1. Introduction

Spectacular progress in micro- and nanofabrication technologies made a number of optical structures, once existing only as theoretical concepts (or fairy tale accessories), come into existence. These range from photonic crystals with a full transmission bandgap [1,2] through optical fibers with manageable dispersion and/or transmission [3–5] to the recent optical (invisibility) cloaks [6–8].

One of the long-standing goals of experimental photonics is to demonstrate unidirectional light transmission, i.e. fabricating a structure that exhibits a significant asymmetry for light waves propagating with opposite wavevectors. While the only practical realization of a one-way light transmission (an optical diode) is based on Faraday effect in rare earth metal doped crystals, several concepts of photonic structures with asymmetric transmission have been conceived. One broad category includes devices containing sub-wavelength metal components, either in the form of a grid of (circular) symmetry-breaking features (resonators) [9–13] or layers [14,15]. Asymmetric light transmission has also been demonstrated in structures based on metallic diffraction gratings [16–19]. Recently, a subwavelength hole array coupled to a diffraction grating has been studied in the context of unidirectional transmission arising from the incidence angle-tuned refraction [20].

Yet another approach uses dispersion properties of symmetry-breaking photonic crystals [21–24] where integrated photonic devices have been presented [25,26]. An all-dielectric multilayer structure proposed theoretically in [27] belongs to this class – for a stack of layers with different indices of refraction combined with a series of diffraction gratings with varying filling fractions, a narrow region of asymmetric transmission was predicted in the UV region.

While many authors limit their works on asymmetric transmission to theoretical studies and/or implement their concepts experimentally only in the microwave or terahertz spectral domains, in this paper we demonstrate the design, optimization, fabrication and characterization of an all-dielectric photonic structure with a significant, broadband asymmetry in transmission of the near-infrared radiation for opposite propagation directions.

Our approach, simplifying the concept of corrugated photonic crystals [21,24] towards manageable fabrication, is based on a two-layer structure made of a quarter wavelength stack (Bragg mirror) topped with a transmission phase diffraction grating consisting of a series of parallel lines. For the optimized structure geometry, the difference in transmission coefficient for opposite propagation directions as high as 0.5 was predicted and measured.

2. The structure design

Multilayer dielectric mirrors (quarter wavelength stacks) are well known for their angle-dependent performance. In particular, a stack designed as a high reflector for a certain wavelength at one incidence angle may become transparent at the same wavelength for another angle of incidence. Combining this phenomenon with a diffractive structure (grating) that directs incident light into a range of orders propagating in different directions is a basic idea behind our asymmetric transmission structure (Fig. 1(a)).

 

Fig. 1 (a) The asymmetric transmission structure (drawn to scale): nine-layer dielectric mirror is topped with a diffraction grating made of parallel lines. The glass substrate at the bottom is not shown. (b) Designed and measured transmission profile of the dielectric mirror with high reflectivity between 850 and 1050 nm. (c) Measured angle-dependent transmission of the dielectric stack only. (d) AFM measured grating line profile. While the line height is measured here with high accuracy, the line width is convolved with the AFM tip shape.

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A nine-layer dielectric Bragg mirror was designed to have high transmission at 780 nm and high reflectivity in the 850-1050 nm range (Fig. 1(b)). These wavelengths were chosen to fulfil several conditions simultaneously. First, the transmission peak at 780 nm overlaps with the femtosecond laser wavelength used for the 3D photolithography and thus unwanted reflections are avoided during laser writing (see details below). At the same time, the line spacing and width in the diffractive structure are limited by the photolithography resolution, being of the order of 0.4 micron, and determine the working spectral range of the structure too.

The structure performance can qualitatively be understood as follows. If a 780 nm wave impinges at normal incidence from the dielectric stack side, it will be transmitted with high efficiency and will be diffracted on the grating into zeroth, first and minus first orders, the sum of the three contributing to the total transmitted intensity. If the same wave arrives at the structure from the other side, first illuminating the grating, and the grating lines geometry is chosen properly, a significant fraction of energy may be transformed into the first and minus first orders, now propagating in the stack at different angles. For high transmission asymmetry, these angles are chosen so that the stack is now highly reflective and thus the light is reflected from the Bragg mirror (compare Fig. 1(c)). While this simple picture explains the asymmetric transmission principle, it is not able to account for effects such as the (polarization-dependent) diffraction efficiency into higher orders – to this end, a series of numerical simulations was performed. Finite Difference Time Domain technique (FDTD) was used to simulate light propagation within the structure. To find the intensity transmission coefficient (T), the Fourier-transformed Poynting vector was integrated over a surface behind the structure, resulting in the transmitted power for each frequency (f). This was then divided by the incident power, yielding T(f).

An open access MEEP package, ver. 1.2.1 [28] was used in all the simulations presented below. A 2D simulation box with the resolution of 10 nm/px was used with periodic boundary conditions and PML absorbing layers at each end. The ellipsoidal shape of the photolithographic voxel, resulting in the rounded-corner grating line cross section, was taken into account. The grating geometry is characterized by two parameters: the height and the filling fraction, which we define as the line width at the base divided by the line-to-line distance. Although the glass substrate was not taken into account in the simulations, we found that it has little effect on the calculated transmission curves.

Figures 2(a) and 2(b) present the calculated transmission coefficients for normal incidence, with the electric field (E) vector parallel and perpendicular to the grating lines, respectively. The line height is 0.9 μm with the filling fraction of 0.6. Both propagation directions are shown (S = >L corresponds to light first propagating in the multilayer stack (S) and then in the grating lines (L)) as well as the transmission asymmetry, defined as the difference T_{S = >L} – T_{L = >S}. Considerable positive transmission asymmetry is visible around 0.78 μm for both polarizations, for E perpendicular to the lines reaching almost 0.5. For this electric field orientation another asymmetry peak appears at 0.93 μm, this time with more light traversing in the L = >S direction (compare the 950 nm curve behavior in Fig. 1(c)). For wavelengths above 0.95 μm the asymmetry vanishes – in this region the grating period becomes shorter than the wavelength and hence only the zeroth diffraction order is present.

 

Fig. 2 Calculated transmission curves for the structure from Fig. 1(a) for the electric field parallel (a) and perpendicular (b) to the lines. Also shown are calculated electric field distributions for both polarizations with waves propagating in two directions, calculated for 0.786 μm incident wavelength.

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Figures 2(c)-2(f) present the electric field distributions before, inside and behind the structure. These images were generated for a continuous wave illumination at 0.786 μm, around the maximum of the asymmetry peak. For both polarizations the field is visibly stronger behind the structure for the S = >L propagation than for the L = >S direction.

The simulations revealed that the magnitude and spectral band of the transmission asymmetry for a given stack design strongly depend on the grating geometry – the line height and the filling fraction. As these parameters can, to some extent, be adjusted in the photolithographic fabrication, we searched for their optimum values, i.e. yielding the highest absolute value of the transmission asymmetry. For a given line spacing, the lowest filling fraction of 0.4 is set by the photolithographic voxel dimension. The color maps in Fig. 3 present the results for the two linear polarizations.

 

Fig. 3 Transmission asymmetry of the structure calculated for varying grating line height and width for the electric field vector parallel (a) and perpendicular (b) to the lines. The structure exhibits the highest asymmetry in the perpendicular polarization for the lines with 0.9 µm height and the filling fraction of 0.6.

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The maps also give an estimate of how sensitive the structure is to fabrication errors, an important parameter for potential practical applications.

3. Fabrication and characterization

For further experiments, the following structure parameters were chosen: the dielectric mirror stack based on quarter wave layers, alternating Nb₂O₅ (5 layers, n(840 nm) = 2.176, d = 109.3 nm) and SiO₂ (4 layers, n(840 nm) = 1.438, d = 165.3 nm) (Laseroptik GmbH), the diffraction grating pitch equal 951 nm, the filling fraction of 0.6 and the line height of 0.9 μm (the optimum values for the perpendicular polarization). 170 μm thick fused silica substrates were ultrasonically cleaned and the electron beam evaporation (Balzers BAK box coater) was used to evaporate both stack materials from electron guns in a heated vacuum chamber under base pressure of 3 × 10⁻⁶ mbar with an oxygen inlet during the process. The layer thickness was controlled by monitoring a monochromatic light transmission. The mirror transmission profile at normal incidence as well as the transmission angular dependence for two wavelengths (high and low reflectivity) were measured; the results are plotted in Figs. 1(b) and 1(c).

The grating lines were fabricated on the mirror surface with a commercial Direct Laser Writing (DLW) workstation using a negative liquid resin (Photonic Professional and IPL respectively, both from Nanoscribe GmbH). The details of the setup and the process can be found in [29]. Upon irradiation with 780 nm infrared femtosecond laser pulses, the liquid resin polymerization is triggered within a volume where the laser light intensity exceeds a certain threshold, defining a three-dimensional writing region – the voxel. In our setup the voxel is approximately a prolate ellipsoid of revolution with the minor and major axes being 420 nm and 1000 nm long respectively.

The structure transmission was measured with femtosecond laser pulses tuned between 690 and 1040 nm (MaiTai, Spectra Physics). The focused beam size was around 50 microns (smaller than the structure lateral dimensions) and the sample was placed in the focal plane on an (x,y,z) positioning stage. The power meter head (Nova II, Ophir) behind the structure was scanned to cover the transmitted beam angles up to 70 degrees from the normal (corresponding to the numerical aperture of 0.94) and the integrated light intensity was recorded.

4. Results and Discussion

Measured angle-integrated light transmission for incident beam propagating in opposite directions is plotted in Fig. 4. While the asymmetry differs for the two perpendicular polarizations – parallel and perpendicular to the grating lines – for both cases there is a significant difference in transmission for a broad range of wavelengths around 780 nm. The asymmetry spans the 700-900 nm range (all the wavelengths measured) for parallel polarization and 740-820 nm band for perpendicular polarization, changing sign in the latter case.

 

Fig. 4 Calculated and measured angle-integrated light transmission in opposite directions (L = >S meaning “from grating lines to stack” and vice versa) (a) and (b) and the transmission asymmetry (c) and (d), for two linear polarizations – parallel ((a) and (c)) and perpendicular ((b) and (d)) to the grating lines. A significant asymmetry in transmission is visible for both polarizations in the range spanning more than 50 nm around 780 nm.

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Overall agreement between the simulated and measured results is visible in the plots with two discrepancies. First, the resonance-like features present in the theoretical data are not recorded in experiments – this is due to the experimental configuration adopted, with broadband (10 nm bandwidth) pulsed source used in the measurements. The recorded asymmetry is also higher than expected for the parallel polarization, the effect resulting from lower transmission in the L = >S direction measured for shorter wavelengths. As we have thoroughly verified that it is not related to the presence of the glass substrate, the origin of this difference remains unclear.

In conclusion, we have designed and fabricated an all-dielectric photonic structure that exhibits a significant transmission asymmetry in the near infrared spectral band around 780 nm. With higher resolution techniques for the diffractive grating fabrication, even higher transmission asymmetry can be reached (compare the map in Fig. 3(b)) and this concept can be directly adopted at shorter wavelength, covering the visible and near UV regions.