Energy 39 (2012) 27e32
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Energy journal homepage: www.elsevier.com/locate/energy
Design of optical antenna for solar energy collection Michele Gallo a, Luciano Mescia a, *, Onofrio Losito a, Michele Bozzetti a, Francesco Prudenzano b a b
Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy Dipartimento di Ingegneria dell’Ambiente e per lo Sviluppo Sostenibile, Politecnico di Bari, V.le del Turismo 8, 74100 Taranto, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 November 2010 Received in revised form 1 February 2011 Accepted 14 February 2011 Available online 22 March 2011
In this paper, an antenna array is designed in order to transform the thermal energy, provided by the Sun and re-emitted from the Earth, in electricity. The proposed antenna array is constituted by four square spirals of gold printed on a low cost dielectric substrate. A microstrip line, embedded into the substrate, is used to feed the array and to collect the thermal radiation. The dispersive behavior of gold at infrared frequencies has been taken into account through the LorentzeDrude model. Simulations have been conducted in order to investigate the behavior of the antenna array illuminated by a circularly polarized plane wave with an amplitude chosen according to the StefaneBoltzmann radiation law. An output current of about 3.8 mA has been simulated at 28.3 THz, i.e. at the frequency of the Earth emitted radiation. Moreover, these infrared antennas could be coupled with other components to obtain direct rectification of infrared radiation. As a consequence, these structures further optimized could be a promising alternative to the conventional photovoltaic solar cells. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Solar radiation Solar antenna Spiral antenna
1. Introduction During the last years, the worldwide energy demand has been strongly increased and as a consequence the deleterious effects due to the combustion of fossil fuels are apparent. Nowadays, renewable energies give a strong contribution to power generation without increasing environmental pollution. In particular, solar energy is largely used because it is a freely available source and the technology utilized to get electricity is relatively low cost. Moreover, the electricity production in solar space power plants could meet the future energy needs of the Earth’s population [1]. The Sun is mainly composed of hydrogen and helium. Thus, within the Sun, a thermonuclear fusion reaction converts the hydrogen into helium releasing huge amounts of energy. The energy created by the fusion reaction is converted in thermal radiation and transferred in the form of electromagnetic waves into the free space. Solar radiation occurs over a wide range of wavelengths, nevertheless the main range of this radiation includes ultraviolet (UV, 0.001 O 0.4 mm), visible (light, 0.4 O 0.7 mm), and infrared radiation (IR, 0.7 O 100 mm). Part of the solar radiation is scattered and reflected by clouds and a part is absorbed by the atmosphere and by the surface of the Earth. By absorbing the incoming solar radiation, the Earth warms up and its temperature rises. * Corresponding author. Tel.: þ39 80 5963808; fax: þ39 80 5963410. E-mail address:
[email protected] (L. Mescia). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.02.026
In general, all heated objects emit electromagnetic radiation. The amount of emitted radiation can be calculated through the StefaneBoltzmann law [2] that is applicable to perfect black bodies, i.e. an object that absorbs and emits radiation uniformly with 100% efficiency. Moreover, the total (over all wavelengths) energy radiated from a black body is proportional to the fourth power of its absolute temperature. The Earth and other planets are not perfect black bodies, as they do not absorb all the incoming solar radiation but they reflect part of it back toward the open space. The ratio between the reflected and the incoming energies is named planetary albedo [3]. The average albedo of the Earth is about 0.3. This fraction of incoming radiation is reflected back into space while the other 0.7 is absorbed. The Earth absorbs this energy and reemits it mainly in wavelength range from 4 to 25 mm. Due to the different spectral properties of the Sun and Earth emission, they are classified as shortwave and longwave radiation, respectively. Solar panels use the incoming solar radiation to produce electricity by exploiting the photovoltaic effect, i.e. a phenomenon which induces an electric voltage between two electrodes attached to a material when the system is exposed to light [4]. Since the incoming solar radiation is an electromagnetic wave radiation at terahertz wavelengths, it can be collected by using optical antennas as it usually occurs at radiowave and microwave frequencies [5]. Optical antennas are essentially scaled-down versions of antennas used in the microwave frequency range, able to convert the energy of free propagating radiation to localized energy.
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M. Gallo et al. / Energy 39 (2012) 27e32
2. Theory Nomenclature 2.1. Spiral antennas c e E h I
k PE R T Z0
G0 1/Gj
3r l s u up Up
speed of light earth emissivity electric field Plank constant black body spectral irradiance Boltzmann constant earth emitted power black body irradiance temperature impedance of the free space damping constant lifetime Complex relative permittivity wavelength StefaneBoltzmann constant angular frequency plasma frequency intra-band plasma frequency
Nevertheless, the antennas operating within the visible region generate a high frequency alternate current which cannot be easily controlled and rectified with the present devices. On the contrary, the Earth mainly emits its thermal energy within the infrared band, and as a consequence the longwave collectors can be easily manufactured as planar structures using well known techniques, such as electron-beam lithography (having a resolution on the order of 0.1 mm). The design of these novel antennas by using well known printing techniques, allows the reduction of costs and a quick prototyping approach. Integrated infrared detectors using dipole antennas [6], bowtie antennas [7], and spiral antennas [8] have been already investigated. Most of the past works have been devoted to experimentally demonstrate the capability of the optical antennas for producing electricity [9,10], but only a few numerical analysis have been performed. Accurate numerical modeling is needed for optical antenna performance prediction, design and refinement as well as to obtain some qualitative properties that may help in the design of more complex antenna array. The identification of the optimal geometric parameters and the frequency-dependent model of the permittivity of the considered materials are essential. To this aim, in this paper, we propose and design an antenna array that, are different from commercial solar panels, collects the longwave radiation emitted from the Earth and convert it into electricity. The array is constituted by four spiral antennas made of a thin film of gold printed on a SiO2 substrate. The feasibility of Earth thermal radiation harvesting has been investigated through simulations by illuminating the array with a circularly polarized plane wave having the amplitude and the frequency of the Earth radiation, properly calculated through the StefaneBoltzmann theory. Moreover, the LorentzeDrude model has been taken into account in order to model the variation of the metal permittivity versus the frequency within the infrared frequency region. The paper is organized as follows. In Section 2 the spiral antenna background is provided and the theory used for calculation of the amplitude and the frequency of the circularly polarized plane wave used into the simulations is illustrated. In Section 3, the numerical results regarding the optimization of the array is described. In Section 4 some main applications are illustrated. Finally Section 5 reports the conclusions.
Due to their broad bandwidth, during the last few years, spiral antennas have been proposed to collect solar energy [7,8]. In fact, as shown in Fig. 1, these antennas allow to concentrate the electric field in the gap (feed point) between two metallic arms which constitutes an appropriate point to transport energy needed to supply other circuitry. Round spiral antennas are generally designed by using Archimedean spiral geometries which have linear growth rates and frequency independent radiative characteristics. Moreover, the frequency independency is limited to a wavelength band determined by the antenna size. Spiral antennas can be constructed as planar structures and they can radiate linearly or circularly polarized waves; they are widely utilized for electronic countermeasures, surveillance, remote sensing, direction finding telemetry, and flush mounted airborne applications [9]. The optimal reception of a spiral antenna occurs when the spiral arm length equals approximately one wavelength, which correspond to a diameter of D ¼ l/p, for the circular spiral, and a side length W ¼ l/4 for the square spiral (see Fig. 1) [9]. According to these relations, square spiral geometries have more advantages in terms of size with respect to a circular spiral because comparable antenna gain can be obtained when the width of the square spiral is approximately 75% of the diameter of the circular spiral antenna.
2.2. StefaneBoltzmann radiation law The design of the antenna array collecting the electromagnetic radiation emitted by the Earth has been performed by illuminating the array with a circularly polarized plane wave. Theoretical considerations have been led in order to set the simulations in the right value of the electric field of the incoming plane wave. The Earth emits thermal radiation at much lower intensity with respect to the Sun because it is cooler. In order to study the thermal radiation emitted by the Earth, it can be approximated as a black body that absorbs all the incoming radiation and emits a temperature-dependent radiation spectrum.
0.06
0.04
0.02
0
-0.02
-0.04
-0.06 -0.06
-0.04
-0.02
0
0.02
0.04
0.06
Fig. 1. Square Archimedean antennas compared with a round spiral antennas.
M. Gallo et al. / Energy 39 (2012) 27e32
The power I of the radiation emitted by a black body at the temperature T per unit of area and wavelength (spectral irradiance) is given by Planck’s law [11]:
2pc2 h
Iðl; TÞ ¼
l5
1 expðhc=lkTÞ 1
(1)
where l is the wavelength, c is the speed of light, T is the temperature expressed in Kelvin degree, I(l,T)dl is the amount of the power emitted in the wavelength range from l to l þ dl per unit of area, unit of time and unit of solid angle, h and k are the Plank and Boltzmann constant, respectively. The power, R, emitted per unit area on the surface of a black body at temperature T over the entire frequency spectrum (irradiance) is given by the StefaneBoltzmann radiation law [2]. In particular, it is directly proportional to the fourth degree of a black body temperature by the relation:
ZþN Iðl; TÞdl ¼ sT 4
RðTÞ ¼
(2)
0
where s is the StefaneBoltzmann constant. Fig. 2 shows the black body radiation at temperature T ¼ 287 K versus the wavelength. The black body spectral irradiance exhibits a maximum close to the wavelength l ¼ 10.6 mm. A steeply and slowly I decreasing occurs at shorter and longer wavelengths, respectively. The temperature T ¼ 287 K corresponds to the mean Earth temperature as estimated by Jones et al. [12]. An accurate estimation of the Earth thermal radiation actually requires a different approach because it reflects part of the incoming energy. The emissivity, e, of the Earth, defined as the ratio between the energy radiated by a material and the energy radiated by a black body at the same temperature, is less than 1. For this kind of bodies, named gray body, the Eq. (2) becomes:
ZþN Iðl; TÞdl ¼ esT 4
RðTÞ ¼
(3)
29
2.3. The dispersion law In the infrared frequency range, dispersive metallic properties with a finite thickness have to be considered because the conductor loss in the terahertz regime could be very significant. Moreover, the frequency dependence of the material permittivity is necessary to accurately model the antenna features. To this aim, the Lorentze Drude (LD) model has been considered to explain the dispersive behavior of the gold [14]. The LD model considers a complex relative permittivity, 3r(u), expressed by:
3r ðuÞ ¼ 3fr ðuÞ þ 3br ðuÞ
(4)
This model is closely related to the electronic band structure and explicitly separates the intra-band effects,
3fr ðuÞ ¼ 1
U2p
(5)
uðu iG0 Þ
while the inter-band contribution is described by the model resembling the Lorentz result for insulators:
3br ðuÞ ¼
k X j¼1
fj u2p
(6)
u2j u2 þ iuGj
where up is the plasma frequency, k is the number of oscillators with frequency uj, strength fj and lifetime i/Gj, Up is the plasma frequency of the intra-band transitions with oscillator strength f0 and damping constant G0. The plot of Eq. (4) for gold is shown in the Fig. 3. The wavelength range considered in the numerical investigation corresponds to the frequency range from 20 to 40 THz. An increase of both real and imaginary part of the relative permittivity versus the wavelength is apparent. The availability of this model allows the calculation of electrical properties of the gold, such as the permittivity and the skin dept. A sixth order model has been here considered to study the material dispersion since excellent agreement between the fit and experimental data has been found [14].
0
Generally, the emissivity value of the Earth depends on gases density (water vapor and carbon dioxide), but a mean value of 0.9 can be considered [13]. By following the indications highlighted in Fig. 2, in order to efficiently collect Earth thermal radiation an antenna array operating at a wavelength around 10.6 mm have to be designed.
3. Numerical results A commercial full-wave 3D electromagnetic solver, CST (Computer Simulation Technology) Microwave Suite 2009 [15], has been used to perform simulations.
4
10
Relative permittivity of Au
Spectral irradiance [Wm-2 μm-1 ]
30
20
10
3
10
- Re{ε r} Im{ε r}
2
10
0 0
20
40 Wavelength [ μm]
60
Fig. 2. Black body radiation at the temperature T ¼ 287 K.
80
7
8
9
10 11 12 Wavelength [μm]
13
14
15
Fig. 3. Real part (full curve), and imaginary part (dotted curve) of the gold permittivity at infrared frequencies calculated by using the LorentzeDrude model.
30
M. Gallo et al. / Energy 39 (2012) 27e32
An array constituted by four spiral antennas printed on a substrate of 500 200 mm2 having permittivity 3s ¼ 4.86 and thickness ts ¼ 1.2 mm is considered. The ground plane and antenna arms are constituted by a gold film having thickness tG ¼ 150 nm. All the dispersive properties of dielectric and gold materials have been considered as input in the numerical solver. Fig. 4 shows the geometry of each element constituting the antenna array. The length of each linear filament composing both the arm A and arm B has been designed in order to expand the radiation patter and to optimize the ability of the antenna array to capture and convert the abundant energy from Earth radiation. The total length of each antenna of the array is 10.6 mm that is the wavelength corresponding to the maximum thermal radiation emitted by the Earth. The radiation characteristic of the proposed receiving antenna array is simulated by considering it as transmitting one. To this aim, a 50 U microstrip line, embedded into the substrate, has been considered to feed the antenna array. Fig. 5 illustrates a sketch of the considered antenna array. The black trace indicates the antenna array arms, the light gray represents the substrate and the full gray the microstrip line within the substrate. The width and length of the microstrip are w ¼ 0.45 mm and L ¼ 29 mm, respectively. Fig. 6 shows the simulated return loss of the antenna array versus the frequency. It can be observed for good performance of the proposed antenna array around the frequency 28.3 THz. It exhibits return loss values below RL (return loss) ¼ 10 dB from 20 to 24.8 THz and from 28 to 29.1 THz. This feature could be used to enhance the antenna array efficiency since Earth radiation can be collected in a wider frequency range. Fig. 7 illustrates the radiation patterns at the frequency of 28.3 THz. The obtained numerical results highlight that the array radiation pattern exhibits a maximum directivity value of 8.61 dBi and a half-power beam large enough to allow the receiving of thermal energy from different directions. Moreover, the pattern contains many lobes and nulls due to the edges of each spiral square element. In order to evaluate the efficiency of the array in collecting the thermal radiation, a number of simulations were performed by illuminating the antenna array with a circularly polarized plane wave. The amplitude of this plane wave cannot be chosen arbitrarily but it depends on the actual thermal power emitted by the Earth. Because the radiation emitted from the Earth has a maximum at the wavelength close to 10.6 mm, the electromagnetic analysis was performed from 7.5(40 THz) to 15 mm (20 THz), by integrating the
y
Fig. 5. Sketch of the linear array constituted by four square spiral antennas fed by a microstrip line embedded into the substrate.
Eq. (3) in this wavelength range. In particular, by considering T ¼ 287 K as the mean Earth temperature and emissivity e ¼ 0.9, the power emitted from the Earth in the considered frequency range was PE ¼ 152.5 W/m2. Since the Earth radiates a circularly polarized plane wave and the considered antenna is linearly polarized, the received power drops to an half. By considering the plane wave propagating power, the relation between the electric field amplitude E and the Earth emitted power PE is
E ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffi 2Z0 PE ¼ 239 V=m
(7)
where Z0 ¼ 377 U is the impedance of the free space. Therefore, in order to obtain reliable results, a plane wave with a magnitude of 239 V/m at the frequency of 28.3 THz was considered in the simulations. Numerical results stated that the best position to collect thermal radiation corresponds to the feed point of each antenna because in these points the electric field is maximum. In fact, in these antenna structures, the incident Earth thermal radiation excites surface waves at the metaledielectric interface which are channeled toward the gap. In particular, the free electrons of the gold flow along the antenna structure and are concentrated at the feed point. Nevertheless, due to technological limits to pick up the electric field
Feed point Arm A
-6
x
Return Loss (dB)
-8 -10 -12 -14 -16
Arm B
-18 -20
Fig. 4. Geometry of each square spiral element constituting the antenna array.
20
22
24
26
28 30 32 34 Frequency (THz)
36
38
40
Fig. 6. Simulated return loss of the linear spiral array versus the frequency.
M. Gallo et al. / Energy 39 (2012) 27e32
31
Fig. 7. Simulated 3D and 2D radiation pattern of the linear spiral array.
in these gaps, the field has been collected at the microstrip line input through a 50 U resistor. The current wave form across this element has been considered as a quantification of the total electric field collected by the array. Fig. 8 depicts the calculated electric current amplitude versus the frequency for a circular polarized plane wave excitation having central frequency of 28.3 THz and band from 20 to 40 THz. The array gives a reliable response between 26 and 30 THz with a maximum value of 3.8 mA at 28.3 THz. In Table 1 are summarized the calculated values of the output current by varying the number of the array elements. The obtained results show that the output current increases by increasing the number of array elements. In addition, a longer array leads to a narrower half-power beam and a higher gain. By
4. Applications The whole antenna array transforms Earth thermal radiation into electricity. Since the Earth mainly emits its thermal energy within the infrared band during the night, it would allow to overcome the main drawback of the current solar technology, i.e. the operation only during the morning. However, this kind of technology could be used in many other applications. As an example, in most industrial process there is waste heat that could be gathered to produce electricity. Because the temperature affects the received wavelength band, the antenna array should be ad hoc designed to operate and collect around the frequency range where the
4 3.5 3 Current (μA)
considering that the output current increases by increasing the number of antenna array elements, a planar array, constituted by several linear array, could be implemented to obtain higher output current. Nevertheless, the increment of the output current with the number of antennas cannot be easily evaluated. In fact, the coupling effects can reduce the array performance and, as a consequence, a carefully numerical and theoretical investigation has to be performed in order to identify the proper solution allowing the minimization of these effects and a further improving of the device performance.
2.5 2 1.5 1
Table 1 Output current of the linear array.
0.5 0 20
22
24
26
28 30 32 34 Frequency (THz)
36
38
40
Fig. 8. Response of the antenna array to a plane wave excitation versus the frequency when a 50 U resistor is connected at the microstrip line input.
Number of the array elements
Output current [mA]
1 2 3 4
1.06 2.08 2.42 3.80
32
M. Gallo et al. / Energy 39 (2012) 27e32
industrial process radiates most of its thermal energy. Moreover, this kind of antenna may also be used to remove heat and to cool electronic devices by substituting, for example, fans mounted in every personal computer, and at the same time it could continuously charge the batteries. Ad hoc designed array antenna should be a good candidate to improve the building thermal insulation and to reduce the energy consumption due to the operation of airconditioners and fans. In fact, by coating the roofs, windows and walls such system could cool down buildings without the external power sources. As a consequence, the proposed technology could be attractive within the recently introduced EU Eco-label scheme relating to buildings [16]. Moreover, due to the employed materials, this technology should be more eco sustainable with respect to the conventional ones. Other possible applications are in biology and in chemistry [17,18], where these antennas can be used as probes for the three-dimensional localization of biomolecular reactions. 5. Conclusions In this paper, a square spiral antenna array able to collect the longwave radiation emitted from the Earth has been numerically investigated through FDTD (Finite Difference Time Domain)-based solver. Simulations have been performed both by feeding the array with a microstrip line embedded into the substrate to calculate the radiation characteristics and by illuminating the array with a circularly polarized plane wave. The magnitude of this plane wave has been properly calculated through the StefaneBoltzmann law by considering the Earth as a gray body. Moreover, in the analysis the dispersive characteristics of the gold at optical frequencies have been explained through the use of the LorentzeDrude model. The array has a resonant frequency at 28.3 THz and return loss values of 10 dB from 20 to 24.8 THz and between 28 and 29.1 THz. A maximum output current of 3.8 mA has been obtained at the frequency of 28.3 THz corresponding to the maximum Earth radiation. The obtained numerical results show that with the right value of width and depth of antenna wire, gap size, shape and materials this
antenna array can efficiently collect energy at infrared wavelengths becoming a valid alternative to the traditional solar cells. In fact, it allows the electricity production also during the night overcoming the main drawback of the PV (Photovoltaic) technology. Therefore, this solution could be an interesting innovation in the area of the renewable energy as well as a promising cooling system to be utilized in buildings and computers. References [1] Zidansek A, Ambro zi c M, Milfelner M, Blinc R, Lior N. Solar orbital power: Sustainability analysis. Energy 2011;36(4):1986e95. [2] Tipler PA, Llewellyn RA. Modern physics. 4th ed.; 2002. 132e141. [3] Rybicki GB, Lightman AP. Radiative processes in astrophysics, vol. 25. New York: John Wiley & Sons; 1979. [4] Goetzberger A, Hoffmann VU. Photovoltaic solar energy generation. Berlin Heidelberg: Springer-Verlag; 2005. [5] Bharadwaj P, Deutsch B, Novotny L. Optical antennas. Adv Opt Photon 2009;1:438e83. [6] Gonzalez FJ, Boreman GD. Infrared Phys 2005;46:418e28. [7] Yu N, Cubukcu E, Diehl L, Bour D, Corzine S, Zhu J, et al. Bowtie plasmonic quantum cascade laser antenna. Opt Express 2007;15:13272e81. [8] Kotter D.K, Novack S.D, Slafer W.D, Pinhero P. Proceedings of ES2008 American Society of Mechanical Engineers; 2008:p. 1e7. _ [9] Saynak U. Novel rectangular spiral antennas. Master Thesis of science. Izmir _ _ October 2007. Institute of Technology: IZM IR; [10] Sarehraz M, Buckle K, Weller T, Stefanakos E, Bhansali S, Goswami, Y, Subramanian K. Photovoltaic Specialists Conference, Conference Record of the Thirty-first IEEE 2005:pp. 78e81. [11] Planck M. Über das Gesetz der Energieverteilung im Normalspektrum. Annalen der Physik 1901;4:553e8. [12] Jones D, New M, Parker DE, Martin S, Rigor IG. Surface air temperature and its changes over the past 150 years. Rev Geophys 1999;37:173e99. [13] Trenberth KE, Fasullo JT, Kiehl J. Earth’s global energy budget. Bull Am Met Soc; 2009:311e23. [14] Rakic AD, Djurisic AB, Elazar JM, Majewski ML. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl Opt 1998;37:5271e83. [15] CST Suite, www.cst.com; 2010. [16] Franzitta V, La Gennusa M, Peri G, Rizzo R, Scaccianoce G. Toward a European Ecolabel brand for residential buildings: holistic or by-components approaches? Energy 2011;36(4):1884e92. [17] Garcia-Parajo Maria F. Optical antennas focus in on biology. Nat Photonics 2008;2:201e3. [18] Alda J, Rico-García JM, López-Alonso JM, Boreman G. Optical antennas for nano-photonic applications. Nanotechnology 2005;16:S230e4.
