## 1. Introduction

Surface electromagnetic waves (also called surface plasmon polaritons, SPPs), predicted by Ritchie in 1957 [1], are coherent electron oscillations at a metal surface. The coherent electron oscillations generate electromagnetic (EM) waves that travel along the dielectric/metal interface [2]. Depending on the metal structures, certain resonant modes of the surface electromagnetic waves can be strongly absorbed (or excited) [2]. This is generally referred to as excitation of surface plasmonic resonance (SPR) modes. SPRs propagate along the metal-dielectric interface. The intensity profile exponentially decreases with the distance from metal-dielectric interface, that is, SPs are confined at the metal-dielectric interface. Such surface confinement effects have been used in Raman scattering, that is, surface-enhanced Raman scattering (SERS) [3–5] and spectroscopy [6, 7] and have been reported with thousands of times sensitivity enhancement [3, 4]. In addition to SERS, the SPR enhancement technology also provides a promising technique to concentrate EM energy on surface area and thus enables high quantum efficiency with a thin active absorption layer in a photodetector. Significant performance enhancements in a quantum dot infrared photodetector (QDIP) have been reported [8–15].

In addition, the SPR modes can also change EM field distribution and thus offers an effective technique for EM field engineering to achieve specific transmission and/or receiving patterns with polarization and detection spectrum engineering capability [11, 16]. In this chapter, a brief review of the fundamental concepts of SPRs will be first given and followed by the description of their applications in infrared detections. SPR-based EM field engineering will also be presented with the discussion of polarization and receiving angle control.

## 2. Review of surface plasmonic resonance

### 2.1. Plasma frequency, complex conductivity and the Drude model

Plasmonic waves are electromagnetic waves. They follow Maxwell equations, which can be expressed as follows in the phasor domain

where

where **4**) can therefore be expressed as follows:

where

where

The current density is related to the speed of the charge

where **7**) and (**8**), one gets:

Taking another partial derivative of *t*, one gets:

Eq. (**10**) can be expressed as follows:

where **11**) can thus be changed to

In phasor domain, Eq. (**12**) can be expressed as follows:

where **1**) and (**13**), one gets

Taking the partial derivative of *t* for Eq. (**8**), one gets

The **15**) becomes

In phasor domain, Eq. (**16**) can be rewritten as follows:

Combining Eqs. (**5**) and (**17**), one gets:

The complex permittivity

The derivations and equations above are for the ideal lossless free-electron gas model. The loss term can be included in the model by introducing a relaxation rate

Eq. (**20**) is the complex permittivity given by the well-known Drude model [17].

### 2.2. Plasmonic waves at the dielectric and metal interface

Following Raether in Ref. [2], one can analyse plasmonic waves using a transmagnetic (TM) plane wave. **Figure 1** shows the incident of a TM plane EM wave with the *H*-field in the y-direction. Note that the phasor expressions of the H-fields follow the convention of **6**) to use this convention.

Under the aforementioned convention, the E-field defined by Eq. (**6**) can be changed to

From Eq. (**21**), the E_{x} can be expressed as follows:

where

where

Since Eq. (**27**) and Eq. (**28**) are valid for any *x*,

When there is no reflection, that is, **27**) and (**28**) become

Combining Eqs. (**29**) and (**30**), one gets the following:

Plugging Eq. (**31**) into Eq. (**26**), one gets the following:

Combing Eq. (**32**) with Eq. (**25**), one can get

Eq. (**33**) can be expressed using relative permittivity

where

**34**) as follows:

where Re(.) and Im(.) are taking the real and the imaginary parts. The plasmonic wave propagates in *x* and *z* directions with loss described by the imaginary parts of the corresponding directions, that is, **36**) can be simplified as follows:

### 2.3. Plasmonic wave excitation in a metallic two-dimensional (2D) sub-wavelength hole array (2DSHA) structure

Surface plasmonic waves can be excited by numerous structures. The metallic 2DSHA structure [18] is one of the commonly used plasmonic structures for performance enhancement in infrared photodetectors [8, 10–12]. **Figure 2** shows a schematic structure with the light incident scheme of the metallic 2DSHA array structure. The 2DSHA structure is a square lattice with the period of

**Figure 3** shows the cross section of the light incidence on the 2DSHA structure. The excited plasmonic waves and the scattered waves by the 2DSHA structure are indicated in the figure.

From E-M field boundary conditions, the following relations hold:

The excitation efficiency

where

### 2.4. Near-field E-field distribution in the 2DSHA structure

The near-field E-field component can be simulated as well. **Figure 4** shows the top (*x*-*y*) and cross-section (*x*-*z*) views of the ^{®}. The incident light is linearly polarized surface normal plane wave with E-field magnitude of 1 V/m. The colour scale bar represents the magnitude of the *E*_{x}.

**Figure 5** shows the top (*x*-*y*) and cross-section (*x*-*z*) views of the **Figures 4** and **5**, both *E*_{x} and *E*_{z} strongly depend on the excitation wavelengths. *E*_{z} is high between 7.6 and 8.5 µm, whereas *E*_{x} is strong between 7.6 and 8.0 µm. *E*_{z} is primarily at the edge of the holes, whereas *E*_{x} is inside the holes. The period of the 2DSHA

From Eq. (35),

where *λ*_{0} is the free space wavelength, *ε*_{m} and *ε*_{d} are the relative permittivity of the metal and GaAs, respectively. The dielectric constant of GaAs in the long-wave infrared region is 10.98 [19]. The dielectric constant of Au is calculated to be −1896 + *i*684 at 7.6 µm [1]. The calculated plasmonic resonant wavelength is *λ*_{sp} = 7.6 µm. At the resonant wavelength (i.e.

## 3. QDIPs in mid-wave infrared (MWIR) and long-wave infrared (MWIR/LWIR) detection

QDIPs are based on intersubband transitions in self-assembled InAs quantum dots (QDs). The simplified band diagram and the schematic structures of a QD infrared photodetector (QDIP) are shown in **Figure 6(a)** and **6(b)**, respectively. The s, p, d, f, represent the energy levels of a QD with the wetting layers (WL). A typical QDIP consists of vertically-stacked InAs quantum dots layers with GaAs capping layers. The electrons are excited by the normal incident light and subsequently collected through the top electrode and generate photocurrent. This is a unipolar photodetector, where only conduction band is involved in the photodetection and photocurrent generation process.

The QDIP technology offers a promising technology in MWIR and LWIR photodetection due to the advantages provided by the three-dimensional (3D) quantum confinement of carriers—including intrinsic sensitivity to normal incident radiation [13], high photoconductive (PC) gain, high quantum efficiency [15] and photoresponsivity [16]. The normal incidence detection capability greatly simplifies the fabrication complexity for a large format (1K × 1K) FPA. The high photoconductive (PC) gain and high photoresponsivity provide a promising way for MWIR and LWIR sensing and detection.

**Figure 7** shows the photodetection spectrum of a QDIP. It covers a broadband IR spectrum from 3 to 9 µm. The insert of **Figure 7** shows an atomic force microscopic (AFM) picture of the QDs by self-assembled epi-growth. The growth gives high-density QDs with uniform sizes. The InAs/GaAs QD material is a mature material system with low substrate cost, high material quality and large wafer growth capability. It can offer low-cost MWIR and LWIR photodetectors and focal plane arrays (FPAs) with simplified fabrication processes and high yield. Detailed QDIP performance, such as photoconductive gains, noise, photoresponsivity and photodetectivity can be found in literature [20–27].

## 4. 2DSHA plasmonic-enhanced QDIPs

### 4.1. Backside configured 2DSHA-enhanced QDIPs

Surface confinement of plasmonic waves enables high absorption using a thin absorption layer and thus leads to significant enhancement in QDIPs [8, 10–13, 15]. We have developed a backside-configured plasmonic enhancement technology by fabricating the 2DSHA plasmonic structures on top of a QDIP and illuminating the QDIP from the opposite side of the plasmonic structure (i. e. backside illumination) [12]. **Figure 8(a)** and **8(b)** show the schematic cross-section structures of the backside-configured plasmonic QDIP and the reference QDIP without the plasmonic structure, respectively. **Figure 8(c)** and **8(d)** show scanning electron microscopic (SEM) images of the plasmonic structures on a QDIP and a close-up view of the plasmonic structure, respectively.

**Figure 9** shows the measured photocurrent spectra of the backside-configured plasmonic QDIP compared with the top-side configured plasmonic QDIP and the reference QDIP. The backside-configured plasmonic QDIP clearly shows higher plasmonic enhancement than those of the top-side configured plasmonic QDIP and the reference QDIP.

**Figure 10(a)** shows the simulated E-field intensities of the top and backside-configured plasmonic structures, respectively. The backside-configured plasmonic structure can induce stronger E-field at the interface and therefore can provide larger plasmonic enhancement [12].

### 4.2. Wavelength-tuning and multispectral enhancement

From Eq. (**42**) and

where (m, n) are the orders of the grating vectors. Therefore, the plasmonic resonance wavelength can be tuned by changing the period of the 2DSHA plasmonic structure. The plasmon resonant peaks *λ*_{sp} of different *(m, n)* orders for various 2DSHA periods *p* are shown in **Figure 11** that exhibits the linear dependence of the resonant peak wavelength *λ*_{sp} with the period *p* of the 2DSHA for different *(m, n)* orders. As predicted by Eq. (**43**), good linearity is obtained for both the (1, 0)th or (0, 1)th and the (1, 1)th order plasmonic resonant peaks.

We define the photocurrent enhancement ratio *R* as follows:

where *I*_{plasmonic} is the photocurrent of the plasmonic QDIP and *I*_{ref} is the photocurrent of the reference QDIP without the 2DSHA structures.

**Figure 12** shows the photocurrent enhancement ratio spectra for all the plasmonic QDIPs with different periods from 1.4 to 2.0 µm. The periods of the 2DSHA plasmonic structures are marked on the curves. The insert shows a microscopic picture of a QDIP with a 2DSHA plasmonic structure. The IR incidence is from the backside of the QDIPs, that is, backside-configured 2DSHA plasmonic structures.

As shown in **Figure 12**, the enhancement wavelengths can be tuned by varying the periods of the 2DSHA plasmonic structures. This allows one to achieve multispectral QDIPs without fabricating an individual filter on each photodetector [28].

### 4.3. Polarization dependence and polarimetric detection

From Eq. (**43**), the plasmonic resonant wavelength depends on the period *p*. By changing the plasmonic lattice from a square lattice to a rectangular lattice with different periods in the x and y directions, one can engineer the resonant wavelengths at different polarizations.

**Figure 13(a)** shows an SEM picture of a rectangular lattice 2DSHA plasmonic structure with the periods of 2.6 and 3.0 µm in the *x*-direction and the *y*-direction, respectively. **Figure 13(b)**–**(d)** shows the transmission spectra of the un-polarized, 90° polarized (i.e. polarization in *y*-direction), and 0° polarized (i.e. polarization in *x*-direction), respectively. The resonant wavelengths correspond to the orders in the *x*- and *y*- directions are marked in the figures. The un-polarized light shows transmission in both (0, 1) and (1, 0) orders. However, the 0° polarized light only shows transmission at the (1, 0) order resonant wavelength and the 90° polarized light only shows transmission at the (0, 1) order.

**Figure 14** shows a microscopic picture of a QDIP with the rectangular lattice 2DSHA structure. The insert shows an SEM picture of the rectangular lattice 2DSHA structure.

**Figure 15(a)** and **(b)** shows the measured detection spectra of the plasmonic QDIP at 90° polarization and 0° polarization, respectively. The photo-response of a reference QDIP without the plasmonic structure is also shown in the figures for comparison. The plasmonic QDIP shows different detection wavelengths at different polarizations.

### 4.4. Angular dependence of the 2DSHA plasmonic enhancement

**Figure 16** shows the schematic view of the top-illuminated 2DSHA plasmonic QDIP with an incident angle

From Eq. (**41**), the coupling efficiency

From Eq. (**45**), the coupling condition can be expressed as follows:

Taking the + sign, one can write Eq. (**46**) in terms of plasmonic resonant wavelength

Eq. (**47**) shows that the enhancement wavelength shifts to shorter wavelengths as the incident angle increases.

**Figure 17** shows the measured photocurrent of the 2DSHA plasmonic QDIP at different incident angles of 0°,

To quantitatively analyse the relationship between the plasmonic wavelength shift and the incident angle, we plot the plasmonic resonant wavelengths **Figure 18** shows the **47**). The interception and the slope are 7.6 and −1.4 µm, respectively. The interception 7.6 µm matches the value **47**). However, the slope of −1.4 µm is smaller than **47**). This may be due to the plasmonic scattering-induced phase distribution in

## 5. Conclusion

In conclusion, 2DSHA plasmonic structures can effectively induce plasmonic resonant waves. The resonant wavelength depends on the period of the plasmonic structure. The surface confinement effect allows one to improve the performance of QDIPs. The plasmonic enhancement also strongly depends on the polarization and the incident angle. The polarization and incident angle dependence allow polarimetric and polarization engineering in QDIP designs.