1. Introduction

Antennas are key devices for transmitting and receiving electromagnetic waves in the RF, microwaves and millimeter spectral regimes. The dimension of an antenna strongly depends on its operating frequency [1–3]. In RF or microwave spectral regimes, the antenna dimension is in centimeters or millimeters, whereas in optical spectral regimes such as visible, near infrared (IR), and middle wave infrared (MWIR) and longwave infrared (LWIR), the antenna dimensions range from a few to hundreds of nanometers (nm) to a few micrometers (µm) [1–3]. The state-of-the-art nanofabrication techniques, such as electron-beam (E-beam) photolithography and focused ion-beam (FIB) milling, allow the fabrication of optical antennas with nm scale accuracy and thus enable the development of optical antennas [1, 2, 4]. Optical antennas and their applications in controlling light sensing and emission properties have been extensively researched [1, 2, 4–6]. For light sensing and imaging applications, optical antennas can collect incident light and focus it in a small region well below the diffraction limit of light [1, 3, 6]. Such effective light collection and the strong light focusing effect not only can enhance the photoresponsivity of a photodetector through effective light collection, but also enable high-resolution light sensing and imaging beyond the diffraction limit of light.

Metallic nanoparticles are promising optical nano-antennas [6, 7]. Light can be coupled to localized surface plasmonic resonance (LSPR) and confined within the small region of the nanoparticles [8–10]. Such nano-antennas have been extensively used to enhance the performance of various devices and optical systems, including surface plasmonic resonance enhanced Raman scattering (SERS) [6, 11, 12], plasmonic solar cells [13, 14], and photodetectors [15].

In addition to the strong subwavelength electric field (E-field) enhancement and confinement effects, optical antennas also change the near-field E-field distribution and their polarizations due to the excitation of the LSPR mode and the antenna re-radiation [16, 17]. Compared with optical antennas for thermal detectors and bulk-material detectors [15, 18], optical antenna near-filed E-field distribution and polarizations are more critical for photodetectors based on low-dimensional materials, such as quantum well infrared photodetectors (QWIP) and quantum dot infrared photodetectors (QDIP). For a QDIP, the photon-electron excitation in quantum dots (QD) involves electron transitions between QD’s discrete energy levels with different quantum selection rules with specific polarization requirement [19]. Because of this, near field $\overrightarrow{E}$ vector components play different roles in the photon-electron excitation process in a QDIP. This makes the knowledge of near-field $\overrightarrow{E}$ vectors of optical antennas essential to the understanding of the optical antenna enhancement in a QDIP. In this letter, we report the analysis of the near-field vector components of the metallic circular disk array (MCDA) optical antenna and their contribution to the QDIP enhancement.

2. Device structure

The MCDA optical antenna is similar to the nanoparticle optical antenna except that due to wavelength scaling effect [3], the dimensions of the optical antennas is a few µm in the MWIR and LWIR wavelength region and the optical antennas are uniform and arranged in a two-dimensional (2D) periodic structure. Figure 1 shows the schematic structure of the MCDA optical antenna array. The MCDA optical antenna array is a square lattice with a period of 2.3 µm. The diameter of the metal circular disks is 1.15 µm and the thickness of the metal (gold) layer is 30 nm.

 

Fig. 1 Schematic structure of the MCDA optical antenna. It is a 2D square lattice with a period of 2.3 µm. The diameter of the metal circular disks is 1.15 µm and the thickness of the metal layer is 30 nm.

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3. Plasmonic near-field simulation

The dipole LSPR mode can be excited in the MCDA optical antenna by illumination lights at resonant wavelengths [20, 21]. The reflection light plus the dipole LSPR re-radiation form the near field $\overrightarrow{E}$ vector. We performed the simulation using CST Microwave Studio® to obtain the near field $\overrightarrow{E}$ vector. Time domain solver and periodical boundary in x-y directions and open boundary conditions in z-direction were used in the simulation. Figure 2(a) shows x-z cross-section view of the $\overrightarrow{E}$ vector distribution the x-z cross-section (cut-plane) is at the center of the circular disk (i. e. y = 0). The optical antenna array is illuminated from the substrate side (i. e. backside-illumination) with a plane-wave light polarized in the x direction. The wavelength of the excitation light is 7.3 µm, and its amplitude is set to 1.0 V/m (i.e. ${\overrightarrow{E}}_{in}=1.0\widehat{x}{e}^{ikz}$ V/m). The dark lines in Fig. 2(a) indicate QD active region. The magnitude scale bar is also shown in Fig. 2. $\overrightarrow{E}$ is in the z-direction across the metal surfaces, whereas it is x-direction in the other region. The directions of $\overrightarrow{E}$vectors are consistent with electromagnetics (EM) boundary conditions. $\overrightarrow{E}$ vectors at the left and the right edges of the metallic circular disk are opposite, indicating different signs of the charges at the edges. Figure 2(b) and (c) show the z-component (i.e. E_z) and the x-component of $\overrightarrow{E}$ vector at the top surface (x-y cross-section), respectively. It clearly shows the excitation of the dipole LSPR mode on the metallic circular disk. The color scale bar shows the intensity level of $\overrightarrow{E}$vectors.

 

Fig. 2 Simulated E vectors at an x-polarized excitation plane-wave IR light with the wavelength of 7.3 µm: (a) x-z cross section at the y = 0 cut-plane (the center of the circular disk); (b) top view of E_z; (c) top view of E_x. LSPR is excited at this resonant wavelength.

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To understand the resonant excitation of the dipole LSPR mode and its near-field $\overrightarrow{E}$ vector distributions, we simulated $\overrightarrow{E}$ vectors at different excitation wavelengths from 6.5 µm to 8.5 µm. The excitation IR lights are chosen to have the same x-polarization and the same amplitude of 1.0 V/m (i.e. ${\overrightarrow{E}}_{in}=1.0\widehat{x}{e}^{ikz}$ V/m).

Figure 3 shows x-z cross-section views of E_x and E_z distributions at various excitation wavelengths. The cut-plane is at y = 0 µm (center of the circular disk). The black lines in the Figs. indicate the QD layers. The first row shows E_x, and the second row shows E_z. E_y is found to be two orders of magnitude smaller than E_x and E_z, and is therefore negligible in the $\overrightarrow{E}$ vector analysis. Since the excitation light is x-polarized, the weak E_y indicates low LSPR scattering in the MCDA optical antenna. The color scale bar (not shown in Fig. 3) is the same as that shown in Fig. 2.

 

Fig. 3 Simulated near-field E_x and E_z distributions at various excitation wavelengths. E_x is primarily at the edge of the circular disk, whereas E_x is under the circular disk. E_z has a larger overlap with the QD layers than E_x at the y = 0 µm cut-plane.

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From Fig. 3, both E_x and E_z depend on the excitation wavelengths. E_x is primarily at the edge of the circular disk, whereas E_z is under the circular disk. E_z has a larger overlap with the QD layers than E_x at the y = 0 µm cut-plane.

Figure 4 shows x-z cross section views of E_x and E_z distributions at the y = 1 µm cut-plane (area away from the metallic circular disks). E_x shows a strong overlap with the QD regions at the excitation wavelength of 7.6 µm at this cut plane. Other cut planes away from the metallic circular disks show similar results. The color scale bar (not shown in Fig. 4) is the same as that shown in Fig. 2.

 

Fig. 4 Simulated near-field E_x and E_z distributions at the y = 1 µm cut-plane. E_x shows a strong overlap with the QD regions at the excitation wavelength of 7.6 µm.

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4. Device fabrication, characterization and analysis

To understand the contribution of E_x and E_z play to the QDIP enhancement, we fabricated the MCDA optical antenna array on a QDIP. The QDIP structure, growth conditions and device processing procedures are similar to QDIPs reported before [22, 23]. Figure 5(a) shows a microscopic picture of the QDIP with the MCDA optical antenna array. Figure 5(b) shows the close-up SEM view of the MCDA optical antenna array. Figure 5(c) shows the schematic structure of the QDIP. The QDIP was grown on a GaAs substrate with 10 layers of QD heterostructures. The active QD region is from 0.2 µm to 0.7 µm below the sample surfaces.

 

Fig. 5 QDIP with the MCDA optical antenna array: (a) microscopic picture; (b) close-up SEM view; (c) schematic structure of the QDIP.

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Figure 6 shows the measured Fourier transform infrared (FTIR) photocurrent spectrum of the QDIPs with the MCDA optical antenna as compared to the reference QDIP. The MCDA optical antenna gives high photocurrent enhancement over the reference QDIP.

 

Fig. 6 Measured photocurrent spectra of the QDIPs with MCDA optical antenna compared to the reference QDIP. he MCDA optical antenna gives high photocurrent enhancement.

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By taking the ratio of the MCDA QDIP and the reference QDIP at different wavelengths, one can obtain the photocurrent enhancement ratio spectrum [22]. Figure 7(a) shows the photocurrent enhancement ratio at wavelengths from 5 µm to 9 µm. An over 13 times photocurrent is obtained at the resonant wavelength of 7.3 µm. Figure 7(b) shows the integrated intensities of the near-field vector components over the QD active region, i.e. ${\displaystyle {\int }_V{\left|E_i\right|}^{2}dV}$(i = x, or z), where V indicates volume integral over the QD active region. As shown in Fig. 7(b), ${\displaystyle {\int }_V{\left|E_x\right|}^{2}dV}$ is larger than ${\displaystyle {\int }_V{\left|E_z\right|}^{2}dV}$. As shown in Fig. 2(a) and (b), E_z is primarily in the circular disk region, whereas E_x is dominant in the other GaAs region. Since the circular disk region only consists of a small fraction of the device region, the volume integral of ${\left|E_z\right|}^2$ is smaller than that of ${\left|E_x\right|}^2$due to the smaller volume E_z spreads. In addition, by comparing Fig. 7(a) and Fig. 7(b), one can find that the spectrum of ${\displaystyle {\int }_V{\left|E_x\right|}^{2}dV}$ more closely resembles the photocurrent enhancement ratio spectrum shown in Fig. 7(a), suggesting that E_x plays a major role in the QDIP enhancement. This also indicates that the overlapping of the near-field vectors with the QD active region is critical for the plasmonic enhancement due to $\overrightarrow{E}$and electric dipole interaction in QDs. The experimental photocurrent enhacement in Fig. 7(a) shows a broader spectral width than the simulation in Fig. 7(b). This might be due to the SPR loss caused by inperfect deivce fabrication, which leads to a broader spectral width in the frequecncy domain.

 

Fig. 7 (a) photocurrent enhancement ratio spectrum of the QDIP with the MCDA optical antenna array; (b) integrated intensities of the near field vector components over the QD active region. ${\displaystyle {\int }_V{\left|E_x\right|}^{2}dV}$ is larger than ${\displaystyle {\int }_V{\left|E_z\right|}^{2}dV}$. ${\displaystyle {\int }_V{\left|E_x\right|}^{2}dV}$ more closely resemble the photocurrent enhancement ratio spectrum, indicating that E_x plays a major role in the QDIP enhancement.

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5. Conclusion

In conclusion, we analyzed the near-field $\overrightarrow{E}$ of the MCDA optical antenna excited at different wavelengths and their distribution and overlapping with the QD active region. At resonant LSPR wavelengths, E_z is primarily in the circular disk region, whereas E_x is mainly in the other GaAs region. E_x has a stronger overlapping and larger intensity integral with the QD active region. The spectrum of ${\displaystyle {\int }_V{\left|E_x\right|}^{2}dV}$ more closely resembles the photocurrent enhancement ratio spectrum. We thus believe E_x plays a major role in the QDIP enhancement. The research also indicates that the overlapping of the near-field vectors with the QD active region is critical for the plasmonic enhancement due to $\overrightarrow{E}$and electric dipole interaction in QDs. The reserach also provides a guideline for the design of other plasmonic optical antenna QDIP photodetectors with various active layer and contacting layer thickness. For QDIP photodetectors with thicker ative layers, one needs to reduce the thickness of the top contacting layer to enasure large overlapping of the near-field vectors with the active region. In addition, the diameter of the plasmonic optical antenna needs to be optimzed to achieve a maximum overlapping of the near-field vectors with the active layer.

Conflict of interest

Xuejun Lu is a co-founder of ANFT. The authors declare no conflict of interest.