1. Introduction

Recent progresses in semiconductor light sources have changed our daily lives. For example, classical light sources, such as incandescent and fluorescent light bulbs, are being replaced gradually with light emitting diodes (LEDs) that capable of improved energy efficiency and reliable lifetime [1–9]. LEDs are also used as a backlight unit (BLU) in liquid crystal displays (LCDs) in conjunction with the technical advances in flat panel displays and considerable growth of the market [10]. Many groups are now focused on a new type of LED that emits selectively one linearly polarized light because it can play a key role in future LED displays as a standalone device [11–14]. However, it is challenging to develop such a polarization-selective LED with a net enhancement in efficiency. The net efficiency must be dropped if the polarization selection in LEDs is achieved by preventing the transmission of undesired polarization states. This paper proposes a novel light emitter that enhances preferentially the light emission with the desired polarization direction and suppresses the emission with the undesired one. The spontaneous emission rates and emission profiles can be manipulated, depending on the polarization direction, by a one-dimensional (1-D) metal grating mirror consisting of ITO and silver. In addition, the highly polarized light emission with enhanced extracted power is implemented in a vertical GaN slab LED structure by optimizing the grating structure and position of the quantum wells (QWs).

2. Design and optimization of a 1-D metal grating mirror

If an electric dipole is located close to a high-reflectivity mirror, as shown in Fig. 1(a) , the spontaneous emission rate and emission profile will change significantly due to interference between the original dipole and the image dipole induced by the mirror [8,9]. To show this quantitatively, we calculated the spontaneous emission enhancement rate of the dipole source with an in-plane polarization direction as a function of the distance between the dipole and mirror, h, using a three-dimensional (3-D) finite-difference time-domain (FDTD) simulation [15–17]. Three types of mirrors, perfect metal, aluminum and silver mirrors were considered and the dispersive properties of the real metals were modeled with the Drude model [18]. The plasma and collision frequencies were obtained by fitting the measured refractive index and extinction coefficient of silver [19] and aluminum [20] over the wavelength range, 400 - 500 nm. The central wavelength (λ) and the spectral linewidth (Δλ) of the dipole source were set to be 450 nm and 25 nm, respectively. The simulation shows that the spontaneous emission rate oscillates with a period of ~λ/2n with changing h (Fig. 1(b)). The spontaneous emission rate was enhanced or suppressed as the dipole and image dipole interferes constructively or destructively, respectively. In Fig. 1(b), the spontaneous emission enhancement reaches unity when the dipole source is far enough from the mirror. Note that the oscillatory response is shifted by the phase delay of light reflected from the mirror, thus the field profile of the reflected light can be manipulated using different metals or designing the mirror structure appropriately. On the other hand, the same interference patterns are generated by the planewave normally incident to the mirror (Fig. 1(c)). The positions of the antinodes and nodes in Fig. 1(c) are in good agreement with those of the respective enhancement maxima and minima in Fig. 1(b). This suggests that spontaneous emission can be enhanced or suppressed when a light source is located at the positions of the antinodes or nodes of the interference pattern, respectively. Therefore, calculating the interference pattern is a convenient and rational protocol for determining the positions of the enhanced or suppressed spontaneous emission rates.

 

Fig. 1 (a) Schematic diagram of an electric dipole located at a distance of h from a metal mirror. (b) Spontaneous emission enhancements were calculated as a function of h using a 3-D FDTD simulation. (c) The electric field intensity profiles calculated using 1-D FDTD simulation as planewave is normally incident to the mirror. In (b) and (c), perfect metal, aluminum and silver were used as a mirror.

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The introduction of a surface pattern in a metal mirror can effectively induce a phase delay of the reflected light that is substantially different from that of a planar mirror. In addition, the phase delay can differ according to the polarization direction of the incident light if the surface pattern is asymmetrically defined. A 1-D grating was introduced to the metal mirror surface, as shown in Fig. 2(a) . Under this condition, the planewaves normally incident to the grating mirror in the transverse-electric (TE) and transverse-magnetic (TM) polarization directions will be reflected, showing polarization-dependent phase delays. If a dipole source is located at the position that corresponds to the antinode of the TE electric field profile and the node of the TM one, for example, the TE spontaneous emission rate is enhanced while the TM rate is suppressed. Hence, a 1-D metal grating mirror can exhibit polarization-dependent spontaneous emission and a resulting high polarization ratio.

 

Fig. 2 (a) Schematic diagram of an ITO/silver grating mirror and TE and TM planewaves incident to the grating mirror. The pitch, width and depth of the grating are a, w and d, respectively. (b), (c), and (d) The TE and TM electric field profiles reflected from the ITO/silver grating mirror were calculated at a = 180 nm, d = 85 nm as a function of w, using a 2-D FDTD simulation. The calculated phase differences between TE and TM are (b) π/4 at w = 170 nm, (c) π/2 at w = 155 nm, and (d) π at w = 115 nm, respectively.

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A two-dimensional (2-D) FDTD simulation was performed to examine this idea regarding the selection of one polarization direction (Figs. 2(b)-2(d)). The 1-D metal grating consisted of silver with a high reflectivity and ITO with a refractive index of n _ITO = 2.0 (Fig. 2(a)) [9]. The background material was GaN with a refractive index of n _GaN = 2.46. The pitch, width and depth of the grating were a, w and d, respectively. The periodic boundary condition along the x-axis with a spatial resolution of 2.5 nm in all axes was applied in the simulation [21]. The electric field profiles of the reflected light were calculated while the TE and TM planewaves were incident from z-axis. A 1-D total-field scattered-field technique was used to separate individually the reflected field from the incident one [22]. In Figs. 2(b)-2(d), the width of the grating changed from w = 170 nm to w = 115 nm, whereas the pitch and depth were fixed to a = 180 nm and d = 85 nm, respectively. The simulations demonstrate that the phase of the reflected TE wave changes significantly with changing w, whereas that of the reflected TM wave is barely affected by w. Consequently, the phase difference between the TE and TM waves depends strongly on w and the maximum phase difference, π, is achieved at w = 115 nm (Fig. 2(d)). In the phase difference of π, the TE field profile is opposite to the TM one. Therefore, the spontaneous emission of only one polarization direction can be enhanced, as discussed above.

Next, all available ranges of w and d were scanned continuously for three different pitches (a = 120 nm, 180 nm, and 240 nm). In Figs. 3(a) -3(c), the phase differences between the reflected TE and TM waves were calculated as a function of w and d, and are plotted in different colors. A phase difference of π appears as a red color. For each a, various combinatorial sets of w and d provide a phase difference of π. In terms of fabrication tolerance in the experiment, one can choose the middle of the widest red color region (white circles in Figs. 3(a)-3(c)) among the sets of structural parameters of the grating mirror. For example, when w = 120 nm and d = 80 nm at a = 240 nm (Fig. 3(c)), the phase difference of π is maintained even with a small deviation of w and d. Figure 3(d) shows the values of w and d maximizing the phase difference as a function of a. Note that the optimal w increases with increasing a whereas the optimal d decreases. The optimized structural parameters of the grating mirror can be found easily in Fig. 3(d).

 

Fig. 3 Calculated phase differences between the TE and TM waves reflected from the ITO/silver grating mirror with (a) a = 120 nm, (b) a = 180 nm, and (c) a = 240 nm. These graphs are plotted as a function of w and d of the grating. The white dashed circles indicate the widest regions of the phase difference of π. (d) Optimal w and d that maximize the phase difference of the reflected light are plotted as a function of a. The data is from (a), (b), and (c).

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3. Results and discussion

Based on the analysis in the previous section, we designed a polarization-selective LED structure and investigated quantitatively the ratio of the spontaneous emission enhancement rates between two polarization directions using a 3-D FDTD simulation. In the GaN LED structure shown in Fig. 4(a) , an infinitely thick GaN slab containing QWs with a thickness of one FDTD grid and a 1-D ITO/silver grating mirror with the structural parameters of Fig. 3(d) were introduced. Since most of radiative recombination takes place at the first layer of the GaN multiple QWs, the one-grid-thick dipole source can describe properly such an actual emitting structure [23]. Ten periods of the grating were considered in the calculation domain, where perfectly matched layer boundary conditions are applied to all six boundaries. The spontaneous emission enhancement rates were calculated using an electric dipole excited in the QW layer. Only a single dipole source was introduced in the simulation to avoid the coherent effect between multiple dipoles. Instead, the simulations were repeated after changing the position of the dipole source in the QW layer between 0 and a/2 in x-axis until all grid points were scanned by the dipole source. The spontaneous emission enhancement rates were then calculated by averaging the value obtained in each simulation. The spatial resolution was 5 nm and the central wavelength and spectral linewidth of the dipole were set to 450 nm and 25 nm, respectively.

 

Fig. 4 (a) Schematic diagram of a GaN LED structure with the QWs and ITO/silver grating mirror. The distance between the QWs and mirror is h. A single electric dipole is excited at (x, h) with changing x from 0 to a/2. (b) Spontaneous emission enhancement rates of the incoherent TE (red line) and TM (blue line) dipoles in the QWs were calculated as a function of h using a 3-D FDTD simulation. The structural parameters of the grating were set to a = 140 nm, w = 100 nm, and d = 95 nm. (c) The TE/TM ratios of the spontaneous emission enhancement rates are plotted as a function of h at w = 90 nm (magenta), w = 100 nm (black), and w = 110 nm (cyan). In the case of w = 100 nm, data was obtained from (b).

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Figure 4(b) shows the spontaneous emission enhancement rates of the TE and TM dipoles calculated as a function of the distance between the QWs and mirror, h. The following structural parameters of the grating mirror were chosen: a = 140 nm, w = 100 nm and d = 95 nm, where these structural parameters are from Fig. 3(d) [24]. As expected, the spontaneous emission enhancement rates of the TE and TM dipoles exhibited out-of-phase oscillatory responses. For example, the TE spontaneous emission rate was suppressed at h ~50 nm or 140 nm whereas the TM one was enhanced at the same distances compared to the dipole oscillation in a free space. On the other hand, at h ~95 nm or 185 nm, the TE spontaneous emission rate was enhanced and the TM one was suppressed. As a result, the ratio between the TE and TM spontaneous emission enhancement rates changed periodically with a period of ~50 nm and reached a maximum of 1.3 at h = 90 nm (black, Fig. 4(c)). This suggests that the spontaneous emission rate of the TE polarized light is 1.3 times higher than that of the TM polarized light and polarization-selective light emission was demonstrated without using an external polarizer.

The TE/TM ratios at w = 90 nm (magenta, Fig. 4(c)) and w = 110 nm (cyan, Fig. 4(c)) were also calculated to examine the fabrication tolerance. Both results showed similar oscillation behavior, even though the TE/TM ratios were slightly smaller than the ratio at w = 100 nm due to a small deviation from the phase difference of π. This confirms the robustness of the fabrication tolerance as discussed in the previous section. Notably, there was abnormal enhancement of the TM spontaneous emission at h < 50 nm. This enhancement was attributed to coupling of the surface plasmon states, which will be in lost by heat dissipation unless a proper extraction structure is employed [25,26]. Therefore, the best value of h is the second maxima point (i.e. ~90 nm) in Fig. 4(c).

The TE/TM polarization ratio was also investigated in a practical vertical GaN slab LED. To consider the effect of the LED structure together with the spontaneous emission rate modified by the metal grating mirror, the extracted power in an ambient medium was calculated at this time. The GaN slab was modeled with a finite thickness in the air background, as shown in Fig. 5(a) , and the extracted powers of the TE and TM polarized light were calculated. The thickness and lateral size of the GaN slab were set to 1 μm and 2 μm, respectively [4,5]. Periodic boundary conditions were applied to the side boundaries to present the indefinite propagation of light guided in the slab. The extracted power was calculated using three incoherent electric dipole sources oscillating in the x, y, and z directions, which are excited at a grid point of the QWs. The TE (−E_y·H_x) and TM (E_x·H_y) parts of the vertical component of the Poynting vector, S_z, were accumulated individually in the detection plane located in the air (Fig. 5(a)). The same procedures were carried out until all grid points in the QWs were scanned by the dipole source, similarly to the simulation in Fig. 4, so that the extracted power and resulting polarization ratio were calculated.

 

Fig. 5 (a) Schematic diagram of a vertical GaN slab LED structure. The background is air and the thickness and lateral size of the GaN slab are 1 μm and 2 μm, respectively. The distance between the QWs and mirror is h. A single electric dipole was excited at (x, h) with changing x from 0 to a/2. (b) The normalized extracted powers with the TE (red line) and TM (blue line) polarization directions were calculated as a function of h at a = 200 nm, w = 120 nm, and d = 85 nm, using 3-D FDTD simulation. The TE/TM ratio was also plotted (green dashed line). (c) The field profiles of the TE part of S_z. Vertical emission is clearly shown. (d) The field profiles of the TM part of S_z. The field profiles in (c) and (d) are calculated at h = 75 nm.

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The normalized extracted power, which is the extracted power divided by the total power generated by the dipoles, was plotted as a function of h at a = 200 nm (Fig. 5(b)). The extracted power with the TE polarization direction was maximized as the power with the minimized TM polarization direction, and vice versa, at h > 40 nm. However, unlike the spontaneous emission enhancement rate of Fig. 4(b), the overall extracted power with the TM polarization (blue line) was much smaller than the power with the TE polarization (red line). Accordingly, the TE/TM polarization ratio increased strongly to a maximum ratio of 15:1 at h ~75 nm (green dashed line) [27]. This polarization ratio is quite different from the ratio obtained by the spontaneous emission rate in Fig. 4, even though both ratios are maximized at similar h values. This difference originated from the significant change in the field profile of a desired polarization state − the vertically emitted field profile only in the TE polarization state (Figs. 5(c) and 5(d)), as well as the enhanced spontaneous emission rate by the 1-D ITO/silver grating mirror

4. Conclusion

A polarization-selective light emitter that utilizes a 1-D ITO/silver grating mirror capable of the preferable excitation of a single polarization state by controlling the spontaneous emission was demonstrated. A TE/TM polarization ratio of 1.3:1 in terms of the spontaneous emission rate was obtained by optimizing the structural parameters of the metal grating mirror and the position of a dipole source. In addition, this polarization ratio was increased up to 15:1 when the extracted power was considered in a vertical GaN slab LED structure. These simulation results are expected to open new opportunities for the design of high-efficiency polarization-selective LEDs without the use of additional optical components, such as a polarizer.