Comptes Rendus Physique

Jean-Jacques Greffet

Revisiting thermal radiation in the near field

Smaïl Tedjini

Apostolos Georgiadis

Tome 18 (2017) – N◦ 2 – février 
Cover illustration / Illustration de couverture : © Daniel de Fornel, Atelier Isatis, Dijon, France.
DOSSIER
Energy and radiosciences / Énergie et radiosciences
Journées scientifiques URSI-France 2016 – Cesson-Sévigné (Rennes), 15–16 March 2016 / 15–16 mars 2016
Coordinators / Coordinateurs : Smaïl Tedjini, Apostolos Georgiadis
• Foreword
Smaïl Tedjini, Apostolos Georgiadis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
• Wireless energy transfer: Dielectric lens antennas for beam shaping in wireless power-transfer applications
Ricardo Gonçalves, Nuno B. Carvalho, Pedro Pinho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
• On energy harvesting for augmented tags
Dahmane Allane, Yvan Duroc, Gianfranco Andia Vera, Rachida Touhami, Smail Tedjini . . . . . . . . . . . . . . . . . . . . . . 86
• Electrostatic vibration energy harvester with 2.4-GHz Cockcroft–Walton rectenna start-up
Hakim Takhedmit, Zied Saddi, Armine Karami, Philippe Basset, Laurent Cirio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
• Multiband rectenna for microwave applications
Abderrahim Okba, Alexandru Takacs, Hervé Aubert, Samuel Charlot, Pierre-François Calmon . . . . . . . . . . . . . . . 107
• Theoretical and practical limits of superdirective antenna arrays
Abdullah Haskou, Ala Sharaiha, Sylvain Collardey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
• Performance of low-power RFID tags based on modulated backscattering
Zeinab Mhanna, Alain Sibille, Richard Contreras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
• Energy and angular momentum transfers from an electromagnetic wave to a copper ring in the UHF band
Olivier Émile, Christian Brousseau, Janine Émile, Kouroch Mahdjoubi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
• Fundamental energetic limits of radio communication systems
Jean-Yves Baudais . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Continued on the next page
Contents (continued)
• Wavelet modulation: An alternative modulation with low energy consumption
Marwa Chafii, Jacques Palicot, Rémi Gribonval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
• Analysis of the faster-than-Nyquist optimal linear multicarrier system
Alexandre Marquet, Cyrille Siclet, Damien Roque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
• Turbo-FSK, a physical layer for low-power wide-area networks: Analysis and optimization
Yoann Roth, Jean-Baptiste Doré, Laurent Ros, Vincent Berg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Guide for authors: http://www.em-consulte.com/getinfoProduit/COMREN/instructionsAuteurs/COMREN.pdf
Electronic Submission: http://ees.elsevier.com/crphysique/


Foreword

Abdullah Haskou

Ala Sharaiha

Sylvain Collardey

C. R. Physique 18 (2017) 118–124Contents lists available at ScienceDirect
Comptes Rendus Physique
www.sciencedirect.com
Energy and radiosciences / Énergie et radioscience
Theoretical and practical limits of superdirective antenna 
arrays
Limites théoriques et pratiques des antennes superdirectives
Abdullah Haskou ∗, Ala Sharaiha, Sylvain Collardey
IETR UMR CNRS 6164, Université de Rennes-1, 263, avenue du Général-Leclerc, CS 74205, 35042 Rennes cedex, France
a r t i c l e i n f o a b s t r a c t
Article history:
Available online 5 December 2016
Keywords:
Superdirective antenna arrays
Parasitic elements
Theoretical and practical limits
Mots-clés :
Réseaux d’antenne superdirectifs
Éléments parasites
Limites théoriques et pratiques
Some applications as Wireless Power Transfer (WPT) require compact and directive 
antennas. However, Electrically Small Antennas (ESAs) have low efficiencies and quasi-
isotropic radiation patterns. Superdirective ESA arrays can be an interesting solution to 
cope with both constraints (the compactness and the directivity). In this paper, the 
theoretical and practical limits of superdirective antennas will be presented. These limits 
can be summarized by the directivity sensitivity toward the excitation coefficients changes 
and the radiation efficiency decrement as the inter-element decreases. The need for 
negative resistances is also a practical limit for transforming these arrays into parasitic 
ones. The necessary trade-offs between the antenna total dimensions (the number of 
elements and the inter-element distance) and the attainable directivity and efficiency are 
also analyzed throughout this paper.
© 2016 Académie des sciences. Published by Elsevier Masson SAS. This is an open access 
article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
r é s u m é
Certaines applications, comme le transfert d’énergie sans fil, nécessitent des antennes 
à la fois directives et compactes. Cependant, les antennes électriquement petites (AES) 
présentent de faibles rendements et des diagrammes de rayonnement quasi isotropes. Les 
antennes compactes superdirectives peuvent être une solution intéressante pour résoudre 
les problématiques concernant la directivité et l’efficacité énergétique. Dans cet article, 
nous présentons les limites théoriques et pratiques des antennes superdirectives. Ces 
limites sont le niveau de directivité en fonction de la sensibilité sur les coefficients 
d’excitation ainsi que la diminution de l’efficacité de rayonnement quand la distance 
inter-éléments diminue. Le besoin de résistances négatives pour concevoir des réseaux 
superdirectifs à éléments parasites est également une limite pratique dont il faut tenir 
compte. Les compromis nécessaires entre les dimensions totales de l’antenne (nombre des 
éléments et distance inter-éléments), la directivité et l’efficacité atteignables sont analysés 
dans cet article.
© 2016 Académie des sciences. Published by Elsevier Masson SAS. This is an open access 
article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).* Corresponding author.
http://dx.doi.org/10.1016/j.crhy.2016.11.003
1631-0705/© 2016 Académie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
A. Haskou et al. / C. R. Physique 18 (2017) 118–124 1191. Introduction
Many emerging radio technologies as the Internet of Things (IoT), wireless sensors, Wireless Power Transfer (WPT) and 
low-power wireless communications require a significant effort on the antenna miniaturization while keeping an acceptable 
performance (in terms of bandwidth, directivity, and efficiency). The effect of the antenna gain (efficiency and directivity) 
on far-field Power Transfer Efficiency (PTE) can be easily seen from the Friis transmission formula. Furthermore, Ick-Jae 
Yoon demonstrated that using directive antennas also improves the PTE in the near-field region [1]. However, antenna 
performance is limited, with some fundamental limits related to its physical dimensions. Multiple researchers addressed the 
fundamental limits of Electrically Small Antennas (ESAs) [2–6]. A.H. Wheeler defined an ESA as an antenna with ka < 1, 
where k = 2π
λ
is the wave number, λ is the free-space wavelength and a is the radius of the smallest sphere enclosing 
the antenna [2]. Due to these fundamental limits, ESAs are characterized by their narrow bandwidths, their quasi-isotropic 
radiation patterns (radiating energy in non-desired directions) and their low efficiencies (high power consumption). These 
characteristics will lead to a considerable loss in the link budget, and, as a consequence, small communications ranges. To 
increase the directivity of ESAs, one can integrate them in arrays. However, the conventional arrays (where the inter-element 
distance is around half a wavelength) lead to a significant increase in their size. At the same time, since the pioneering 
work of I. Uzkov [7], there has been a renewed interest in superdirective arrays (the inter-element distance is set to a small 
fraction of the wavelength) [8–18]. While decreasing the distance increases the attainable directivity, it also increases the 
mutual coupling, hence it can have a considerable effect on the array efficiency.
In [17], we detailed the design procedure of small parasitic superdirective arrays. In this paper, the theoretical and prac-
tical limits of superdirective antennas will be presented. The necessary trade-offs between the antenna overall dimensions, 
the attainable directivity and efficiency will be detailed. This analysis is validated via the full-wave simulation and the 
measurement of a three-element array.
The rest of the manuscript is organized as follows: superdirective antenna limits are discussed in section 2. The results 
are validated via the design of a three-element array in section 3. Finally, conclusions are drawn in section 4.
2. Theoretical limits of superdirective arrays
Consider an array of antennas located at positions rn , n = 1, 2, . . . , N with respect to a fixed rectangular (xyz) coordinate 
system. The complex far field radiated by the array in (θ, φ) is given by:
f (θ,φ) =
N∑
n=1
An fn(θ,φ)e
jkr̂rn (1)
where An are the complex excitation coefficients, fn(θ, φ) are the complex radiated far fields and r̂ is the unit vector in the 
far-field direction (θ, φ). The array directivity is given by:
D(θ,φ) = | f (θ,φ)|
2
1
4π
´ 2π
0
´ π
0 | f (θ,φ)|2 sin(θ)dθ dφ
(2)
The Uzkov–Altshuler current excitation coefficients that maximize the directivity in the direction (θ0, φ0) are given by [7,8]:
a0n = [H∗mn]−1e−jkr̂0rm f ∗m(θ0, φ0) fn(θ0, φ0) (3)
where r̂0 is the unit vector in the far field direction (θ0, φ0), and Hmn is given by:
Hmn = 1
4π
2πˆ
0
π̂
0
fm(θ,φ) f
∗
n (θ,φ)e
jkr̂(rm−rn) sin(θ)dθ dφ (4)
Now let us consider an array of N isotropic radiators equally spaced by a distance d along the z axis with the first element 
located in the coordinate system origin. The calculated excitation coefficients of three- and four-element arrays are given in 
Figs. 1 and 2. These excitation coefficients reveal that, for an array of a fixed number of elements, high excitation magnitudes 
are required for small distances, and, as the distance increases, the excitation magnitude decreases. For d = 0.5λ all the 
excitation magnitudes are equal. It can be noticed that the symmetric elements (1,2 for N = 2, 1,3 for N = 3, 1,4, and 2,3 for 
N = 4) have equal excitation magnitudes. It can also be noticed that for a fixed spacing, increasing the number of elements 
significantly increases the excitation magnitudes. By applying these excitation coefficients, the maximum directivity that 
can be obtained as a function of the inter-element distance is given in Fig. 3(a). It may be noticed that when the distance 
between the elements approaches zero, the array directivity approaches N2. Increasing spacing decreases the directivity in 
the main direction and increases it in the backward direction (Fig. 3(b)). At 0.5λ, the directivity in both end-fire directions is 
equal to N (refer to Fig. 3(c)). Fig. 3(d) shows the power radiated by the array for power-normalized excitation coefficients, 
i.e. (
∑N
n=1 A2n = 1). This power is calculated as follows:
E-mail address: abdullah.haskou@univ-rennes1.fr (A. Haskou).
120 A. Haskou et al. / C. R. Physique 18 (2017) 118–124Fig. 1. Three d-spaced isotropic array optimal excitation coefficients. (a) Magnitude and (b) phase.
Fig. 2. Four d-spaced isotropic array optimal excitation coefficients. (a) Magnitude and (b) phase.
P rad = 12
‹
S
Re(E × H∗)ds ≈ 1
2η
‹
S
|E|2ds ≈ 1
2η
2πˆ
0
π̂
0
|E|2r2 sin(θ)dθ dφ (5)
where η is the intrinsic impedance of the medium (air), r is the radius of the sphere over which the radiated power is 
calculated, and E is the total far-field electric field and can be calculated as in Eq. (1). We can notice that, for the same 
distance, as the number of the elements increases, the radiated power decreases, and, as a consequence, so does the array 
radiation efficiency. To study the sensitivity of the array toward the excitation coefficients, we re-calculated the directivity 
when the coefficients magnitudes are estimated with an error of 5% or the phases are shifted by 5◦ . Fig. 4 shows the 
obtained results (since the symmetric elements have equal magnitudes, the array sensitivity toward the errors in these 
elements’ excitation is also the same, so they are not shown). It may be noted that, for small spacing, the array is very 
sensitive to the changes in the coefficients. It is also possible to notice that, for a fixed distance, increasing the number of 
the elements increases the array sensitivity. For a distance d = 0.1 λ, an error of 5% in the estimation of the first element’s 
magnitude reduces directivity by 1.1%, 10.2%, or 56.1% in case of an array of two, three, or four elements, respectively. It is 
also observed that, for an array of N elements, the array is more sensitive to the changes in the coefficients of the middle 
elements. This is due to the fact that the magnitudes of these coefficients are higher. After presenting the theoretical limits 
of superdirective arrays, we will show in the next section some practical limits via the design of a three-element array.
3. Design of a three-element array
The superdirective antenna array design methodology detailed in [17] was used to design a three-element array. The 
unit-element used in this array is a miniaturized half-loop antenna printed on a 0.8-mm-thick Rogers RO4003 substrate 
and integrated in a PCB of 8 × 8 cm2 [18]. It has a resonance frequency around 864 MHz with a directivity of 2.4 dBi 
and a radiation efficiency of 89.4%. The proposed antenna geometry is shown in Fig. 5(a). The inter-element distance d1 is 
varied from 0.69 cm ≈ 0.02 λ to 6 cm ≈ 0.17λ to investigate its effect on the antenna’s maximum directivity and radiation 
efficiency. Fig. 5(b) shows the array directivity compared to Harrington’s fundamental limit on the directivity of an antenna 
with the same size ka given by D = (ka)2 + 2ka [6]. As expected, it can be noticed that for very small distances, the 
A. Haskou et al. / C. R. Physique 18 (2017) 118–124 121Fig. 3. The performance of N-element d-spaced isotropic array. (a) Directivity in the main end-fire direction, (b) directivity in the backward end-fire direc-
tion, (c) 2D total directivity radiation pattern for d = 0.01 (continuous), d = 0.25 (dashed), and d = 0.01 (dashed–dotted), and (d) normalized transmitted 
power.
Fig. 4. The effect of the error in the coefficients estimation on the directivity of N-element d-spaced isotropic array. (a) N = 2, (b) N = 3, and (c) N = 4.
122 A. Haskou et al. / C. R. Physique 18 (2017) 118–124Fig. 5. Proposed superdirective array. (a) Array geometry and (b) simulated total directivity.
Fig. 6. The value of the required loads for converting the array into a parasitic one. (a) Real part and (b) imaginary part.
Fig. 7. Parasitic array simulated radiation efficiency.
driven array is very sensitive to the excitation coefficients, and a small error in the calculation of these coefficients leads 
to an important decrement in the antenna’s directivity. As distance increases, this sensitivity decreases and, starting from 
d1 = 3.5 cm ≈ 0.08λ, interesting directivity values can be attained. The value of the required loads for transforming the 
array into a parasitic one is given in Fig. 6. As it can be noticed, some negative resistances are required, and since the design 
of negative resistances using non-Foster circuits is not an easy task, neglecting these resistances significantly decreases the 
attained directivity compared to the fully driven array. Finally, Fig. 7 shows that, as expected due to the coupling decrement, 
the parasitic array radiation efficiency increases with the inter-element distance. A prototype of the antenna array for 
d1 = 6 cm ≈ 0.17 λ was fabricated and measured (Fig. 8(a)). In this array, the second element is excited, while the others 
are loaded. Fig. 8(b) shows the antenna input reflection coefficient magnitude in dB. As it can be noticed, the antenna has 
a simulated/measured resonance at 863/868 MHz with a S11 < −10 dB bandwidth of 1.7/5 MHz. The higher losses in the 
measurement may be attributed to the UFL cable used for measurement. Fig. 8(c) shows the antenna’s 3D total directivity 
A. Haskou et al. / C. R. Physique 18 (2017) 118–124 123Fig. 8. Simulated and measured parameters corresponding to a three-element array with 6-cm spacing. (a) Fabricated prototype, (b) input reflection coeffi-
cient magnitude in dB, and (c) 3D total directivity radiation pattern.
Fig. 9. Simulated and measured parameters corresponding to 2D total directivity radiation patterns for a three-element array with 6-cm spacing. (a) E-plane, 
(b) H-plane.
radiation pattern. The figure shows a directive pattern with a directivity of 8.8/8.5 dBi toward the z-axis. This directivity 
is larger by about 1.4 dB than Harrington’s normal directivity limit for an antenna with the same size factor (ka = 1.6). 
The HPBWs in the E (XoZ ) and H (Y oZ ) planes are, respectively, 72◦/73.1◦ and 64◦/67.5◦ , and FBR is 5.8 dB/4.1 dB (Fig. 9). 
The antenna presents a radiation efficiency of 34.7%/37%.
124 A. Haskou et al. / C. R. Physique 18 (2017) 118–1244. Conclusion
In this article, we have shown the theoretical and practical limits of the design of superdirective antenna arrays. These 
limits can be summarized by the array’s sensitivity to excitation coefficients and the small efficiencies for very closely 
spaced arrays, and the need for negative resistances for transforming the arrays into parasitic ones. In general, the design of 
superdirective antenna arrays is a trade-off between the antenna dimensions (the number of elements and the inter-element 
distance) and the attained directivity and efficiency. Superdirective and efficient arrays can be designed through a careful 
consideration of these trade-offs.
Acknowledgements
This work has been funded by the French National Research Agency (ANR-11-INFR-014) as part of the project “SOCRATE”, 
and with the support of the “Images et réseaux” cluster of the Brittany region, France.
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Tome 18 (2017) – N◦ 7–8 – septembre–octobre 
Cover illustration: Left: the Sainte-Croix dam and its water reservoir contribute to the supply of water and 
renewable energy across the PACA region (see E. Branche, this issue, pp. 469–478). Top right: view of the 
ITER tokamak that will be assembled in this ”well” at the centre of the Tokamak Complex building in 
Saint-Paul-les-Durance, France (see B. Bigot, this issue, pp. 367–371). Bottom right: photovoltaic farm, 
Néoules (Var, France). Photo: D. Lincot (see D. Lincot, this issue, pp. 381–390).
Illustration de couverture : À gauche : barrage de Sainte-Croix et son réservoir d’eau, qui contribuent à 
l’approvisionnement en eau et en énergie renouvelable pour toute la région Provence-Alpes-Côte d’Azur (PACA) 
(voir E. Branche, ce dossier, pp. 469–478). À droite, en haut : vue du Tokamak ITER qui va être assemblé dans le 
« puits » au centre de ce bâtiment central du Tokamak, à Saint-Paul-les-Durance, France (see B. Bigot, ce dossier, 
pp. 367–371). À droite, en bas : ferme photovoltaïque de Néoules (Var, France). Photo : D. Lincot (voir D. Lincot, ce 
dossier, pp. 381–390).
DOSSIER
Demain l’énergie
Coordinators / Coordinateurs : Patricia de Rango, Daniel Bellet, Adrien Bidaud, Henri Mariette
• Foreword
Patricia De Rango, Daniel Bellet, Adrien Bidaud, Henri Mariette . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
• ITER: A unique international collaboration to harness the power of the stars
Bernard Bigot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
• Fundamentals of reactor physics with a view to the (possible) futures of nuclear energy
Xavier Doligez, Sandra Bouneau, Sylvain David, Marc Ernoult, Abdoul-Aziz Zakari-Issoufou, 
Nicolas Thiollière, Adrien Bidaud, Olivier Méplan, Alexis Nuttin, Nicolas Capellan . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
• The new paradigm of photovoltaics: From powering satellites to powering humanity
Daniel Lincot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
• Spatial Atomic Layer Deposition (SALD), an emerging tool for energy materials. Application to new-generation 
photovoltaic devices and transparent conductive materials
David Muñoz-Rojas, Viet Huong Nguyen, César Masse de la Huerta, Sara Aghazadehchors, Carmen Jiménez, 
Daniel Bellet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
Continued on the next page
Contents (continued)
• Storage of thermal solar energy
Benoît Stutz, Nolwenn Le Pierres, Frédéric Kuznik, Kevyn Johannes, Elena Palomo Del Barrio, 
Jean-Pierre Bédécarrats, Stéphane Gibout, Philippe Marty, Laurent Zalewski, Jerome Soto, Nathalie Mazet, 
Régis Olives, Jean-Jacques Bezian, Doan Pham Minh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
• Buildings: The new energy nexus
Daniel Quénard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
• “Smart buildings” integrated in “smart grids”: A key challenge for the energy transition by using physical 
models and optimization with a “human-in-the-loop” approach
Frédéric Wurtz, Benoît Delinchant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
• Lighter structures for transports: The role of innovation in metallurgy
Alexis Deschamps, Guilhem Martin, Rémy Dendievel, Hugo P. Van Landeghem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
• LEDs for lighting: Basic physics and prospects for energy savings
Bruno Gayral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
• Use of vegetal biomass for biofuels and bioenergy. Competition with the production of bioproducts and 
materials?
Christine Chirat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
• The multipurpose water uses of hydropower reservoir: The SHARE concept
Emmanuel Branche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
• Energy transitions after COP21 and 22
Sébastien Balibar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
Guide for authors: https://www.elsevier.com/journals/comptes-rendus-physique/1631-0705/guide-for-authors
Electronic Submission: http://ees.elsevier.com/crphysique/


Benoît Stutz

Nolwenn Le Pierres

Frédéric Kuznik

Kevyn Johannes

Elena Palomo Del Barrio

Jean-Pierre Bédécarrats

Stéphane Gibout

Philippe Marty

Laurent Zalewski

Jerome Soto

Nathalie Mazet

Régis Olives

Jean-Jacques Bezian

Doan Pham Minh

Storage of thermal solar energy

Abderrahim Okba

Alexandru Takacs

Hervé Aubert

Samuel Charlot

Pierre-François Calmon

Multiband rectenna for microwave applications

Yoann Roth

Jean-Baptiste Doré

Laurent Ros

Vincent Berg

Turbo-FSK, a physical layer for low-power wide-area networks: Analysis and optimization

Lisa Glaser

Renate Loll

CDT and cosmology

Not a member yet

Revisiting thermal radiation in the near field

Foreword

Theoretical and practical limits of superdirective antenna arrays

Dossier Sommaire

Editorial Board

Foreword

Storage of thermal solar energy

Multiband rectenna for microwave applications

Turbo-FSK, a physical layer for low-power wide-area networks: Analysis and optimization

CDT and cosmology

2,036

2,321