Efficient optical coupling in AlGaN/GaN quantum well infrared photodetector via quasi-one-dimensional gold grating

S. Wang; W. Tian; F. Wu; J. Zhang; J. N. Dai; Z. H. Wu; Y. Y. Fang; Y. Tian; C. Q. Chen

doi:10.1364/OE.23.008740

1. Introduction

In recent years, AlGaN/GaN MQWs have attracted increasing attention and are taken as one of the most promising materials for infrared photodetectors based on intersubband transitions (ISBT) [1–4]. Due to the large conduction band offset (1.75 eV in AlN/GaN MQWs) [5] and strong electron-phonon interaction [6–8] in AlGaN/GaN MQWs, the devices can be operated in a wide region of 0.7-70 μm at ultrafast speed. Particularly, AlGaN/GaN MQWs are the only material that can realize ultraviolet and infrared double band detectors on the same wafer. The excellent properties of the material open inspiring prospects for important applications, especially in the military. For infrared photodetectors, the majority of applications are related to imaging by using small-pixel and large-area focal plane arrays (FPAs) [9], which requires planar device geometry and normal illumination. However, according to the intersubband absorption selection rules [10], infrared absorption in QWIPs is possible only when the electric field of the incident light has a component perpendicular to MQWs. Therefore, special corrugated surface or grating structures are necessary to deflect the incident light away from the direction normal to MQWs, fulfilling the ISBT. Since Ebbesen et al. found that metal films with two-dimensional subwavelength periodic perforated hole array exhibit extraordinary optical transmission [11], properties of SPP have been applied to improve the performance of photoelectric devices such as solar cells [12–15], light-emitting diodes (LED) [16–19], photodetectors [20–22] and so on. SPP at the interface between a metal and a dielectric material has a combined character of electromagnetic wave and surface charge [23]. Essentially, it is a kind of special electromagnetic wave which travels along the metal/dielectric interface [24], changing the direction of energy flow and inducing the electric field component perpendicular to the surface. Recently, the enhancement of infrared absorption in QWIPs has been demonstrated via a two-dimensional periodic metallic hole array on the top of InGaAs/InAlAs MQWs [21] and InGaAs/InP MQWs [22]. Nevertheless, few efforts have been made on enhancing the infrared absorption in AlGaN/GaN QWIP operated in the atmospheric window of 3–5 μm via LSP or SPP. In addition, the mechanism responsible for the significant enhancement of optical coupling has not been clearly explained. These issues prompt us to look for some other new structures associated with plasmon resonance to enhance optical absorption of AlGaN/GaN QWIP in mid-infrared, satisfying the planar device geometry and normal illumination which are essential in FPAs.

In this letter, a comparative study of one-dimensional, quasi-one-dimensional and two-dimensional gold gratings for electric field distribution, current density and energy flow in AlGaN/GaN QWIP has been conducted by an algorithm of FEM in detail. With the optimized quasi-one-dimensional gold grating, the |E_z|² in MQWs is remarkably enhanced, showing 2 times and 1.3 times increase at 4.65 μm compared with that obtained via a one-dimensional gold grating and a two-dimensional gold grating, respectively. The significant enhancement primarily benefits from the strong near-field coupling of the electromagnetic resonances between the incident light and the plasmon modes [24]. Further calculation shows that a coupling efficiency of 85% can be obtained. It indicates that the performance of the AlGaN/GaN QWIP will be potentially improved.

2. Theoretical model

The proposed quasi-one-dimensional gold grating is patterned on the AlGaN/GaN QWIP whose operation wavelength is 4.65 μm, as illustrated in Fig. 1(a). The detailed structure of the QWIP can be found in our previous study in [4]. The parameters related to the grating are denoted as: Λ₁ and Λ₂ for the pitch of the adjacent square holes along the x- and y-axes, respectively, d for the width of each aperture hole and h for the grating height. Considering the periodicity of the grating, Fig. 1(b) shows the basic unit of the geometry under investigation, illuminated by normal incident light along z-axis from the top, which is a y-polarization plane wave with electric field E₀ = 1 V/m. For the theoretical analysis, we use the algorithm of FEM to model the structure. To simplify the problem without sacrificing the accuracy of calculation, the bottom contact layer is truncated from 700 nm below quantum well region by a 1-μm-thick perfectly matched layer (PML) [25] for the complete absorption of electromagnetic wave. Wherever in the cap layer, MQWs or bottom contact layer of the QWIP, carrier densities are almost of the same order of magnitude. So the conductivity of Al_xGa_1-xN can be simplified as the same value of 1000 S/m. The infrared refractive indices of AlN and GaN epitaxial films are 2.1~2.2 [26] and 2.3 [27], respectively. In the simulation, the relative dielectric constant of the cap layer, MQWs and bottom contact layer are set as 5.05, 5.09 and 5.12 separately by linear interpolation.

Fig. 1 Schematics of (a) AlGaN/GaN QWIP with quasi-one-dimensional gold grating and (b) basic unit of the simulated geometry on different sides.

Download Full Size | PDF

In the mid-infrared, a good fit can be obtained with a Drude model dielectric function defined as [28]

ε (ω) = ε_{\infty} - \frac{ω_{p}^{2}}{ω^{2} + i ω ω_{τ}}

where ω is the angular frequency of incident light, ɛ_∞ is the permittivity in high frequency. We assume the value of ɛ_∞ can be appropriately set as 1 for the reason that it represents band-to-band transitions and the energy of mid-infrared radiation is too small to induce the transitions between the valence band and conduction band. Moreover, ω_p = 1.37 × 10¹⁶ rad/s and ω_τ = 4.065 × 10¹³ rad/s represent the plasma oscillation frequency and damping constant in Au [28], respectively.

3. Results and discussion

The electromagnetic field distribution in AlGaN/GaN MQWs with quasi-one-dimensional gold grating is carefully optimized at the wavelength of 4.65 μm. Then the width of the square hole d is set as 1 μm, the lattice constant along x-axis Λ₁ as 1.1 μm, Λ₂ along y-axis as 2 μm and the thickness of gold layer h as 100 nm. For n-type QWIPs, they are only sensitive to the electric field component along the MQWs growth direction (z-axis). Therefore, the |E_z|² in MQWs can effectively represent the amount of light that can be absorbed by QWIP. Figure 2(a) shows the simulated spectrum of averaged |E_z|² across the whole quantum well region between 30 nm and 230 nm under the Au/semiconductor interface. It is clear that |E_z|² in MQWs is enhanced for all radiation wavelengths, especially at 4.65 μm where our QWIP works, indicating that the selected parameters are appropriate. As illustrated in Fig. 2(b), the amplitude of E_z (|E_z|) decays exponentially with the increasing distance away from the Au/semiconductor interface, which is a significant characteristic of SPP [23]. As a result, the resonance peak at 4.65 μm should be attributed to the interaction of the incident light and SPP, which is determined by the geometry of the etched hole array.

Fig. 2 (a) Averaged |E_z|² across the whole quantum well region at a normal incidence for different wavelengths; (b) |E_z| in the square center (x = 0.55 μm, y = 0.5 μm) as a function of the distance (z) away from the Au/semiconductor interface at 4.65 μm; (c) dispersion diagram of SPP generated at the Au/semiconductor interface; (d) dispersion diagram of SPP detailed with enlarged scale line.

Download Full Size | PDF

For a metal/dielectric interface, the SPP wave vector (k_sp) can be derived from Maxwell equations given by [29]

k_{s p} = \frac{ω}{c} \sqrt{\frac{ε_{m}^{'} ε_{d}}{ε_{m}^{'} + ε_{d}}}

where ω is the angular frequency and c is the speed of light in vacuum. To identify the cause of the enhancement, we consider the dispersion diagram of SPP generated at the Au/semiconductor interface, derived from Eq. (2) and shown in Fig. 2(c). The momentum of SPP (red line) is always larger than that of the normal light (blue line) in GaN, preventing SPP directly excited by the incident light at a smooth metal/dielectric interface. However, the momentum difference can be compensated via the quasi-one-dimensional gold grating. When the incident light is coupled into SPP, the resonant momentum can be depicted as [29]

{\vec{k}}_{s p} = \vec{k} + i {\vec{G}}_{x} + j {\vec{G}}_{y}

where

\vec{k}

is the wave vector of the incident light in the x-y plane with

\vec{k} = 0

for normal incidence,

{\vec{G}}_{x}

and

{\vec{G}}_{y}

are the reciprocal lattice vectors of a square lattice with

| {\vec{G}}_{x} | = 2 π / Λ_{1}

,

| {\vec{G}}_{y} | = 2 π / Λ_{2}

(in this letter, Λ₁ = 1.1 μm, Λ₂ = 2 μm) and i, j are the unit vectors along x- and y-axes, respectively. The only difference among quasi-one-dimensional, one-dimensional and two-dimensional gold gratings is the distance between adjacent metallic holes along x-axis. When the distance is equal to zero, it is the one-dimensional grating. It will be two-dimensional grating provided that it is approximate to the distance along y-axis. And it will become the quasi-one-dimensional grating with the distance along x-axis decrease to dozens of nanometers. In this letter, the distance along x-axis is only 100 nm resulting in little influence on the conventional diffraction effect compared with one-dimensional grating when the incident light is in the mid-infrared region. Then the grating becomes quasi-one-dimensional gold grating. In comparison with the mid-infrared incident light, Λ₁ is too small and the value of i can only be set as zero. When considering (i, j) = (0, 1) or (0, −1), the resonant wavelength of SPP corresponds to 4.6 μm, as illustrated in Fig. 2(d). Surprisingly, theoretically derived resonant wavelength from Eqs. (2) and (3) well matches the calculated results by FEM in Fig. 2(a), suggesting that mid-infrared absorption of the AlGaN/GaN QWIP can be effectively enhanced and controlled via the normal incident light coupling with SPP.

To highlight the significant enhancement of |E_z|² via the proposed structure, Fig. 3(a) shows the spectrums of averaged |E_z|² across the whole quantum well region considering one-dimensional (Λ₁ = 1 μm, Λ₂ = 2 μm), quasi-one-dimensional (Λ₁ = 1.1 μm, Λ₂ = 2 μm) and two-dimensional gold gratings (Λ₁ = 2 μm, Λ₂ = 2 μm) with the same h = 100 nm and d = 1 μm. These distinct peaks show that all the three gratings can obviously enhance the E_z in MQWs which can be absorbed by QWIP. It can be noticed that, for our AlGaN/GaN QWIP, the quasi-one-dimensional gold grating is much more effective than the other two. As illustrated in Fig. 3(b), the enhancement of |E_z|² obtained via the quasi-one-dimensional gold grating is 2 (black arrow) and 1.3 (red arrow) times higher than via the one-dimensional and two-dimensional gold gratings at 4.65 μm, respectively. In view of the comparatively poor enhancement of |E_z|² via one-dimensional gold grating, here we only make a comparison of the latter two gratings. Compared with the two-dimensional gold grating with two SPP resonant peaks whose value are 3.25 μm and 4.6 μm, the quasi-one-dimensional gold grating eliminates the short ( ± 1, ± 1) resonant peak at 3.25 μm which will influence the performance of QWIP. Furthermore, it can be deduced from Fig. 3(b) that the full width at half maximum (FWHM) of |E_z|² spectrum for quasi-one-dimensional gold grating is much wider than that obtained via the two-dimensional grating, which will make great sense when the operation wavelength of the QWIP shifts under certain circumstance. As illustrated in Fig. 4, the FWHM of |E_z|² spectrum for the quasi-one-dimensional gold grating is 0.78 μm, 2 times larger than that for the two-dimensional gold grating, verifying our deduction.

Fig. 3 (a) Averaged |E_z|² across the whole quantum well region at a normal incidence for different wavelengths: one-dimensional gold grating (black line), quasi-one-dimensional gold grating (red line) and two-dimensional gold grating (blue line); (b) |E_z|² enhancement ratios M: |E_z|²_{_avg0} for quasi-one-dimensional grating, |E_z|²_{_avg1} for one-dimensional grating and |E_z|²_{_avg2} for two-dimensional grating.

Download Full Size | PDF

Fig. 4 FWHM of |E_z|² spectrums and relevant peak wavelengths of three patterned gratings.

Download Full Size | PDF

The electric field distribution and energy flow at 4.65 μm are also investigated in three different gratings mentioned above to reveal the underlying mechanism in the enhanced |E_z|². Figure 5 compares the |E_z| distribution and time-averaged Poynting vector 10 nm under the Au/semiconductor interface. The time-averaged Poynting vector represents the energy flow in the x-y plane, which clearly shows that the electromagnetic wave from the adjacent edges couple with each other along y-axis, generating SPP standing waves with the interference patterns in Fig. 5. It can also be noticed that the |E_z| distributions of the three devices are very strong from the edges of square holes perpendicular to the polarization orientation of incident light. This phenomenon is mainly owing to SPP resonantly excited by the coupling between free surface charges of the metal and the incident electromagnetic wave [19]. Interestingly, the |E_z| and time-averaged Poynting vector in Fig. 5(b) and Fig. 5(c) are much stronger than that in Fig. 5(a), meaning that SPPs generated in the devices with quasi-one-dimensional or two-dimensional gold grating are much stronger. Specially, a little fraction of the energy flow couples between the adjacent square holes along x-axis and LSP is excited in the right angle. Therefore, it is not only the SPP but the LSP generated via the quasi-one-dimensional and two-dimensional gold gratings that is responsible for the significant enhancement of |E_z|² in quantum well region. As illustrated in Fig. 6, higher charge density is also obtained via the quasi-one-dimensional and two-dimensional gold gratings compared with the one-dimensional gold grating because the distribution of charge is denser at the surface of metal with smaller radius of curvature. For the latter two gratings, due to the square holes patterned in the gold film, the equivalent radius of curvature is much smaller, resulting that the charge density at the gold surface is larger and stronger SPP and LSP are excited at the same time which help to induce electric field component along MQWs growth direction. However, whatever the |E_z|, time-averaged Poynting vector or charge density is almost the same for the quasi-one-dimensional and two-dimensional gold gratings which indicates similar SPP and LSP intensity. For the two gratings, the duty ratios of the air holes are 25% and 45.5%, respectively which suggests that the Fresnel reflection loss of the quasi-one-dimensional gold grating is much weaker and more incident light will be coupled into SPP and LSP. The smaller periodicity of the quasi-one-dimensional gold grating along x-axis also enables 1.8 times more plasma excitation source than the two-dimensional gold grating. Accordingly, strong enhancement of |E_z|² in quantum well region is realized via the quasi-one-dimensional gold grating because of the following three advantages: weaker Fresnel reflection loss, more plasma excitation source and higher charge density.

Fig. 5 Distribution of |E_z| in the x-y plane 10 nm under the Au/semiconductor interface at 4.65 μm: (a) one-dimensional gold grating; (b) quasi-one-dimensional gold grating; (c) two-dimensional gold grating. The black arrows represent the normalized time-averaged Poynting vector.

Download Full Size | PDF

Fig. 6 Current density in the x-y plane 10 nm under the Au/semiconductor interface at 4.65 μm: (I) one-dimensional gold grating; (II) quasi-one-dimensional gold grating; (III) two-dimensional gold grating.

Download Full Size | PDF

The averaged |E_z|² across the whole quantum well region reaches 0.85 (V/m)² at the operation wavelength of the AlGaN/GaN QWIP. To characterize the enhancement of |E_z|² via the quasi-one-dimensional gold grating at different location of the quantum well region, the function $F = {\iint_{Z = S} | E_{Z} |}^{2} d x d y / {\iint_{Z = S} | E_{0} |}^{2} d x d y$ is defined, where E₀ is the electric field of the incident light and E_z is the z component of the induced electric field over the x-y plane locating at the distance s away from the Au/semiconductor interface. As illustrated in Fig. 7, |E_z|² is 1.66 times stronger than |E₀|² at the Au/semiconductor interface which indicates a strong resonance of incident light and plasmon modes. At the very beginning and the end of quantum well region (green region), the defined function F is up to 1.15 (s = 30 nm) and 0.675 (s = 230 nm), respectively, directly indicating that a large amount of electric field component perpendicular to quantum well region exists in MQWs. When considering the actual structure of the QWIP, electromagnetic wave arriving at the bottom contact layer/AlN and AlN/c-sapphire interfaces will be reflected to the MQWs strongly and SPP can be excited again at the Au/semiconductor interface when the momentum difference is compensated, inducing more E_z for the QWIP to make response. It should be pointed out that, from the inset of Fig. 7 (blue line), the |E_z|² is about 3 times higher compared with the sum of |E_x|² and |E_y|² in quantum well region. The results indicate that the composition of electric field is efficiently converted into E_z via the quasi-one-dimensional gold grating.

Fig. 7 Averaged |E_z|² enhancement over the x-y plane (F) as a function of the distance (s) away from the Au/semiconductor interface. The green region represents the AlGaN/GaN quantum well region. The inset shows the proportion of E_z component in quantum well region.

Download Full Size | PDF

AlGaN/GaN QWIP can effectively make response when the electric field in MQWs has a component E_z along the MQWs growth direction. The photocurrent is proportional to the averaged |E_z|² across the whole quantum well region [30]. Therefore, in order to highlight the effects of the proposed grating, the optical coupling efficiency $η = {∭_{Δ v} | E_{z} |}^{2} d x d y d z / ∭_{Δ v} {| E_{0} |}^{2} d x d y d z$ is defined, where Δv represents the volume of quantum well region. When Λ₁ = 1.1 μm, Λ₂ = 2 μm, d = 1 μm, t = 100 nm, the optical coupling efficiency η reaches 85% at 4.65 μm, which further confirms that the performance of the photodetector will be potentially improved.

4. Conclusions

In summary, a new kind of grating, quasi-one-dimensional gold grating is numerically investigated. By comparing the electric field distribution, time-averaged Poynting vector and current density at the Au/semiconductor interface of three different grating structures, it shows that the quasi-one-dimensional gold grating can provide more plasma excitation source and higher charge density. These promising results indicate that the effective electric field component can be greatly enhanced by the plasmon resonance under normal illumination, resulting in a high optical coupling efficiency of 85% in quantum well region. More inspiringly, the small-pixel and large-area focal plane arrays based on AlGaN/GaN QWIP operating in mid-infrared will be finally realized via the quasi-one-dimensional gold grating.

Acknowledgments

This work was supported by the National Basic Research Program of China (Grant No. 2012CB619302, 2010CB923204), the National Natural Science Foundation of China (Grant No. 60976042, 51002058, 10990102), the Science and Technology Bureau of Wuhan City (Grant No. 2014010101010003).

References and links

1. J. S. Yang, H. Sodabanlu, M. Sugiyama, Y. Nakano, and Y. Shimogaki, “Blueshift of intersubband transition wavelength in AlN/GaN multiple quantum wells by low temperature metal organic vapor phase epitaxy using pulse injection method,” Appl. Phys. Lett. 95(16), 162111 (2009). [CrossRef]

2. C. C. Huang, F. J. Xu, X. D. Yan, J. Song, Z. Y. Xu, L. B. Cen, Y. Wang, J. H. Pan, X. Q. Wang, Z. J. Yang, B. Shen, B. S. Zhang, X. S. Chen, and W. Lu, “Intersubband transitions at atmospheric window in Al_xGa_1−xN/GaN multiple quantum wells grown on GaN/sapphire templates adopting AlN/GaN superlattices interlayer,” Appl. Phys. Lett. 98(13), 132105 (2011). [CrossRef]

3. D. Hofstetter, J. Di Francesco, P. K. Kandaswamy, and E. Monroy, “Intersubband spectroscopy probing higher order interminiband transitions in AlN-GaN-based superlattices,” Appl. Phys. Lett. 98(7), 071104 (2011). [CrossRef]

4. W. Tian, W. Y. Yan, X. Hui, S. L. Li, Y. Y. Ding, Y. Li, Y. Tian, J. N. Dai, Y. Y. Fang, Z. H. Wu, C. H. Yu, and C. Q. Chen, “Tunability of intersubband transition wavelength in the atmospheric window in AlGaN/GaN multi-quantum wells grown on different AlGaN templates by metalorganic chemical vapor deposition,” J. Appl. Phys. 112(6), 063526 (2012). [CrossRef]

5. P. K. Kandaswamy, H. Machhadani, C. Bougerol, S. Sakr, M. Tchernycheva, F. H. Julien, and E. Monroy, “Midinfrared intersubband absorption in GaN/AlGaN superlattices on Si (111) templates,” Appl. Phys. Lett. 95(14), 141911 (2009). [CrossRef]

6. K. Driscoll, A. Bhattacharyya, T. D. Moustakas, R. Paiella, L. Zhou, and D. J. Smith, “Intersubband absorption in AlN/ GaN/ AlGaN coupled quantum wells,” Appl. Phys. Lett. 91(14), 141104 (2007). [CrossRef]

7. H. Machhadani, Y. Kotsar, S. Sakr, M. Tchernycheva, R. Colombelli, J. Mangeney, E. Bellet-Amalric, E. Sarigiannidou, E. Monroy, and F. H. Julien, “Terahertz intersubband absorption in GaN/AlGaN step quantum wells,” Appl. Phys. Lett. 97(19), 191101 (2010). [CrossRef]

8. N. Péré-Laperne, C. Bayram, L. Nguyen-Thê, R. McClintock, and M. Razeghi, “Tunability of intersubband absorption from 4.5 to 5.3 μm in a GaN/Al 0.2 Ga 0.8 N superlattices grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 95(13), 131109 (2009). [CrossRef]

9. A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electron. Rev. 12(2), 221–245 (2004).

10. B. F. Levine, “Quantum-well infrared photodetectors,” J. Appl. Phys. 74(8), R1–R81 (1993). [CrossRef]

11. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

12. J. K. Mapel, M. Singh, M. A. Baldo, and K. Celebi, “Plasmonic excitation of organic double heterostructure solar cells,” Appl. Phys. Lett. 90(12), 121102 (2007). [CrossRef]

13. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008). [CrossRef] [PubMed]

14. W. L. Bai, Q. Q. Gan, F. Bartoli, J. Zhang, L. K. Cai, Y. D. Huang, and G. F. Song, “Design of plasmonic back structures for efficiency enhancement of thin-film amorphous Si solar cells,” Opt. Lett. 34(23), 3725–3727 (2009). [CrossRef] [PubMed]

15. H. H. Shen and B. Maes, “Combined plasmonic gratings in organic solar cells,” Opt. Express 19(106Suppl 6), A1202–A1210 (2011). [PubMed]

16. L. H. Smith, J. A. E. Wasey, and W. L. Barnes, “Light outcoupling efficiency of top-emitting organic light-emitting diodes,” Appl. Phys. Lett. 84(16), 2986–2988 (2004). [CrossRef]

17. D. M. Yeh, C. F. Huang, C. Y. Chen, Y. Ch. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008). [CrossRef] [PubMed]

18. C. H. Lu, C. C. Lan, Y. L. Lai, Y. L. Li, and C. P. Liu, “Enhancement of Green Emission from InGaN/GaN Multiple Quantum Wells via Coupling to Surface Plasmons in a Two-Dimensional Silver Array,” Adv. Funct. Mater. 21(24), 4719–4723 (2011). [CrossRef]

19. H. S. Zhang, J. Zhu, Z. D. Zhu, Y. H. Jin, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on a multilayered M-shaped nano-grating,” Opt. Express 21(11), 13492–13501 (2013). [CrossRef] [PubMed]

20. R. D. R. Bhat, N. C. Panoiu, S. R. J. Brueck, and R. M. Osgood Jr., “Enhancing the signal-to-noise ratio of an infrared photodetector with a circular metal grating,” Opt. Express 16(7), 4588–4596 (2008). [CrossRef] [PubMed]

21. W. Wu, A. Bonakdar, and H. Mohseni, “Plasmonic enhanced quantum well infrared photodetector with high detectivity,” Appl. Phys. Lett. 96(16), 161107 (2010). [CrossRef]

22. S.-Q. Zhai, J.-Q. Liu, F.-Q. Liu, and Z.-G. Wang, “A normal incident quantum cascade detector enhanced by surface plasmons,” Appl. Phys. Lett. 100(18), 181104 (2012). [CrossRef]

23. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

24. W. Wang, D. Zhao, Y. T. Chen, H. M. Gong, X. X. Chen, S. W. Dai, Y. Q. Yang, Q. Li, and M. Qiu, “Grating-assisted enhanced optical transmission through a seamless gold film,” Opt. Express 22(5), 5416–5421 (2014). [CrossRef] [PubMed]

25. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127(2), 363–379 (1996). [CrossRef]

26. J. H. Edgar, “EMIS Datareviews Series,” in Properties of Group III Nitrides, W. J. Meng, ed. (INSPEC, 1994).

27. T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997). [CrossRef]

28. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1120 (1983). [CrossRef] [PubMed]

29. H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).

30. R. Zhang, X. G. Guo, J. C. Cao, and H. C. Liu, “Near field and cavity effects on coupling efficiency of one-dimensional metal grating for terahertz quantum well photodetectors,” J. Appl. Phys. 109(7), 073110 (2011). [CrossRef]

Efficient optical coupling in AlGaN/GaN quantum well infrared photodetector via quasi-one-dimensional gold grating

Abstract

1. Introduction

2. Theoretical model

3. Results and discussion

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (7)

Equations (3)

Optics Express