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1.INTRODUCTIONSilicon integrated photonics is nowadays mainstream technology that will merge with the existing electronic CMOS integrated circuits to reduce the power consumption in data processing facilities and enhance the data streaming performance within a single integrated circuit. The concepts of silicon technology were developed in a series of investigations of photonic properties of silicon in 1980’s[1-5], including early studies of light propagation losses in silicon planar waveguides in the near IR part of the electromagnetic spectrum[1,4]. Silicon integrated photonic platform is compatible with CMOS integrated circuits technology, and is successfully using more than 50 years of engineering development in wafer processing techniques, in particular optical lithography[5-14]. On the other hand, silicon integrated technology has an inherent disadvantage: it is founded on a mature silicon technology, where incremental advancements over the many decades have resulted in steady growth, but is most likely not capable to produce a major technological disruptive breakthrough. Soft matter, in particular liquid crystals, has the potential for disruptive technological breakthrough in photonics, which was actually demonstrated by the emergence of flat Liquid Crystal Displays (LCDs) in the 1990’s. LCDs have not only completely replaced bulky cathode ray tubes in TVs and instrumentation, but have also enabled an extremely great number of novel devices, including portable cell phones that could not be realized using the cathode ray tube technology. Unlike solid state silicon technology that is using high temperatures to process wafers, soft matter is stable near room temperature and must be processed at moderate temperatures. Furthermore, the fluidity and soft nature of soft matter makes it possible to design new materials using simple mixing of different liquids, or dissolving solid materials to dope liquids with optical gain material, using microfluidic flow control and even using the self-assembly properties of soft matter. Unlike mainstream silicon photonics, research initiatives in soft matter photonics are rather sparse and research efforts are quite limited. Some time ago we demonstrated that liquid crystals could be used as tunable optical micro-resonators[15,16], micro-lasers[17] and optical fibers[18] with excellent wave-guiding properties. It was also demonstrated that self-assembly could be used to bind together different soft matter micro-photonic elements to form a kind of micro-photonic circuitry[19-22]. Because liquid crystals and soft matter are poor conductors of electric current, soft matter photonics is inherently an all-optical platform, where the flow of light is controlled by light. We present the first step towards realization of soft matter micro-photonic circuitry, i.e. design, production and characterization of multimode optical waveguides made of polymer that are directly printed on glass using two-photon polymerization technique, known as Direct Laser Writing (DLW) technique. DLW has been extensively used in a number of micro-optical and micro-photonic applications. DLW has been used to produce multimode optical waveguides on glass that were coupled with a light-sensitive optical micro-cavity[23], thus realizing light-tunable optical filter. It has also been demonstrated that DLW patterned surfaces provide an excellent alignment of nematic[24-26], columnar[27], and lyotropic chromonic liquid crystals[28]. An example of a 3D micro-device produced entirely by DLW and using liquid crystals as tunable electro-optic material was also demonstrated recently[29]. Optical properties of the photosensitive resins that are used for two-photon polymerization (TPP) have been studied in considerable detail, both in bulk and printed form[30]. The absorption of light in these materials has been studied in the liquid (non-polymerized) state and after UV curing and thermal treatment. However, there is insufficient knowledge on the propagation losses for polymer micro-waveguides that are printed using the DLW technique. Here we present our study of propagation of light through multimode optical waveguides that are printed on borosilicate glass covered with a 500 nm thin layer of low refractive index fluoropolymer CYTOP. We printed waveguides using two different resins: (i) The IP-S resin that shows good alignment of NLCs on DLW patterned surfaces[26], but has a refractive index close to glass, (ii) high refractive index resin IP-n162. Waveguides of different length and cross-section have been terminated on both ends with two rectangular prisms. Propagation losses have been measured using the cut-back method (i.e. different lengths of waveguides) by focusing light from a tunable laser onto one of the prisms. The light intensity exiting on the other side of the waveguide was measured using a camera. We present propagation losses for IP-S and IP-n162 waveguides with a cross section of 10μm × 10μm and discuss the accuracy of measuring propagation losses in DLW printed waveguides with two input-output coupling prisms. 2.MATERIALS AND METHODSWe use 3D laser lithography system (Photonic Professional GT+, Nanoscribe GmbH & Co.KG) operating in galvo mode using the 63 × objective that has a printing area of 200 μm. Two different resins were tested, the IP-S resin (Nanoscribe GmbH & Co.KG) with refractive index of 1.486 not polymerized and 1.515 after polymerization, and IP-n162 resin with refractive index of 1.604 in liquid state and 1.622 after polymerization at 589 nm. The waveguides were printed on 22 mm × 22 mm borosilicate glass coverslips (ROTH) of 170±5 μm thickness. The coverslips were first cleaned by hand wiping using lint free cloths and acetone, which was followed by 15 min ultrasound cleaning in 1% water solution of detergent (Hellmanex II) at 35°C. This was followed by 15 min ultrasound cleaning in pure deionized water to remove the traces of detergent. Finally, the slides were dried in an isopropanol degreaser. The coverslips were then spin-coated with fluorinated polymer CYTOP (CTX-809A, Asahi Glass Co., Ltd) that has refractive index of 1.34. A 60:40 % wt solution of CTX-809A and solvent CT-SOLV9AP is spin coated at 1000 RPM onto cleaned substrates and baked at 205°C for 1 hour. This produces a fluoropolymer film of thickness ~ 500 nm that serves as low-refractive index optical isolation layer between borosilicate glass and DLW printed polymer waveguide. CYTOP coated substrates are placed for 5 min into a UVO cleaner (UVO-Cleaner 256-220, Jelight Company, INC.). After 5 min the substrates are blown with nitrogen and a small amount of IPS/IP-n162 resin is drop-casted onto the substrate. A 63× objective NA (Zeiss - 1.4NA Oil Dic, Plan polycromat) is inserted into the printer. The substrates are loaded onto the substrate holder of Nanoscribe and inserted with resin side down into the machine and optical contact is established between the resin and the objective lens. The objective is then carefully moved toward the substrate until the interface of the resin and CYTOP layer is easily found in focus due to the high refractive index mismatch of >0.2. The printing of waveguides is therefore performed in dip-in laser lithography mode (DILL). After printing, the substrates were dipped twice, first for 12 min into PGMEA solvent (Sigma Aldrich), and, second for 1 min in isopropanol. Finally the substrates with printed waveguides and prisms were dried at 40°C for 30 min. For control purposes, some of printed waveguides were imaged using SEM. The substrates with the printed structures were cut to the appropriate size for imaging and coated with the 10 nm of pure Au. The imaging was performed by Field emission SEM Zeiss SUPRA VP, using secondary electrons (SE) to reveal the topography of the imaged structures. The printed structures were imaged either from top or tilted by 30° to obtain the correlative side view as well. Propagation losses in printed multimode waveguides were measured using an inverted optical microscope (Nikon Eclipse, TE), a tunable pulsed laser (Opolette HE 355 LD, Opotek, USA) and precision camera (Flir BFS-U3-50S5C). Camera gain and exposure time were kept the same during all experiments to enable quantitative light intensity analysis. Laser light from the tunable laser system was sent to the microscope objective (ZIESS 20×, NA=0.8 field of view 400 μm) and focused to the input surface of a 45° micro-prism (10 μm × 10 μm footprint). The objective was set to a position to have the exit prism in focus. The intensity pattern of light, exiting on the other 45° micro-prism was monitored with the camera. While monitoring the total intensity of the exiting light, the input beam focus was precisely moved within the x-y plane of the prism surface until maximum of light intensity was reached. The whole procedure was repeated for different lengths L of the waveguide. The result was a set of measured light intensities for different waveguides lengths, I(L). This set of data was the fitted to an exponentially decaying function of waveguide’s length, I(L) = I°e−βL, where β is the propagation loss. 3.RESULTS AND DISCUSSIONFigures 1(a,b) show the CAD model of a waveguide. Each waveguide is designed as a series of single-printed layers that are stacked on each other with a period that is called slicing, as presented in Fig. 1a. In our case we use slicing of 100 nm, which means that neighboring printed layers are strongly overlapping. Namely, the printing voxel has a dimension of ~700 nm along the optical axis of the objective that gives around 600 nm of overlapping of neighboring layers. Individual slices are printed by moving the laser focus along the waveguide, which is followed by displacing the focus for 100 nm perpendicularly to the printed line. Then, subsequent lines are printed along the same direction, which is along the waveguide. The separation between neighboring lines is hatching distance, which is set to 100 nm for all prints. As a final step, contouring is applied, which means that the laser spot is moving along the edges of a printed slice, thereby smoothening the 100 nm finishing polymer layer of the waveguide. Figure 1(c) shows SEM image of 50 μm long waveguide with a 10 μm × 10 μm cross section made of high refractive index IP-n162 resin. The surface of the resin looks quite smooth, but more detailed analysis using fluorescent confocal analysis reveals that the structures printed with IP-n162 are quite porous, because it can be infiltrated with fluorescent dye. The porosity and potential swelling of structures made of IP-n162 is also indicated by the apparently swollen upper surface of the waveguide in Fig. 1(c). We use optical microscopy to measure the propagation losses in as-printed wavegudes using the cut-back method. The appearance of IP-n162 waveguides under an optical microscope for various wavelengths of measuring light is shown in Figure 2. Figure 3(a) shows the photographs of 580 nm laser beam transmission through 10 μm × 10 μm waveguides on Cytop of different lengths from 10 μm to 170 μm. The measured intensity at the reflected prism for different waveguide lengths is shown in Figure 3(b). At the wavelength of 580 nm (yellow) the transmission losses in IP-n162 waveguides are of the order of ~14 dB/cm. The propagation losses in IP-n162 DLW printed multimode waveguides are quite high and we explored in more detail the micro-structure of printed waveguides. We exposed printed IP-n162 DLW printed scaffolds to a liquid crystal doped with 0.1% w.t. of fluorescent dye. We used a confocal fluorescence microscope to take 3D images of these samples. We noticed in 3D fluorescent images that after some time the IP-n162 DLW printed scaffolds became fluorescent. This clearly indicates the nanoscale porosity of DLW printed scaffold using IP-n162 resin. In the next step, we repeated the fluorescence test using scaffolds printed with IP-S resin and no diffusion of fluorescent dye was observed into the DLW printed IP-S scaffolds. In the next step, we printed IP-S multimode waveguides of 10 μm × 10 μm cross section and variable lengths. By using the stitching function of the Nanoscribe GT printer, we split the waveguides bigger than the print field into individual segments, which are printed separately. This makes it possible to print waveguides up to the maximum 900μm length L to increase the accuracy of the measurements of the propagation losses using the cut-back method. Namely, if the propagation losses of waveguides are lower than ~10 dB/cm, the maximum length of ~170 μm of single-print waveguides using the 63× objective results in small attenuation of propagation light at the exit prism, which in turn results in poor accuracy of the measurement of β. This was resolved by increasing the length L of DLW printed waveguides up to 900 μm by stitching individual prints. We also performed SEM imaging of IP-S DLW printed waveguides and we found that the surfaces are smooth, the printed IP-S waveguides are not swollen after in contact with fluorescent LC and there are no printing features seen on the surface of IP-S waveguides. Propagation properties of 585 nm light through 10 μm × 10 μm cross section waveguides printed with IP-S resin on 500 nm CYTOP on glass are shown in Figure 4. The transmission of the printed waveguides is ~90% at the maximum printed length of L=900 μm. This corresponds to propagation losses of 7.3±1.5 dB/cm, which is a reasonably good result for this stage of research. We found that the losses can nearly completely be attributed to the absorption of light in the IP-S resin. Light propagation through the printed waveguides is also simulated numerically using the finite-difference time-domain (FDTD) method [31] implemented in the MEEP software [32] We perform simulations of light propagation along the lateral cross-section only. Panel (a) of Figure 5 shows the refractive index profile and introduces the geometrical parameters of the structure: the waveguide length L, its height and the prism size, both D. Under the left prism, we place a continuous source shaped as a Gaussian beam with a wavelength of λ = 532 nm and a waist size of w0 = 2.5 μm with focus at the substrate-waveguide boundary. The polarisation is linear in the z-axis direction. The profile of the z-component of the electric field Ez (x, y) in a waveguide of length L = 40 μm and thickness D = 5 μm is shown in panel (b). At the entrance prism, light undergoes total internal reflection which provides coupling into the waveguide, but some light still escapes at and around the corners. At the planes labelled IN, 1, …, 9, OUT, we measure the Poynting flux of light in the direction of propagation, i.e. on the IN plane along , on the 1, …, 9 planes in the direction and on the OUT plane in the direction. As shown in the inset of panel (b), light is mostly lost at the first prism, the flux is then approximately constant along the waveguide, and finally, part of the light energy is lost at the exit prism as well. For a constant beam waist w0 = 2.5 μm, total losses, measured as a ratio between Poynting fluxes measured at IN and OUT planes, decrease with increasing D (entrance prism size and waveguide thickness). In a waveguide with D = 10 μm, the relative loss of light energy is even greater at the exit prism than at the entrance prism, as shown in panels (c,d) of Figure 5. The reason is that the beam at the entrance prism is much narrower than the size of the prism, but on the way to the exit prism, it becomes wider and already extends to the sharp corners, where the losses are significant. The experimental measurement of the waveguide attenuation is sensitive to the illumination setup, since the measured output flux (at the OUT plane) varies greatly with: (1.) the displacement of the incoming beam with respect to the centre of the prism Δx, and (2.) the incident angle α, defined as the angle between the direction of beam propagation and the normal to the substrate-waveguide interface. The change of the flux at the OUT plane due to the variation of Δx and α is demonstrated in panels (e-h) of Figure 5. For example, a displacement of the beam with waist size w0 = 2.5 μm at the prism of the waveguide of thickness D = 5 μm for Δx = 0.5 μm to the right results in a decrease of the measured flux already by 5%. Interestingly, it is not optimal to target the centre of the prism since the maximum flux at the OUT plane is measured if the beam is shifted by Δx = −0.2 μm to the left. Even more than the displacement of the beam, the measured flux is affected by the angle of incidence α. For given refractive indices (nP = 1.5 for the prism and n = 1.0 for surrounding air), the limiting angle for total internal reflection is βc ≈ 41.8°. For a normal beam incidence (α = 0°), the angle of incidence at the prism surface is β = 45°, which satisfies the condition for total internal reflection, but a tilt of the beam α by just a few degrees in negative direction causes the reflection on the entrance prism to be no longer perfect. Alternatively, the angle of incidence to the surface of the entrance prism can be increased in positive direction, but the consequence is a decreased flux of the beam at the OUT plane due to the imperfect reflection at the exit prism. Overall, as shown in panel (h), the orthogonal incidence (α = 0°) is optimal. For example, tilting the beam by α = −3° decreases the flux at the OUT plane by almost 20%. 4.CONCLUSIONSWe demonstrate that 2-photon DLW technique can be used to print low-loss polymer waveguides on glass with optical isolation. For waveguides that were DLW printed using the IP-S resin, the losses at 550 nm are of the order of ~5 dB/cm, which means that only ~10% of light is lost in a millimeter-long waveguide. This means that for research purposes the IP-S and IP-n162 waveguides are excellent. We anticipate that propagation losses are even lower in the red and near IR part of the spectrum. However, propagation losses lower than 1dB/cm are difficult to measure using the micro-prism couplers, which means that new methods need to be designed or the existing method has to be refined. Nevertheless, the DLW printing of more complex polymer photonic circuits seems to be a promising direction. ACKNOWLEDGEMENTSThis result is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant agreement No. 884928-LOGOS). REFERENCESSoref, R. A., and Lorenzo, J. P.,
“All-Silicon Active and Passive Guided-Wave Components for λ= 1.3 and 1.6 μm,,”
IEEE J. Quant. Electr., QE-22
(6), 873
–879
(1986). https://doi.org/10.1109/JQE.1986.1073057 Google Scholar
Lorenzo, J. P. and Soref, R. A.,
“1.3 μm electro-optic silicon switch,”
Appl. Phys. Lett.,, 51
(1), 6
–8
(1987). https://doi.org/10.1063/1.98887 Google Scholar
Soref, R. A., Bennett, B. R.,
“Electrooptical Effects in Silicon,”
IEEE J. Quant. Elect.,, QE-23
(1), 123
–129
(1987). https://doi.org/10.1109/JQE.1987.1073206 Google Scholar
Weiss, B. L ., Reed, G. T., Toh, S. K., Soref, R. A. and Namavar, F.,
“Optical Waveguides in SIMOX Structures,”
IEEE Photon. Tech. Lett., 3
(1), 19
–21
(1991). https://doi.org/10.1109/68.68035 Google Scholar
Little, B. E., Foresi, J. S., Steinmeyer, G., Thoen, E. R., Chu, S. T., Haus, H. A., Ippen, E. P., Kimerling, L. C., Greene, W.,
“Ultra-Compact Si–SiO Microring Resonator Optical Channel Dropping Filters,”
IEEE Photon. Tech. Lett., 10
(4), 549
–551
(1998). https://doi.org/10.1109/68.662590 Google Scholar
Taillaert, D., Bogaerts, W., Bienstman, P., Krauss, T. F., Van Daele, P., Moerman, I., Verstuyft, S., De Mesel, K., Baets, R.,
“An Out-of-Plane Grating Coupler for Efficient Butt-Coupling Between Compact Planar Waveguides and Single-Mode Fibers,”
IEEE J. Quant. Elect.,, 38
(7), 949
–955
(2002). https://doi.org/10.1109/JQE.2002.1017613 Google Scholar
Almeida, V. R., Panepucci, R. R., Lipson, M.,
“Nanotaper for compact mode conversion,”
Opt. Lett.,, 28
(15), 1302
–1304
(2003). https://doi.org/10.1364/OL.28.001302 Google Scholar
Almeida, V. R., Barrios, C. A., Panepucci, R. R., Lipson, M.,
“All-optical control of light on a silicon chip,”
Nature, 431
(28 October 2004), 1081
–1084
(2004). https://doi.org/10.1038/nature02921 Google Scholar
Dumon, P., Bogaerts, W., Wiaux, V., Wouters, J., Beckx, S., Van Campenhout, J., Taillert, D., Luyssaert, B., Bienstman, P., Van Thourhout, D., Baets, R.,
“Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography,”
IEEE Photon. Tech. Lett., 16
(5), 1328
–1330
(2004). https://doi.org/10.1109/LPT.2004.826025 Google Scholar
Liu, A., Jones, R., Liao, L., Samara-Rubio, D., Rubin, D., Cohen, O., Nicolaescu, R., Paniccia, M.,
“A high-speed silicon optical modulator based on a metal–oxide–semiconductor capacitor,”
Nature,, 427
(12 February 2004), 615
–618
(2004). https://doi.org/10.1038/nature02310 Google Scholar
Bogaerts, W., Baets, R., Dumon, P., Wiaux, V., Taillaert, D., Luyssaert, B., Van Campenhout, J., Bienstman, P., Van Thourhout. D.,
“Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology,”
J. Lightwave Tech., 23
(1), 401
–412
(2005). https://doi.org/10.1109/JLT.2004.834471 Google Scholar
Rojo Romeo, P., Van Campenhout, J., Regreny, P., Kazmierczak, A., Seassal, C., Letartre, X. Hollinger, G., Van Thourhout, D., Baets, R., Fedeli, J.M., Di Cioccio, L.,
“Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs,”
Opt. Exp., 14
(9), 3864
–3871
(2006). https://doi.org/10.1364/OE.14.003864 Google Scholar
Chang, Hsu-Hao, Fang, A. W., Sysak, M. N., Park, H., Jones, R., Cohen, O., Raday, O., Paniccia, M. J., and Bowers, J. E.,
“1310 nm silicon evanescent laser,”
Opt. Exp., 15
(18), 11466
–1147
(2007). https://doi.org/10.1364/OE.15.011466 Google Scholar
Lipson, M.,
“The revolution of silicon photonics,”
Nature Materials,, 21
(September 2022), 974
–975
(2022). https://doi.org/10.1038/s41563-022-01363-6 Google Scholar
Humar, M., Ravnik, m. Pajk, S., and Muševič, I.,
“Electrically tunable liquid crystal optical microresonators,,”
Nat. Photonics, 3 595
–600
(2009). https://doi.org/10.1038/nphoton.2009.170 Google Scholar
Humar, M. and Muševič, I.,
“Surfactant sensing based on whispering-gallery-mode lasing in liquid-crystal microdroplets,”
Optics Express, 19 19836
–19844
(2011). https://doi.org/10.1364/OE.19.019836 Google Scholar
Humar, M., and Muševič, I.,
“3D microlasers from self-assembled cholesteric liquid-crystal microdroplets,,”
Opt. Express, 18 26995
–27003
(2010). https://doi.org/10.1364/OE.18.026995 Google Scholar
Peddireddy, K., Jampani, V. S. R., Thutupalli, S., Herminghaus, S., Bahr, Ch. and Muševič, I.,
“Lasing and waveguiding in smectic A liquid crystal optical fibers,,”
Optics Express, 21 30233
–30242
(2013). https://doi.org/10.1364/OE.21.030233 Google Scholar
Musevic, I.,
“Nematic colloids, topology and photonics,”
Phil. Trans. Royal Soc. A, 371
(20120266),
(2013). https://doi.org/10.1098/rsta.2012.0266 Google Scholar
Musevic, I., Skarabot, M., Humar, M.,
“Direct and inverted nematic dispersions for soft matter photonics,”
J. Phys. Cond. Matter, 23
(28), 284112-1
–284112-7
(2011). https://doi.org/10.1088/0953-8984/23/28/284112 Google Scholar
Coles, H. and Morris, S.,
“Liquid-crystal lasers,”
Nature Photonics, 4 676
–685
(2010). https://doi.org/10.1038/nphoton.2010.184 Google Scholar
Cipparrone, G., Mazzulla, A., Pane, A., Hernandez, R. J., Bartolino, R.,
“2011 Chiral self-assembled solid microspheres: A novel multifunctional microphotonic device,”
Adv. Mat., 23 5773
–5778 https://doi.org/10.1002/adma.v23.48 Google Scholar
Nocentini, S., Riboli, F., Burresi, M., Martella, D., Parmeggiani, C., and Wiersma, D. S.,
“Three-Dimensional Photonic Circuits in Rigid and Soft Polymers Tunable by Light,”
ACS Photonics,, 5 3222
–3230
(2018). https://doi.org/10.1021/acsphotonics.8b00461 Google Scholar
Lee, Chee Heng, Yoshida, H., Miura, Y., Fujii, A., and Ozaki, M.,
“Local liquid crystal alignment on patterned micrograting structures photofabricated by two photon excitation direct laser writing,”
Appl. Phys. Lett., 93 173509
(2008). https://doi.org/10.1063/1.2952765 Google Scholar
Zhang, B., Plidschun, M., Schmidt, M. A., Kitzerow, H.-S.,
“Anchoring and electro-optic switching of liquid crystals on nano-structured surfaces fabricated by two-photon based nano-printing,”
Opt. Mat. Express,, 13
(12), 3467
–3480
(2023). https://doi.org/10.1364/OME.503100 Google Scholar
Jagodič, U., Vellaichammy, M., Škarabot, M., Muševič, I.,
“Surface alignment of nematic liquid crystals by direct laser writing of photopolymer alignment layers,”
Liq. Cryst.,
(2023). https://doi.org/10.1080/02678292.2023.2242297 Google Scholar
Tokuoka, K., Yoshida, H., Miyake, Y., Lee, C. H., Miura, Y., Suzuki, S., Fujii, A., Shimizu, Y., and Ozaki, M.,
“Planar Alignment of Columnar Liquid Crystals in Microgroove Structures,”
Mol. Cryst. Liq. Cryst., 510 1260
–1267
(2009). https://doi.org/10.1080/15421400903060185 Google Scholar
Guo, Y., Shahsavan, H., Davidson,Z. S., and Sitti, M.,
“Precise Control of Lyotropic Chromonic Liquid Crystal Alignment through Surface Topography,”
ACS Appl. Mat. Interf, 11 36110
–36117
(2019). https://doi.org/10.1021/acsami.9b12943 Google Scholar
He, Z., Tan, G., Chanda, D., Wu, S.-T.,
“Novel liquid crystal photonic devices enabled by two-photon polymerization,”
Opt. Exp., 27
(8), 11472
–11491
(2019). https://doi.org/10.1364/OE.27.011472 Google Scholar
Hasan, M., Blair, S.,
“Maximizing transmittance in two-photon 3D printed materials for micro-optics in the visible,”
Opt. Mat. Express, 12
(3), 895
–906
(2022). https://doi.org/10.1364/OME.448819 Google Scholar
Taflove, A., Oskooi, A., and Johnson, S. G., Advances in FDTD computational electrodynamics: photonicsand nanotechnology, Artech house(2013). Google Scholar
Oskooi, A. F., Roundy, D., Ibanescu, M., Bermel, P., Joannopoulos, J. D., and Johnson, S. G.,
“Meep: A flexible free-software package for electromagnetic simulations by the fdtd method,,”
Computer Physics Communications, 181
(3), 687
–702
(2010). https://doi.org/10.1016/j.cpc.2009.11.008 Google Scholar
|