Grating splitters play important roles in various optical systems, such as ultrashort pulse splitting^[1–3], optical communications^[4], optical interconnection networks^[5–8], complex vector beam shaping^[9,10], augmented reality (AR)^[11,12], interferometry^[13], and fiber grating mask^[14,15]. In the past decades, a variety of two-port grating splitters in the resonant region have been investigated extensively, with characteristics of compact structure, high diffraction efficiency, broad bandwidth, and stable performance. These two-port grating splitters could be divided into two main categories. One type is the grating splitter under Littrow mounting^[16,17]. In this case, the grating splitter is usually used under monochromatic light illumination, because the zeroth order possesses no dispersion power. The other type is the grating splitter under normal incidence^[18,19], whose efficiencies of the ±1st orders are naturally equal to each other with the same dispersion power due to its symmetrical grating configuration. In order to take full use of dispersion power of the ±1st orders, an ultrabroad waveband is highly desired for those symmetric grating splitters. On the other hand, the efficiencies of the ±1st orders should be as high as possible, although the efficiency of grating splitters under normal incidence is usually lower than that under Littrow mounting because of the existence of the undesired zeroth order. In addition, for practical applications, a polarization-independent beam splitter would be more favorable than a polarization-dependent one due to its versatility. Recently, Wang^[20] had successfully designed a rectangular reflective broadband polarization-independent two-port grating splitter under normal incidence conditions. However, the bandwidth with the ±1st-order diffraction efficiency over 46% is only 23 nm at a central wavelength of 1550 nm.

In this work, an encapsulated metal-dielectric reflective grating configuration is chosen with consideration of its advantages of protecting the grating surface and reducing the Fresnel loss^[21]. Moreover, the connection-layer-based grating structure usually possesses the advantage of wideband property^[22,23]. The unified method^[24–26] is used here for designing such grating splitters, which enable one to quickly choose grating parameters to realize high efficiency in a wide waveband. Based on this method, a reflective broadband high-efficiency polarization-independent two-port grating splitter is optimized effectively. For a center wavelength of 800 nm, a 46.4 nm bandwidth for the efficiency (defined as the ratio of the energy of light diffracted only at the first order to the whole incident field) over 46% can be achieved under normal incidence, which is improved greatly compared with previous works.

Figure 1 illustrates the schematic of the encapsulated metal-dielectric grating configuration for two-port beam splitters. As shown in Fig. 1, the grating region is embedded into a cover layer with refractive index of n1 and a substrate layer with refractive index of n3. The grating region is mainly divided into three layers: an encapsulated grating layer with thickness of h1 (with refractive index of nr for grating ridge and ng for grating groove), a connecting layer with thickness of h2, and another reflective metal layer with thickness of h3. The period of the grating is p, and the ridge width of the grating is b. Then, the duty cycle f is defined as f=b/p. When a non-polarized light is impinged into the grating region under normal incidence, the diffractive light is propagated along the vertical direction, and then it is reflected by the metal layer. The reflective light is again diffracted by the encapsulated grating layer, and finally it exits from the grating region. In this Letter, the cover layer, the substrate, the connecting layer, and also the grating ridge are chosen as fused silica (reflective index n3=1.45 at 800 nm), and the reflective layer is chosen as an Ag slab (refractive index nAg=0.094–5.212i at the central wavelength) with thickness of h3=100nm.

A unified method^[24–26] is a powerful tool to design various gratings working with a broad waveband, where the unified grating structures are approximately wavelength-independent. It should be noted that this unified design of wavelength-independent gratings is based on the fact that the material dispersion should be low enough, and its refractive index is assumed to be fixed over the working waveband. In this work, the fused silica is chosen as the main material of the grating. Since it is a low dispersion material at the designed waveband, the unified method is employed here for designing the grating structure. Under such a condition, the diffraction efficiency of the gratings depends on unified grating parameters, P and D (where P and D are defined as the ratios of grating period p and depth h1 to the working wavelength, respectively). Since the grating configuration is symmetrical here, the efficiencies of the ±1st orders are completely equal to each other. Therefore, we use the absolute efficiency of light diffracted only at the first order to represent the grating efficiency η in this Letter.

Here, for the grating configuration mentioned above, the thickness of the grating region is divided into two parts, the thickness of encapsulated grating layer h1 and the thickness of connecting layer h2. In order to obtain a clear efficiency distribution map versus unified parameters P and D, we firstly set the ratio of depths of those two layers as h2=α×h1. Before final optimization, the duty cycle f and the proportional coefficient α should be determined in advance. Then, the rigorous coupled wave analysis (RCWA) theory^[27] is used for calculating the grating efficiency without considering material dispersion, and the simulated annealing algorithm^[28] is used to execute the optimization. The cost function is defined as with where ηmin(P,D)=Min(ηTE,ηTM) is the minimum of the ηTE and ηTM for each pair of unified parameters (P,D), with ηTE and ηTM being the efficiency for TE and TM polarizations, respectively. By maximizing the cost function, the parameters of f=0.687 and α=0.332 are obtained quickly. Then, the relationship between the grating efficiency η and those two unified parameters (P,D) could be obtained.

Figure 2 depicts the contour map of theoretical grating efficiency η as a function of those two unified parameters, P and D, where Figs. 2(a) and 2(b) are results for TE and TM polarizations, and Fig. 2(c) denotes the result of Min(ηTE,ηTM). It is shown that the influence of incident wavelength on the efficiency distribution could be well predicted by analyzing its effect on P and D. For a specific grating with profile parameters (f, α, h1, h2, and p) determined, the change of the incident wavelength only induces the linear variation of P and D under the framework of the unified design method. Therefore, the optimized grating structure corresponds to a trajectory described by a straight line through the origin. As shown in Fig. 2(c), we could use a straight line to cross through the high-efficiency area surrounded by the white rectangle, which indicates that there is an optimal grating solution with efficiency over 46% under both TE and TM polarizations for a broad working waveband. Moreover, a longer length of the straight line crossing the high-efficiency area suggests a broader working band. For more clarity, a partial enlarged contour of the part surrounded by the white rectangle in Fig. 2(c), with efficiency higher than 46% under both TE and TM polarizations, is replotted in Fig. 3. Then, we use a straight line (the red dot line in Fig. 3) crossing through the origin to pass through the high-efficiency region as long as possible. Also, as shown in Fig. 3, the two intersection points PL (1.344, 1.745) and PH (1.428, 1.855) with the efficiency outline of 46% are marked out. Here, the slope of the straight line is 0.77 with P ranging from 1.344 to 1.428. Setting A and B, the lower and upper limits of the unified period P, the working bandwidth ranges from p/B to p/A with efficiency η over 46%. In this work, the feasible value of the period p could be chosen from 1.344λ to 1.428λ. Here, the period of the grating is set as 1.38λ, which makes the central wavelength located at the center of the spectral bandwidth, and the corresponding depth h1 is 1.796λ. Since the unified design method is used, the grating parameters can be flexibly adjusted when the working wavelength is changed. Here, as an example, the upper and lower limits of the working waveband of a grating splitter are p/A=1.38λ/A=821.4nm and p/B=1.38λ/B=773.1nm for femtosecond laser pulse splitting at the central wavelength of 800 nm. It suggests that the theoretical spectral bandwidth of 773.1–821.4nm with efficiency over 46% could be achieved under normal incidence for both TE and TM polarizations. In addition, the results shown in Fig. 3 indicate large manufacture tolerances for the grating period and etching depth of the encapsulated grating layer for such a grating splitter designed by the unified method. It is seen that the efficiency is still higher than 46% when P varies from 1.341 to 1.398 or D varies from 1.746 to 1.864 [two crossing blue lines with the four intersection points P1 (1.796, 1.398), P2 (1.796, 1.341), D1 (1.764, 1.382), and D2 (1.846, 1.382) marked out]. It suggests that the thicknesses of encapsulated grating layer and also the connecting layer both exhibit large tolerances, since the ratio of thicknesses of those two layers is a constant. The third layer, i.e., the Ag slab, works as a reflective mirror, and its influence on the grating performance can be ignored if the thickness is large enough (it is set as 100 nm, which is large enough to work as an effective reflective layer).

According to the analysis above, the optimal grating parameters could be fully determined as p=1.104μm, h1=1.434μm, h2=0.476μm, α=0.332, and f=0.687. In order to verify the validity of the unified method used here, the grating efficiency versus the working wavelength is replotted by a strict numerical calculation method while considering material dispersion, besides the efficiency curve predicted by the unified method, as shown in Fig. 4. It is seen that the curve is very close to that predicted by the unified design method, which indicates that the approximation by considering the refractive index as a constant is reasonable during the unified design procedure. Also, it is seen that the bandwidth with efficiency over 46% for both TE and TM polarizations is 775.3–821.7nm (about 46.4 nm). For easy comparison, similar to the linewidth of lasers^[29], the normalized spectral bandwidth of a beam splitter is defined as σ=Δλ/λ0, where Δλ is the waveband, and λ0 is the central working wavelength. Then, the normalized spectral bandwidth of the grating splitter designed here is greatly improved compared with previous work reported by Wang^[20].

In conclusion, an encapsulated metal-dielectric reflective grating is presented for broadband polarization-independent two-port beam splitting under normal incidence at the central wavelength of 800 nm. Due to the symmetrical grating configuration, the ±1st orders with equal diffraction efficiency possess the same dispersion power. A unified method is used for designing such grating splitters, which enables one to quickly find the feasible area for realizing the broadband performance. The results indicated that a bandwidth of 46.4 nm could be achieved for the diffraction efficiency over 46% at the central wavelength of 800 nm. This kind of broadband two-port polarization-independent beam splitter has wide applications in ultrashort pulse splitting, coherent beam combination, complex vector beam shaping, and so on.