to their crystal symmetry and the refractive index contrast, such as a diamond, a Yablonovite, an inverse opal and a woodpile PhC structures [9–11]. Various defects in perfect 3D PhC structures can create localized photonic modes such as optical waveguides and nanocavities in 3D [11,12]. The light trapped in such defects makes 3D PhCs suitable for many photonic devices.
In the last decade, the woodpile structure has become very attractive for two main reasons: i) it can be prepared by layer-by-layer process using the simple planar technologies [13] and ii) it forms the complete PBG at specific conditions. The woodpile was introduced by Ho et al. [14] and first demonstrated at optical frequencies by Lin et al. [15]. It was published that the complete PBG can be obtained in the woodpile 3D PhC structure only if the permittivity of used material is ɛ ≥ 4.6 [16]. The first woodpile 3D PhC structures were prepared from high index materials such as silicon and titanium dioxide using sputtering and electron beam patterning [17]. There were fabricated many woodpile and inverse woodpile structures with complete PBG in near-infared (NIR) and infrared (IR) spectral range [18–20].
The woodpile structure was used in some interesting applications. Several investigations of defect cavities in the woodpile structures were presented to calculate the resonant cavity modes. It was shown that the resonant frequencies of the cavity can be adjusted by the size of the defect at a certain position [11,21]. Some research groups presented the defect waveguides in the woodpile for the particle accelerating [22,23] and for 3D light guiding [24]. Ogawa et al. made a light emitting diode (LED) with InGaAsP active layer covered by GaAs woodpile structure to control a light emission [25]. There was fabricated superprism device consisting of a waveguide-coupled woodpile structure [26]. The superprism phenomena is wavelength dependent anomalous refraction of light between PhC structure and a homogeneous medium. The refraction angle is found to be very sensitive to the change of the incident angle and the wavelength under the proper conditions. Such an effect arises from the anisotropy of the bands in the photonic crystal and such dispersion effects could be hundreds of times stronger than in the conventional prism [26,27].
It is still challenging to obtain complete PBG in visible (VIS) spectral range due to complication in transparency and high refractive index of materials and also the fabrication techniques to produce submicrometer periods. Subramania et al. nano-lithographically fabricated titania woodpile PhC using multilevel electron beam direct write and physical vapor deposition technique [28]. The electron beam lithography and the etching of silicon nitride was used for preparation of the woodpile structure by Dhuey et al. [10]. Among the various approaches, the polymer-based 3D woodpile PhCs have attracted considerable interest as they can be easily fabricated by femto-second ultrafast direct laser writing (DLW) method in single-step process. Generally, the dielectric constant of polymers is ɛ ≤ 2.5 and it is impossible to achieve complete PBG in the polymer woodpiles. There were published some results of the polymer woodpile structures with partial PBG in IR frequency ranges [29–31]. To achieve the partial PBG in VIS spectral range is still challenging. Fischer et al. combined DLW with the concept of stimulated emission depletion (STED) to improve the resolution limit of DLW and successfully fabricated the polymer woodpile structures for VIS spectral range [32].
Our goal is to fabricate the woodpile structure with partial PBG in VIS spectral range using the single-step 3D laser lithography technique based on DLW. For preparation, we used a commercial DLW system Photonic Professional GT from Nanoscribe GmbH. For the woodpile structure we used IP-Dip negative photosensitive polymer. This material is currently very attractive and progressively used for fabrication of many photonic structures and devices especially due to its very good optical and mechanical properties [33–36]. Crucial for the design of such structures is the detailed knowledge of the refractive index and its dispersion. Gissibl et al. made refractive index measurements of exposed IP-Dip in VIS and NIR spectral range and found the refractive index characteristic using Cauchýs model [37]. Fullager et al. measured dielectric response of IP-Dip after the polymerization in infrared region (∼1.67 – 40 µm) [38]. Their experiences and results with IP-Dip polymer were used for design and experimental fabrication of the woodpile structure.
In consideration to the very small refractive index of used IP-Dip polymer (n = 1.52 at 780 nm unexposed), only partial PBGs in some directions are expected. The width of partial PBG is modulated using the second crucial parameter for optical properties – the symmetry of the woodpile structure. We designed the woodpile structure with face-centered cubic (fcc) lattice symmetry, considering that fcc lattice has the most spherical Brillouin zone, thus creates the widest PBG. We simulated the dispersion diagrams for the woodpile 3D PhC structure with fcc symmetry, in which we found positions of partial PBGs in some directions. Simulation results were compared with optical transmission measurements.
2. Woodpile structure and dispersion diagram
The woodpile represents a diamond-like structure formed by a stack of alternating four-layered sequences of parallel dielectric columns with rectangular profile of width w and height h. It is characterized by horizontal period a representing the distance between two adjacent dielectric columns in xy plane and vertical period c, which represents the height of four stacking layers in vertical direction (c = 4 h). If c = a√2, the woodpile forms an fcc lattice [11,39]. Detail of arrangement of dielectric columns in the woodpile structure, unit cell and the structure parameters are shown in Fig. 1.
For the simulation of dispersion diagram of the woodpile structure, an RSoft Photonic Component Design Suite simulation tool BandSOLVE with plane-wave expansion (PWE) numerical method was used. In general case, the woodpile lattice is a body-centered tetragonal (bct) lattice. This can be considered as an fcc lattice that has been rotated and stretched in the vertical direction. Each crystal structure is characterized by a set of symmetry points. To construct a dispersion diagram, we identified the symmetry points of the first Brillouin zone and connected them by straight lines representing wave vector k in fcc Brillouin zone (Fig. 2(a)). The orientation of the woodpile structure relative to the Brillouin zone is shown in Fig. 2(b).
Fig. 2. (a) The first Brillouin zone of fcc lattice and (b) orientation of the woodpile structure relative to the directions in reciprocal space during the simulation.
There are two main aspects forming the PBG in the woodpile structure: i) refractive index contrast of used materials and ii) filling factor (ff), which represents a ratio of column width to horizontal period ff = w/a. The very low contrast of dielectric constants of used materials (ɛcolumns = 2.34 and ɛair = 1) will produce only partial PBGs in defined directions. The filling factor will control the PBG position and width in dispersion diagram [16]. Figure 3 shows the dispersion diagram of the woodpile structure based on IP-Dip polymer with ff = 50%. In dispersion diagrams we found the partial PBGs in <001 > and <111 > directions corresponding to Γ - X and Γ - L. While Γ - L direction shows wider PBG (0.45 – 0.50) than Γ - X (0.54 – 0.57), the Γ - X has PBG at higher values of normalized frequency. It is useful for achieving the PBG at shorter wavelengths at the same horizontal period. Also, we prefer Γ - X direction for the simple orientation of the woodpile structure during transmission measurements and applications.
Fig. 3. Dispersion diagram with partial PBG in Γ - X direction for the woodpile structure with fcc lattice symmetry and ff = 50%.
We simulated dispersion diagram for the woodpile structure of fcc lattice symmetry with the introduced material parameters (ɛcolumns = 2.34, ɛair = 1). In simulation we changed filling factor in the range of 10 – 80% (so the values of w were changed from 0.050–0.400 µm with respect to the horizontal period a = 0.500 µm). The goal was to find the appropriate partial PBG with maximal width and normalized frequency for possible realization of the woodpile structure with PBG in VIS spectral region. In the following calculations, we focused on a detail analysis in Γ - X direction. We found partial PBG in dispersion diagrams in the filling factor interval ff = 10 – 80%. The dispersion diagrams of the woodpile structures with the values of ff close to the limits at which we obtain partial PBG in Γ - X direction as is shown in Fig. 4. Figure 4(a) shows partial PBG for ff = 20% with position at normalized frequency range a/λ = 0.62 – 0.64. For the woodpile structures with horizontal period a = 0.500 µm it corresponds to the wavelength range of Δλ = 781 – 806 nm. The partial PBG for ff = 70% with position at normalized frequency range a/λ = 0.50 – 0.52 corresponding to the wavelength range Δλ = 961 – 1000 nm is shown in Fig. 4(b). It means that 0.500 µm horizontal period produces partial PBG in NIR spectral region very close to the VIS spectral range. The widest partial PBG was found in dispersion diagrams in the interval of filling factors ff = 40% – 50%. Outside of the filling factor interval ff = 10 – 80%, the PBG in the Γ - X direction was not found and the limit values of ff at 10% and 80% show very narrow PBG.
Fig. 4. Dispersion diagrams with partial PBGs in Γ - X direction for the woodpile structure with horizontal period a = 0.500 µm and (a) ff = 20% and (b) ff = 70% with inset pictures showing the detail of columns width relative to horizontal period a.
The dependence of normalized frequency a/λ on filling factor obtained from a series of simulations of PBG for different filling factors is shown in Fig. 5. From this graph, we can see the position and width of partial PBGs as a function of filling factor. For better representation, the area of partial PBG was filled. Such PBG representation is very useful for general analysis of IP-Dip based the woodpile structures in Γ - X direction and it clearly characterizes the PBG limits. PBG in units of normalized frequency can be simply interpreted as a wavelength range for defined values of horizontal period a.
By our simulations, we characterized the parameters for PBG formation in IP-Dip polymer-based woodpile structures in Γ - X direction. Regarding to our numerical calculations, there can be designed application-tailored woodpile structures with any desired PBG in proposed interval of normalized frequencies (blue area in Fig. 5). The spectral range of PBG is then function of the horizontal period a and the PBG width can be modulated by the ff. It opens wide-ranging application area for woodpile structures as band-pass filters for integrated photonics, light emitting diodes and photodiodes.
3. Fabrication and analysis of PBG in the woodpile structures
For the fabrication of the woodpile structures, we used a commercial 3D laser lithography system Photonic Professional GT from Nanoscribe GmbH. This DLW system works on principle of non-linear optical lithography based on two-photon absorption (TPA) in the volume of photosensitive material. As excitation light, the high-energy near infrared femtosecond laser pulses are used. The laser pulses are focused in the volume of a photosensitive polymer and non-linear TPA initiate polymerization process within the focal point. Arbitrary 3D structures can be fabricated by moving the focused laser beam in three directions in the photoresist. The excitation light source is a Ti-sapphire femtosecond laser working at wavelength of 780 nm with 100 fs pulse width and 80 MHz repetition rate. The laser beam is focused by objective lens with 63× magnification and a high numerical aperture NA = 1.4 to spatial unit called voxel. The resolution limit of DLW system Photonic Professional GT is determined by voxel dimensions, which are better than 0.200 µm in lateral direction and 0.500 µm in axial direction. These voxel dimensions were adjusted by laser power and scanning speed during the fabrication process.
For fabrication of the woodpile 3D PhC structure negative IP-Dip photosensitive polymer was used. We chose this polymer due to its good optical properties, high mechanical stability, good adhesion to glass substrate and the highest resolution for Dip in Laser Lithography (DiLL), which was used in our experiment [40]. In this configuration, IP-Dip serves as immersion and photosensitive material at the same time by dipping the microscope objective into the liquid photoresist. Refractive index of IP-Dip is well characterized by Cauchýs equation [37, 41,].
The sample preparation consists of several steps. First, we prepared script in program Describe from Nanoscribe GmbH to design the woodpile structures with defined periods. The woodpile structures consist of 20 layers arranged in cylinder shape with a diameter of 40 µm. Next, the lithography process was provided by exposure of the IP-Dip photosensitive polymer applied on a glass substrate with scanning speed 40000 µm/s and laser power in range of 20mW to 40mW. Several woodpile structures with different values of horizontal period a, were fabricated on one glass substrate. After the laser writing process, the sample was developed in PGMEA developer, rinsed in isopropyl alcohol and finally dried with nitrogen.
The goal of this paper was to prepare the woodpile structures and to analyze partial PBGs by measurements in VIS and NIR spectrum. Therefore, we prepared the woodpile structures with horizontal periods starting from a = 0.300 µm to a = 0.500 µm with step 0.050 µm and a = 0.700 µm to a = 0.900 µm with step 0.100 µm. We analyzed existence of partial PBGs in Γ - X directions of woodpile structures in transmission measurements at normal incidence of unpolarized white light. Transmission in VIS and NIR spectral range was analyzed by spectrometers OceanOptics USB2000 and NIRQuest 512. The light from multi-mode optical fiber with core diameter of 50 µm coupled to halogen lamp passed through the woodpile structure. Transmission spectrum was measured using single-mode optical fiber with core diameter of 9 µm coupled to spectrometer. Generally, the IP-Dip photoresist shows very weak absorption for spectral range over 500 nm. The producer declares absorption of IP resists close to 10% measured on the 981 µm thick layer in this spectral range. All the processed woodpile structures were fabricated with height of up to 5 µm, so the absorption can be neglected.
Firstly, we investigated the woodpile structures with partial PBG laying in NIR spectral range. The positions of partial PBGs of these woodpile structures were estimated from dispersion simulations for the woodpile structure with horizontal period a = 0.500 µm. All the woodpile structures with horizontal periods starting from a = 0.700 µm should exhibit expected PBG in spectral range of NIRQuest spectrometer. However, due to the considerable shrinkage effect [30,42], the woodpile structures with period a = 0.700 and 0.800 µm show PBG on the border of the spectral range of used spectrometers NIRQuest and OceanOptics HR 2000. We observed PBG just for the woodpile structure with the proposed horizontal period of a = 0.900 µm.
The quality of the fabricated woodpile structures was analyzed using a scanning electron microscope (SEM). In Fig. 6(a) we can see SEM image indicating the real reduced woodpile structure parameters caused by considerable (20%) shrinkage effect (a = 0.720 µm and w = 0.170 µm), from which we calculated the filling factor to be ff = 24%. For this filling factor and according to the simulation from Fig. 5, we estimated the wavelength range for the PBG to be Δλ = 1137 – 1190 nm. The experimentally measured PBG range shows wider spectral dip of Δλ = 1035 – 1200 nm achieving more than 30% transmission decrease (Fig. 6(b)).
Fig. 6. (a) SEM image of the fabricated woodpile structure with the dimensions a = 0.720 µm and w = 0.170 µm and (b) transmission spectrum of the woodpile structure designed for NIR spectral range with expected position of partial PBG from simulations.
After promising results from the woodpile structure for NIR spectral range, our motivation was to fabricate the woodpile structures for VIS spectral range. Firstly, we focused on investigation of the woodpile structure with horizontal period of a = 0.500 µm. The SEM analysis also confirmed shrinkage effect (Fig. 7(a)) with real parameters w = 0.171 µm and a = 0.475 µm, what corresponds to ff = 35% and calculated PBG position at wavelength range Δλ = 826 – 877 nm (Fig. 7(b)). From SEM measurements, we also recognized the column width broadening in the second woodpile layer caused by laser writing process. The first and the second layers were processed in perpendicular writing process, with the same voxel orientation. It will affect the different column width in perpendicular directions. For the second layer we estimated the ff increasing up to ff = 50% what explains the extension of the measured PBG. For the ff = 50%, the simulated position and the wavelength range of PBG of the woodpile structure with horizontal period a = 0.500 µm in Γ - X direction were estimated from the Fig. 5 at wavelength range Δλ = 877 – 943 nm. In measured spectrum (Fig. 7(b)) we can observe decrease at wavelength range Δλ = 791 – 931 nm, what nearly covers the simulated PBG if two filling factors 35% and 50% are considered.
Fig. 7. (a) SEM image of the fabricated woodpile structure with the real dimensions of horizontal period a = 0.476 µm and column width w = 0.171 µm and (b) transmission spectrum of the woodpile structure with expected positions of partial PBGs for different filling factors of ff = 35 and 50%.
Our experimental results document the stable column width of 0.170 µm in one direction and 0.230 µm in perpendicular direction. It favors this technology to fabricate the woodpile structures with minimal horizontal period of app. 0.300 µm having PBG in VIS spectral range. For the next experimental investigations, we focused on fabrication process of the woodpile structures with horizontal periods a = 0.300, 0.350, 0.400 and 0.450 µm. The spectral transmission characteristic (Fig. 8) shows partial PBGs of the fabricated woodpile structures with evident blue shift of PBG for the decreasing horizontal periods. The woodpile structures with period up to 0.400 µm cover the VIS spectral range starting from app. 500 nm. The transmission decay overcomes 20% for all woodpile structures. The woodpile structures consist of 20 layers with different vertical periods with respect to horizontal periods. Thus, the final height starts from app. 2.12 µm for 0.300 µm horizontal period up to 3.53 µm for 0.500 µm period. This leads to weak decreasing of PBG effect on transmission as is shown for lower horizontal periods in measured spectrum.
Fig. 8. Transmission spectrum of the woodpile structures with different horizontal periods a (0.300, 0.350, 0.400, 0.450 and 0.500 µm). Spectra were vertically shifted by step of 20% with respect to nominal 0.400 µm spectrum.
From the simulations and experimentally determined column widths, we determined partial PBG in our woodpile structures with horizontal periods in the range of 0.300 µm to 0.500 µm with respect to relevant values of filling factor ff (Fig. 9). The dark grey area shows the PBG for column width of 0.230 µm calculated for the range of period 0.300 - 0.500 µm and the light grey area represents PBG for column width of 0.170 µm as was documented from SEM analysis of woodpile columns processed in two perpendicular directions. The slight process nonuniformity of column widths spreads the PBG interval as is shown in the Fig. 9. The calculated PBG interval is compared with experimentally obtained PBG for fabricated structures. Comparison of calculated PBG interval covers well the experimentally measured PBG and documents the spreading of PBG given by slight nonuniformity of woodpile columns processed in two perpendicular directions.
Fig. 9. PGB intervals determined as a function of horizontal periods calculated for different column widths (dark grey w = 0.230 µm, light grey w = 0.170 µm) and comparison with the measured PBGs of prepared woodpile structures (solid lines).
4. Summary
The main goal of this study was to prove experimental preparation of the polymer-based woodpile structures using the attractive IP-Dip polymer achieving the partial PBG in the NIR and VIS spectral range. For fabrication of the woodpile structures with partial PBG in VIS spectral range, we used single-step 3D laser lithography technique based on DLW.
In theoretical consideration to the very small refractive index of used IP-Dip polymer, only partial PBGs in specified directions were expected. We simulated complex dispersion diagrams for the woodpile 3D PhC structure with fcc symmetry, in which we found partial PBGs in Γ - X direction. Using conventional DLW lithography system, we prepared a series of low-periodic woodpile structures with PBG in NIR and VIS spectral range attacking the yellow-green spectral range. The prepared structures consist of only 5 vertical periods (20 layers) and document more than 20% transmission decay in the PBG region. We carefully analyzed the filling factor effect on the PBG properties as well.
The massive employment of IP-Dip polymer in 3D single-step technologies and this study could open the interesting way, how to prepare the fully functional woodpile structures with partial PBG for applications in VIS spectral range. The prepared structures can be easily applied at the end of optical fibers or light emitting diodes.
Funding
Vedecká Grantová Agentúra MŠVVaŠ SR a SAV (1/0069/19, 1/0540/18, 1/0886/17); Agentúra na Podporu Výskumu a Vývoja (16-0129).
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