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Abstract
Better performances of two-dimensional (2D) grating are required recently, such as polarization independence, high efficiency, wide bandwidth and so forth. In this paper, we propose a 2×2 2D silver cylindrical array grating with excellent polarization-independent high diffraction efficiency (DE) over communication band for beam splitting. The grating was calculated by rigorous coupled wave analysis (RCWA) and can achieve over 24% DE of four first diffraction orders at 1550 nm with nonuniformity of 1.43% in both transverse electric (TE) and transverse magnetic (TM) polarizations, which is a significant improvement over previous reports. The holographic exposure technology, wet chemical development process and electron beam evaporation were used to fabricate the 2D grating. The correctness and accuracy of the calculation are fully verified with the measurement result of fabricated grating. Excellent performances of the 2D splitter we proposed will have great potential for applications in optical communication, semiconductor manufacturing and displacement measurement.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Information transmission by light is an irreversible trend and the explosive growth of workload of the communication network system can be relieved by multi-direction synchronous transmission, which means that an incident beam is separated into multiple beams with equal power in different directions at necessary position [1]. Traditional beam splitters include optical crystals [2,3], optical waveguide structure [4,5], diffraction grating [6–8] and so forth. Using the birefringence effect of optical crystals to split light is a way with least resistance. However, it is difficult to package with integrated optical circuits and fabricate due to its bulky size, which makes it impossible to be used in high-precision transmission. Optical waveguide structures that transfer light along the waveguide by coupling can split a ray into several beams and retain advantages of easy integration, compact size, and large bandwidth [9,10]. However, these structures are not only too complex to produce using electron beam lithography, but also too hard to apply on a large scale [11]. Benefiting from the excellent phase modulation ability of the diffraction grating, the directions and number of beams are easily controlled by changing geometric parameters [12,13]. Different from optical crystal, the effective working surface area of diffraction grating only needs to be larger than the spot area of laser under normal incidence, so it is compact and easy to be integrated into optical circuit. Compared with the intricate optical waveguides structure, the structure of the diffraction grating is uncomplicated. A simple periodic structure is extremely easy to manufacture and can also maintain advantages of optical waveguide structure [14]. It is worth mentioning that a beam splitting diffraction grating can be used as a beam combination diffraction grating with the same efficiency in theory. However, the influences of the errors in the phase values of each beam, and the matching and positioning of the beam combination diffraction grating will lead to the decrease of beam combining efficiency [15].
In recent years, with the development of grating vector theory and microfabrication technology, using diffraction gratings as the beam splitter has attracted much attention. Vast approaches of achieving grating-based beam splitter have been presented [16–19]. In Ref. [16], a polarization independent sandwiched grating was proposed as a 1×2 beam splitter under Littrow mounting, with the diffraction efficiencies in the −1st order and the 0th order more than 45% for both TE and TM polarizations. However, this special incidence condition makes it impossible to simply integrate with photonic devices and complex multi-layer structure derails it from reality. Kota Ito et al. [17] reported a 1×2 dielectric surface-relief grating which couples normal incident light to the −1st/+1st-order transmission diffraction with a 49.6% efficiency for each. Jijun Feng et al. [18] designed and manufactured a polarization-independent 1×3 fused-silica grating of which efficiency totals more than 82% under normal incidence. Bowen Gong et al. [19] proposed a polarization-independent 1×5 splitter under normal incidence based on two-layer grating with the efficiency of each order more than 13%, yet Ta2O5 is too tough to etch.
Although diffraction gratings used as beam splitters have been developed for a long time, most of known designed diffraction gratings are one-dimensional(1D) gratings and far too little attention has been paid to two-dimensional(2D) diffraction gratings due to its high degree of difficulties in designing and manufacturing. However, compared with 1D diffraction gratings, 2D diffraction gratings can achieve multi-dimensional light splitting, hence it provides more application possibilities. Eero Noponen et al. [20] designed a binary surface-relief 3×3 grating of which efficiency totals more than 89% under normal incidence, but the DE of each order is unevenly distributed with high nonuniformity. In Ref. [21], a 2D gold nanocylinder 2×2 grating was fabricated for displacement measurement, which is used at 780 nm incident wavelength under normal incidence condition, and four first orders with measured DE more than 21.8% are obtained. There is no doubt that the efficiency of the 2D grating proposed in the work has been significantly improved, but it still can be improved to a higher level.
The specific objective of this study is to design and fabricate a novel polarization-independent 2×2 high DE beam splitter over communication band based on a two-dimensional silver cylindrical array grating. With optimized parameters, the theoretical efficiency of (±1, 0), (0, ±1) orders for TE and TM polarizations exceeds 24% at the wavelength of 1550 nm under vertical incidence, with total efficiency of over 97%, which, to the best of our knowledge, is superior to previous reported results. The diffraction properties with varied incident wavelength over C-band are given. Moreover, the manufacturing tolerances as well as the dependence of the DE on incident angle and grating period are also analyzed. Meanwhile, the experimental data has been obtained which is consistent with the theoretical data, revealing the feasibility of its fabrication and promising prospect in the application of optical communication as a beam splitter.
2. Structure and materials
As a special structure, the diffraction grating can modulate the direction and energy of light propagation by changing its structure parameters and operating the wavelength and incident angle. According to the diffraction equation of 2D gratings, it can be expressed as [20]
where ϕ and θ are the azimuth angle and polar angle of the incident light; ϕm,n and θm,n represent the counterparts of the diffracted light in (m, n) order; Λx and Λy denote the period in the x direction and the y direction, respectively. It is worth mentioning that the influence of polarization state is greatly weakened when light strikes the grating surface under normal mounting, hence polarization independence can be realized easily. On the other hand, working under normal incidence condition is easier to match with the system optical path, eliminating the error caused by the derivation of the incident angle and improving system compatibility. Selecting the same period of x-axis and y-axis is not only the key to cut down the impact of incident light azimuth, but also the key to reduce the difficulty of fabrication by using holographic exposure. Consequently, in order to achieve the high DE of (0, ±1) and (±1, 0) orders, higher orders should be evanescent, thus direction of (m, n) diffraction order can be written as while the grating period should meet the following requirementIn this paper, we propose a 2×2 high DE beam splitter based on 2D silver cylindrical array grating under normal mounting. The grating period Λ is 1666.66nm (line density 600l/mm), and the incident wavelength λ is 1550nm. According to Eqs. (1)–(4), only (0, 0) order and the four first orders ((0, ±1) and (±1, 0)) exist.
As shown in Fig. 1, on the SiO2 substrate, a silver (Ag) layer is deposited with inclined cylinder patterns to form the grating structure, of which ψ is the sidewall angle and h1 is the height. We choose the Ag film h2 as a reflective layer due to its considerable broadband high reflection in the near infrared region. The refractive index of Ag film at the operating wavelength of 1550 nm is 0.40960 + i10.048, which is referred in Ref. [22]. To avoid the degradation of the silver surface, a thin layer (about 10 nm) of SiO2 or Si3N4 can be deposited on the silver layer with little effect on the grating performance. In the case of 2D grating under normal incidence, the TE and TM polarizations are ambiguous. Hence, it is necessary to redefine these two polarizations. In this work, the TE polarization is defined as the wave of which the electric field is perpendicular to the x-axis, while the TM polarization perpendicular to the y-axis, which are marked in coordinate axis.
Fig. 1. Schematic view of the proposed 2D grating: (a) side, (b) a single cycle and (c) front views of the structure.
3. Parameter optimizations
Owing to the discrete rotational symmetry, the diffraction grating has the inherent advantage of polarization independence in most instances [23]. DE of (±1, 0) orders in TE polarization is the same as that of (0, ±1) orders in TM polarization, which is equivalent to 90° rotation of incident azimuth. In addition, the completely equal DE of diffraction orders in same plane will appear in the case of vertical polarization, such as (1, 0) order and (−1, 0) order. Therefore, it is enough to calculate the DE of (−1, 0) and (0, −1) orders to achieve polarization-independent beam splitting. We will only discuss TE polarization condition in following parts. The diffraction grating that we proposed is a periodic structure with just one kind of material. Multi-parameters optimization was carried out in our design because multiple parameters of the grating influence the DE and bandwidth of the grating. To achieve higher efficiency for 4 uniform diffraction orders is the goal of optimizing the beam splitter, which can improve the signal-to-noise (SNR) ratio and signal contrast. Therefore, cylindrical height h1, duty cycle f and sidewall angle ψ need to be considered in the optimization process.
According to our experimental results, the structure sidewall angle of each single period cell obtained by holographic exposure is approximately a fixed value which should be fixed at 70°. Moreover, as a reflective layer, the thickness of Ag h2 has been set at 100 nm properly to reduce the impact on duty cycle expansion after chemical development process. As mentioned in the previous work [24–26], rigorous coupled wave analysis (RCWA, also called Fourier modal method, FMM) method is used to transform the electromagnetic field in the grating region and then obtain a series of superposition of plane waves by using Fourier expansion. The amplitude of each diffraction order can be obtained by solving Maxwell's Equation with grating structure parameters through boundary condition. In the numerical calculation of the 2D circular platform grating in this paper, we layered the grating region and calculated each layer with RCWA. Finally, the complex amplitude of the diffraction order was determined by the matrix iteration algorithm and the corresponding DE is obtained. Simulated annealing (SA) algorithm, a method to solve unconstrained and bounded constrained problems, imitates the physical process of minimizing the system energy for the purpose of reducing faultiness by lowering the temperature slowly after heating the material. With the decrease of material temperature, the search range of the algorithm narrows gradually and exits when the termination condition is satisfied [27,28]. The optimization function is defined as CF = 1 - [η(total)TE - |(η(−1,0)TE - η(0, −1)TE)|], where η(−1,0)TE, η(0, −1)TE and η(total)TE are diffraction efficiencies of (−1, 0) and (0, −1) orders and total of the four first orders for TE polarization, respectively. After the optimization, the best parameters came out with f = 0.77, ψ = 70°, h1 = 565 nm, the DE of η(−1,0)TE = 24.77% and η(0, −1)TE = 24.07% and η(total)TE = 97.68% is obtained. Considering the Ag reflectance of S-(99.56%) and P-(99.56%) polarized light at 1550nm under normal incidence [21], most of reflection light efficiency distribute in four first orders uniformly.
The best theoretical DE given by Xie’ s 2×2 splitter based on 2D grating shows 22.9% and 22.7% in (0, ±1) orders and (±1, 0) orders respectively in the TE polarization. The theoretical DE of the grating we design can be higher although Xie’s grating has achieved good results. In Fig. 2, we evaluate the relationship between duty cycle f or Ag thickness h1 and the efficiencies of diffraction orders (±1, 0) and (0, ±1). Considering the rationality of fabrication process, the structure will no longer be an inclined cylinder pattern, but will change to a rhomboid hole when the duty cycle keeps increasing until 1, so it is necessary to limit the duty cycle within a reasonable range. As shown in Fig. 2, on the premise that the structure can be fabricated and has sufficiently high DE, feasible structure parameters are circled with black lines. The irregular feasibility region within the black lines shows that diffraction efficiencies of the four first orders are all greater than 20% and less than 25% when the duty cycle is from 0.59 to 0.79 with the duty cycle tolerance of 0.2 and the Ag thickness h1 is from 490 nm to 650 nm with the depth tolerance of 160 nm. The diameter of the bottom of each period inclined cylinder patterns D can be defined as duty cycle multiplied by the period, which means that when the duty cycle tolerance is 0.2, fabrication tolerance of D will reach 330 nm. It is attainable to control the grating etching accuracy within 10 nm by using dry etching technology. Therefore, the corresponding requirement for duty cycle can be relieved greatly. Considering the outstanding fabrication tolerance, the grating has been fabricated in our work.
Fig. 2. DE of the 2D grating versus duty cycle and Ag thickness with ψ = 70°: (a) (−1, 0) order, (b) (0, −1) order.
Figure 3 shows the influence of incident angle on diffraction orders with optimized parameters. Firstly, in the special case where the incident angle is 0°, the DE of (±1, 0) or (0, ±1) order is always equal at 1550 nm. Secondly, the DE of the (0, ±1) diffraction orders will increase if the incident angle increases, but the DE of (±1, 0) orders will gradually decrease asymmetrically. In addition, the (1, 0) or (−1, 0) diffraction order will disappear at a certain incident angle value which can be defined by
In our design, θ is 3.99°. As seen from the vector diffraction theory, the energy of the disappeared (1, 0) order (θ = 3.99°) or (−1, 0) order (θ = -3.99°) and the significant decline of (0, ±1) orders will mainly transfer to the (0, 0) order or vanish on the grating surface [20]. Apart from this, the DE of four first orders are more than 20% from −2.67° to 2.67° at 1550nm, which is enough to restrain the incident angle alignment error in optical applications.
The higher DE means the greater utilization of light intensity in the effective diffraction order and can reduce unnecessary energy attenuation, which is critical in the field of optical communication. The excessive zero-order reflected light will return along the original path and interfere with the entire optical system, resulting in interfering the measurement resolution of the edge, and reducing the system accuracy and SNR. Therefore, it is necessary to define the extinction rate (ET) about first orders DE and (0, 0) order DE η(0, 0) to judge the diffraction properties, which is given by [29]
Under optimized parameters, the DE of the (0, 0) order is 0.0367% with ET = 24.23 dB, which is relatively high. Ignoring the energy of the (0, 0) order, the difference between (−1, 0) order and (0, −1) order is defined as nonuniformity of splitter, which is given by [21]
In areas circled in black lines in Fig. 2, values of EU are less than 10%. In particular, the value of EU is only 1.43% with optimized parameters at 1550nm, which could be a critical improvement for optical applications. Figure 4 shows the DE and EU corresponding to the grating period under normal incidence with the optimized grating parameters. Both the DE of (−1, 0) order and (0, −1) order are over 23.3% and the difference between the DE of (−1, 0) order and (0, −1) order is less than 2% with grating period from 1655 nm to 1680 nm. At the same time, EU is less than 4%. Therefore, the high efficiency and polarization-independence of the grating we proposed can still be achieved when the grating period shifts away from 1666.66 nm.
Fig. 4. DE and splitter nonuniformity corresponding to grating period under normal incidence with the optimized grating parameters.
4. Experimental tests and discussion
The holographic exposure technology has been used in fabricating discrete rotationally symmetric 2D periodic surface mask, which is achieved by exposing twice on the substrate coated with photoresist at angles of 0° and 90° respectively. In Fig. 5(a), photoresist (Model S1805, Shipley, USA) was evenly spin coated on the smooth and dry surface of 25mm×25 mm quartz substrate. Graphite coating on the back of quartz substrate can effectively absorb transmitted light and reduce the reflection light during exposure, avoiding interference of reflection light to affect the contrast of the exposure pattern. In Fig. 5(b), we expose the photoresist layer in a holographic exposure lithography system along the X-direction with 441 nm light (He - Cd Laser, IK4171I - G, KIMMON, JAPAN). In Fig. 5(c), we obtain one-dimensional pattern after one successful exposure, then rotate the substrate 90 degrees and expose again to obtain the required 2D pattern. In Fig. 5(d), wet chemical development process is used to remove exposed photoresist layer and initial 2D mask is obtained. In Fig. 5(e), 100nm silver layer is deposited on 2D mask through Electron Beam Evaporation. As shown in Fig. 5(f), the panoramic image was given and 3D appearance of the fabricated grating was viewed by Bruker Dimension 5000 atomic force microscopy (AFM). Finally, the discrete rotationally symmetric 2D periodic grating has been finished and geometrical parameters of grating with f = 0.65, h1 = 525nm and ψ = 70° have been measured by AFM. The difference between measured and optimized parameters, which is called form error, is mainly caused by second exposure process with insufficient interference contrast.
Fig. 5. (a)∼(e) The fabricated process of Ag coated grating with a size 25mm×25 mm. (f) The practicality picture and the 3D appearance by AFM.
To evaluate the diffraction property of the grating, the polarized beam of the Tunable Laser Controller (TLB - 6700, New Focus, USA) is perpendicularly emitted to the grating surface, and the DE can be obtained by measuring the amplitude of the diffraction light of each order. Figure 6 shows three relationships between the DE of each order and the incident wavelength: the measurement result, the simulation result of optimized parameters and the simulation result of measured parameters that are obtained by AFM. The DE of the grating at 1520–1570nm(C-band) is always higher than 21% with the fabricated grating parameters and it’s noted that the value of η(−1,0)TE = 22.24% and η(0, −1)TE = 22.30% and EU = 0.135% at the special wavelength 1550nm is obtained. In addition, simulation results of measured parameters and experimental results are basically consistent and the gap between them is mainly caused by form error in the manufacturing process and incident angle alignment error in the measurement process, which verifies the reliability of the simulation calculation. According to experiment result, 10.93% energy loss is mainly composed of (0, 0) diffraction order efficiency and metal absorption at 1550 nm. The value of unexpected (0, 0) diffraction order accounts for about 7% from C-band in measurement results. Nonetheless, it can be solved by approaching the best optimization parameters in fabricating products, because we can see that the DE of simulation results with optimized parameters is always around 24%. Furthermore, the energy absorption introduced by metal layer is acceptable because it broadens the reflective bandwidth.
Fig. 6. The calculated and measured DE corresponding to incident wavelength from 1520 nm to 1570 nm under normal incidence.
The morphology of grating surface is mainly influenced by dual interference beam intensity and contrast, exposure time, wet chemical development process time and so forth. The preferable surface can be controlled easily by adjusting process parameters. By theoretical calculation, with the increase of the sidewall angle, the performance of tolerance is improved and considerable solutions can be obtained. In our work, silver film is directly deposited on the photoresist 2D mask, causing a lot of uncertainties to the following process. We believe that the surface flatness and smoothness of the mask pattern can be improved by the introduction of reaction ion beam etching (RIBE). Using electron beam lithography can avoid the interference of the second exposure process caused by holographic lithography, and the side wall of the structure will be steeper. Therefore, the DE will be improved further by selecting fabrication process properly.
5. Conclusion
In conclusion, a novel polarization-independent 2×2 high DE beam splitter based on 2D silver cylindrical array grating under normal incidence for communication band is proposed and fabricated. The simulation and optimization of the DE are based on RCWA and SA algorithm, respectively. After, the highest DE of (±1, 0) orders and (0, ±1) orders are more than 24% and polarization independence can be achieved with the duty cycle of 0.77, side wall angle of 70° and Ag cylinder height of 565 nm. The holographic exposure technology, wet chemical development process and Electron Beam Evaporation are carried out to fabricate the final discrete rotationally symmetric 2D periodic surface pattern. Within moderate manufacture tolerance, the 2D grating has been fabricated and the correctness of the simulation is verified successfully. Therefore, this 2D grating is beneficial to improve beam splitting ability and achieve high SNR and accuracy, which has considerable application potentials in optical communication, semiconductor manufacturing and displacement measurement.
Funding
Guangzhou Science and Technology Program key projects (202007010001); Fundamental Research Funds for the Central Universities (21619343).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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