1. Introduction

In recent years, photodetectors generating contrasting photocurrents in response to circularly polarized light (CPL) with opposite helicity have attracted attention [1–6] due to their potential applications in spin information processing [7], quantum teleportation [8] and computation [9], and circular dichroism spectroscopy [10]. One rational approach to realizing a compact circular-polarization-sensitive photodetector that uses no bulky optical components is to replace the material constituting the photoactive layer in a conventional photodetector with chiral molecules possessing dissymmetric absorption depending on the helicity of the incident CPL. In this case, the dissymmetric photocurrent is determined by the dissymmetry in absorption quantified either by the circular dichroism value [11]:

Alternatively, one can modify a local electromagnetic environment in the photoactive region so that the dissymmetry in photocurrent is amplified beyond what is expected from the CD value or is induced even with a photoactive layer having no intrinsic chirality [14]. For example, a previous study demonstrated that depending on the helicity of incident CPL, the electromagnetic field intensity can be selectively enhanced near Z-shaped plasmonic structures, generating hot electrons injected into Si over a Schottky barrier [6]. A circular-polarization-sensitive photodetector based on this mechanism yielded a high $g_{\textrm {A}}$ of 1.1 and a near-unity $\eta _{\textrm {A}}$ at $\lambda$ = 1340 nm [6]. Although inherently very fast [15], hot electron injection has a disadvantage that a significant number of hot electrons are thermally relaxed before being injected [16,17], resulting in a low $\eta _{\textrm {E}}$ of 0.2 %. In addition, the dissymmetry factor of photocurrent is only $\sim$70 % of $g_{\textrm {A}}$, meaning that the device architecture was not fully optimized. To realize a high-performance circular-polarization-sensitive-photodetector, it is essential to develop a new optoelectronic platform that can induce high $g_{\textrm {A}}$ while being compatible with photoactive materials suitable for high $\eta _{\textrm {E}}$.

Here, we numerically demonstrate that a circular-polarization-sensitive organic photodetector (CP-OPD) based on a chiral plasmonic nanostructure can achieve both high $g_{\textrm {A}}$ and $\eta _{\textrm {E}}$. In this structure, which consists of a dielectric interposed between a chirally patterned metal layer and a flat metal layer (henceforth referred to as the chiral MDM structure), a plasmon mode featuring a high photonic density of states in the dielectric region is excited only for incident CPL with its helicity matched to the twisted direction of the chiral nanopattern. A key feature of our CP-OPD is that the circular dichroic response is almost decoupled with the engineering of the organic donor–acceptor photoactive layer required for a high internal quantum efficiency ($\eta _{\textrm {I}}$). This is in contrast to previously demonstrated CPL detectors, in which chiral molecules function as both the absorber and the agent that distinguishes the helicity of CPL [1–4]. To fully utilize the plasmonic hotspots in a rational manner, we first investigate the electromagnetic properties of the chiral MDM structure, revealing that the circular dichroic plasmon mode originates from the hybridization of surface plasmon polaritons (SPPs) at the dielectric–top metal and dielectric–bottom metal interfaces. Based on this understanding, we establish a design principle of the plasmonic CP-OPD and comprehensively optimize the device architecture in terms of the geometrical and material parameters.

2. Simulation geometry

Figure 1a shows a chiral MDM structure consisting of a subwavelength-thick dielectric layer sandwiched between top and bottom electrodes, where the top electrode is perforated in a shape of periodically arranged windmills. The region enclosed by the black dashed lines represents a unit cell, with width $\Lambda$ in the $x$ and $y$ directions, possessing a four-fold rotational symmetry, and the origin ($\mathcal {O}$) of the coordinate system is at the center of the square indicated by the red dashed lines. The thicknesses of the top electrode, the bottom electrode, and the dielectric gap are denoted by $t_{\textrm {T}}$, $t_{\textrm {B}}$, and $t_{\textrm {D}}$, respectively. The length and the width of the voids are denoted by $l_{\textrm {V}}$ and $w_{\textrm {V}}$, respectively, and the line width of the metal pattern is indicated by $w_{\textrm {L}}$. Because the thickness of the transparent uppermost layer representing a glass substrate is typically much larger than the wavelength of CPL propagating in the $-\mathbf {\hat {z}}$ direction [Fig. 1(a), red arrow], it is set to be infinite. Organic molecules are chosen as the dielectric material for the following reasons: large absorption coefficient ($\alpha$) allows for sufficient light absorption in the subwavelength-thick layer; the direction of the transition dipole moment of molecules can be controlled [12,18], which is advantageous to fully optimize the chiral light–matter interactions [12]. In Section 3.1, where chiral plasmonic resonances of the chiral MDM structure are investigated, the relative permittivity ($\varepsilon _{\textrm {r}}$) of the dielectric layer is assumed to be 3.24, a typical value for organic semiconductors [19]. In Section 3.2, the dielectric layer is described by the complex relative permittivity tensor ($\bar {\bar {\varepsilon }}_{\textrm {r}}$) to reflect the anisotropic and absorptive characteristics of the constituent molecules. The top and bottom electrodes are composed of silver because it is known to form efficient charge injection and extraction electrodes upon employing appropriate interfacial layers [20] and to have low optical loss [21]. The wavelength-dependent $\varepsilon _{\textrm {r}}$ values of silver are taken from the literature [22], and the $\varepsilon _{\textrm {r}}$ values of the voids and the glass substrate are assumed to be 3.24 and 2.25, respectively, at all wavelengths. All materials are assumed to be nonmagnetic and homogeneous. For all calculations, COMSOL Multiphysics software, a finite element modeling tool, is used.

 

Fig. 1. (a) Schematic of the simulation geometry of the chiral MDM structure investigated in this study. (b) The volume average of $|\tilde {\mathbf {E}}|^2$ in the top electrode (top left) and the dielectric gap (top right) under $r$-CPL (red) and $l$-CPL (blue) illumination. Also shown are the associated dissymmetry factors in the top electrode (bottom left) and the dielectric gap (bottom right).

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Figure 1(b) shows the volume average of $|\tilde {\mathbf {E}}|^2$ calculated using the following equation:

3. Results and discussion

3.1 Analysis of chiral plasmonic resonances

To understand the characteristics of the electromagnetic resonance arising at $\lambda$ = 660 nm, we investigate the electromagnetic field distributions in the chiral MDM structure. Figures 2(a) and 2(b) are the $|\tilde {E}_{z}|^{2}$ and $|\tilde {E}_{xy}|^{2}$ (= $|\tilde {E}_{x}|^{2} + |\tilde {E}_{y}|^{2}$) profiles in the $yz$-plane at $x = \Lambda /2$, and Figs. 2(c) and 2(d) are the $|\tilde {E}_{z}|^{2}$ and $|\tilde {H}_{xy}|^{2}$ (= $|\tilde {H}_{x}|^{2} + |\tilde {H}_{y}|^{2}$) profiles in the $xy$-plane at $z = -$40 nm (the midpoint on the $z$-axis in the dielectric gap), respectively. $\tilde {E}_i$ (or $\tilde {H}_i$) is the complex amplitude of the $i$ component of the $\mathbf {E}$ [or magnetic ($\mathbf {H}$)] field. In each figure, the left and right profiles correspond to the cases of $r$-CPL and $l$-CPL illumination, respectively. In the case of $r$-CPL the electromagnetic field is localized in the dielectric gap, whereas in the case of $l$-CPL it is localized around the top electrode. $H_{x}(\Lambda /2, y, z)$ and the induced current density ($J$, arrows) at time $\tau _{\textrm {H}}$ when |${H}_{x}$| is maximized are plotted in Fig. 2(e), where the length of the arrows is proportional to $\log {J}$. For the $r$-CPL, current loops are observed across the top and bottom electrodes, indicating that the plasmonic hotspots formed in the dielectric gap are attributed to a magnetic resonance. When the $\mathbf {k}$ vector of the incident CPL is tilted in the $yz$-plane, the resonance frequency varies linearly with the angle of incidence (Fig. 3), implying that the resonance is excited by grating-coupled SPPs with the aid of the reciprocal lattice vector of the periodic chiral grating ($\mathbf {k} = \frac {2m\pi }{\Lambda }\hat {\mathbf {x}}+ \frac {2n\pi }{\Lambda }\hat {\mathbf {y}}$, where $m$ and $n$ are integers) [23,24]. In addition, the ${H}_{x}$ profiles at $z = -$40 nm [Fig. 2(f)], where four anti-nodes are observed in the case of $r$-CPL, indicate that $m = n = 1$ [24].

 

Fig. 2. (a) $|\tilde {{E}}_{z}|^{2}$ profiles at $x = \Lambda /2$. (b) $|\tilde {{E}}_{xy}|^{2}$ profiles at $x = \Lambda /2$. (c) $|\tilde {{E}}_{z}|^{2}$ profiles at $z = -$40 nm (the midpoint on the $z$-axis in the dielectric layer). (d) $|\tilde {{H}}_{xy}|^{2}$ profiles at $z = -$40 nm. (e) ${H}_{x}$ profiles at $x = \Lambda /2$. (f) ${H}_{x}$ profiles at $z = -$40 nm. The arrows in (e) represent the induced current density. The left and right panels in (a)–(f) correspond to the cases of $r$-CPL and $l$-CPL illumination, respectively.

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Fig. 3. The optical power absorbed in the bottom electrode as a function of the frequency $f$ (or wavelength $\lambda$) and the incident angle $\theta$ under (a) $r$-CPL and (b) $l$-CPL illumination. The $\mathbf {k}$ vector is in the $yz$-plane and $\theta$ is the angle between $\mathbf {k}$ and $-\mathbf {\hat {z}}$. The linear dependence of the resonance frequency on $\theta$ (dashed lines) indicates that the resonance features originate from the grating-coupled SPPs.

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To further investigate the grating-coupled SPPs, $|\tilde {\mathbf {E}}|^{2}$ averaged over a plane normal to the $z$-axis within a unit cell is plotted as a function of $t_{\textrm {D}}$ and $\lambda$ (Fig. 4). The $z$-position of the plane is chosen to be at the interface between the dielectric and the bottom electrode ($z = -t_{\textrm {D}}$) to better identify the wavelengths of the magnetic resonance by reducing the background originating from the non-resonantly coupled electromagnetic field localized around the top electrode. In the case of $r$-CPL [Fig. 4(a)], when $t_{\textrm {D}}\;>$ 200 nm the branch denoted by $\textrm {SPP}_{\textrm {D}}$ is observed at $\lambda \approx$ 610 nm, which, as $t_{\textrm {D}}$ decreases below 200 nm, splits into the red- and blue-shifted branches, indicated by $\textrm {SPP}_{\textrm {R}}$ and $\textrm {SPP}_{\textrm {B}}$, respectively. In the $l$-CPL case [Fig. 3(b)], the resonance features in the region with $t_{\textrm {D}}\;>$ 200 nm are almost identical to those in the $r$-CPL case in the same region, but the SPP$_{\textrm {R}}$ branch is absent. Next, we investigate the ${E}_{z}$ profile corresponding to a representative point on each branch: point A ($\lambda =$ 612 nm, $t_{\textrm {D}} =$ 240 nm) where the $\textrm {SPP}_{\textrm {D}}$ branch begins to separate, point B ($\lambda =$ 660 nm, $t_{\textrm {D}} =$ 80 nm) on the SPP$_{\textrm {R}}$ branch where the maximum |$g_{\textrm {I}}$| (Fig. 1) is observed, and point C ($\lambda =$ 570 nm, $t_{\textrm {D}} =$ 140 nm) on the SPP$_{\textrm {B}}$ branch. Figures 5(a) and 5(b) show the ${E}_{z}(\Lambda /2, y, z)$ profiles at point A, captured at time $\tau _{\textrm {E}}$ when $|{E}_{z}|$ is maximized and at $\tau _{\textrm {E}} + T/4$, where $T$ is the period of the electromagnetic wave, respectively. These two profiles exhibit the characteristics of bonding and antibonding modes, respectively, suggesting that they result from the hybridization of the SPPs propagating along the metal–dielectric interfaces at $z = {0}\;{\textrm{nm}}$ and $-t_{\textrm {D}}$ [25]. For the bonding case, the polarity of ${E}_{z}$ is maintained along the $z$-axis in the dielectric region, whereas for the antibonding case, there exists a horizontal plane with $E_z = 0$ at which the polarity is reversed [25]. Furthermore, when $t_{\textrm {D}}$ is large ($>\;{200}\;{\textrm{nm}}$), these two modes are degenerate. When $t_{\textrm {D}}$ decreases below 200 nm, the features of the antibonding (or bonding) mode are observed only in the $\textrm {SPP}_{\textrm {B}}$ (or $\textrm {SPP}_{\textrm {R}}$) branch, as shown in Figs. 5(c) and 5(d). Interestingly, unlike in the case of the SPP$_{\textrm {B}}$ branch [Fig. 5(d)], the field distribution of the $\textrm {SPP}_{\textrm {R}}$ branch [Fig. 5(c)] strongly depends on the helicity of CPL, resulting in large |$g_{\textrm {I}}$| in the dielectric gap [Fig. 1(b)]. It is this characteristic of the chiral MDM structure that we exploit in the design of CP-OPDs having both high $g_{\textrm {A}}$ and $\eta _{\textrm {A}}$. The two slightly tilted horizontal features with low intensities in Fig. 4 originate from Fabry–Perot resonances, where the total reflection from the chiral MDM structure significantly increases (data not shown).

 

Fig. 4. The surface average of $|\tilde {\mathbf {E}}|^2$ at the dielectric–bottom metal interface ($z = -t_{\textrm {D}}$) as a function of the thickness of the dielectric layer $t_{\textrm {D}}$ and the wavelength $\lambda$ (or frequency $f$) of the incident $r$-CPL (a) and $l$-CPL (b). The dotted lines in (a) are a guide to the eye, drawn to better identify the resonance conditions.

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Fig. 5. $E_z$ profiles in the $yz$-plane at $x = \Lambda /2$ corresponding to point A (a,b), point B (c), and point C (d) in Fig. 4. The profiles in (a, c, d) are captured when |$E_z$| is maximized ($\tau = \tau _{\textrm {E}}$), while the profile in (b) is captured at $\tau = \tau _{\textrm {E}} + T/4$. The left and right plots in each figure correspond to the cases of $r$-CPL and $l$-CPL illumination, respectively.

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3.2 Circular-polarization-sensitive organic photodetectors

When the dielectric gap is composed of an optical absorption layer sandwiched between two nonabsorbing layers facilitating charge transport and extraction, the chiral MDM structure can generate charge carriers in response to incident CPL. When a conventional organic photodetector having a planar multilayer structure is illuminated with a planewave with $\mathbf {k} \parallel \hat {\mathbf {z}}$ (normal incidence), the $\mathbf {E}$ profile, composed entirely of the $xy$ component, has a local maximum at a distance of about a quarter wavelength from the back metal electrode [26,27]. In contrast, in the case of the chiral MDM structure, $\mathbf {E}$ inside the dielectric region is primarily composed of the $z$ component, which is strongly concentrated at the metal–dielectric interfaces as shown in Fig. 2(a). Because of these different electromagnetic properties of the two types of structures, it is not appropriate to apply to the plasmonic CP-OPDs the approaches typically used for conventional OPDs to maximize the optical absorption, i.e., the uses of an optical spacer [27] and molecules lying flat to the substrate [18]. Thus, to realize plasmonic CP-OPDs based on the chiral MDM structure that have both high $\eta _{\textrm {A}}$ and $g_{\textrm {A}}$, a new design principle is needed.

The structure of the plasmonic CP-OPD with $t_{\textrm {D}} =$ 80 nm is schematically illustrated in Fig. 6(a), where the thicknesses of the optical absorption layer and the lower charge transport layer are denoted by $t_{\textrm {A}}$ and $d$, respectively. The anisotropic characteristic of the absorption layer is described by the complex permittivity tensor

 

Fig. 6. (a) Layer structure of the plasmonic CP-OPD. The absorption efficiencies of the CP-OPD with $t_{\textrm {A}} = {5}\;{\textrm{nm}}$ and $\alpha$ = 1×10⁵ cm$^{-1}$ as a function of $d$ and the orientation of $\mathbf {p}$ under $r$-CPL (b) and $l$-CPL (c) illumination. (d) The dissymmetry factor of absorption calculated from (b,c). The absorption efficiencies for case $p_\bot$ as a function of $\alpha$ and $t_{\textrm {A}}$ under $r$-CPL (e) and $l$-CPL (f) illumination. (g) The dissymmetry factor calculated from (e,f). In (e–g), the value of $t_{\textrm {A}}$ (in nm) is shown for each line.

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The values of $\eta _{\textrm {A}}^{\sigma }$ and $g_{\textrm {A}}$ are calculated as functions of $d$ and the orientation of $\mathbf {p}$ for the CP-OPD with $t_{\textrm {A}} = {5}\;{\textrm{nm}}$ under $r$-CPL and $l$-CPL illumination at $\lambda = {660}\;{\textrm{nm}}$ [Figs. 6(b–d)]. For all values of $d$, $\eta _{\textrm {A}}^r$ is found to be larger in case $p_\bot$ than in case $p_{\parallel }$ [Fig. 6(b)]. The $r$-CPL illumination excites the plasmonic mode belonging to the SPP$_{\textrm {R}}$ branch with $\mathbf {E}$ composed primarily of $E_{\textrm {z}}$ [Fig. 2(a)], and thus the molecules with $\mathbf {p} \parallel \hat {\mathbf {z}}$ absorb more strongly than the molecules with $\mathbf {p} \perp \hat {\mathbf {z}}$. For both orientations, $\eta _{\textrm {A}}^r$ has local maxima at $d = 0$ and 75 nm because $|\tilde {E}_z|^2$ (or $|\tilde {E}_{xy}|^2$) in case $p_{\bot }$ (or $p_{\parallel }$) is concentrated at the top and bottom metal–dielectric interfaces as shown in Figs. 2(a) and 2(b). Unlike $\eta _{\textrm {A}}^r$, $\eta _{\textrm {A}}^l$ is almost identical for both orientations [Fig. 6(c)], where $\eta _{\textrm {A}}^l$ is close to zero at $d = 0$ and monotonically increases with $d$, except for an initial slight decrease for $p_\bot$ case. This result is a direct consequence of the field profile, $|\tilde {E}_z|^2$ for case $p_\bot$ and $|\tilde {E}_{xy}|^2$ for case $p_\parallel$, which concentrates at the top metal–dielectric interface and rapidly decreases away from it, as shown in the right panels of Figs. 2(a) and 2(b). The highest |$g_{\textrm {A}}$| is found to be $1.51$ at $d= {0}\;{\textrm{nm}}$ for case $p_\parallel$ and $1.63$ at $d= {5}\;{\textrm{nm}}$ for case $p_\bot$ [Fig. 6(d)]. Although these two values are comparable, $\eta _{\textrm {A}}^{r}$, which is the relevant absorption efficiency in this study because the twisted direction of the chiral MDM structure [Fig. 1(a)] is designed to resonantly match $r$-CPL, is much higher in case $p_\bot$ than in case $p_\parallel$. Therefore, to achieve both high |$g_{\textrm {A}}$| and $\eta _{\textrm {A}}$, the absorption layer must be composed of molecules with $\mathbf {p} \parallel \hat {\mathbf {z}}$ and be positioned close to the bottom electrode.

To further optimize the performance of the CP-OPD, we investigate the dependence of $\eta _{\textrm {A}}$ and $g_{\textrm {A}}$ on $\alpha$ and $t_{\textrm {A}}$ for case $p_\bot$. The thickness of the lower charge transport layer ($d =$ 10 nm) is chosen to be as small as possible to maximize $g_{\textrm {A}}$ [Fig. 6(d)], and at the same time to be large enough to prevent exciton quenching by the bottom electrode [27,28]. Figures 6(e) and 6(f) show $\eta _{\textrm {A}}^r(\alpha )$ and $\eta _{\textrm {A}}^l(\alpha )$, respectively, calculated for different $t_{\textrm {A}}$, from which $g_{\textrm {A}}(\alpha )$, shown in Fig. 6(g), is calculated using Eq. (2). The dependence of $\eta _{\textrm {A}}^r$ on $\alpha$ and $t_{\textrm {A}}$ is somewhat complex: an increase of $\alpha$ (or $t_{\textrm {A}}$) does not always result in a gain in $\eta _{\textrm {A}}^r$, and for $t_{\textrm {A}}$ $\leq$ 40 nm, local maxima ranging from 25.2 to 29.4 % exist. $\eta _{\textrm {A}}^l$, on the other hand, increases monotonically with $\alpha$ for all $t_{\textrm {A}}$. In the case of $\eta _{\textrm {A}}^r$, the increase in $\alpha$ of the absorbing molecules, which are located in the high-field region, decreases the volume average of $|\tilde {E}_z|^{2}$ in the absorption layer, as shown in Figs. 7(a) and 7(c). This tradeoff between $|\tilde {E}_z|^{2}$ and $\alpha$ leads to the presence of local maxima of $\eta _{\textrm {A}}^r$. In the case of $\eta _{\textrm {A}}^l$, on the other hand, the absorbers are excited by the tail of the SPP wave localized at the top metal–dielectric interface. As a result, the effect of $\alpha$ on $|\tilde {E}_z|^{2}$ is much weaker compared to the case of $\eta _{\textrm {A}}^r$ [Figs. 7(b) and 7(d)], and hence $\eta _{\textrm {A}}^l$ increases monotonically with $\alpha$.

 

Fig. 7. The volume integral of $|\tilde {E}_{\textrm {z}}(\lambda ,\alpha )|^2$ in the absorption layer with $t_{\textrm {A}}$ = 20 nm under $r$-CPL (a) and $l$-CPL (b) illumination, calculated with $\alpha$ varying from 1×10⁴ to 2×10⁵ cm⁻¹ in 1×10⁴ cm⁻¹ increments. (c) The volume integral of $|\tilde {E}_{\textrm {z}}(\lambda ,\alpha )|^2$ in the absorption layer (blue), the imaginary part of the $z$-component of the relative permittivity (Im($\tilde {\varepsilon }_{z}$), orange) of the absorption layer, and their product (red), which is proportional to $\eta _{\textrm {A}}$ [Eq. (6)], under $r$-CPL (c) and $l$-CPL (d) illumination with $\lambda =$ 660 nm. In the case of $r$-CPL, the tradeoff between the volume integral of $|\tilde {E}_{\textrm {z}}|^2$ and Im($\tilde {\varepsilon }_{z}$) is clearly shown, resulting in a maximum of $\eta _{\textrm {A}}$ at $\alpha =$ 6×10⁴ cm⁻¹. In the case of $l$-CPL, on the other hand, $\eta _{\textrm {A}}$ increases monotonically with $\alpha$ because the $|\tilde {E}_{\textrm {z}}(\lambda )|^2$ integral decreases much more slowly compared to the $r$-CPL case.

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As the values of $\alpha$ and $t_{\textrm {A}}$ change, $g_{\textrm {A}}$ may vary significantly while $\eta _{\textrm {A}}^r$ remains nearly constant. For example, compared to the CP-OPD with $\alpha =$ 8.5×10⁴ cm$^{-1}$ and $t_{\textrm {A}} =$ 35 nm$, g_{\textrm {A}}$ of the CP-OPD with $\alpha =$ 4.5×10⁴ cm$^{-1}$ and $t_{\textrm {A}} =$ 20 nm doubles from 0.7 to 1.4, while $\eta _{\textrm {A}}^r$ is $\sim$28 % for both devices. The values of $\alpha$ and $t_{\textrm {A}}$ can be chosen depending on the application. For applications requiring high $g_{\textrm {A}}$, the CP-OPD with $\alpha$ = 1×10⁴ cm$^{-1}$ and $t_{\textrm {A}}=$10 nm is desirable, yielding $|g_{\textrm {A}}|$ = 1.7 and $\eta _{\textrm {A}}^r =$ 8.8 %. On the other hand, for applications whose primary figure of merit is $\eta _{\textrm {A}}^r$, the device with $\alpha$ = 5×10⁴ cm$^{-1}$ and $t_{\textrm {A}}=$10 nm, with the corresponding values of $|g_{\textrm {A}}|$ and $\eta _{\textrm {A}}^r$ being 1.6 and 23.8 % respectively, is preferred despite slightly lowered $g_{\textrm {A}}$. We note that the values of $\eta _{\textrm {A}}^\sigma$ shown in Fig. 6, calculated for CPL incident from the semi-infinite glass substrate, are a good approximation to the external quantum efficiency ($\eta _{\textrm {E}}^\sigma$, the number of electrons collected at the electrode divided by the number of incident photons) because (i) a near-unity internal quantum efficiency ($\eta _{\textrm {I}}$, the number of electrons collected at the electrode divided by the number of incident photons) is commonly achieved in the visible spectrum for single donor–acceptor heterojunction OPDs [20,29,30], ensuring $\eta _{\textrm {E}}^\sigma = \eta _{\textrm {A}}^\sigma \eta _{\textrm {I}}^\sigma \simeq \eta _{\textrm {I}}^\sigma$ and (ii) reflection at the glass–air interface can easily be minimized at the operational wavelength by application of an anti-reflection coating.

Finally, we investigate the effects of the metallic loss of the chiral plasmonic nanocavity on $\eta _{\textrm {A}}^{\sigma }$ and $g_{\textrm {A}}$. Figures 8(a) and 8(b) show the $\eta _{\textrm {A}}^{r}$ and $\eta _{\textrm {A}}^{l}$ spectra, respectively, for the CP-OPD with $t_{\textrm {A}}$ = 20 nm and $\alpha$ = 1×10⁴ cm⁻¹, calculated by varying the Im($\tilde {\varepsilon }_{\textrm {r}}$) value of silver composing the top and bottom electrodes while fixing the Re($\tilde {\varepsilon }_{\textrm {r}}$) value. As a reference, the data calculated using Im($\tilde {\varepsilon }_{\textrm {r}}$) = 0.19 , which corresponds to the value of a silver film taken from the literature [22], are denoted by the red dashed lines in Figs. 8(a) and 8(b). As Im($\tilde {\varepsilon }_{\textrm {r}}$) decreases, both $\eta _{\textrm {A}}^{r}$ and $\eta _{\textrm {A}}^{l}$ peak with increasingly higher intensities, due to the reduction of the metallic loss competing for absorption with the absorption layer and the concomitant increase in the quality factor of the cavity resonance. Figure 8(c) shows the values of $\eta _{\textrm {A}}^{r}$ (filled squares), $\eta _{\textrm {A}}^{l}$ (open squares), and |$g_{\textrm {A}}$| (gray triangles) at $\lambda ={660}\;{\textrm{nm}}$, as a function of Im($\tilde {\varepsilon }_{\textrm {r}}$). Except in the highly lossy region where Im($\tilde {\varepsilon }_{\textrm {r}}$) $>\;0.27$, an increase in Im($\tilde {\varepsilon }_{\textrm {r}}$), which is required to increase |$g_{\textrm {A}}$|, necessarily decreases $\eta _{\textrm {A}}^r$, presenting a tradeoff between |$g_{\textrm {A}}$| and $\eta _{\textrm {A}}^r$. In addition, |$g_{\textrm {A}}$| approaches zero as Im($\tilde {\varepsilon }_{\textrm {r}}$) decreases, consistent with a previous study showing that asymmetric transmission of CPL depending on the helicity occurs only for a lossy planar metamaterial possessing two dimensional chirality [31].

 

Fig. 8. Absorption efficiencies of the CP-OPD with $t_{\textrm {A}}$ = 20 nm and $\alpha$ = 1×10⁴ cm⁻¹ under $r$-CPL (a) and $l$-CPL (b) illumination, calculated with Im($\tilde {\varepsilon }_{\textrm {r}}$) of the top and bottom electrodes varying from 0 to 0.38 in 0.038 increments. The data denoted by red dashed lines correspond to the Im($\tilde {\varepsilon }_{\textrm {r}}$) value of a silver film ($=0.19$) taken from the literature [22]. (c) Dissymmetry factor of absorption at $\lambda$ = 660 nm (gray triangles) calculated from (a,b) and absorption efficiencies at $\lambda = {660}\;{\textrm{nm}}$ under $r$-CPL (filled squares) and $l$-CPL (open squares) illumination.

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4. Conclusions

We have demonstrated that both high $\eta _{\textrm {E}}$ and $g_{\textrm {A}}$ are achievable in a CP-OPD based on the chiral MDM structure. Under CPL illumination whose helicity matches the twisted direction of the chiral pattern, plasmonic hotspots, originating from the hybridization of SPP waves at the dielectric–top metal and the dielectric–bottom metal interfaces, were found to be selectively excited in the dielectric region where photoactive molecules are located. By studying the electromagnetic properties of the CP-OPD, we established a design principle for the maximization of $\eta _{\textrm {E}}$ and $g_{\textrm {A}}$. The resulting CP-OPD attains $\eta _{\textrm {E}}$ = 23.8 % and |$g_{\textrm {A}}$| = 1.6 , representing significant improvements compared to previously demonstrated circular-polarization-sensitive photodetectors (Table 1). We also note that owing to the the vertical geometry and the ultrathin device thickness, the response time of our plasmonic CP-OPD is likely to be significantly shorter than that of chiral photodetectors with the lateral thin-film transistor geometry [1,5]. According to the reciprocity principle [32,33], the proposed chiral MDM structure is also expected to be utilized as an optoelectronic platform for organic circularly polarized light-emitting diodes.

Table 1. Dissymmetry factor of photocurrent ($g_{\textrm {Ph}}$) and external quantum efficiency ($\eta _{\textrm {E}}$) of previously demonstrated circular-polarization-sensitive photodetectors compared with those of our photodetector.

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