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Polarization-independent asymmetric light transmission in all-dielectric photonic structures
Optical Materials 73 (2017) 484e488
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Polarization-independent asymmetric light transmission in alldielectric photonic structures Lukasz Zinkiewicz a, *, Michal Nawrot a, Jakub Haberko b, Piotr Wasylczyk a a b
Photonic Nanostructure Facility, Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warszawa, Poland AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Al. Mickiewicza 30, 30-059, Krakow, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 March 2017 Received in revised form 8 August 2017 Accepted 29 August 2017
We design, optimize and fabricate an all-dielectric photonic structure, having a significant, polarizationindependent asymmetry in light transmission for opposite incident wave directions. The device, consisting of a dielectric Bragg mirror topped with a regular grid of micrometer-sized pillars, acting as a diffraction grating, is potentially scalable into industrial production. The light propagation simulation results are confirmed by direct measurement of the difference in light transmission, reaching 0.55 near 780 nm, and exceeding 0.2 over a spectral range spanning from 750 to 820 nm. © 2017 Elsevier B.V. All rights reserved.
Keywords: Photonic crystal Diffraction grating Asymmetric transmission
1. Introduction One of the holy grails of experimental photonics is to create a unidirectional light transmission structure which exhibits a significant difference in transmission for light propagating with opposite wave vectors. While the only practical realization of this concept, commonly used in laboratories, is a device based on Faraday effect in rare earth metal doped crystals, many other ideas have been tested too. These can be categorized into structures containing sub-wavelength metal components in the form of nonsymmetric features [1e5], metallic diffraction gratings [6e10] or holes [11e14]. Additionally, a class of devices based on symmetry breaking photonics crystals has been presented [12,15e18]. These includes fibers [19] and state of the art devices containing silicon on-chip optical diode [20,21], as well as a complex structure, combining layers of different indices of refraction with a series of diffraction gratings with varying filling fractions, where a narrow region of asymmetric transmission was predicted in the UV region [22]. The common drawback of most unidirectional transmission devices is their polarization-dependent performance usually a significant asymmetry in transmission is achieved for one linear (or circular) polarization only. In our approach described herewith we
* Corresponding author. E-mail address: [email protected] (L. Zinkiewicz). http://dx.doi.org/10.1016/j.optmat.2017.08.046 0925-3467/© 2017 Elsevier B.V. All rights reserved.
overcome this disadvantage in a few micron thick, all-dielectric structure that exhibits polarization-independent asymmetry in transmission of near-infrared light (peaked at 780 nm). 2. The structure design Working principle of our structure is based on the concept presented in Ref. [23], but with higher symmetry guaranteeing polarization-independent transmission, unlike in the previous demonstrations that had different transmission asymmetry for different input polarizations. The device consists of a dielectric stack (S) with wavelength and angle of incidence dependent reflectance, topped with a rectangular grid of uniformly and equally spaced pillars (P), acting as a diffraction element (see Fig. 1). The dielectric stack is a Bragg mirror, designed to have high transmittance at 780 nm and high reflectance for longer wavelengths (850e1050 nm) (see Fig. 2 (a)). This choice of transmission characteristics was associated with the operating wavelength of our 3D photolithography setup, used in the next step of the device fabrication process - the dielectric stack has to be transparent at 780 nm, to avoid unwanted reflections of the lithographic laser beam. Additionally, the resolution limitations of the technology (features down to 400 nm in lateral size can be fabricated) restricted the asymmetric transmission wavelength range to the near infrared band of the spectrum. Materials used in the fabrication process were SiO2 and Nb2O5 for the dielectric stack low and high refractive index layers
L. Zinkiewicz et al. / Optical Materials 73 (2017) 484e488
Fig. 1. Schematic model of the all-dielectric structure (drawn to scale), consisting of a Bragg mirror topped with a square grid of the 3D-printed pillars. The glass substrate is not shown and the rendered colors were chosen for clarity: light blue - silica (SiO2), dark blue - niobia (Nb2O5), purple - acrylic resin (IP-L). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
respectively, and a commercial polymer UV curable resin (IP-L) for the pillars. Their optical properties and the structure dimensions are described in detail in section 3. When light at 780 nm is incident on the structure at zero angle of incidence from the stack side (S0P), a high fraction is transmitted through the Bragg mirror and even though it is diffracted afterwards by the pillar grating, the total (angle integrated) transmission is high. On the other hand, light incident from the pillars side (P0S) is first diffracted and then its substantial part propagates through the stack at an angle for which the transmission drops significantly this results in low transmittance. To reach the highest asymmetry possible, the structure parameters need to be adjusted to diffract a large fraction of light. At the same time a high absolute transmission and broadband asymmetry region is needed and optimizing these two simultaneously poses a significant challenge. FDTD simulations of electromagnetic field propagation in our structure were performed, using an open access MEEP environment, ver. 1.2.1 [24]. A 3D simulation box with the resolution of 50 px/micron was used, which corresponds to approximately 16 pixels per the shortest wavelength in the highest refractive index material (n ¼ 2.176). We have checked that increasing the resolution by up to a factor of 2 did not considerably change our simulation results. We have also verified that the simulation time was long enough for the results to converge. Periodic boundary conditions were used in the
485
directions perpendicular to the incident beam and PML absorbing layers at the top and bottom. The structure was illuminated with short plane wave pulses, corresponding to vacuum wavelengths between 0.67 mm and 1.43 mm. The pillar geometry was adjusted to follow the ellipsoidal shape of the photolithographic voxel, as measured for our fabrication setup. Specifically, an ellipsoid of revolution can be inscribed in the curvature of the pillar edge, as seen in the cross-section through the center of the pillar in Fig. 3 (a), with the axes rx ¼ 200 nm and ry ¼ 500 nm, corresponding to the size of the lithographic voxel. The refractive index of the pillar dielectric material was set to n ¼ 1.48. In separate simulations we have verified that the glass substrate did not considerably alter the simulation results other than adding Fabry-Perot fringes (which would not be measurable in the experiment due to relatively broad spectrum of our laser), so it can be neglected in simulations. For the initial grating parameters: height h ¼ 960 nm, diameter D ¼ 571 nm and the spacing between consecutive pillars x ¼ 951 nm, Fig. 3 (b) shows calculated, angle-integrated light transmission in two opposite directions: from the pillars side (P0S) and from the stack side (S0P), as well as their difference the asymmetry in transmission - peaked at 786 nm and exceeding 0.6. To maximize the result, we have explored the pillar geometry parameter space (height and diameter), looking for the maximum values of the asymmetry at 780 nm - see Fig. 3 (c). This map also gives an estimate of the structure high tolerance to fabrication errors - an important parameter for potential applications, e.g. the deviation in the pillar height of up to 20% (1:0±0:2 mm) does not decrease the transmission difference significantly. Further, we varied the distance between pillars, creating similar maps and plotting the maximum asymmetry value for each pillar spacing (Fig. 3 (d)). An optimum value of the grating pitch (x) of 1:07±0:05 mm was thus found. 3. Fabrication and characterization The dielectric Bragg mirror had nine quarter wave layers, (5 layers, n(840 nm) ¼ 2.176, alternating Nb2O5 thickness ¼ 109.3 nm) and SiO2 (4 layers, n(840 nm) ¼ 1.438, thickness ¼ 165.3 nm) (Laseroptik GmbH), manufactured with the electron beam evaporation (Balzers BAK box coater). Niobia
Fig. 2. Measured (points) and calculated (lines) transmission profiles of the dielectric stack. (a) High transmission of the Bragg mirror was designed and measured at around 785 nm, while the photonic bandgap spans the range between 850 and 1000 nm, both for normal light incidence. High and low transmittance wavelengths of 785 and 950 nm respectively (dashed vertical lines) were chosen to demonstrate angle-dependent characteristics of the mirror, which are the key to the structure working principle (see details in text). (b) Measured (symbols) and calculated (lines) mirror angle-dependent transmission proles show decreasing transmittance at 785 nm for two polarizations: p (black) and s (blue) with increasing angle of incidence. On the contrary, transmittance rises (or remains nearly constant) at 950 nm, again for both polarizations (p - olive, s - green). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. FDTD light propagation numerical simulations leading to the optimum structure dimensions. (a) The simulation box includes the Bragg mirror and one of the pillars with rounded edges to account for the ellipsoidal lithographic voxel. Left: side view, right: top view. The structure dimensions are described in the text. (b) Calculated total (angleintegrated), polarization-independent light transmission curves from the stack (S0P, black) and from the pillar side (P0S, red), and their difference (blue), reveal maximum asymmetry (exceeding 0.6) at 782 nm (dashed line). (c) Calculated asymmetry in transmission at around 780 nm optimized for varying pillar height (h) and diameter (D). Region of the highest asymmetry (surrounded by the white dashed line) gives an estimate of the fabrication errors tolerance. (d) Calculated maximum asymmetry, retrieved from parameter maps similar to this in (c), for different pillar spacing (x) (black squares) - an optimum pillar spacing of x ¼ ð1:07±0:05Þ mm (dashed line) is visible. The line was fitted to guide the eye only. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
(Nb2O5) was used in the mirror stack due to its high refractive index (n(785 nm) ¼ 2.1798, n(950 nm) ¼ 2.1603), low dispersion (dn ð785 dl dn ð950 dl
mm1 , nmÞ ¼ 0:0863 mm1 ) and negligible absorption in the nmÞ ¼ 0:1595
near infrared spectral band between 700 and 900 nm (the Sellmeier coefficients are given in Table 1). Silica (SiO2) is the preferred material of choice for the low refractive index layers in the spectral band used in our experiments (n(785 nm) ¼ 1.4536, n(950
¼
nm)
1.4511,
mm1
dn ð950 dl
dn ð785 dl
nmÞ ¼ 0:0179
mm1 ,
nmÞ ¼ 0:0133 (see Table 1)). Final grating parameters, resulting from numerical calculations, were chosen to be: the diffraction grating pitch x ¼ 1020 nm, the pillar diameter D ¼ 550 nm and height h ¼ 850 nm. The grating pillars were then fabricated with the 3D photolithography, using commercially available setup (Photonic
Professional, Nanoscribe GmbH) [28]. A femtosecond fiber laser beam pulse train (100 fs, 100 MHz, 780 nm central wavelength) is focused (100, 1.4 NA Plan-Apo objective, Zeiss GmbH) within a droplet of photosensitive resin (IP-L, Nanoscribe GmbH; n(785 nm) ¼ 1.5072, n(950 nm) ¼ 1.5048, dn ð785 nmÞ ¼ 0:0199 mm1 , dn ð950 nmÞ ¼ 0:0104 mm1 dl dl (see Table 1)), placed on the substrate from the Bragg mirror side. A piezo XYZ positioning stage, combined with an acousto-optic modulator controlling the laser power, allows exposure and thus two-photon absorption triggered polymerization of an arbitrarily chosen shape on the mirror surface. The commercial IP-L acrylic resin was chosen, as it features high printing resolution, low
Table 1 Sellmeier coefficients for niobia (Nb2O5) [25], silica (SiO2) [26] and IP-L resin [27], used for calculating refractive index dispersion (see details in the text). Equation in a 2 2 2 form of n2 1 ¼ b21 l þ b22 l þ b23 l was used for silica and niobia, and n ¼ A þ B2 þ l c1 l c2 l c3 l C for IP-L. 4 l
Nb2O5 SiO2
IP-L
IP-L
b1
c1 [mm2]
b2
c2 [mm2]
b3
c3 [mm2]
1.019290 0.696166
0.061508 0.004679
2.479507 0.407943
0.032825 0.013512
0 0.897479
0 97.934003
A
B [mm2]
C [mm4]
1.5003
3:6771,103
3:5288,104
A
B [mm ]
C [mm4]
1.5003
3:6771,103
3:5288,104
2
Fig. 4. The fabricated structure dimensions were verified with scanning electron microscope (SEM) and atomic force microscope (AFM) measurements. (a) A top view SEM image of the fabricated 100 100 mm structure, providing the grating pitch and the pillar diameter measurements. The scale bar is 10 mm. (b) An AFM measured profile of the structure along the white scale bar line drawn in (a), providing the measurement of the column height with respect to the glass substrate surface. The profile is a result of the convolution of the column and the AFM tip shapes.
L. Zinkiewicz et al. / Optical Materials 73 (2017) 484e488
487
Fig. 5. (a) Measured angle-integrated light transmission through the fabricated structure in opposite directions (P0S meaning from grating pillars to stack and vice versa). Results are shown for five linear polarizations, rotated by 0, 15, 30, 45 and 90 (from dark to light blue/red respectively) to one of the structure edges. (b) Experimental results (green, various shades correspond to different polarizations as in (a)), showing the polarization-independent asymmetry exceeding 0.2 in the range of 750e820 nm, agree well with simulation (dashed line), smoothed in 10 nm bins to account for the broad laser spectrum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
shrinkage and has been extensively tested and optimized for multiphoton polymerization [29]. Final dimensions of the structure were verified by AFM and SEM imaging (see Fig. 4. (a), (b)). The structure transmission was measured in the spectral range between 690 and 880 nm, using linearly polarized, tunable femtosecond laser (MaiTai, SpectraPhysics) focused on the sample to the spot smaller than the overall structure size. Typically, five main diffraction orders in a range of ±70 degrees were observed: the zero order and four side orders, originating from the diffraction structure. The intensity of each order was recorded (Nova II power meter, Ophir) for zero angle of incidence from two opposite sides and for different positions of the sample axes with respect to the light polarization direction.
4. Results and discussion The measured integrated light transmission (sum of all diffraction orders) through the structure is shown in Fig. 5 (a) for light incident from opposite directions, for five different linear polarizations, oriented at 0, 15, 30, 45 and 90 with respect to structure edge (white line in Fig. 4. (a)). The measured difference in transmittance coefficients exceeds 0.5 around 780 nm and 0.2 in the range 750e820 nm, whilst the absolute transmission is above 0.5 in this region. The experimental data is compared with the simulation results in Fig. 5 (b), with the latter averaged in 10 nm-wide intervals to account for our pulsed laser spectrum width. In conclusion, we have designed, optimized and manufactured all-dielectric photonic structure with asymmetric light transmission for the opposite incident wave vectors. This was demonstrated in the near-infrared spectral range and is independent from the light polarization. By using e.g. hot embossing the structure can be scaled up to the industrial fabrication and may find applications in integrated photonic devices.
Funding This work has been generously supported by the National Science Centre (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.
Acknowledgements We acknowledge prof. Tomasz Szoplik for drawing our attention to the subject of asymmetric transmission. J.H. acknowledges the use of TeraACMIN computer cluster at the Academic Centre for Materials and Nanotechnology, AGH-UST, Krakow, Poland. References [1] M. Kang, J. Chen, H. Cui, Y. Li, H. Wang, Asymmetric transmission for linearly polarized electromagnetic radiation, Opt. Express 19 (2011) 8347e8356, http://dx.doi.org/10.1364/OE.19.008347. [2] A. Schwanecke, V. Fedotov, V. Khardikov, S. Prosvirnin, Y. Chen, N. Zheludev, Nanostructured metal film with asymmetric optical transmission, Nano Lett. 8 (2008) 2940e2943, http://dx.doi.org/10.1021/nl801794d. [3] E. Plum, V. Fedotov, N. Zheludev, Asymmetric transmission: a generic property of two-dimensional periodic patterns, J. Opt. 13 (2011) 024006, http:// dx.doi.org/10.1088/2040-8978/13/2/024006. [4] M. Mutlu, A. Akosman, A. Serebryannikov, E. Ozbay, Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling, Phys. Rev. Lett. 108 (2012) 213905, http:// dx.doi.org/10.1103/PhysRevLett.108.213905. [5] C. Menzel, C. Helgert, C. Rockstuhl, E. Kley, A. Tnnermann, T. Pertsch, F. Lederer, Asymmetric transmission of linearly polarized light at optical metamaterials, Phys. Rev. Lett. 104 (2010) 253902, http://dx.doi.org/10.1103/ PhysRevLett.104.253902. [6] M. Stolarek, D. Yavorskiy, R. Kotynski, C. Rodriguez, J. Lusakowski, T. Szoplik, Asymmetric transmission of terahertz radiation through a double grating, Opt. Lett. 38 (2013) 839e841, http://dx.doi.org/10.1364/OL.38.000839. [7] S. Cakmakyapan, H. Caglayan, A. Serebryannokov, E. Ozbay, One-way transmission through the subwavelength slit in nonsymmetric metallic gratings, Opt. Lett. 35 (2010) 2597e2599, http://dx.doi.org/10.1364/OL.35.002597. [8] J. Xu, C. Cheng, M. Kang, J. Chen, Z. Zheng, Y. Fan, H. Wang, Unidirectional optical transmission in dual-metal gratings in the absence of anisotropic and nonlinear materials, Opt. Lett. 36 (2011) 1905e1907, http://dx.doi.org/ 10.1364/OL.36.001905. [9] Z. Zhu, K. Liu, W. Xu, Z. Luo, C. Guo, B. Yang, T. Ma, X. Yuan, W. Ye, One-way transmission of linearly polarized light in plasmonic subwavelength metallic grating cascaded with dielectric grating, Opt. Lett. 37 (2012) 400810, http:// dx.doi.org/10.1364/OL.37.004008. [10] D. Yavorskiy, M. Stolarek, J. Lusakowski, R. Kotynski, Asymmetric transmission of radially polarized thz radiation through a double circular grating, Opt. Express 22 (2014) 30547e30552, http://dx.doi.org/10.1364/OE.22.030547. [11] Z. Li, M. Mutlu, E. Ozbay, Highly asymmetric transmission of linearly polarized waves realized with a multilayered structure including chiral metamaterials, J. Phys. D. Appl. Phys. 47 (2014) 075107, http://dx.doi.org/10.1088/00223727/47/7/075107. [12] T. Xu, H. Lezec, Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial, Nat. Commun. 45 (2014) 4141, http:// dx.doi.org/10.1038/ncomms5141. [13] P. Rodrguez-Ulibarri, M. Beruete, M. Navarro-Ca, A. Serebryannikov, Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures, Phys. Rev. B 88 (2013) 165137, http://
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dx.doi.org/10.1103/PhysRevB.88.165137. [14] V. Klimov, I. Treshin, A. Shalin, P. Melentiev, A. Kuzin, A. Afanasiev, V. Balykin, Optical tamm state and giant asymmetry of light transmission through an array of nanoholes, Phys. Rev. A 92 (2015) 063842, http://dx.doi.org/10.1103/ PhysRevA.92.063842. [15] A. Serebryannikov, One-way diffraction effects in photonic crystal gratings made of isotropic materials, Phys. Rev. B 80 (2009) 155117, http://dx.doi.org/ 10.1103/PhysRevB.80.155117. [16] A. Cakmak, E. Colak, A. Serebryannikov, E. Ozbay, Unidirectional transmission in photonic-crystal gratings at beam-type illumination, Opt. Express 18 (2010) 22283e22298, http://dx.doi.org/10.1364/OE.18.022283. [17] A. Serebryannikov, A. Cakmak, E. Ozbay, Multichannel optical diode with unidirectional diffraction relevant total transmission, Opt. Express 20 (2012) 14980e14990, http://dx.doi.org/10.1364/OE.20.014980. [18] E. Colak, A. Serebryannikov, P. Usik, E. Ozbay, Diffraction inspired unidirectional and bidirectional beam splitting in defect-containing photonic structures without interface corrugations, J. Appl. Phys. 119 (2016) 193108, http:// dx.doi.org/10.1063/1.4949509. [19] B. Singh, S. Rawal, R. Sinha, Chirped photonic crystal with different symmetries for asymmetric light propagation, Appl. Phys. A 122 (2016) 1e7, http:// dx.doi.org/10.1007/s00339-016-0134-4. [20] C. Wang, X. Zhong, Z. Li, Linear and passive silicon optical isolator, Sci. Rep. 2 (2012) 674, http://dx.doi.org/10.1038/srep00674. [21] A. Cicek, M. Yucel, O. Kaya, B. Ulug, Refraction-based photonic crystal diode, Opt. Lett. 37 (2012) 2937e2939, http://dx.doi.org/10.1364/OL.37.002937. [22] A. Mandatori, M. Bertolotti, C. Sibilia, Asymmetric transmission of some two-
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Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Polarization-independent asymmetric light transmission in alldielectric photonic structures Lukasz Zinkiewicz a, *, Michal Nawrot a, Jakub Haberko b, Piotr Wasylczyk a a b
Photonic Nanostructure Facility, Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warszawa, Poland AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Al. Mickiewicza 30, 30-059, Krakow, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 March 2017 Received in revised form 8 August 2017 Accepted 29 August 2017
We design, optimize and fabricate an all-dielectric photonic structure, having a significant, polarizationindependent asymmetry in light transmission for opposite incident wave directions. The device, consisting of a dielectric Bragg mirror topped with a regular grid of micrometer-sized pillars, acting as a diffraction grating, is potentially scalable into industrial production. The light propagation simulation results are confirmed by direct measurement of the difference in light transmission, reaching 0.55 near 780 nm, and exceeding 0.2 over a spectral range spanning from 750 to 820 nm. © 2017 Elsevier B.V. All rights reserved.
Keywords: Photonic crystal Diffraction grating Asymmetric transmission
1. Introduction One of the holy grails of experimental photonics is to create a unidirectional light transmission structure which exhibits a significant difference in transmission for light propagating with opposite wave vectors. While the only practical realization of this concept, commonly used in laboratories, is a device based on Faraday effect in rare earth metal doped crystals, many other ideas have been tested too. These can be categorized into structures containing sub-wavelength metal components in the form of nonsymmetric features [1e5], metallic diffraction gratings [6e10] or holes [11e14]. Additionally, a class of devices based on symmetry breaking photonics crystals has been presented [12,15e18]. These includes fibers [19] and state of the art devices containing silicon on-chip optical diode [20,21], as well as a complex structure, combining layers of different indices of refraction with a series of diffraction gratings with varying filling fractions, where a narrow region of asymmetric transmission was predicted in the UV region [22]. The common drawback of most unidirectional transmission devices is their polarization-dependent performance usually a significant asymmetry in transmission is achieved for one linear (or circular) polarization only. In our approach described herewith we
* Corresponding author. E-mail address: [email protected] (L. Zinkiewicz). http://dx.doi.org/10.1016/j.optmat.2017.08.046 0925-3467/© 2017 Elsevier B.V. All rights reserved.
overcome this disadvantage in a few micron thick, all-dielectric structure that exhibits polarization-independent asymmetry in transmission of near-infrared light (peaked at 780 nm). 2. The structure design Working principle of our structure is based on the concept presented in Ref. [23], but with higher symmetry guaranteeing polarization-independent transmission, unlike in the previous demonstrations that had different transmission asymmetry for different input polarizations. The device consists of a dielectric stack (S) with wavelength and angle of incidence dependent reflectance, topped with a rectangular grid of uniformly and equally spaced pillars (P), acting as a diffraction element (see Fig. 1). The dielectric stack is a Bragg mirror, designed to have high transmittance at 780 nm and high reflectance for longer wavelengths (850e1050 nm) (see Fig. 2 (a)). This choice of transmission characteristics was associated with the operating wavelength of our 3D photolithography setup, used in the next step of the device fabrication process - the dielectric stack has to be transparent at 780 nm, to avoid unwanted reflections of the lithographic laser beam. Additionally, the resolution limitations of the technology (features down to 400 nm in lateral size can be fabricated) restricted the asymmetric transmission wavelength range to the near infrared band of the spectrum. Materials used in the fabrication process were SiO2 and Nb2O5 for the dielectric stack low and high refractive index layers
L. Zinkiewicz et al. / Optical Materials 73 (2017) 484e488
Fig. 1. Schematic model of the all-dielectric structure (drawn to scale), consisting of a Bragg mirror topped with a square grid of the 3D-printed pillars. The glass substrate is not shown and the rendered colors were chosen for clarity: light blue - silica (SiO2), dark blue - niobia (Nb2O5), purple - acrylic resin (IP-L). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
respectively, and a commercial polymer UV curable resin (IP-L) for the pillars. Their optical properties and the structure dimensions are described in detail in section 3. When light at 780 nm is incident on the structure at zero angle of incidence from the stack side (S0P), a high fraction is transmitted through the Bragg mirror and even though it is diffracted afterwards by the pillar grating, the total (angle integrated) transmission is high. On the other hand, light incident from the pillars side (P0S) is first diffracted and then its substantial part propagates through the stack at an angle for which the transmission drops significantly this results in low transmittance. To reach the highest asymmetry possible, the structure parameters need to be adjusted to diffract a large fraction of light. At the same time a high absolute transmission and broadband asymmetry region is needed and optimizing these two simultaneously poses a significant challenge. FDTD simulations of electromagnetic field propagation in our structure were performed, using an open access MEEP environment, ver. 1.2.1 [24]. A 3D simulation box with the resolution of 50 px/micron was used, which corresponds to approximately 16 pixels per the shortest wavelength in the highest refractive index material (n ¼ 2.176). We have checked that increasing the resolution by up to a factor of 2 did not considerably change our simulation results. We have also verified that the simulation time was long enough for the results to converge. Periodic boundary conditions were used in the
485
directions perpendicular to the incident beam and PML absorbing layers at the top and bottom. The structure was illuminated with short plane wave pulses, corresponding to vacuum wavelengths between 0.67 mm and 1.43 mm. The pillar geometry was adjusted to follow the ellipsoidal shape of the photolithographic voxel, as measured for our fabrication setup. Specifically, an ellipsoid of revolution can be inscribed in the curvature of the pillar edge, as seen in the cross-section through the center of the pillar in Fig. 3 (a), with the axes rx ¼ 200 nm and ry ¼ 500 nm, corresponding to the size of the lithographic voxel. The refractive index of the pillar dielectric material was set to n ¼ 1.48. In separate simulations we have verified that the glass substrate did not considerably alter the simulation results other than adding Fabry-Perot fringes (which would not be measurable in the experiment due to relatively broad spectrum of our laser), so it can be neglected in simulations. For the initial grating parameters: height h ¼ 960 nm, diameter D ¼ 571 nm and the spacing between consecutive pillars x ¼ 951 nm, Fig. 3 (b) shows calculated, angle-integrated light transmission in two opposite directions: from the pillars side (P0S) and from the stack side (S0P), as well as their difference the asymmetry in transmission - peaked at 786 nm and exceeding 0.6. To maximize the result, we have explored the pillar geometry parameter space (height and diameter), looking for the maximum values of the asymmetry at 780 nm - see Fig. 3 (c). This map also gives an estimate of the structure high tolerance to fabrication errors - an important parameter for potential applications, e.g. the deviation in the pillar height of up to 20% (1:0±0:2 mm) does not decrease the transmission difference significantly. Further, we varied the distance between pillars, creating similar maps and plotting the maximum asymmetry value for each pillar spacing (Fig. 3 (d)). An optimum value of the grating pitch (x) of 1:07±0:05 mm was thus found. 3. Fabrication and characterization The dielectric Bragg mirror had nine quarter wave layers, (5 layers, n(840 nm) ¼ 2.176, alternating Nb2O5 thickness ¼ 109.3 nm) and SiO2 (4 layers, n(840 nm) ¼ 1.438, thickness ¼ 165.3 nm) (Laseroptik GmbH), manufactured with the electron beam evaporation (Balzers BAK box coater). Niobia
Fig. 2. Measured (points) and calculated (lines) transmission profiles of the dielectric stack. (a) High transmission of the Bragg mirror was designed and measured at around 785 nm, while the photonic bandgap spans the range between 850 and 1000 nm, both for normal light incidence. High and low transmittance wavelengths of 785 and 950 nm respectively (dashed vertical lines) were chosen to demonstrate angle-dependent characteristics of the mirror, which are the key to the structure working principle (see details in text). (b) Measured (symbols) and calculated (lines) mirror angle-dependent transmission proles show decreasing transmittance at 785 nm for two polarizations: p (black) and s (blue) with increasing angle of incidence. On the contrary, transmittance rises (or remains nearly constant) at 950 nm, again for both polarizations (p - olive, s - green). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. FDTD light propagation numerical simulations leading to the optimum structure dimensions. (a) The simulation box includes the Bragg mirror and one of the pillars with rounded edges to account for the ellipsoidal lithographic voxel. Left: side view, right: top view. The structure dimensions are described in the text. (b) Calculated total (angleintegrated), polarization-independent light transmission curves from the stack (S0P, black) and from the pillar side (P0S, red), and their difference (blue), reveal maximum asymmetry (exceeding 0.6) at 782 nm (dashed line). (c) Calculated asymmetry in transmission at around 780 nm optimized for varying pillar height (h) and diameter (D). Region of the highest asymmetry (surrounded by the white dashed line) gives an estimate of the fabrication errors tolerance. (d) Calculated maximum asymmetry, retrieved from parameter maps similar to this in (c), for different pillar spacing (x) (black squares) - an optimum pillar spacing of x ¼ ð1:07±0:05Þ mm (dashed line) is visible. The line was fitted to guide the eye only. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
(Nb2O5) was used in the mirror stack due to its high refractive index (n(785 nm) ¼ 2.1798, n(950 nm) ¼ 2.1603), low dispersion (dn ð785 dl dn ð950 dl
mm1 , nmÞ ¼ 0:0863 mm1 ) and negligible absorption in the nmÞ ¼ 0:1595
near infrared spectral band between 700 and 900 nm (the Sellmeier coefficients are given in Table 1). Silica (SiO2) is the preferred material of choice for the low refractive index layers in the spectral band used in our experiments (n(785 nm) ¼ 1.4536, n(950
¼
nm)
1.4511,
mm1
dn ð950 dl
dn ð785 dl
nmÞ ¼ 0:0179
mm1 ,
nmÞ ¼ 0:0133 (see Table 1)). Final grating parameters, resulting from numerical calculations, were chosen to be: the diffraction grating pitch x ¼ 1020 nm, the pillar diameter D ¼ 550 nm and height h ¼ 850 nm. The grating pillars were then fabricated with the 3D photolithography, using commercially available setup (Photonic
Professional, Nanoscribe GmbH) [28]. A femtosecond fiber laser beam pulse train (100 fs, 100 MHz, 780 nm central wavelength) is focused (100, 1.4 NA Plan-Apo objective, Zeiss GmbH) within a droplet of photosensitive resin (IP-L, Nanoscribe GmbH; n(785 nm) ¼ 1.5072, n(950 nm) ¼ 1.5048, dn ð785 nmÞ ¼ 0:0199 mm1 , dn ð950 nmÞ ¼ 0:0104 mm1 dl dl (see Table 1)), placed on the substrate from the Bragg mirror side. A piezo XYZ positioning stage, combined with an acousto-optic modulator controlling the laser power, allows exposure and thus two-photon absorption triggered polymerization of an arbitrarily chosen shape on the mirror surface. The commercial IP-L acrylic resin was chosen, as it features high printing resolution, low
Table 1 Sellmeier coefficients for niobia (Nb2O5) [25], silica (SiO2) [26] and IP-L resin [27], used for calculating refractive index dispersion (see details in the text). Equation in a 2 2 2 form of n2 1 ¼ b21 l þ b22 l þ b23 l was used for silica and niobia, and n ¼ A þ B2 þ l c1 l c2 l c3 l C for IP-L. 4 l
Nb2O5 SiO2
IP-L
IP-L
b1
c1 [mm2]
b2
c2 [mm2]
b3
c3 [mm2]
1.019290 0.696166
0.061508 0.004679
2.479507 0.407943
0.032825 0.013512
0 0.897479
0 97.934003
A
B [mm2]
C [mm4]
1.5003
3:6771,103
3:5288,104
A
B [mm ]
C [mm4]
1.5003
3:6771,103
3:5288,104
2
Fig. 4. The fabricated structure dimensions were verified with scanning electron microscope (SEM) and atomic force microscope (AFM) measurements. (a) A top view SEM image of the fabricated 100 100 mm structure, providing the grating pitch and the pillar diameter measurements. The scale bar is 10 mm. (b) An AFM measured profile of the structure along the white scale bar line drawn in (a), providing the measurement of the column height with respect to the glass substrate surface. The profile is a result of the convolution of the column and the AFM tip shapes.
L. Zinkiewicz et al. / Optical Materials 73 (2017) 484e488
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Fig. 5. (a) Measured angle-integrated light transmission through the fabricated structure in opposite directions (P0S meaning from grating pillars to stack and vice versa). Results are shown for five linear polarizations, rotated by 0, 15, 30, 45 and 90 (from dark to light blue/red respectively) to one of the structure edges. (b) Experimental results (green, various shades correspond to different polarizations as in (a)), showing the polarization-independent asymmetry exceeding 0.2 in the range of 750e820 nm, agree well with simulation (dashed line), smoothed in 10 nm bins to account for the broad laser spectrum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
shrinkage and has been extensively tested and optimized for multiphoton polymerization [29]. Final dimensions of the structure were verified by AFM and SEM imaging (see Fig. 4. (a), (b)). The structure transmission was measured in the spectral range between 690 and 880 nm, using linearly polarized, tunable femtosecond laser (MaiTai, SpectraPhysics) focused on the sample to the spot smaller than the overall structure size. Typically, five main diffraction orders in a range of ±70 degrees were observed: the zero order and four side orders, originating from the diffraction structure. The intensity of each order was recorded (Nova II power meter, Ophir) for zero angle of incidence from two opposite sides and for different positions of the sample axes with respect to the light polarization direction.
4. Results and discussion The measured integrated light transmission (sum of all diffraction orders) through the structure is shown in Fig. 5 (a) for light incident from opposite directions, for five different linear polarizations, oriented at 0, 15, 30, 45 and 90 with respect to structure edge (white line in Fig. 4. (a)). The measured difference in transmittance coefficients exceeds 0.5 around 780 nm and 0.2 in the range 750e820 nm, whilst the absolute transmission is above 0.5 in this region. The experimental data is compared with the simulation results in Fig. 5 (b), with the latter averaged in 10 nm-wide intervals to account for our pulsed laser spectrum width. In conclusion, we have designed, optimized and manufactured all-dielectric photonic structure with asymmetric light transmission for the opposite incident wave vectors. This was demonstrated in the near-infrared spectral range and is independent from the light polarization. By using e.g. hot embossing the structure can be scaled up to the industrial fabrication and may find applications in integrated photonic devices.
Funding This work has been generously supported by the National Science Centre (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.
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