Holographic waveguide display with a combined-grating in-coupler

Jingjing Guo; Yan Tu; Lanlan Yang; Lili Wang; Baoping Wang

doi:10.1364/AO.55.009293

1. INTRODUCTION

An eyewear waveguide display system is a see-through display device worn in front of human eyes to overlay virtual images onto ambient scenery. This device is attractive and inspiring because it enables users to read messages, data and images or even watch videos while being immersed in the real world. Additionally, all the display items can follow head movement and the screen is hands-free. So it has been applied to military operation, pilot training, and the entertainment industry [1].

In the optical system of a waveguide display, a coupler is responsible for either guiding light into a waveguide or directing waves out. Prisms or planar gratings in various profiles were once chosen as the coupler, but they had problems including bulky size, low diffraction efficiency, color distortion, and ghost imaging [2,3]. Later, researchers found that the ultrathin size and low secondary diffraction of volume holographic gratings (VHGs) made them excellent waveguide couplers in the visible spectrum, ideal for eyewear waveguide displays [4–6]. When a well-designed VHG is illuminated by light at the Bragg condition, the optical field is redistributed, and most of its energy concentrates into one diffraction order. Compared with the transmission variety, reflection VHGs show less color crosstalk so they are widely used in waveguide displays. However, according to Kogelnik’s coupled wave theory [7], the diffraction efficiency of a reflection hologram monotonically increases with coupling constant. Because the coupling constant of transverse-magnetic (TM) is lower than transverse-electric (TE), this difference will yield a reduction in TM diffraction efficiency. Because the light emitted by an LED or OLED based microdisplay is unpolarized, the diffraction efficiency of the VHG will approximately equal the average of the TM and TE mode. Hence, the out-coupling luminance can be improved if the diffraction efficiency of the TM harmonics is increased.

This paper proposes a novel holographic waveguide display using a combined-grating as the in-coupler. The diffraction efficiency of both TM and TE waves have been enhanced, especially for TM waves. The optical characteristics of the combination of a subwavelength metal grating and a VHG were analyzed using a finite-element method, including diffraction efficiency, diffraction light field, wavelength selectivity, coupling efficiency, and angular selectivity. The configuration was used as the in-coupler of a holographic waveguide system to increase the luminance efficiency. Also, the out-coupling diffraction efficiency and the luminance efficiency of this novel holographic waveguide system were studied. The results for TM polarized, TE polarized, and unpolarized incident light are discussed in detail.

2. HOLOGRAPHIC WAVEGUIDE DISPLAY WITH COMBINED-GRATING

A. Structure Overview

Figure 1 shows the scheme of the novel holographic waveguide display (HWD) with the combined-grating for the in-coupler. The image is generated by the microdisplay and collimated by the convex lens. When the collimated image strikes the VHG and satisfies the Bragg condition, it is modulated by the interplay of the VHG and the metal grating, causing light to be coupled into the waveguide. Then the light is guided to the exit pupil and finally diffracted out of the waveguide by the out-coupler.

Fig. 1. Scheme of the holographic waveguide display using a combined-grating. The metal grating is etched on the upper surface of the VHG in nanoscale and is used to enhance the diffraction efficiency of the TM polarized light.

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Herein, two reflection-type VHGs are attached on the same side of the planar waveguide. An ultrathin metal grating is etched on a dielectric substrate and then attached upside down to the upper surfaces of the in-coupling VHG I. The grooves of the metal grating are assumed to be filled with a liquid that is index matched to the substrate. The period of the metal grating is assumed to be smaller than the wavelength of the incident light.

Generally, the out-coupling VHG is mirror symmetric to the in-coupling one. But in the case of the metal grating, the diffraction angle and the incident angle are nonreciprocal according to the grating equation. If the same metal grating is etched on the out-coupling VHG, light in the waveguide in the form of the total-reflection cannot be diffracted into the human eye. Additionally, part of the ambient light is blocked. So, here no metal grating is applied as the out-coupler.

A single reflection VHG coupler exhibits a higher diffraction efficiency for TE polarized than TM polarized light. In order to direct more TM polarized light into the waveguide, a subwavelength metal grating is used in combination with the VHG because its diffraction efficiency is higher for TM polarized than in TE polarized light, which is opposite of a dielectric grating.

Figure 2 shows the structure of the in-coupler, which consists of the VHG and the metallic nanograting. The VHG grating vector $k_{v}$ is oblique from the $z$ axis at the angle $ϕ$ , and its value is given by $k_{v} = 2 π / Λ_{v}$ . Here, the grating period of the VHG satisfies the Bragg condition

Λ_{v} = λ / (2 n \sin θ_{B}),

where

n

is the average refractive index, and

θ_{B}

is the Bragg angle of the grating. For a reflection-type grating,

θ_{B}

is given by

θ_{B} = π / 2 - ϕ + θ_{0}

, where

θ_{0}

is the incident angle. The thickness of the VHG is

d_{v}

. For a metal planar grating, the grating vector

k_{m}

is along the

x

axis and can be expressed as

k_{m} = 2 π / Λ_{m}

, where

Λ_{m}

is the metal grating period. It should satisfy the grating equation

Λ_{m} = λ / (n \sin θ_{s} + \sin θ_{0}),

here

θ_{s}

is the diffraction angle. The metal grating is a binary one whose width of ridge is

a

and depth is

d_{m}

.

Fig. 2. Structure of the VHG and the metal grating.

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To eliminate stray light as much as possible, the reflected light from the two gratings ( $R_{- 1, v}$ and $R_{- 1, m}$ in Fig. 2) should be parallel, which means the diffraction angles of the VHG ( $θ_{s, v}$ in Fig. 2) and the metal grating ( $θ_{s, m}$ in Fig. 2) should be designed to be equal. Additionally, the gap between the two reflected beams should be smaller than the Rayleigh criterion. For the out-coupler, the light propagating in the waveguide is incident onto the out-coupling grating at a large angle, which cannot be diffracted out of the waveguide by the same metal grating. So, an isolated VHG is used as the out-coupler.

B. Modeling Method

We first design the in-coupling combined-grating to obtain a high diffraction efficiency and then theoretically analyze the out-coupling diffraction efficiency and the luminance efficiency when it is applied to a holographic waveguide display system.

Some theoretical methods have been developed and widely used to solve grating diffraction problems, such as rigorous coupled-wave analysis (RCWA) [8] and Kogelnik’s coupled wave theory [7]. But these methods are not suitable for a composite grating with two different periods. Here, the finite-element-method (FEM) can be used to solve this complicated problem. It transforms the whole structure into a union of multiple subdomains and finds a solution of scalar wave equation for every element. Finally, the sum of the solutions in each element leads to the final one [9]. Thus, FEM breaks the limits of period and is applicable for multiperiod problems.

Figure 3 shows the combined-grating model established in a FEM solver, and herein the dashed rectangle frame is an enlarged image of the metal grating. Perfect matched layers (PMLs) cover the whole structure except the incident light port. Here, PMLs are used to simulate electromagnetic waves that propagate into unbounded domains, which act like absorbing walls to absorb all radiated waves with negligible reflections. The structure of the VHG is described in Ref. [10]. The waveguide and the substrate are all silica ( $n = 1.52$ ). The refractive index of the index matching liquid is 1.52. The VHG is dichromated gelatin (DCG), whose refractive index is 1.52, the index modulation is 0.03, and the thickness is 10 μm. The slanted angle of VHG is designed to be 22°. The metal grating is binary with the filling factor ( $a / Λ_{m}$ ) of 0.5. This choice was made due to its common use in applications. The waveguide is 30 μm-thick, and the substrate is 10 μm-thick. In practice use, the thickness of the substrate is 30 μm, which is much larger than a wavelength. In order to save computational resources, we reduce the value since that it has been demonstrated to have no influence on the optical distribution. We use a Gaussian beam to replace the microdisplay. The beam is incident vertically from the bottom center of the waveguide and has a diameter of 10 μm and power $P_{in}$ of 1 W. The line AB is perpendicular to the diffraction light. The diffraction power $P_{R}$ can be calculated by integrating the Poynting vector along the line AB. The in-coupling diffraction efficiency ${DE}_{in}$ can be calculated by

{DE}_{in} = \frac{P_{R}}{P_{in}} \times 100 % .

Fig. 3. Combined-grating simulation model.

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After exploring the optical characteristics of the combined-grating, we also examine the out-coupling diffraction efficiency and luminance efficiency while using it as an in-coupler. High efficiencies are required to obtain a bright image. Figure 4 shows the simplified holographic waveguide simulation model. Herein the VHG II is mirror symmetric to the VHG I, and the incident material is air. The design parameters are the same as the combined-grating simulation model. The line CD is parallel to the bottom boundary of the waveguide and covers the width of the out-coupling light. The out-coupling power $P_{out}$ can be calculated by integrating the Poynting vector along the line CD. So the out-coupling diffraction efficiency ${DE}_{out}$ can be calculated by

{DE}_{out} = \frac{P_{out}}{P_{in}} \times 100 % .

Fig. 4. Simplified holographic waveguide simulation model.

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The diffraction efficiency of TM ( ${DE}_{TM}$ ) and TE ( ${DE}_{TE}$ ) polarizations are calculated separately, and the unpolarized light ( ${DE}_{un}$ ) is approximated by the average of these two polarizations [11], like

{DE}_{Un} = \frac{1}{2} ({DE}_{TE} + {DE}_{TM}) .

In order to ensure the accuracy of the calculation, the meshing size is smaller than 80 nm. Especially, considering the possible plasmon phenomenon, the maximum size is 5 nm in the internal domain of the metal grating and around the interface between the metal grating and the VHG or the substrate, as shown in Fig. 5.

Fig. 5. Meshing near the metal grating.

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3. OPTICAL PROPERTIES OF COMBINED-GRATING

A. Diffraction Efficiency

Figures 6(a) and 6(b) show the interplay of the metal grating and the VHG on the in-coupling diffraction efficiency when the incident wavelength is 525 nm. The dashed line represents the in-coupling DE of a single VHG. When the metal grating period increases from 450 to 550 nm (here the grating depth is set as 80 nm), the ${DE}_{in}$ on the diffraction order $R_{- 1}$ increases both for TE and TM polarization. One interesting observation is that, as shown in the dotted rectangle in Fig. 6(a), when $Λ_{m}$ is close to the $x$ component of the volume holographic grating period (497 nm), ${DE}_{in}$ enhances extraordinarily. Herein the comodulation effect of TM-polarized component is more significant than the TE one. Figure 6(b) shows that the influence of the grating depth is not obvious with the grating period of 495 nm, ${DE}_{in}$ rises slowly as the grating depth increases to 80 nm and after that it stabilizes. When the metal grating period is 495 nm and the thickness is 80 nm, the DE reaches the peak (89.2% at the TM incidence and 95.0% at the TE one). The maxima and the relative variation ratios compared to a single VHG are listed in Table 1. The combined-grating increases DE by 16.4% for TM mode, by 4.3% for TE mode, and by 10.0% for unpolarized light.

Fig. 6. In-coupling diffraction efficiency versus: (a) the metal grating period with the depth of 80 nm; (b) the grating depth with the period of 495 nm. The wavelength is 525 nm.

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Table 1. Diffraction Efficiency Increment of the Combined-Grating Structure^a

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B. Diffraction Light Field

When the wavelength is 525 nm, Fig. 7 illustrates the magnetic field norm distribution on the surface at TM incidence with the metal grating period of 495 and 450 nm, while Fig. 8 is the electric field norm for the TE mode. When the metal grating period is 495 nm [Fig. 7(a)], the same as the $x$ component of the volume holographic grating period, the $R_{- 1}$ diffraction angles of both gratings are coincident with each other, and the field intensity of other diffraction orders ( $R_{0}$ , $R_{1}$ , $T_{- 1}$ , $T_{0}$ , and $T_{1}$ ) of the metal grating are suppressed for both polarizations. On the contrary, when the grating period difference of two gratings is not matched, e.g., too large [Fig. 7(b)], the diffraction light $R_{- 1}$ is divergent, and this kind of stray light will result in “ghost” images at the out-coupler.

Fig. 7. Magnetic field norm (unit: A/m) at TM incidence with the metal grating period of: (a) 495 nm; (b) 450 nm. The wavelength is 525 nm.

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Fig. 8. Electric field norm (unit: V/m) at TE incidence with the metal grating period of: (a) 495 nm; (b) 450 nm. The wavelength is 525 nm.

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C. Wavelength Selectivity

The wavelength selectivity of the in-coupling gratings is shown in Fig. 9, wherein the solid line is the diffraction efficiency of the in-coupler with the combined-grating, and the dashed line is the diffraction efficiency of the in-coupler with a single VHG. Meanwhile, the black and red lines show the diffraction efficiency of the TM and TE modes, respectively. The full-width at half-maximum (FWHM) of this design is 14 nm for TM mode and 18 nm for TE mode, the same as that of a single VHG. The additional diffraction exhibited by the combined grating in the red and blue wavelengths is due to the wide spectral bandwidth of the metal grating, which can be eliminated by the out-coupling VHG.

Fig. 9. In-coupling wavelength selectivity.

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D. Coupling Efficiency

Assuming the optical source is a green LED with a central wavelength of 525 nm and an FWHM of 35 nm, its normalized luminance is plotted in Fig. 10.

Fig. 10. Normalized luminance curve of a green LED.

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The in-coupling efficiency $η_{c}$ can be described as

η_{c} = \frac{\int L (λ) \cdot {DE}_{in} (λ) d λ}{\int L (λ) d λ},

where

L (λ)

is the LED spectra, and

{DE}_{in} (λ)

is the in-coupling diffraction efficiency. Based on our simulation results of diffraction efficiency of the in-coupler and LED spectra, we obtain the

{DE}_{in}

of the TM and TE modes by Eq. (3).

The results are listed in Table 2; the in-coupler with combined-grating increases the coupling energy efficiency by 61.6% for the TM mode, by 27.5% for the TE one and by 41.3% for unpolarized light.

Table 2. In-Coupling Efficiency Increment of the Combined-Grating^a

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E. Angular Selectivity

Figure 11 shows the angular selectivity of the combined-grating and the VHG. When the optical axis is oblique from the $z$ axis in the $x z$ plane, the FWHM of the combined-grating is $\pm 1.8 °$ for TM polarization and $- 2.2 ° \sim 1.8 °$ for TE one, which is almost the same as the single VHG. But it is obvious that the diffraction efficiency of the combined-grating is higher than the single VHG in the full field view.

Fig. 11. Angular selectivity.

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4. OPTICAL PROPERTIES OF HOLOGRAPHIC WAVEGUIDE DISPLAY SYSTEM WITH COMBINED-GRATING AS IN-COUPLER

As is discussed above, the introduction of the metal grating enhances the in-coupling diffraction efficiency and therefore increases the coupling energy. The optimal metal grating period is 495 nm, and the thickness is 80 nm. Here we apply the combined-grating to the holographic waveguide display system and analyze the spectra response and the luminance efficiency.

A. Spectra Response

Regardless of the propagation losses in the waveguide, the out-coupling spectrum response of the holographic waveguide is the product of the in-coupling and the out-coupling grating. As shown in Fig. 12, the FWHM for both polarizations is the same, while the peak diffraction efficiency of our configuration is higher than the HWD with only VHG. The corresponding result is listed in Table 3. Herein, the out-coupling diffraction efficiency of TM and TE increases 9.9% and 3.7%, respectively. For unpolarized light, it increases 6.3%.

Fig. 12. Out-coupling spectra response.

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Table 3. Diffraction Efficiency of the Holographic Waveguide System^a

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B. Luminance Efficiency

Luminance efficiency represents the optical energy utilization. Taking the spectral sensitivity of human visual perception of brightness into consideration, the luminance efficiency can be described as

η_{L} = \frac{\int L (λ) \cdot V (λ) \cdot {DE}_{out} (λ) d λ}{\int L (λ) d λ},

here

V (λ)

is the human eye photopic luminosity curve, and

{DE}_{out} (λ)

is the out-coupling diffraction efficiency of the holographic waveguide display. In Table 4, we see that the luminance efficiency of our structure is 13.1% and 19.1% for TM and TE polarization, respectively. Compared to the traditional structure, our configuration improves the luminous efficiency for TM incidence by 26.8%, TE incidence by 9.0%, and unpolarized incidence by 15.6%.

Table 4. Luminance Efficiency of the Holographic Waveguide System^a

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5. CONCLUSION

This paper proposes and theoretically analyzes a novel holographic waveguide display system using a subwavelength metal grating combined with a volume holographic grating as the waveguide in-coupler. When the image source is a green LED with the central wavelength of 525 nm, the optimized thickness and period of the metal binary grating are 80 and 495 nm, respectively. The diffraction efficiency increases 16.4% for TM incidence, 4.3% for TE, one and 10.0% for unpolarized light. When the combined-grating is used as an in-coupler of a holographic waveguide system, the luminance efficiency increases 26.8%, 9.0%, and 15.6% for these three polarizations, respectively. This design could help improve the energy utilization ratio of the holographic waveguide display.

Funding

National Key Research Program (2016YFB0401201).

REFERENCES

1. J. Rolland and O. Cakmakci, “Head-worn displays: the future through new eyes,” Opt. Photon. News 20(4), 20–27 (2009). [CrossRef]

2. L. Eisen, M. Meyklyar, M. Golub, A. A. Friesem, I. Gurwich, and V. Weiss, “Planar configuration for image projection,” Appl. Opt. 45, 4005–4011 (2006). [CrossRef]

3. T. Levola, “7.1: Invited paper: novel diffractive optical components for near to eye displays,” in SID Symposium Digest of Technical Papers (Wiley, 2006), pp. 64–67.

4. H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17, 185–193 (2009). [CrossRef]

5. T. Oku, K. Akutsu, M. Kuwahara, T. Yoshida, E. Kato, K. Aiki, I. Matsumura, S. Nakano, A. Machida, and H. Mukawa, “15.2: High-luminance see-through eyewear display with novel volume hologram waveguide technology,” in SID Symposium Digest of Technical Papers (Wiley, 2015), pp. 192–195.

6. M. Piao and N. Kim, “Achieving high levels of color uniformity and optical efficiency for a wedge-shaped waveguide head-mounted display using a photopolymer,” Appl. Opt. 53, 2180–2186 (2014). [CrossRef]

7. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969). [CrossRef]

8. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]

9. T. Grosges, A. Vial, and D. Barchiesi, “Models of near-field spectroscopic studies: comparison between finite-element and finite-difference methods,” Opt. Express 13, 8483–8497 (2005). [CrossRef]

10. J. Guo, Y. Tu, L. Yang, L. Wang, and B. Wang, “Design of a multiplexing grating for color holographic waveguide,” Opt. Eng. 54, 125105 (2015). [CrossRef]

11. A. H. Mahamat, F. A. Narducci, and J. Schwiegerling, “Design and optimization of a volume-phase holographic grating for simultaneous use with red, green, and blue light using unpolarized light,” Appl. Opt. 55, 1618–1624 (2016). [CrossRef]

Polarized Mode	${DE}_{in}$ of a Single VHG, ${DE}_{in, 1}$ (%)	${DE}_{in}$ Maximum of the Combined-Grating, ${DE}_{in, 2}$ (%)	Relative Variation Ratio, $δ {DE}_{in}$ (%)
TM	76.6	89.2	16.4
TE	91.0	95.0	4.3
Unpolarized	83.8	92.1	10.0

Polarized Mode	Single VHG, $η c 1$ (%)	Combined-Grating, $η c 2$ (%)	Relative Variation Ratio, $δ η c$ (%)
TM	21.8	35.2	61.6
TE	31.2	39.7	27.5
Unpolarized	26.5	37.5	41.3

Polarized Mode	HWD with Only VHG, ${DE}_{out, 1}$ (%)	HWD with Combined-Grating, ${DE}_{out, 2}$ (%)	Relative Variation Ratio, $δ {DE}_{out}$ (%)
TM	59.6	65.5	9.9
TE	81.6	84.6	3.7
Unpolarized	70.6	75.1	6.3

Polarized Mode	HWD with Only VHG, $η L 1$ (%)	HWD with Combined-Grating, $η L 2$ (%)	Relative Variation Ratio, $δ η L$ (%)
TM	10.3	13.1	26.8
TE	17.6	19.1	9.0
Unpolarized	13.9	16.1	15.6

Polarized Mode	${DE}_{in}$ of a Single VHG, ${DE}_{in, 1}$ (%)	${DE}_{in}$ Maximum of the Combined-Grating, ${DE}_{in, 2}$ (%)	Relative Variation Ratio, $δ {DE}_{in}$ (%)
TM	76.6	89.2	16.4
TE	91.0	95.0	4.3
Unpolarized	83.8	92.1	10.0

Holographic waveguide display with a combined-grating in-coupler

Abstract

1. INTRODUCTION

2. HOLOGRAPHIC WAVEGUIDE DISPLAY WITH COMBINED-GRATING

A. Structure Overview

B. Modeling Method

3. OPTICAL PROPERTIES OF COMBINED-GRATING

A. Diffraction Efficiency

B. Diffraction Light Field

C. Wavelength Selectivity

D. Coupling Efficiency

E. Angular Selectivity

4. OPTICAL PROPERTIES OF HOLOGRAPHIC WAVEGUIDE DISPLAY SYSTEM WITH COMBINED-GRATING AS IN-COUPLER

A. Spectra Response

B. Luminance Efficiency

5. CONCLUSION

Funding

REFERENCES

Cited By

Figures (12)

Tables (4)

Equations (7)

Applied Optics