Efficient full-spectrum utilization, reception and conversion of solar energy by broad-band nanospiral antenna

Huaqiao Zhao; Huotao Gao; Ting Cao; Boya Li

doi:10.1364/OE.26.00A178

1. Introduction

Traditional photovoltaic (PV) cells, as limited by the bandgap of semiconductors, are difficult to obtain higher conversion efficiency [1]. Current state-of-the-art PV efficiency is ~29% for single-junction cells, and ~46% for mutijunction cells [2]. In the 1970s, a novel concept of rectifying-antenna (rectenna), which uses a nanoantenna coupled to a rectifier to transform the collected solar power into DC power, was proposed by Bailey based on the wave character of light [3]. In recent years, with the increasing demand of clean renewable energy and the fast development of nanotechnology, the solar rectenna system has once again drawn worldwide researchers’ concern due to its attractive high efficiency (greater than 85% theoretically possible [4,5]), which makes it a hopeful substitution of PV cells.

However, the harvesting efficiency is not as high as expected in the researches using conventional nanoantennas. Sarehraz [6] analyzed a typical half-wave dipole with a 15% solar bandwidth, and found that the efficiency is less than 1%. Vandenbosch and Ma [7,8] reported the efficiency for silver dipole nanoantennas over the wavelength range 300-1200 nm, and found the maximum upper bounds to be about 65.4% when the loss in the antenna was solely considered, 54% when the loss in the antenna and 2^nd polynomial rectifier impedance model were considered, and 39% when the loss in the antenna and the equivalent circuit impedance model were considered. El-Toukhy et al. [9] designed a tapered dipole nanoantenna with a total harvesting efficiency of 79.2% (only the loss in the antenna was considered). However, these researches didn’t take into account the randomly polarized characteristic of solar radiation, which would make the efficiency of a linearly polarized dipole drop to half [10]. Moreover, nanodipoles are narrow-band due to their resonant nature, and only a small part of the broad-band solar spectrum can be used. Nanobowties [11–13] may have broader wavelength bands than nanodipoles, but compared with the wide solar spectrum, their bands do not broaden essentially because they are also resonant antennas. Wang et al. [13] designed a sector nanobowtie integrated with a metal-insulator-metal (MIM) diode for infrared energy harvesting, and found the power conversion efficiency to be 3.4% at the resonant wavelength.

In order to achieve an efficient collection of solar energy, a suitable nanoantenna should have several characters [10,14,15]. First, a wider wavelength band is necessary to make the most of solar energy in the visible and infrared band. Second, the impedance matching between nanoantenna and rectifier should be as perfect as possible to reduce the reflection loss. Third, the loss in the nanoantenna itself should be smaller to increase the power delivered to the antenna terminals. Fourth, a larger effective area for the nanoantenna is needed. Finally, randomly polarized solar radiation should be accepted by the nanoantenna.

Obviously, conventional nanodipoles as well as nanobowties could not meet the requirements above. Spiral antenna, as a classical ultra-wide band (UWB) antenna at radio frequencies (RF) [16], is a suitable candidate that may meet them simultaneously. In fact, the consideration of spiral antennas for the harvesting of solar radiation is not new. However, most of nanospiral antennas were investigated for thermal radiation harvesting in the mid-infrared region (MIR, 3-50 μm) [17–23]. Their properties such as input impedance, radiation and polarization in the visible (380-780 nm) and near-infrared (NIR, 780-3000 nm) regime are seldom investigated, and their applications in solar energy harvesting are not analyzed systematically. In this work, a nanospiral antennas is used to realize the full-spectrum utilization, reception and conversion of solar energy from 300 nm to 3000 nm, which corresponds to more than 98% of the solar radiation energy. The result suggests that the maximum harvesting efficiency of the nanospiral can in principle be as high as 80% (for a rectifier resistance of 200 Ω) under AM1.5 flux condition.

It’s worth noting that there is no suitable rectifier for solar rectenna system to date. MIM diodes, including metal-oxide-metal (MOM) diodes [4,15,22,24–27] and metal-vacuum-metal (MVM) diodes [28,29], are assumed as potential solutions, but the high impedance and low responsivity do not meet the requirements for visible and NIR rectification. Berland [4] reported MIM diodes providing impedance ranged from 2 to 10 kΩ and responsivity of ~1 A/W (at bias about 500 mV, but drops off closer to zero bias), depending on the fabrication process. Bean et al. [26] measured their tunnel diode with a resistance 200 kΩ when the zero-bias responsivity reaches 0.45 A/W. Mayer et al. [28] showed their MVM diode with resistance as high as 10⁶-10¹¹ Ω and responsivity 0.72-35.8 A/W, depending on the work function of the metal. Apparently, the properties of MIM diodes are closely bound to the materials and the fabrication process. We have demonstrated that if the MIM diode resistance is designed in the order of 1 kΩ, the nanospiral can yield a harvesting efficiency of 47.2%, which is higher than that of traditional PV cells.

In the paper, the total harvesting efficiency including the effects of impedance matching, radiation, polarization and effective area will be discussed in section II. Nanoantenna topology and software validation are described in section III. Detailed nanoantenna properties are reported in section IV and the results for solar energy harvesting in section V. Finally, conclusion is drawn in section VI.

2. Theory

Although nanoantennas work at optical frequencies, they still satisfy the classical electromagnetic theories [7,30]. The equivalent circuit [15,22] for a nanoantenna coupled to a rectifier diode is shown in Fig. 1. The nanoantenna is modeled as a voltage source in series with the impedance of the nanoantenna and the MIM rectifier diode is modeled as a nonlinear resistor in parallel with a capacitor.

Fig. 1 Equivalent circuit of a nanoantenna coupled to a MIM rectifier diode.

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The power received by the rectifier is

P_{r e c} = \frac{1}{2} {| V_{o p e n} |}^{2} \frac{R_{r e c}}{{| Z_{a n t} + Z_{r e c} |}^{2}}

where

Z_{a n t} = R_{a n t} + j X_{a n t}

,

Z_{r e c} = R_{r e c} + j X_{r e c}

and

V_{o p e n}

are the antenna impedance, the rectifier impedance, and the open-circuit voltage at the antenna terminals when no load is connected, respectively. According to antenna theories [31], the open-circuit voltage can be expressed as

| V_{o p e n} | = 2 \sqrt{\frac{R_{a n t} A_{e f f} η_{p o l}}{Z_{0}}} | E_{i n} |

where

Z_{0}

= 377 Ω is the intrinsic impedance of free space,

| E_{i n} |

is the amplitude of incident electric field,

η_{p o l}

is the polarization efficiency between nanoantenna and incident wave, and

A_{e f f}

is the effective area, which is related to the free space wavelength

λ

, antenna directivity

D

and radiation efficiency

η_{r a d}

. Here we assume that the direction of the maximum reception of the antenna is the same as the incident light.

A_{e f f} = \frac{λ^{2} D η_{r a d}}{4 π}

Due to the reciprocity theorem, the radiation efficiency of a transmitting antenna equals its reception efficiency, and mainly depends on the loss in the antenna itself. The ideal case of no loss ( $η_{r a d} = 1$ ) corresponds to the maximum effective area,

A_{e f f}^{m a x} = \frac{λ^{2} D}{4 π}

The final expression for the power received by the rectifier can be expressed as

P_{r e c} = η_{p o l} η_{r a d} η_{m a t} A_{e f f}^{m a x} S_{i n}

where

η_{m a t}

is the impedance matching efficiency, whose original definition [31] is shown in Table 1, and can be expressed as follows [8]:

η_{m a t} = \frac{4 R_{a n t} R_{r e c}}{{| Z_{a n t} + Z_{r e c} |}^{2}}

and

S_{i n}

is the incident power density (W/m²)

Table 1. Definitions of Related Efficiencies in the Solar Rectenna

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S_{i n} = \frac{{| E_{i n} |}^{2}}{2 Z_{0}}

It must be noted that $P_{r e c}$ in Eq. (5) is the power which is received but not rectified by the diode. We assume that $η_{d i o d e}$ is the efficiency of rectifying the power received by the diode [15,28], and the DC power can be expressed as

P_{d c} = η_{d i o d e} P_{r e c}

Solar radiation has a continuous spectral irradiance $I_{i n}$ (W/m²/nm) over a wide wavelength band, and the incident power density $S_{i n}$ in the wavelength band from $λ$ to $λ + Δ λ$ can be calculated with $S_{i n} (λ) = I_{i n} (λ) Δ λ$ . The total harvesting efficiency of the nanoantenna for solar energy collection can be defined as the ratio of the total DC power rectified by the diode to the total incident power,

\begin{matrix} η_{t o t a l} = \frac{P_{d c}^{t o t a l}}{P_{i n}^{t o t a l}} \\ = \frac{\int_{λ_{1}}^{λ_{2}} η_{p o l} (λ) η_{r a d} (λ) η_{m a t} (λ) η_{d i o d e} (λ) A_{e f f}^{m a x} (λ) I_{i n} (λ) d λ}{\int_{λ_{1}}^{λ_{2}} A_{e f f}^{m a x} (λ) I_{i n} (λ) d λ} \\ = \frac{\int_{λ_{1}}^{λ_{2}} A_{e f f}^{m a x} (λ) I_{r e c} (λ) η_{d i o d e} (λ) d λ}{\int_{λ_{1}}^{λ_{2}} A_{e f f}^{m a x} (λ) I_{i n} (λ) d λ} \end{matrix}

where

λ_{1}

and

λ_{2}

are the starting and ending wavelength of the band investigated, respectively.

The parameter $I_{r e c}$ can be defined as the receiving spectrum of the nanoantenna with $I_{r e c} = η_{p o l} η_{r a d} η_{m a t} I_{i n}$ .

Compared with the harvesting efficiency defined in [8], Eq. (9) has considered not only the loss in the nanoantenna and the impedance matching efficiency between nanoantenna and rectifier, but also the maximum effective area, the polarization efficiency between nanoantenna and incident wave, and the diode rectification efficiency.

It can be seen that the total harvesting efficiency is a function of multiple component efficiencies. In order to facilitate understanding, their respective original definitions [8,15,31] are listed in Table 1.

It’s worth mentioning that the responsivity of a rectifier diode is also an important influence factor, which means the ratio between the rectified DC current and the power flowing into the rectifier [15,28], as discussed in the introduction. Actually, the effect of the responsivity has been considered into the diode rectification efficiency [28]. Unfortunately, no suitable diode for solar energy harvesting application exists to date. Here we don’t aim to model a new rectifier topology. This paper mainly investigates the full-spectrum collection of solar energy from the perspective of broad-band nanospiral antenna, which would in turn provide guidance for the diode design. Therefore, we assume that the MIM diode has an ideal rectification efficiency ( $η_{d i o d e} = 1$ ). Thus, the maximum total harvesting efficiency is actually the upper bound of the solar rectenna harvesting efficiency [7,8].

3. Nanoantenna topology and simulation consideration

3.1 Nanoantenna topology

In this study, a symmetrical Archimedean nanospiral antenna with two turns, as shown in Fig. 2(a), is used for solar energy harvesting. For comparison, a nanodipole (Fig. 2(b)) resonating in the visible regime is also investigated. Their geometric parameters in x-y plane have been listed in Table 2. Both of them have a thickness of 40 nm at z axis. The nanostructures are surrounded by free space. Actually in the realistic manufacture process, nanoantennas have to be supported by a substrate, which would influence the directivity and radiation efficiency of the nanoantenna due to the plasmonic effects [7,32]. Moreover, the substrate layers in practice are much thicker than the wavelength and can be assumed to cover the half space below the nanoantenna [32], and the efficiency in this case recovers about the same value as in the case without substrate [7]. Since our research focus is the influence of different antenna structures on solar energy harvesting, here the substrate is not considered, but it really deserves more attention. The nanoantennas are assumed to be composed of silver, whose permittivity has been modeled by fitting the experimental data in [33]. Full-wave time domain numerical software CST based on the finite integration technique (FIT) [34] is used for simulation.

Fig. 2 (a) Nanospiral antenna, (b) nanodipole antenna.

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Table 2. Dimensions for the Nanospiral and Nanodipole

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3.2 Simulation consideration

The analysis of grid convergence is carried out first because FIT uses hexahedral meshes, whose sizes may influence the calculation accuracy. Figure 3 shows the field enhancement in the nanospiral gap at different minimum mesh sizes. It can be seen that the enhancement values for different wavelengths have all stabilized when the mesh size is reduced to 0.75 nm.

Fig. 3 Field enhancement in the nanospiral gap at different minimum mesh sizes for wavelength 500 nm, 1000 nm and 2000 nm.

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In order to check the validity of the mesh generation with a minimum size of 0.75 nm, a gold nanodipole with L = 230 nm and g = 10 nm in [35] is simulated with FIT method. Figure 4 shows the relative intensity at the antenna gap center for the FIT model and that reported in [35] by Green’s tensor technique (GTT). It’s evident that there is an excellent agreement between both methods. In the following study, a minimum mesh size of 0.75 nm will be used to ensure the calculation accuracy.

Fig. 4 Wavelength dependent relative intensity at the gap center of a gold dipole (L = 230 nm, g = 10 nm) using GTT method in [35] and FIT method with a minimum size of 0.75 nm.

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4. Nanoantenna property

4.1 Impedance property

As defined in [36,37], the input impedance of a nanoantenna, which is the ratio of the applied optical voltage at the gap to the induced optical displacement current flowing into the terminals, could be derived by feeding the nanoantenna at the gap, i.e., gap excitation [37]. The nanodipole impedance has been explored in depth [38,39], and it is found that the simple wavelength scaling is no longer valid at optical frequencies due to the plasmons in the metal. However, the nanospiral impedance has been rarely studied. Figure 5 shows the resistance and reactance of the nanospiral and the nanodipole, respectively. It is evident that the nanospiral has a relatively flat impedance behavior in the major wavelength band, except at wavelengths lower than 400 nm and larger than 2000 nm because of the truncation of spiral structures. Whereas the impedance of the nanodipole varies dramatically over the whole wavelength band. It appears that the impedance of the nanospiral is less affected by plasmons than that of the nanodipole. In fact, this impedance difference between nanospiral and nanodipole is determined by their geometrical structures. According to the theory of UWB antenna [31], the nanospiral is self-compensated and the location of effective working zone changes with different wavelengths; therefore it can maintain constant impedance over a wide wavelength band.

Fig. 5 Resistance (a) and reactance (b) of the nanospiral and the nanodipole.

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As discussed in section II, the wide-band characteristic of nanoantenna impedance could ensure perfect matching with rectifiers in the full spectrum. The total harvesting efficiency that has considered the impedance matching between nanoantenna and rectifier will be shown in section V.

4.2 Radiation property

As illustrated in Eq. (8), the total harvesting efficiency not only depends on the impedance matching between nanoantenna and rectifier, but also on the radiation efficiency and the maximum effective area which is connected with antenna directivity. Radiation efficiency, defined as the ratio between the total radiated power and the input power at the feeding port, is mainly related to the loss in the antenna itself [7–9], as shown in Table 1. Due to the reciprocity, the radiation efficiency of a transmitting antenna is equal to the efficiency when it acts as a receiving one. Figure 6 shows the calculated radiation efficiency of the nanospiral and that of the nanodipole, respectively. The nanospiral has a high radiation efficiency of more than 80% in the wavelength band from 500 nm to 2000 nm, however the nanodipole reaches its maximum at the resonant wavelength and declines outside the resonance range. Their different behaviors indicate again that the nanospiral is a wide-band antenna while the nanodipole is a narrow one.

Fig. 6 Radiation efficiency for the nanospiral and the nanodipole.

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Figure 7 shows the maximum directivity for both nanoantennas. It’s clear that the directivity of the nanospiral has a maximum value about 3.5 in the visible band, and slightly decreases outside that band because of the truncation of the spiral structure, but it is still larger than that of the nanodipole, which is about 1.5 over the whole wavelength range. Their three-dimensional patterns at the visible and NIR wavelengths are plotted in Fig. 8. The nanospiral has a stronger direction performance and a narrower far-field radiation beam at wavelength of 600 nm than that of 2000 nm. It is a valuable result because a stronger directivity corresponds to a larger effective area, which means more solar power in the visible can be accepted. In contrast, the nanodipole is omnidirectional on the plane perpendicular to the antenna, and its radiation patterns at different wavelengths are similar.

Fig. 7 Directivity at positive z-axis for the nanospiral and the nanodipole.

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Fig. 8 Three-dimensional radiation patterns for (a) the nanospiral at wavelength 600 nm, (b) the nanodipole at wavelength 600 nm, (c) the nanospiral at wavelength 2000 nm and (d) the nanodipole at wavelength 2000 nm.

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As illustrated in Eq. (3), the high radiation efficiency and large directivity for the nanospiral will result in a large effective area, which allows more power received by the nanoantenna to be delivered to the rectifier instead of being consumed by the antenna itself.

4.3 Polarization property

The polarization of a nanoantenna is another important factor that influences its application in solar energy harvesting. Because solar radiation is randomly polarized, nanoantennas with different polarization will receive different amount of power when illuminated by optical wave, and this variation can be evaluated by the polarization efficiency [31], as defined in Table 1. For the nanospiral and nanodipole, Fig. 9 shows their respective polarization efficiency under the circularly-polarized plane wave incident along z axis. It’s evident that the polarization efficiency of the nanospiral is close to 100% from 500 nm to 1000 nm, which indicates that the nanospiral has a good circular polarization in this region and may receive any polarized solar radiation. Whereas for the nanodipole, a constant value of 50% is derived in the whole wavelength band due to the linear polarization, and it means that the power incident on the nanodipole will drop to half. It should be noted that two orthogonal nanodipoles are possible to overcome the linear polarization [40], but they are still limited by the narrow-band nature. The nanospiral, by contrast, has a characteristic of wide-band polarization efficiency.

Fig. 9 Polarization efficiency with incident circularly-polarized plane wave for the nanospiral and the nanodipole.

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5. Solar energy harvesting

5.1 Field enhancement

A notable feature of the optical nanoantenna is the strong electric field enhancement in the antenna gap [29,41]. By launching a circularly polarized plane wave at normal incidence on the structures with an E-field magnitude of 1V/m, the enhancement in the gap terminals for the nanoantenna could be obtained, which is also called plane wave excitation [37]. Figure 10 has illustrated the E-field distribution in the gap for the nanospiral and the nanodipole, respectively. Figure 11 has plotted their variation dependent on wavelengths. As shown in these figures, E-field is enhanced in the gap for both nanoantennas in the visible regime. However, at the longer wavelengths, the nanospiral has much stronger E-field enhancement, yet the nanodipole almost losses its enhancement function.

Fig. 10 E-field enhancement in x-y plane for the nanospiral and the nanodipole illuminated by a circularly-polarized plane wave of 1V/m at wavelength of (a) 600 nm, (b) 2000 nm.

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Fig. 11 Wavelength dependent E-field enhancement at the center of the antenna gap for the nanospiral and the nanodipole illuminated by a circularly-polarized plane wave of 1V/m.

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In fact, E-field enhancement in the gap is inherently linked with the resistance, directivity, radiation and polarization of the nanoantenna. This is because the path integral of E-field across the gap is equal to the open-circuit voltage at the antenna terminals, and this voltage is related to the antenna properties, as given in Eq. (2). The nanospiral can offer a stronger E-field enhancement in the gap, and this means that the voltage across the rectifier can be increased, which would be beneficial not only to the conduction of diode, but also to rectifier designing. Therefore, the field enhancement in the gap can be viewed as a comprehensive figure of merit to quantify the ability of nanoantenna for solar energy harvesting. It is worth noting that the nanospiral has weaker E-field enhancement in the visible region than in the infrared, as shown in Fig. 11, because the enhancement is proportional to the free space wavelength. Some measures may be taken to enhance the E-field in the visible, such as increasing the directivity by placing an extended hemispherical lens in front of the nanoantenna [42], which is not described in detail here.

5.2 Solar energy harvesting under AM1.5

Due to the analysis of nanoantenna properties above, the solar energy harvesting under AM1.5 flux [43] from 300 nm to 3000 nm can be obtained by Eq. (9), which includes the effects of the loss in the antennas, impedance matching, polarization efficiency and effective area. The rectifier (MIM diode) junction capacitance is assumed to be approximately 5 × 10⁻¹⁷ F for a 40 × 40 nm² cross section [8,15]. Figure 12 shows the total harvesting efficiency for different rectifier resistances. The maximum harvesting efficiency about 80% can be achieved in principle for the nanospiral coupled to a rectifier resistance of 200 Ω, while about 10% for the nanodipole under the same conditions. As discussed in section II, this maximum efficiency represents the upper bound of the solar rectenna harvesting efficiency. The efficiency limitation of 80% for the nanospiral is close to the efficiency of 85% speculated in [4,5]. Figure 13 shows their respective receiving spectra. Apparently, different types of nanoantennas differ greatly in the solar energy harvesting application. The receiving spectrum of the nanospiral is close to the solar spectral irradiation, which means that most of the solar energy in the visible and NIR regime can be received by the nanospiral system. Whereas the nanodipole, as a narrow-band antenna, produces a receiving spectrum much different from the solar irradiation, and only a small part of solar energy in its resonant band can be received.

Fig. 12 Total harvesting efficiency of the nanospiral and the nanodipole with different rectifier resistance and a constant capacitance of 5 × 10⁻¹⁷ F.

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Fig. 13 Receiving spectrum under solar irradiance AM1.5 for the nanospiral and the nanodipole, when coupled to a rectifier with resistance of 200 Ω and capacitance of 5 × 10⁻¹⁷ F.

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Table 3 has listed the total efficiency in Fig. 12 for some typical diode resistances and their respective received power. We can see that the nanospiral has higher efficiency and more received power than the nanodipole for any rectifier resistance. The result shows that the suitable rectifier diode should offer a resistance in the order of 200 Ω. However, there is no such rectifier at optical frequency to date. MIM diode is deemed as a potential candidate, but the current MIM diode generally offers a resistance of several kilohms. The total efficiency and received power for both nanoantennas will decrease rapidly with increasing diode resistance to 1 kΩ, 10 kΩ or 100 kΩ. When the resistance reaches the order of 1kΩ, the received power of the nanodipole is 6.61 pW and its efficiency is only 6.3%, but the nanospiral still has an appreciable received power of 74.9 pW and an efficiency up to 47.0%, which is even higher than that of conventional PV cells. It shows that the nanospiral could be coupled to a high diode resistance more easily than the nanodipole.

Table 3. Total Harvesting Efficiency and Received Power

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6. Conclusion

In this paper, the full-spectrum collection of solar energy has been investigated based on FIT method. The nanospiral has stronger E-field enhancement in the gap than a nanodipole counterpart. After considering the nanoantenna impedance, radiation, polarization and effective area, a maximum harvesting efficiency about 80% can be achieved in principle for the nanospiral coupled to a rectifier resistance of 200 Ω under AM1.5 flux from 300 nm to 3000 nm, which is much higher than that of the nanodipole under the same conditions. Moreover, the nanospiral could be coupled to a high diode resistance more easily than the nanodipole. The nanospiral proposed shows the advantage in the full-spectrum utilization, reception and conversion of solar energy due to its broad-band character and good properties of impedance, radiation and polarization. With the progress of nanotechnology, the nanospiral rectenna, as a novel concept of solar energy harvesting, is expected to be a new clean and renewable energy technology in the future.

Funding

Natural Science Foundation of Hubei Province (2014CFA093).

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Efficiency	Definition	Explanation
$η_{p o l}$	${\| {\vec{e}}_{i n c} \cdot {\vec{e}}_{a n t} \|}^{2}$	${\vec{e}}_{i n c}$ , the unit vector of the E-field for the incident wave ${\vec{e}}_{a n t}$ , the unit vector of the E-field for the receiving antenna
$η_{r a d}$	$\frac{P_{r a d}}{P_{r a d} + P_{l o s s}}$	$P_{r a d}$ , the power radiated from the antenna $P_{l o s s}$ , the power dissipated in the antenna
$η_{m a t}$	$\frac{P_{r e c}}{P_{r e c}^{m a x}}$	$P_{r e c}$ , the power received by the diode rectifier $P_{r e c}^{m a x}$ , the maximum $P_{r e c}$ for perfect matching case
$η_{d i o d e}$	$\frac{P_{d c}}{P_{r e c}}$	$P_{d c}$ , the DC power rectified by the diode
$η_{t o t a l}$	$\frac{P_{d c}^{t o t a l}}{P_{i n}^{t o t a l}}$	$P_{d c}^{t o t a l}$ , the total DC power rectified by the diode $P_{i n}^{t o t a l}$ , the total input power

	Antenna	Rectifier diode resistance
	Antenna	200 Ω	1 kΩ	10 kΩ	100 kΩ
$η_{t o t a l}$	nanospiral	79.2%	47.0%	6.7%	0.7%
$η_{t o t a l}$	nanodipole	10.4%	6.3%	1.0%	0.1%
$P_{r e c}^{t o t a l}$	nanospiral	126.2 pW	74.9 pW	10.6 pW	1.1 pW
$P_{r e c}^{t o t a l}$	nanodipole	11.0 pW	6.61 pW	1.07 pW	0.11 pW

Efficiency	Definition	Explanation
$η_{p o l}$	${\| {\vec{e}}_{i n c} \cdot {\vec{e}}_{a n t} \|}^{2}$	${\vec{e}}_{i n c}$ , the unit vector of the E-field for the incident wave ${\vec{e}}_{a n t}$ , the unit vector of the E-field for the receiving antenna
$η_{r a d}$	$\frac{P_{r a d}}{P_{r a d} + P_{l o s s}}$	$P_{r a d}$ , the power radiated from the antenna $P_{l o s s}$ , the power dissipated in the antenna
$η_{m a t}$	$\frac{P_{r e c}}{P_{r e c}^{m a x}}$	$P_{r e c}$ , the power received by the diode rectifier $P_{r e c}^{m a x}$ , the maximum $P_{r e c}$ for perfect matching case
$η_{d i o d e}$	$\frac{P_{d c}}{P_{r e c}}$	$P_{d c}$ , the DC power rectified by the diode
$η_{t o t a l}$	$\frac{P_{d c}^{t o t a l}}{P_{i n}^{t o t a l}}$	$P_{d c}^{t o t a l}$ , the total DC power rectified by the diode $P_{i n}^{t o t a l}$ , the total input power

	Antenna	Rectifier diode resistance
	Antenna	200 Ω	1 kΩ	10 kΩ	100 kΩ
$η_{t o t a l}$	nanospiral	79.2%	47.0%	6.7%	0.7%
$η_{t o t a l}$	nanodipole	10.4%	6.3%	1.0%	0.1%
$P_{r e c}^{t o t a l}$	nanospiral	126.2 pW	74.9 pW	10.6 pW	1.1 pW
$P_{r e c}^{t o t a l}$	nanodipole	11.0 pW	6.61 pW	1.07 pW	0.11 pW

Efficient full-spectrum utilization, reception and conversion of solar energy by broad-band nanospiral antenna

Abstract

1. Introduction

2. Theory

3. Nanoantenna topology and simulation consideration

3.1 Nanoantenna topology

3.2 Simulation consideration

4. Nanoantenna property

4.1 Impedance property

4.2 Radiation property

4.3 Polarization property

5. Solar energy harvesting

5.1 Field enhancement

5.2 Solar energy harvesting under AM1.5

6. Conclusion

Funding

References and links

Cited By

Figures (13)

Tables (3)

Equations (9)

Optics Express

Geometric parameters	nanospiral	nanodipole
g	10 nm	10 nm
α	90°	90°
W	40 nm	40 nm
r₀	50 nm	-
G	40 nm	-
L	-	210 nm

Geometric parameters	nanospiral	nanodipole
g	10 nm	10 nm
α	90°	90°
W	40 nm	40 nm
r₀	50 nm	-
G	40 nm	-
L	-	210 nm