Toward Indoor Simulations of OPV Cells for Visible Light Communication and Energy Harvesting

The massive deployment of IoT connected devices brings up different modern problems, such as radiofrequency spectrum saturation and energetic requirements. Organic photovoltaics are good candidates for indoor energy harvesting and data reception in a simultaneous lightwave information and power transfer scenario applied for IoT, at which the non-directive channel significantly contributes to the optical system performance. However, achieving the channel impulse response of diffuse links requires complex numerical approaches. This article presents the first ever OPV model used in a Monte-Carlo ray-tracing simulation, associated to theoretical and experimental validation. Finally, for the first time, an optical simulation with an OPV receiver is realized in a cubic environment, from which the received optical power and generated current distributions were obtained. Results show that the employed OPV is suited for indoor energy harvesting to supply low power IoT nodes, and with proper dedicated front-end, could manage to receive optical data in a SLIPT scenario.


I. INTRODUCTION
With the expansion of connected objects, the radiofrequency (RF) spectrum is poised to become saturated [1], leading to interest in the terahertz domain and beyond.Wireless communications in the optical domain (optical wireless communication -OWC) have already demonstrated their potential for indoor communication, fulfilling important requirements for some of the internet of things (IoT) demands.By limiting this concept to the visible spectrum, the visible light communication (VLC) technology emerges as a promising technology that takes advantage of indoor The associate editor coordinating the review of this manuscript and approving it for publication was Guido Lombardi .
lighting for both illumination and data transfer.This was further extended as a network concept in 2011 by Harald Haas, who brought to the spotlight the LiFi term [2], [3], [4], [5].
In classical VLC approaches, a light emitting diode (LED) is used as transmitter, ensuring the conversion of the modulated electrical signal into intensity-modulated (IM) optical waves.Smart lighting systems playing the role of VLC access points have already been deployed and they show great interest for the community in the context of indoor IoT for their reliability and light spectrum recycling [6].After propagation in free-space, possibly including reflections and transmissions on/through elements of the environment, a photodiode (PD) converts the optical signal into electrical data by generating a current proportional to the received optical power (the so-called direct detection (DD) method) [7].The received current is generally converted to voltage by a transimpedance amplifier (TIA) [8].However, this approach requires external power for the current-voltage conversion and to guarantee an ideal operation point of the PD (photoconductive or photovoltaic mode), which represents an important drawback for autonomous systems.
On the energetic side, ambient energy harvesting (EH) is particularly interesting to supply power to connected IoT devices, such as sensors and actuators [9].The innumerous possible usages of these devices in the IoT context, i.e. smart homes, smart cities and smart factories, can easily result in complexity of access for reparation and recharging.From all possible solutions, different EH techniques are available, among which photovoltaic (PV) energy [10], thermal EH [11], RF EH [12] and hybrid configurations [13] stand out.Under indoor situations, obtaining electrical energy from artificial lighting seems promising for the development of autonomous IoT nodes for their high power density, compared to other sustainable sources [14].Over the past few years, the PV community has displayed significant interest in this area [15], [16], [17], [18], [19].
Today, emerging solar cells (i.e. 3 rd generation) are considered as highly relevant PV technologies compared to more conventional inorganic devices (silicon-based systems or thin film technologies), due to their rising performance under full sun and potentially low manufacturing costs and energy payback times [20], [21].Recent studies have shown the importance of organic photovoltaics (OPVs) for energy harvesting in indoor IoT context [22], [23], [24], [25], [26].
In this context, some studies analyzed the use of PV devices (replacing PDs) as OWC receivers, allowing the simultaneous reception of data (which comes from the AC component of the optical signal) and energy (coming from the DC component) [27], [28], [29], [30], [31], [32], [33], bringing up the simultaneous lightwave information and power transfer (SLIPT) concept.This topology allows the recycling of indoor energy towards autonomous low power IoT nodes while establishing a VLC link through the same optical channel [34].By selecting an appropriate operating point, the solar cell can provide an acceptable output signal voltage that can be further decoded while still supplying power to the receiver and the involved electronics.Different receiver circuit strategies were also recently developed, aiming the trade-off between energy harvesting and communication performances according to the solar cell operating point [35], [36], [37].
Even though these works validated the performance of solar cells for SLIPT scenarios, they were carried out in line-of-sight (LOS) conditions, obtaining the best data rate and energy harvested when emitter and receiver are aligned, mostly at very short distances (<1 m).No work has analyzed their performance in real and complex indoor IoT scenarios considering all different factors that can impact the receiver capabilities, while only one analyzed the non-line-of-sight (NLOS) contribution on the PV receiver [38].Actually, signal dispersion due to multipath propagation is generally associated with the reflection of light on different elements of the environment [39].Consequently, it is important to characterize the optical channel to optimize the performance of the system according to the desired scenario, i.e. to determine the best position and direction of both transmitter and receiver and their ideal optoelectronics features to reach the ultimate communication and EH performance.
In this context, we propose a theoretical and experimental approach to model OPV devices, enabling the evaluation and prediction of EH and communication performance in realistic scenarios based on LOS and NLOS configurations.The established model is used in a Monte Carlo ray tracing (MCRT) software, developed in our laboratory [40], [41], allowing us to obtain the channel impulse response for different optical link configurations.From the simulation results, the received optical power can be computed, which is further extended to illuminance using the luminous efficiency function.From the experimental measurement of the OPV receiver responsivity, which considers different internal parameters of photosensitive devices, the optical power estimation can be converted into short-circuit current, further extended to generated electrical power at maximum power point (MPP) condition.
The experimental validation of our methodology is based on a real OPV device of several cm 2 (LAYER®technology) inkjet-printed by the French start-up Dracula Technologies (Valence, France).Such tool opens the door to advanced modeling of energy and data link budgets for various devices and nodes of the IoT ecosystem, and for multiple scenarios being targeted by the SLIPT concept.To the best of the authors' knowledge, this is the first OPV modelling used in optical simulation devoted to energy harvesting and communication purposes with experimental validation.
The essential steps required for conducting indoor simulations using the specified OPV are illustrated in Fig. 1, detailed in subsequent sections of the article.Each component is accompanied by its own methodology and corresponding results.The article is structured as follows: In Section II, we examine pertinent literature, emphasizing the significant contributions of our work to the existing body of knowledge.In Section III, we review the optical channel impulse response equation and describe the responsivity angular dependence of photosensitive devices in general.In Section IV, we detail the materials used for all experiments.Thus, the measurement of the responsivity angular dependence is reported, allowing the implementation of an OPV receiver model into the simulator associated to empirical validation.In Section V, we discuss two experiments, the first consisting in a LOS link and the second in a LOS and NLOS link, experimentally validating the model used for simulations.In Section VI, we simulate a VLC scenario in a 5 m × 5 m × 3 m room, composed by surfaces with spectral reflection coefficients described in [42].The large spectra simulation provides us the channel impulse response for different positions of the OPV receiver, acquiring then a spatial distribution of the generated current (considered in short circuit conditions), which was then extended to energy harvesting performance under maximum power point operation thanks to previously measuring the current voltage characteristics of the device for different artificial illuminations.Finally, in Section VII, we conclude the work.

II. RELATED WORKS
Indoor environments present unique challenges for EH systems, including limited access to natural sunlight.PV devices offer a viable solution by harnessing ambient light sources such as indoor lighting to generate electrical energy.Furthermore, their communication capabilities have been showcased in the context of VLC, with subsequent expansion into the realm of SLIPT.This section briefly underscores key literature that explores the utilization of PV devices in indoor environments for EH and/or VLC applications.

A. PV DEVICES FOR INDOOR EH
In the present state of IoT, ambient light EH has garnered significant attention across various applications, outlined as follows.
In [43], the authors developed a full autonomous wireless sensor network (WSN) node by employing six commercial flexible PV modules (2.66 cm × 2.075 cm) to monitoring ambient conditions such as temperature, humidity, pressure, acceleration and light intensity.The study simulated an office setting with a consistent 300 lux illumination, finding that the PV panel could generate approximately 275 µW under these conditions.This energy output was deemed sufficient to power other electronic components, including sensors, a microcontroller, and a RF transceiver for data transmission.In [44], the authors employed an oversized OPV module (11 cm × 23 cm) in indoor settings (ranging from 400 lux to 1000 lux) over a period of 21 months.While the actual generated power remains undisclosed, the OPV effectively powered all other electronic components with the assistance of a battery.Yet, the precise OPV dimensions needed to power the setup, factoring in the final system size, remain uncertain.In [45], the authors developed a full autonomous indoor WSN by employing a 5.81 cm × 4.86 cm amorphous silicon (α-Si) PV cell, considering a constant 200 lux illumination (generating around 137.1 µW) to design the circuit.Finally, Meli et al. developed an autonomous sensor node operating at incredibly low illuminances (5 lux) [46].The system, associated to energy management strategies, supplied a touch detector, a real-time clock and a microcontroller with four 98 mm 2 PV cells.
Expanding the application of indoor PV EH to the medical field, Tran et al. developed a highly efficient IoT node for medical surveillance employing a large and flexible amorphous silicon thin-film solar panel measuring 19 cm × 4 cm in dimensions [47].Despite the architecture's inability to directly charge the battery, it still enhances its longevity under indoor conditions (irradiances lower than 3 mW/cm 2 ).This underscores the significance of the current strategy.

B. PV DEVICES FOR SLIPT
By employing a PV cell/module in an environment featuring VLC, the IoT node not only harvests energy from indoor ambient light but also detects its intensity to decode optical data.With a customized front-end circuit, the receiver can distinguish between data and energy.While the previous section showcased intriguing real-world indoor lighting EH for IoT systems, the SLIPT concept is relatively novel, and no study has yet presented a fully autonomous and operational system under practical indoor conditions.We then briefly highlight some significant findings regarding indoor SLIPT.
In [48], the first full autonomous IoT node was developed using light for both communication and energy transmission, but it only worked within a short distance of 1 m between the light source and the receiver.A 11 cm × 16.5 cm silicon (Si) PV module was used to power the entire node with a corresponding irradiance of 5 mW/cm 2 , achieving around 4.8 kbit/s.In [49], a 9.36 cm 2 α-Si module was used to receive a 2.6 kbit/s error free data at 1 m distance.Carrascal et Al.considered a constant 200 lux illumination to estimate the PV device EH performance, obtaining a maximum of 96.9 µW output power.
Hammoud et al. theoretically simulated the optical channel in a 3 m × 3 m × 3 m empty room with two optical sources, focusing on the SLIPT context [50].Their study was purely theoretical, involving only LOS simulations, and assumed a constant power conversion efficiency (PCE) of 18%.
Other contributions to the field focus on characterizing the performance of PV devices in energy harvesting and communication, but they do not take into account real-life complex IoT environments as most are realized under LOS configuration.For those interested in delving deeper into the topic, we suggest the following reference for a better understanding [51].

C. OUR CONTRIBUTION
As detailed in Section II-A, the applicability of PV devices for indoor EH is large.However, most works estimate a constant illumination to simulate indoor situation, being able to model the best EH architecture for the proposed scenario.Moreover, other studies utilized autonomous systems in undisclosed indoor settings, effectively monitoring the surroundings but lacking any forecast of the energy harvesting potential before the measurements.Additionally, actual experimental studies on SLIPT do not encompass scenarios beyond LOS conditions.In [50], a simulation (also in LOS link) was realized, but without any experimental validation of the proposed approach.
Ultimately, in our work, we experimentally validate the simulation of an OPV considering both LOS and NLOS links.This capability enables us to simulate the device across various indoor scenarios, allowing a short-circuit current estimation (extended to generated power), contributing to the current state-of-the-art for both indoor EH and SLIPT in the following ways: 1) By analysing the power distribution across an indoor IoT environment, we can optimize the placement and orientation of WSN nodes to suit specific applications, while also refining EH systems and techniques; 2) In the context of SLIPT, we employ the same strategy outlined in point 1), while considering the maximum bandwidth constrained by the optical channel.This allows for the optimization of the receiver system to fulfill specific quality of service requirements; 3) The simulations can be readily extended to IoT scenarios involving mobility, addressing both energy harvesting and communication aspects.

III. OPTICAL PROPAGATION AND OPV CHARACTERISTICS
In this section, a review of the optical channel impulse response is realized, highlighting some important parameters in optical communications, as well as the wavelength dependence of non-directive paths.The angular dependence of the receiver responsivity R(λ, ), a parameter that indicates the ratio between the short-circuit current and the incident optical power, is also described.We consider that no concentrator or optical filter is employed at the reception and that the source is punctual and follows a Lambertian radiation pattern with directivity m 1 [52].The radiant intensity I of Lambertian sources follows a cosine power behavior, as shown in (1), where I 0 is the maximum irradiance (obtained at normal radiation) and θ is the angle of radiance (equivalent to elevation angle in polar coordinates) [7]: The directivity m 1 characterizes the ability of the Lambertian source to focus the optical power P t in a specific direction.This attribute is directly correlated with the half-power angle θ 1/2 , which identifies the angle at which the radiant intensity I equals half of its peak value I 0 .The relation between both variables can be seen in ( 2) [7].
Equation ( 2) illustrates that sources with higher directivity m 1 concentrate more optical power per steradian, resulting in a decrease in θ 1/2 .

A. CHANNEL CHARACTERISTICS
The channel impulse response describes how the channel responds to an impulse (or Dirac δ(•)) optical input, in function of the time t, and depends on the direct and diffuse paths followed by the optical signal.In wide spectrum communications, it also has a strong wavelength dependence due to the spectral reflectivity of surfaces that induce non-direct rays [42].However, the channel impulse response depends on each wavelength λ independently, and is then noted as h(t;λ).
For multiple sources, it can be expressed as shown in (3) [42].
where k represents the number of light reflections before achieving the receiver and N is the number of sources in the link.Thus, h

) corresponds to LOS contributions and h (k)
n corresponds to the NLOS ones.The channel behavior is analyzed by determining different characteristics obtained from h(t; λ), such as the static gain (channel DC gain) and the delays leading to temporal dispersion of the channel.For most analysis, we consider only one source for the optical link without loss of generality.In the end of the current section, the review is then brought to a multiple source scenario.
The ratio between the average transmitted optical power P t , emitted by the source, and received optical power P r that arrives at the photoreceiver active surface A r , i.e. the surface that absorbs the photons, is described by the channel DC gain H 0 , which can be split into two different components, LOS (H LOS ) and NLOS (H NLOS ), and is defined as follow [7]: In LOS paths, the impulse response h (0) (t) has no actual wavelength dependence (for indoor scenarios) and is described by a time-shifted impulse function with amplitude H LOS , as shown in (5), where d is the distance between emitter and receiver and c is the speed of the light in vacuum.This equation considers that the incidence angle on the receiver surface and that the radiance angle θ are both inferior to 90 • [7].
In LOS links, the channel DC gain H LOS is obtained by integrating the impulse response h (0) (t) over the specified time period.For NLOS links, the same principle applies, but the integration needs to be performed separately for each individual wavelength.
By considering that the solid angle subtended by the active surface A r and the punctual source is infinitesimal (which can be considered as valid for many real cases in a first approximation, where d ≫ A r ), H LOS can be analytically obtained as follow [7]: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
In LOS only scenarios, the knowledge of the source optical power P t allows to determine the power that arrives at the receiver P r using ( 6) and (4).However, in complex situations where NLOS rays play an important role in the total power collected by the receiver, multiple reflections on different surfaces must be considered.The channel impulse response for a finite number of reflections has to be computed, which can easily increase the complexity by considering high reflection orders and multiple wavelengths (like for white LED).
Thus, the received power spectral distribution (PSD) r (λ) is related to the PSD of the source t (λ) by ( 7) [53], where the integral represents the channel DC gain as a function of the wavelength.The total received optical power considering the band of interest (for VLC, the whole visible band) is described by (8) [54].
The PSD t (λ) can be obtained according to its normalized emitted power S(λ) (note that S (λ) dλ = 1) as shown in (9), which results in P r described by (10).
We define then in (11) h λ (t) as the channel impulse response pondered by the normalized PSD of the source S(λ), resulting in the received optical power P r defined by (12).
The channel DC gain H 0 in wide spectrum links is then obtained by (13).
Although diffuse channels provide good reliability for systems susceptible to blockage, they can be time dispersive.The channel impulse response pondered by the source normalized PSD h λ (t) can provide some important parameters of multipath channels, for instance the mean delay spread µ and root mean square delay spread D rms of the configuration, defined by ( 14) and ( 15) respectively [53].
Approaches based on MCRT allow the evaluation of the impulse response h(t; λ) for multiple independent wavelengths and multiple sources in cases of complex scenarios, even considering a large number of reflections.For configurations with N sources, the received optical power P r can be obtained for each source independently, as defined by ( 16) [42].
Finally, for identical optical sources (in both normalized PSD S(λ) and transmitted power), the total received optical power is: Beyond the optical channel, systems based on photodetectors convert the received optical power P r into electric power.Thus, some of the most important photosensitive devices characterizations are realized under short-circuit conditions, described in the next section for an OPV.

B. OPV SHORT CIRCUIT CURRENT I SC
For the analysis presented in this article, the authors exploited the single-diode model for the OPV electrical representation (see Fig. 2), a first level approximation that is well accepted by the community for its performance accuracy in static operations [55].The model describes the solar cell internal electrical properties, such as voltage drop and recombination losses.Multiple load values R L result in different obtainable output current I out and output voltage V out , going from the shortcircuit condition, at which the current is at its maximum I sc , up to the open circuit condition, at which the voltage is at its maximum V oc .Changing the operation point of the OPV results in different static and dynamic performances.To obtain the actual generated current I ph we require knowledge of all internal parameters of the device (D, R sh , R s ), which is further achievable with I (V ) curves measurements, a static characterization well known by the photovoltaic community.
The responsivity describes the device's capability to convert optical power into short-circuit current I sc , while also accounting for the internal losses of the device.Different factors can influence the device's responsivity, including the materials used in each layer of the structure, their energy band gaps, incident light wavelength and the angle of incidence, affecting photon-electron interaction cross-sections and potential reflections due to layer stacking.For each experiment described in next sections, the OPV operates in short circuit condition and only the I sc is measured, without any specific extraction of the actual generated current I ph .
With the responsivity R(λ) (which is found in most commercial photodetectors datasheets), we can extend the MCRT analysis to obtain the short-circuit current from the received power in a desired simulation scenario.However, this parameter has an angular dependence, which is described in the next section.

C. RELATIVE RESPONSIVITY R rel ( )
The angular dependence of the responsivity of photosensitive devices, i.e. the ability to generate current as a function of the angle of incidence of the optical power for a given wavelength, is important for systems modelling and performance predictions.In the most general case, the real responsivity R real (λ, ) depends on both wavelength λ and incident angle simultaneously, and as a matter of fact, these variables are not independent, which means that different can result in different spectral responsivity R(λ) [56], [57].Since the short-circuit current depends on angular factors, it is mostly impossible to analytically compute it in complex scenarios, and simulation tools have to be used.However, the full implementation of R real (λ, ) inside a simulator is not trivial, so, in a first approach, let us consider that λ and are independent variables so that the responsivity can then be expressed as follow [56]: where R rel ( ) is the relative responsivity, a normalized function that defines the global behavior of the photosensitive device according to the incident angle.The independent variables hypothesis is actually valid for low variations of the responsivity spectra according to the incident angle [58].The short-circuit current I sc angular dependence can be explicitly seen in ( 19) [7]: The incidence angle dependence can be found in both received optical power P r , following a cos( ) pattern in LOS (seen in ( 6)) and NLOS links, and short-circuit current I sc , following an arbitrary function R rel ( ).However, these two dependences are necessarily linked in a way that I sc rely on the received optical power (and therefore on cos( )) and on the conversion capability (R rel ( )).
Thus, similar to the source, the photoreceiver can also describe different angular behavior for the generated current, defined by the function R rel ( ) cos( ).Some devices manifest Lambertian responses, at which the short-circuit current follows a cosine power expression with associated half-current angle 1/2 (please note that the term half-power angle is inaccurate, since R rel ( ) describes the conversion capability of the device), which can also be associated to the receiver directivity.Although R rel ( )cos( ) can be easily found in Si-based commercial photodiodes datasheets, it is an unknown parameter for most photovoltaic devices, including thin film OPVs.We therefore perform its experimental characterization in Section IV.Finally, Fig. 3 shows a simple diagram that contains all main variables that are analyzed in the current work.

IV. OPV ANGULAR CHARACTERIZATION
In this section, we describe the materials used for all experimental work, the methodology to characterize R rel ( )cos( ) and the obtained results.

A. MATERIALS
In subsequent sections, all experimental work is realized with the same material.A single OPV cell provided by Dracula Technologies and based on their LAYER®technology was used as photoreceiver, and an OSRAM LE CW E3B high power white LED was used as optical source.Fig. 4 shows the OPV device, with 4.7 cm length and 0.66 cm width, fabricated on a flexible substrate using entirely inkjet printing technique.The LED source has a 65 • half-power angle θ 1/2 , which corresponds to a directivity m 1 of 0.8048.Its normalized emitted power was measured using BLACK-Comet, a dedicated spectrometer developed by StellarNet Inc, and is shown in Fig. 5. Thus, the OPV spectral responsivity R(λ) (equally shown in Fig. 5) was obtained by external quantum efficiency characterization (no-bias, DC mode) with the QE-T system, developed by Enlitech.
The characterization and OPV model validation (Sections IV and V respectively) are based on the short-circuit I sc current measurement, realized with a Keithley 2621B source-measure unit.
For each experiment, we employed a meticulously constructed bench, developed in XLIM laboratory (refer to Fig. 6).This setup, initially devised to establish a LOS link, facilitates adjustments to the receiver incident angle while preserving the source-receiver distance and source orientation constant.To avoid any undesired reflected rays or ambient noise, all the structure is painted with high absorbing black mate ink and measurements are realized under dark conditions.This experimental bench can be adjusted to include NLOS link by including reflective surfaces by the receiver (used in Section V-B for NLOS validation).To measure the spectral reflectance of these surfaces, a dedicated spectrophotometer (Agilent Cary 300) was employed.Further OPV characterizations are described in supporting information.Its I (V ) curve under 1000 lux (realized with a Dalle LED Philips 60 × 60cm, 4385K) is shown Supp.Fig. 1, which presents an open-circuit voltage of 0.64 V and 306 µA short-circuit current.Its P(V ) characterization under the same condition is also shown in supporting information, Supp.Fig. 2, obtaining a maximum output power of 137µW at maximum power point (0.525V).

B. METHODOLOGY
As detailed in Section III, it is not possible to analytically obtain the optical power that arrives on a photoreceiver (and by consequence the short-circuit current) in NLOS links.Therefore, to obtain the R rel ( ) function, we must rely upon the LOS equation described in (6).With ( 19), ( 7), ( 5) and ( 6), the short-circuit current of a receiver in a LOS configuration can be mathematically described as follows: By fixing the distance d, keeping the source always pointing towards the receiver (θ = 0 • ) and changing the angle of incidence, the current varies according to and can be measured, obtaining then the angular dependence of the current I sc ( ).In this way, the terms that do not depend on the incident angle are constant and the R rel ( )cos( ) function can be obtained.However, experiments are susceptible to errors, which would directly affect R rel ( ), a function that is intrinsically normalized.It can then be obtained by (21), where I SCmax is the maximum value of the measured current, normally obtained in direct LOS configuration (θ = 0 • and For the measurement, a LOS link was employed while fixing the distance d = 25.1 cm and the angle of irradiance θ = 0 • , with means of the developed bench (see Fig. 6).
Because R rel ( )cos( ) is normalized, the real value of the transmitted optical power P t is not relevant, but the stabilization of the emitting LED is crucial over the experiment.For better robustness, the characterization is realized for negative and positive values of in order to verify any deviation of the OPV response from the expected polar symmetry in such LOS configuration.We also note that this angular characterization can depend on the selected horizontal orientation of the OPV device on the test bench.

D. CHARACTERIZATION RESULTS
Fig. 7 shows the R rel ( ) cos ( ) measured from the OPV, which almost perfectly fits a Lambertian pattern presenting a half-current angle 1/2 of 60 • , resulting in a unitary directivity.In fact, this demonstrates that this particular OPV responsivity has no specific angular dependence, as R rel ( ) = 1.Interestingly, we note that this is the most common behavior of commercial Si-based photodiodes (fact that can be verified in most datasheets), consequently, a photodiode simulation model can be employed for indoor MCRT simulation for this particular OPV cell.This fact was not a priori so obvious considering that OPV cells are based on a stack of materials of thickness in the order of visible wavelengths.For the given distance, a perfect azimuth symmetry was observed with aid of multiple experiments, as consequence, the short-circuit current depends only on the polar angle, which is expressed by the incident angle dependence.
Knowing that the simulator is already designed to operate with different Lambertian receivers, the OPV device was then implemented by accounting for its rectangular dimensions (4.7 cm and 0.66 cm) and experimental R rel ( ) cos( ) with half-current angle of 60 • .

V. OPV MODEL VALIDATION A. METHODOLOGY
To validate the simulation results using the OPV receiver, two different experiments were realized, the first based on a LOS link, and the second based on a LOS and NLOS link.
The simulator can provide the impulse response h(t; λ) in any modelled configuration, being then extended to the received PSD r (λ) with (7).For 60 • half-current Lambertian receivers, R rel ( ) = 1, consequently I sc can be directly obtained from ( 19), ( 7) and ( 9), as follows: Considering the angular characterization of the device presented in the previous section, the photodiode model is hence directly applicable to the OPV cell provided by Dracula Technologies.In the following parts, the simulations are therefore confronted to experimental measurements made using our characterization bench described in Section IV-A.Fig. 8 depicts the methodology employed to validate the OPV model through MCRT simulation.Among the different sources of errors arising between our simulated and experimental currents, the accuracy of the LED emitter calibration (its normalized PSD and P t ) is the most important factor.Therefore, a (pessimistic) ±5% error bar is systematically considered on the experimental current to account for these uncertainties.
To determine the simulated current, it is necessary to know the value of the emitted PSD t (λ) .To this end, we used the BLACK-Comet spectrometer in a perfect alignment configuration ( = 0 • and θ = 0 • ) to measure the received power at the given distance d and so to obtain the corresponding emitted power using (6).

B. LOS LINK 1) SCENARIO DESCRIPTION
Dracula Technology's OPV was placed in the configuration shown in Fig. 6, with its length aligned to the bench rotation axis.With the distance d = 15.4 cm, the short-circuit I sc was measured for different incident angles and was compared to the simulated current.
In fact, for LOS links, a ray propagation software is not necessary, as the channel DC gain can be described by the analytical expression (6), has no wavelength dependence and can be easily calculated.We also aim to compare the experiment and simulation with the theoretical short circuit current, derived from ( 6) and (22).

2) RESULTS
Finally, Fig. 9 shows the obtained theoretical (in blue), simulated (in yellow), and experimental (in red) short-circuit currents I sc for multiple incident angles .
We notice that the experimental results are very close to the simulated ones and follow the theoretical behavior, within the accuracy of our experimental measurements.This LOS result is a preliminary validation of the OPV model, which allows an accurate prediction of the current generated by the photovoltaic device in LOS scenarios.In Section V-B, a hybrid scenario consisting of LOS and NLOS contributions is simulated and validated through experimentation.

VOLUME 12, 2024
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

C. LOS + NLOS LINK 1) SCENARIO DESCRIPTION
The experimental validation of the OPV model in LOS + NLOS link is essential for future simulations in complex situations, especially for indoor IoT applications.In this context, for increased accuracy, the reflected light component H NLOS must or surpass H LOS , denoting that materials with high reflectance in the visible spectrum must be pondered.In Section V-A, the simulation did not contemplate any particular wavelength analysis as the LOS channel attenuation is constant for all optical spectrum.However, materials have different reflectances for different wavelengths, which must be accounted for precise prediction of the short-circuit current provided by the OPV receiver.
Reflection surfaces are made of materials which reflect the light in different ways, modeled by the bidirectional reflectance distribution function (BRDF) [59].Some of them are perfectly diffuse (Lambertian BRDF), other ones are perfectly specular (dielectric BRDF), and the rest, i.e. most of them in fact, are part diffuse and part directive (Blinn-Phong BRDF for instance).Although most materials that compose indoor complex scenarios are often considered as Lambertian, these three BRDF are implemented in the simulator.
Our characterization bench was then adapted to include NLOS contributions in the experiment.Two metal plates were placed at 10 cm from the center of the structure, where the OPV is hold (with its length in the same axis as the rotation bench), and to avoid any specular reflections, both walls were covered with white paper, a mostly diffuse material with spectral reflectance ρ paper (λ) that follows a Lambertian pattern.
The spectral reflectance ρ paper (λ) was measured under normal incidence.The obtained measurements as well as the source normalized emitted power can be seen in Fig. 10.
Interestingly, the reflectance is almost constant over the entire visible spectrum at around 0.8.As detailed in Section III, large spectra diffuse simulations require more processing time than narrowband spectra ones due to the FIGURE Spectral reflectance of white paper (used in Section V), of the materials that compose the room [42] for the simulation (used in Section VI) and the normalized emitted power of the source.
spectral reflectance ρ(λ) of surfaces that compose the environment.As each wavelength can be analyzed separately, we can then perform multiple simulations for different λ.After obtaining all results considering the total spectra of interest, the channel impulse response h(t; λ) is obtained, which can be extended to short circuit results with (22).
The spectrum of interest goes from 380 nm up to 740 nm.It was then discretized with a 10 nm step and a single-inputsingle-output simulation was realized for each wavelength.Two different scenarios were analyzed: the first containing both paper walls and the second with only one paper wall on the right side.For each situation, five incident angles were chosen, from −20 • to 20 • with a 10 • step (see Fig. 11).In the literature, it has been demonstrated that considering 3 reflections in a Monte-Carlo based simulations in conventional indoor scenarios is sufficient to well estimate the channel [60].However, in the current situation, the distances between Tx, Rx and the walls are in the order of centimeters, increasing the reflection dependence of the system.Thus, in our configuration, we have to consider ten reflections, according to one million rays with ray-gathering simulation algorithm [40] to provide both realistic and sufficiently converged impulse response h(t; λ).We also kept the ±5% error bars on the experimental current to account for our experimental accuracy.Aiming to experimentally verify the reflected rays influence on the system, the LOS channel contribution is also simulated.

2) RESULTS
First, we remark from Fig. 12 that for both scenarios, the measured and simulated results are very close, which shows the validity of the model implemented for the OPV cell in the MCRT simulator while accounting LOS and NLOS rays.Fig. 12 also confirms the impact of the reflected rays, increasing the short circuit current by 21% for the first scenario (at which the NLOS component is more significant) and by 10% for the second one.
In the case of scenario 2 where the left wall is removed, the total gain decreases and approaches the value corresponding to a LOS link, as shown in Fig. 12 (b).
We emphasize that the real current generated by OPV devices is governed by the cell's behavior (parasitic resistances, ideality factor, etc.).In short-circuit conditions, our methodology enables the prediction of short-circuit current with a good accuracy.These predictions can easily be extended to the generated power P out under various load conditions through the preliminary knowledge of the cell's electrical characteristics under different illuminations, obtained through conventional I (V ) curves measurements.In Section VI, we explore, for the first time, a realistic simulation under indoor conditions, from which we are able to predict the power harvested by an OPV receiver exposed to multiple LED sources.

VI. INDOOR SIMULATION
For simplicity, we chose the same scene described in [42] for the OPV simulation, with the same spectral reflectance but different source PSD.The spectral reflectance of materials that compose the environment and the source normalized emitted power are shown in Fig. 10.Contrary to our NLOS experiment, all materials have reflectance that deeply depends on the wavelength.For the simulation, four LEDs with half-power angle of 60 • were fixed at the ceiling facing downward, and the OPV was placed 10 cm above the ground facing upward.The rectangular OPV cell was then considered at 400 different positions in the X and Y axis, with its length aligned to the X axis, allowing to precisely map the received optical power P r (and consequently the short-circuit current I sc ) for each placement.Thirty-seven different wavelengths were used for the simulation, going from 380 nm up to 740 nm with 10 nm step, providing a good trade-off between precision and processing time.A convergence analysis was carried on, showing that 5 million rays with ray-gathering algorithm provided good accuracy for the simulation.Table 1 shows some of the simulation parameters.With the channel impulse response h(t; λ) (that for N sources is the sum of each h n (t; λ), as shown in (3)) obtained through simulation at each position, h λ (t) could be computed with (11).
A. RESULTS AND DISCUSSIONS Fig. 13 shows the pondered channel response obtained in two positions: the first in the centre (in blue), where most contributions arise from the LOS channel; and the second in the corner (in red), from which we highlight  The spectral reflectance of each surface that composes the environment has major importance on the received power spectra r (λ).As the receiver approaches the corners of the scene, the NLOS component significantly increases, being then in the same order of magnitude to the LOS one.An interesting attenuation of lower wavelengths was observed at different in the environment by comparing the normalized received PSD to the normalized emitted PSD, demonstrating the reflectance influence on the wide spectrum link.
From h λ (t), the delay spread could be computed with ( 14) and ( 15), obtaining 1.13 ns at the centre, increasing up to 3 ns at the corner.For communications with negligible inter-symbol interference (ISI), the maximum channel bandwidth B channel is limited to B channel ≤ 1 10×D rms [61], [62], resulting in 89 MHz and 33 MHz at the centre and corner respectively.In fact, large area photodetectors, such as the current OPV, are associated with large geometric capacitance, which limits their response time, considering a classical first-order low pass filter behaviour, that will decrease the system bandwidth.In consequence, the maximum achievable data rate in the simulated scenario is expected to be limited by the OPV itself, not by the channel multipath characteristics.
Dividing the received optical power spectra r (λ), obtained out of (7), by the active surface A r will result in the spectral irradiance E(λ) in W/m 2 .The illumination E v spatial distribution in the environment at the OPV height can be finally achieved by wavelength-weighing the spectral irradiance according to the luminous efficiency function [53] (see Fig. 14).The obtained illumination varies from 550 lx (in the corner of the room) up to 990 lx (in the centre), which is in accordance with the International Organization for Standardization, that defines the ideal illumination in workspaces between 300 lx and 1500 lx [63].
Similar to the illumination, the short-circuit current I sc distribution can be obtained with post processing using the simulation result h(t; λ) and (22).The lowest obtained current in this scenario is 150µA, generated at the corners of the environment and associated to an illumination of 550 lx, rising up to 280 µA at the centre, associated to 990 lx.Analysing the diagonal axis of the room, starting from any corner, the short-circuit current I sc extracted by the rectangular OPV can be compared with a hypothetical short-circuit current when the diffuse rays are not considered for the indoor scenario, i.e.only taking into account LOS contributions (see Fig. 15).FIGURE 15.Simulated short-circuit current (in blue) and maximum output power (in red) generated by the OPV at the diagonal axis of the room when considering only LOS rays (dashed line) and LOS + NLOS rays (full line).
We can finally draw attention to the importance of considering the diffuse light in indoor scenarios.An increase of the short-circuit LOS current of approximately 95 µA is noticeable for each analysed position, representing an improvement of 172% at the corners and of 51% at the centre of the current scenario.In a limited access indoor IoT environment, the diffuse optical power represents a major factor for system modelling and prediction, important for both ambient energy harvesting and VLC.
The I sc can be further extended to energy harvesting performances by previous measurements of the OPV I (V ) and P(V ) curves at different light intensities (see Supp.Fig. 3 and Supp.Fig. 4, in supporting information).For each characterization, different parameters can be obtained, for instance the maximum output electrical power P max , achieved at the MPP (see Supp.Fig. 5).The aforementioned static characterizations were realized under the same PSD than those used in the previous experiments in order to obtain precise power estimation.In a variable illumination going from 500 lux up to 1000 lux, the OPV cell provided a quasi-linear output power response from 78 µW to 150 µW .Using a smooth fitting function, the maximum output power, considering the OPV operating in the MPP, can be extrapolated for each simulated position from the obtained I sc and E v .
From the post processing results, we notice that the device can provide a minimum 77 µW at the corner, increasing up to 147 µW at the centre of the room (see Fig. 15).Extending the results to 300 lux, we estimate around 46 µW generated by the current OPV, resulting in a power density of 15.08 µW /cm 2 .Contrastingly, in [43] (also for 300 lux), the PV panel attained a power density of 8.30 µW/cm 2 under identical illuminance conditions.Similarly, the OPV is expected to generate 10.05 µW/cm 2 under 200 lux, while in [45], the α-Si panel obtained 4.86 µW/cm 2 under the same illuminance.This underscores once more the remarkable performance OPVs for indoor IoT integration.
From the LOS rays, the maximum output power generated by the OPV cell can also be predicted when no diffuse channel is considered at the scenario (see Fig. 15).An underestimation of 50 µW is observed in all simulated positions, representing an increase of 185% at the corners and of 51% at the centre, which once more demonstrate the importance of diffuse light consideration for better system modelling in indoor IoT scenarios.
The simulation has shown the importance of OPV for indoor energy harvesting, which can generate decent power when positioned only 10 cm above the ground.Expanding the results for the IoT context, these power levels are interesting to supply different wireless nodes with variable communication protocols even at low illumination, such as a LoRA Backscatter (10 µW -20 µW ) and passive Wi-Fi (50 µW -70 µW ) [14], [64].On the communication aspect, sending trough light can be particularly effective for autonomous Light-based Internet-of-Things (LIoT) nodes while simultaneously harvesting ambient data [65].
Classical VLC configurations typically employ a TIA to convert the output current into a corresponding output voltage.In this setting, the solar cell operates either in photovoltaic mode (no bias voltage applied) or photoconductive mode (reverse bias voltage applied) [66].In the first, the output current represents the device's short circuit current as its voltage is zero.By incorporating the actual short-circuit current I sc along with noise analysis, the system signal-to-noise ratio (SNR) can be determined, facilitating the calculation of the theoretical maximum data rate with associated modulations.
Although the communication (channel data rate limitation) and energy harvesting (P max ) analysis were studied alone, the simulation of the OPV short-circuit current in IoT environments is in fact the first step for more complex simulations involving the receiver front-end adapted to the SLIPT concept.With the knowledge of the internal characteristics of the device, such as shunt or series resistances, appropriate equivalent and receiver circuits can be developed according to the communication/power requirements.

VII. CONCLUSION
In this work, we reviewed the wide-band optical propagation equations for general link scenarios (LOS + NLOS) while considering the relative responsivity R rel ( ) of the device.We also successfully demonstrated an optical channel MC simulation with a ray-tracing algorithm using a flexible, lowcost inkjet-printed OPV as receiver.
Our approach was based on an apprehensible connection between theory, simulation and experiment.Exploring the radiometric equations and simulation results, the channel impulse response and the OPV short-circuit current can be predicted for different optical link scenarios while accounting for its internal losses.
These preliminary simulation results, although realized in a simple cubic room, demonstrate the interest of optical channel simulations for complex indoor environments.In scenarios targeted for massive IoT nodes deployment, different surfaces induce non-directive paths, which plays an important role in the optical data/energy transmission.The simulation, paired up with the overwhelming indoor performance and flexibility of OPVs, illustrate the appeal of inkjet-printed organic electronics to supply low power connected devices.Thus, the analysis will be further evaluated for communication purposes by extending the static condition to the SLIPT context, taking into consideration different aspects that can influence the data transfer and energy harvesting performance.
Furthermore, this work invites future analysis on the front-end circuit simulation, emphasizing SLIPT context for IoT.The current work can also be fully extended to complex IoT scenarios simulations involving different obstacles and elements for both energy harvesting and data transfer.A simulator model of flexible receivers with experimental validation is also an interesting prospect that can be carried on from this work.

FIGURE 1 .
FIGURE 1. Tasks described in each section of the article.

FIGURE 2 .
FIGURE 2. OPV single diode electrical model with load R L .

FIGURE 3 .
FIGURE 3. Diagram containing all variables analyzed in the current work.

FIGURE 4 .
FIGURE 4. OPV based on LAYER®technology.Fabricated by Dracula Technologies.

FIGURE 6 .
FIGURE 6. Experimental bench used in each experiment.

FIGURE 8 .
FIGURE 8. Flowchart of employed methodology for the OPV model validation employing MCRT simulations.

FIGURE 9 .
FIGURE 9. Theoretical generated current using LOS link equation (23) (in blue), experimental current (in red) with 5% error bar and current obtained from simulation results (in yellow).

FIGURE 12 .
FIGURE 12. Measured current in NLOS scenario with 5% measurement error (in blue) with associated expected current obtained with simulation (in red) and LOS component obtained with simulation (in yellow).(a): Scenario 1; (b): Scenario 2.

FIGURE 13 .
FIGURE 13.Simulated h λ (t ) at the centre (in blue) and at the corner (in red).
the multipath channel due to different peaks in different time values.

FIGURE 14 .
FIGURE 14. Illuminance level at the OPV height in the simulated room.