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Abstract
This article considers the design and use of multipath lenses (MPLs) for optical wireless communications (OWC). The MPL increases the maximum permissible exposure (MPE) for eye safety and allows for an increase of transmission power of small-sized emitters like laser diodes (LDs). A prototype of a freeform MPL has been fabricated and characterized. The MPL allows an increase of the optical transmission power by 13 dB, which corresponds to an improvement in the maximum range by a factor of 4.5. The lens transforms the elliptical emission pattern of an edge-emitting LD into a rectangular field-of-view (FOV) with homogenous power distribution. The transmission efficiency through the MPL is 0.905.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The continuously increasing mobile data traffic [1,2] and the demand for low latency data transfer has motivated the development of 5G technology and future 6G systems [1,3]. Optical wireless communications (OWC) also known as “Light-Fidelity” (Li-Fi) have emerged within the last decade as an alternative to radio frequency (RF) technologies. The spatial confinement of the optical channels mitigates interference issues and allows low-latency communication with high reliability.
OWC uses laser diodes (LDs) or light-emitting diodes (LEDs) within the transmitter to convert the electrical signal into the optical domain. Due to stimulated emission, LDs outperform LEDs in regards to their bandwidth and efficiency [4]. Their bandwidth ranges from several hundreds of megahertz to several gigahertz [4] which enables data rates in the range of Gbit/s even with simple modulation schemes like On-Off Keying (OOK) [5–7]. Consequently, there is a high interest in using LDs also for indoor OWC [8,9]. To ensure eye safety, the LD optical output is restricted to sub-milliwatt range or a few milliwatt depending on the wavelength [10–12]. The power restriction limits link range and the field of view (FOV). As a result, the link is restrained to a simple point-to-point data transfer [5,6].
To overcome the power limitations, LD arrays [13–16] and different kinds of diffusers [8,12,17–20] are used. They come with several drawbacks, for instance reduced efficiency, increased complexity, or low flexibility.
In this work, we present a freeform multi-path lens (MPL). Like other freeform lenses, it can be fabricated by injection molding, which is known for its low costs for high-volume production [21]. The MPL increases the maximum permissible exposure (MPE) via the expansion of the angular subtense $\alpha$ of the source. Thereby, the allowed optical output power ${\Phi _{\textrm{TX}}}$ of the laser source is increased. In addition, the MPL converts the source emission profile into the desired FOV shape. A prototype with a rectangular FOV is fabricated and experimentally characterized.
The rest of the paper is organized as follows. Chapter 2 considers the regulation of the LD output by IEC 60825-1 [11]. The article reviews how the MPE can be increased by means of different optical setups and the MPL. Chapter 3 discusses the basic concept behind an MPL and describes the design process. A short overview of freeform design methods is given. Thereby, ray mapping is considered in more detail. Chapter 4 presents the MPL prototype and measurement results regarding optical performance and eye safety. The results are discussed in chapter 5. Chapter 6 provides a summary.
2. Fundamentals
2.1 Eye safety regulations
The optical receiver power ${\Phi _{\textrm{RX}}}$ is determined by the optical transmitter power ${\Phi _{\textrm{TX}}}$ and the channel attenuation. A higher communication range or a larger FOV goes along with stronger signal attenuation within the channel. A higher transmitter power ${\Phi _{\textrm{TX}}}$ compensates for that additional loss and thereby increases the coverage of the OWC link.
The optical transmitter power ${\Phi _{\textrm{TX}}}$ cannot be increased arbitrarily. Optical radiation can damage the human eye and skin, therefore its power is closely regulated. In this work, we focus our considerations on eye safety since Li-Fi systems are typically deployed in non-restricted indoor areas. A high irradiance $E$ is able to induce thermal damage to the cornea, while a high radiance L leads to thermal or photochemical retina damage. Therefore, IEC 60825-1 [11] defines the maximum permissible exposure (MPE).
For laser transmitters the radiance is the most relevant parameter. The high directivity of the laser source and its small output aperture results in a very small apparent source that is then focused, leading to high power densities at the retina. Physically speaking, the issue arises from the very small Étendue of the output aperture since it exhibits a small spatial extend and a rather small emission angle. In contrast, the Étendue in light-emitting diodes (LEDs) is much larger due to larger emission volume and isotropic spontaneous emission.
Figure 1 shows a sketch of the measurement setup defined by IEC 60825-1 [11] for determining the accessible exposure and the MPE. A lens is used to form an image of the source onto a detector. The aperture in front of the lens models the human pupil. The measurement distance r is chosen at the most hazardous position. However, the minimum distance is 100 mm [11,12]. The distance b is chosen in such a way, that the most hazardous arrangement is evaluated. An important parameter for the MPE is the angular subtense $ \alpha$, which is the angle covered by the apparent source viewed from point space [12]. The angular subtense $ \alpha$ is defined by the size of the apparent source and the distance to the evaluated position [12]. By applying the thin lens equation and paraxial ray approximation, $\alpha$ can be expressed by the image size B and the distance b [22].
Table 1 shows the calculation of the MPE for $ 700 \ \textrm {nm} \le { \lambda } \le 1050 \ \textrm {nm}$. Interested readers are referred to IEC 60825-1 [11] for definitions of other wavelengths. IEC 60825-1 [11] distinguishes between point sources $({\alpha \le {\alpha_{\textrm{min}}}} )$ and extended sources $(\alpha > {\alpha _{\textrm{min}}})$. C4, C6, C7, and T2 are correction factors. The exposure time is denoted by tex. For invisible infrared light, we assume to worst-case, i.e. infinite exposure. Assuming a fixed wavelength of $ \lambda = 850\; {\textrm {nm}}$ the only variable within the equations is C6 which depends on the angular subtense $ \alpha$ of the apparent source. Thus, the key for using a higher optical output ${\Phi _{\textrm{TX}}}$ lies in the increase of $ \alpha$.
Table 1. Calculation of the MPE according to IEC 60825-1 [11]. Parameter: $700 \ \textrm {nm} \le {\boldsymbol \lambda } \le 1050 \textrm {nm}$, ${{\boldsymbol t}_{{ ex}}}{\boldsymbol \; } > {\boldsymbol \; }10{\boldsymbol \; }{ s}$, ${{\boldsymbol C}_7} = 1$, ${{\boldsymbol \alpha }_{\textrm{ min}}} = 1.5{\boldsymbol \; }{\textrm{ mrad}}$, ${{\boldsymbol \alpha }_{\textrm{ max}}} = 1.5{\boldsymbol \; }{\textrm{ mrad}}$, ${{\boldsymbol t}_{{\boldsymbol e}{ x}}} > {{\boldsymbol T}_2}$.
2.2 Methods for increasing the angular subtense
Figure 2 (a) – (d) show different practical approaches to increase the size of the image formed onto the human eye’s retina.
Fig. 2. Setups of increasing the angular subtense $ \alpha$. (a) Array of LDs; (b) LD with common diffuser or color converter; (c) LD with collimator and holographic or engineered/tailored diffuser; (d) LD and freeform multi-path lens.
In Fig. 2 (a) an LD array is utilized. Every source has a different origin from the eye’s perspective. The human eye focuses the radiation of each source onto a different point. Thereby, the emission power is spread over a larger area of the retina, and the irradiance is decreased. This approach was realized by using vertical-cavity surface-emitting laser (VCSEL) arrays [12–16]. The VCSEL array is a promising candidate due to its fairly low fabrication effort compared to other laser arrays [13]. Nevertheless, it is still more complex than a single radiation source.
In Fig. 2 (b) a single laser source is combined with a commercial diffuser, which scatters the light into arbitrary directions. From the eye’s perspective, the diffuser is like a source with a larger size. The advantage of this approach is its low complexity and cost-effectiveness. The scattering angle can be adjusted by using smaller or larger structures. However, the control over the scattering direction is weak. As a result, the efficiency of common diffusers is low. Zafar et al. [8] state efficiency of about 0.7. However, efficiency depends strongly on the FOV and degrades for small FOVs. Moreover, it is not possible to get a homogenous irradiance pattern. In the case of visible light communications (VLC), the diffuser might be replaced by a color converter. A phosphorus-based converter turns blue laser light into white light [18,19].
The engineered diffuser is shown in Fig. 2 (c). It is characterized by a defined microstructure [23]. It overcomes the low efficiency of the common diffuser [8]. The microstructure requires the incidence of collimated light. Therefore, typically one or two collimator lenses are required [20]. This increases system complexity. The efficiency of the diffuser is typically > 0.9 [8]. The fabrication of the diffusers is typically sophisticated due to the small structure size which is in the range of some tens of µm [23]. O’Brien et al. [17] use a holographic diffuser to increase the size of the apparent source. The holographic diffuser also requires an additional collimator.
Figure 2 (d) shows the new solution based on an MPL. The increase of the apparent source size is achieved by dividing the emitted radiation into several ray bundles. This can be done with a lens with two refracting interfaces. Each ray bundle carries only a fraction of the total power ${\Phi _{\textrm{TX}}}$ but illuminates the full FOV or a defined part of it. Each ray bundle originates from another point from the eye’s perspective and thus is focused onto a dedicated point onto the retina. The MPL does not require additional collimators. It can be fabricated at a low cost in a high-volume injection molding process. The approach is similar to illumination engineering, where multi-channel lenses are used to reduce glare [24]. Recently, multi-channel freeform lenses are also used in AR and VR for imaging optics [25].
3. Design
3.1 System concept
The MPL shapes the FOV and increases the MPE. In this approach, the MPL consists of multiple facets. Each facet is a freeform surface, which is tailored to the source, its position, and the FOV. The calculation procedure is described in section 3.2.
For ensuring a certain laser class the MPL has to avoid exceeding the MPE for every single peak, the envelope of all peaks, and all possible groups of peaks. The MPL performance from the eye safety perspective is determined by its size, the number of facets, and the FOV angle. For a simple lens with two refractive interfaces, the MPL size is given by the LD emission angle and the distance between the LD and the MPL. The amount of facets determines how many discrete points are formed onto the retina. Increasing this number leads to a lower power per peak. The MPL size and the FOV determines how far the peaks of the source image are spread over the detector. A large MPL size and a larger FOV angle ${\theta _{\textrm{FOV}}}$ increases the spreading of the peaks. For small ${\theta _{\textrm{FOV}}}$ the distinct points move towards each other. At some point, the distinct points merge into one single peak. The smaller the FOV, the weaker the curvature of every single facet of the MPL. For the extreme case of ${\theta _{\textrm{FOV}}}$ = 0°, i.e. collimation of laser light, the MPL merges into a lens with a continuous surface.
The amount and size of the facets can be estimated as follows: The ray bundle from a single facet is focused sharply and can be treated as point source similar to the LD output without a lens. The difference lies in the power of the focus point. It is less than the total output since the power is distributed over the facets. For a given wavelength $\lambda$ the MPE of a point source is calculated according to A in Table 1. The power of a facet ray bundle ${\Phi _\textrm{f}}$ must not exceed the MPE. In practice, a margin of 3 dB is typically considered, i.e. ${\Phi _\textrm{f}} = MPE/2$. According to Eq. (1), ${\Phi _\textrm{f}}$ is given by integration of the solid angle $d{\mathrm \Omega }$ over the source intensity I.
3.2 Calculation procedure
3.2.1. Freeform design methods
The surface of the MPL is generated by calculating the single facets subsequently and using the endpoint of the previous facet as a starting point for the next facet.
Freeform surfaces can be calculated by using direct methods or numerical optimization [26]. In the case of numerical optimization, several lens parameters are defined and optimized by iterative calculation and simulation. Optimization algorithms like damped-least squares or gradient descent are used [26,27]. Due to the time consuming optimization for every single facet, these algorithms are clearly not the ideal choice.
Direct methods on the other hand use defined calculation algorithms to construct the surface. These algorithms are applied subsequently to every facet for MPL construction. Various approaches are known, for instance several ray mapping algorithms [28–34], solving Monge-Ampere equations [35–38], the simultaneous-multiple-surface-method (SMS) in 2D [39], and in 3D [26]. Some of them use iterative calculation with optimization, but in contrast to the numerical optimization design approach, ray tracing simulation is not required for each iteration.
3.2.2. Ray mapping
Ray mapping methodology is popular in illumination design research [28–32,34,40] due to high design flexibility and high efficiency. It was already applied to OWC optics [41–44]. Within the so-called energy mapping a mathematical power transfer problem is formulated, which has to be solved by the freeform surface.
Figure 3 (a) illustrates the principle of the energy mapping. The power density within the source space ${{\mathrm \Omega }_\textrm{s}}$ is transferred into the target space ${{\mathrm \Omega }_\textrm{t}}$. Therefore, a transfer function $\phi :{{\mathrm \Omega }_\textrm{s}} \to {{\mathrm \Omega }_\textrm{t}}$ is defined, which transfers each infinitesimal part of the source space ${\sigma _s}$ into an infinitesimal part of the target space $ {\sigma _t}$.
Fig. 3. (a) Power transfer from the source space $ {{\mathrm \Omega }_\textrm{s}}$ into the target space $ {{\mathrm \Omega }_\textrm{t}}$. (b) Surface construction by geometrical ray tracing. The normal vectors ${{\boldsymbol n}_{i,j}}$ are highlighted in light green. The tangent vectors ${{\boldsymbol t}_{i,j}}$ are colored in dark blue. The sketch was modified from Wang et al. [34].
Due to its small output aperture, a LD can be approximated as a zero-Étendue source. By assuming a zero-Étendue source, the position vectors of the infinitesimal area elements $ {\sigma _s}$ and ${\sigma _t}$ represent the input and output vectors ${{\boldsymbol v}_{i,j}}$ and ${{\boldsymbol o}_{i,j}}$ respectively for the surface construction. For each facet of the MPL $N \times M$ surface points are calculated. Thereby, a facet consists of i curves with j points each, where $i = [{1,2 \ldots ,N} ]$ and $ j = [{1,2 \ldots ,M} ]$.
By using the law of refraction the vector field $N$ of the surface normal vectors can be calculated from the input and output vectors ${{\boldsymbol v}_{i,j}}$ and ${\boldsymbol \; }{{\boldsymbol o}_{i,j}}$. A continuous surface with the normal vector field $N$ exists, if Eq. (2) is satisfied [28,29,45,46]. To find a continuous surface, typically a curl-free $N$ is wanted.
We calculate a curl-free transfer function $\phi$ and assume, that this $\phi$ will lead to a vector field ${\boldsymbol N}$ with sufficient low curl. Although this assumption is not fully correct, it is known, that it yields good results [29]. The lower the curl is, the more similar the surface is to the ideal surface. Here we use the algorithm proposed by Wu et al. [40] to calculate a function $\phi$ with minimum curl, since it provides fast convergence. The algorithm is based on solving a L2 Monge-Kantorovich mass transfer problem [40,47].The final transfer function $\phi$ has to ensure, that the same radiation flux flows through the surface elements ${\sigma _s}$ and $ {\sigma _t}$. From a mathematical point of view, $\phi ({{\sigma_s}} )$ has to satisfy Eq. (3) [29,40].
The input and output vectors ${{\boldsymbol v}_{i,j}}$ and ${{\boldsymbol o}_{i,j}}$ are derived from the grid of the source and target space ${{\mathrm \Omega }_s}$ and ${{\mathrm \Omega }_t}$. Figure 3 (b) illustrates the principle of surface construction. By using the law of refraction the normal vector of each point ${{\boldsymbol n}_{i,j}}$ is derived from ${{\boldsymbol v}_{i,j}}$ and $ {{\boldsymbol o}_{i,j}}$. All points of the ith curve lie in the same plane. For calculation of the first curve, the designer defines the initial point ${{\boldsymbol P}_{1,1}}$ with its normal vector ${{\boldsymbol n}_{1,1}}$ and calculates the remaining points ${\boldsymbol \; }{{\boldsymbol P}_{1,j}}$ subsequently. The tangent vector ${{\boldsymbol t}_{1,j}}$ is generated by rotating ${{\boldsymbol n}_{1,j}}$ within the plane towards the direction of ${\boldsymbol \; }{{\boldsymbol P}_{1,j + 1}}$.${\boldsymbol \; }{{\boldsymbol P}_{1,j + 1}}$ is found by the intersection of ${{\boldsymbol v}_{1,j + 1}}$ and ${{\boldsymbol t}_{1,j}}$. As soon as the first curve is finished, the other curves are calculated analogously. If the vector field $N$ exhibits minimum curl, the continuous surface transforms ${{\boldsymbol v}_{i,j}}$ precisely into $ {{\boldsymbol o}_{i,j}}$. Further details about the surface construction procedure can be found in the work of Wang et al. [34].
3.2.3. Lens design
An MPL prototype is designed for an edge-emitting LD with ${\Phi _{\textrm{TX}}} = 190\; \textrm{mW}$ and $\lambda$ = 850 nm. The LD has an elliptical output profile that is converted into a FOV with a rectangular cross-section with a half-angle of ${\theta _{\textrm{FOV}}} = 7^\circ$ along the X- and Y-axis. Table 2 summarizes the system parameters of our prototype.
Table 2. Summary of the design parameters.
A transfer function $\phi$ with minimum curl is generated by solving the differential equation system from Eq. (3). Each facet is discretized by ${N_{pts}} = 40 \times 40 = 1600$ points. From the grid of the source and target space the input and output vectors ${{\boldsymbol v}_{i,j}}$ and ${{\boldsymbol o}_{i,j}}$ are derived as previously described. Next, the surface construction from Fig. 3 (b) yields the surface points $ {{\boldsymbol P}_{i,j}}$. Those points are interpolated by using non-uniform rational B-splines (NURBS) of 3rd polynomial order. The procedure is repeated for each facet until one quarter of the lens was calculated. The total amount of calculated points is 57600. The other three quarters are created by mirroring on the X- and Y-axis. The geometry is exported in IGES format and simulated in Zemax OpticStudio 17.
3.3 Optical simulations
3.3.1 Optical performance
Figure 4 (a) and (b) shows ray tracing simulations of the LD without MPL and with MPL respectively. The simulation model is ideal and does not contain any rounding between the facets, i.e. the rounding radius is rr = 0. The simulation proves that the lens transforms an elliptical output profile into a rectangular one with homogeneous power distribution. The lens captures 96.5% of the emitted power. The simulated transmitter efficiency is $ {\eta _{\textrm{TX}}} = 0.87$. The loss caused by Fresnel reflections is 9.5% of $ {\Phi _{\textrm{TX}}}$.
Fig. 4. Optical ray tracing simulations. (a) Emission profile of the LD without MPL at z = 5 m. (b) Output profile of the LD with MPL at $ z = 5\; \textrm{m}$. (c) Image of the apparent source according to IEC 60825-1 [11].
Figure 4 (c) illustrates the simulated image of the apparent source produced by the MPL according to IEC 60825-1 [11]. It can be seen, that the use of the MPL leads to the formation of multiple smaller peaks instead of a single high-power peak. Each discrete peak is formed by a different illuminated lens facet.
3.3.2. Multipath propagation
Depending on the modulation scheme and the data rate, the faceted structure of the lens leads to inter-symbol-interference (ISI) due to multipath propagation. ISI is a well-known problem in OWC [48], typically caused by reflections within the optical channel. In case of the MPL, the receiver detects rays from different facets. The different path lengths cause different propagation durations and lead to ISI. Figure 5 (a) illustrates the situation with three rays with the path lengths ${l_1}$, ${l_2}$, ${l_3}$ with ${l_1} < {l_2} < {l_3}$. If the receiver is at the FOV edge, the path difference reaches the maximum. For evaluation, the setup from Fig. 5 (a) is simulated within a ray tracing simulation. The origin of the source rays is at (x;y;z)=(0; 0; 1.5 mm). The receiver has a diameter of 1 mm and its center is placed at (x;y;z)=(0; 50 mm; 500 mm). $5 \cdot {10^6}$ rays are traced but only 803 rays hit the receiver. Figure 5 (b) shows the distribution of the path lengths of these rays.
Fig. 5. (a) Sketch of the simulation setup with three rays with a path length of l1, l2, and l3. The sketch is not in scale. (b) Simulated distribution of the path length of single rays through the MPL to a detector at z = 500 mm. The rays are all equal in power.
The structure of the histogram in Fig. 5 (b) depends on the MPL, the receiver and the alignment between them. The maximum path difference for the traced samples is approx. 3.5 mm, which corresponds to $\mathrm{\Delta }t = 11.67\textrm{ps}$ in air. If we assume a tolerable jitter of 10% of the bit duration of a non-return-to-zero On–off keying (NRZ-OOK) signal, we can reach a data rate of $1/({\mathrm{\Delta }t/0.1} )= \; 8.6\; \textrm{Gbit}/\textrm{s}$ with this MPL. Only 9% of the rays exceed a path length 502.5 mm. This low probability corresponds to low power. If we ignore the jitter-condition for path-differences > 2 mm (l > 502.5 mm), a data rate of 15 Gbit/s is possible. In this case, the jitter degrades the signal quality, which corresponds to a link budget penalty of 0.4 dB. Higher data rates can be reached by reducing the MPL size or by using higher-order modulation schemes. For most OWC transceivers the MPL is not the limiting bottle neck regarding data rate.
4. Measurements
4.1. Prototype
The lens prototype was fabricated by injection molding. The mold tool was produced by using an ultra-precision milling process. The milling head had a rounding radius of 190 µm. We use a black polycarbonate (PC) as the mold material. Figure 6 shows a perspective view and a bottom view of the lens. From Fig. 6 (a) the faceted structure of the top side (1) can be observed. The rectangular surrounding structures (2) are used for mounting and have no optical purpose. The lens is mounted within a custom-designed transceiver case, which exhibits the negative of the lens mounting structures as indentation. The lens was designed for an edge-emitting LD with $\lambda = 850 \ \textrm {nm}$ and $ {\Phi _{\textrm{TX}}} = 190 \ \textrm{mW}$. Comparing the reflections (3) and (4) in Fig. 6 (b), a clear deviation from the ideal lens shape can be seen at the lens center. The distance between the source and the bottom surface is $ {z_\textrm{l}} = 25\; \textrm{mm}$.
4.2. Optical performance
The transmitter is placed without and with MPL inside a motorized three-axis measurement stage. At the opposite side a $\emptyset$3 mm Si-photodiode (PD) is used for photocurrent measurement. The distance between the transmitter and the photodiode is set to $z = 222\; \textrm{mm}$ which is the maximum possible distance within the measurement stage. From the received photocurrent in Fig. 7 (a) we see the elliptical emission profile of the LD. Figure 7 (b) shows the resulting emission profile after its transformation into a rectangular shape. However the transformation is not ideal, which can be especially seen at the corners. This is caused by the fairly low distance z, i.e. Figure 7 (b) does not show the geometrical far field. Therefore, another measurement is carried out by illuminating a white screen at $z = 1\; \textrm{m}$ and using a commercially available digital camera. The result in Fig. 7 (c) shows a more rectangular shape. However, the edges of the profile are still noticeably blurred.
Fig. 7. Measured emission profiles. (a) LD without MPL at $z = 222\; \textrm{mm}$ with $\emptyset$3 mm PD. (b) LD with MPL at $z = 222\; \textrm{mm}$ with $\emptyset$3 mm PD. (c) Photograph of an illuminated screen at $z = 1\; \textrm{m}$. The white line highlights the anticipated FOV.
The transmission efficiency through the MPL is measured by using the power meter Thorlabs PM100USB and the sensor S121C. 90.5% of the power that hits the MPL is transferred to its output.
4.3 Eye safety performance
Figure 8 shows a photograph of the lens in use. A commercial digital camera Sony Cyber-shot DSC–HX is able to resolve the illuminated facets and verify the multi-path principle.
Eye safety measurements with and without MPL are carried out in accordance with IEC 60825–1 [11]. To determine the size of the apparent source (${B_\textrm{x}},{B_\textrm{y}}$) we form an image of the source onto a CMOS beam profiler of type WinCamD-LCM. The optical power ${\Phi _\textrm{m}}$ is measured with the power meter PM100USB and the sensor S121C. The measurement distance to the MPL is 100 mm, which represents the most hazardous position for the human eye. The image is formed by multiple measurements due to the large image size. Only one quadrant is measured and the others are generated by mirroring. Figure 9 (a) shows the measurement as a heat map from the top. Figure 9 (b) and Fig. 9 (c) show the measurement along the X- and Y-axis respectively. The observable pattern is very similar to the simulation from Fig. 4 (c). The single source is divided into multiple discrete peaks, where each peak corresponds to an illuminated MPL facet.
Table 3 shows the numerical measurement results. The size of the image in Fig. 9 is rated according to the full width at half maximum (FWHM) in x- and y-direction. Due to the discrete nature of the peaks, we take the next peak within the actual FWHM for calculation. The apparent source size along both axis is denoted with Bx and By. The average of both is Bavg. The margin shows how much ${\Phi _\textrm{m}}$ is below or over MPE for laser class 1 operation. A negative margin means, that the limit is exceeded by the given value.
Table 3. Eye Safety measurement for laser class 1 according to IEC 60825-1 [11] and Table 1. Parameters: ${\boldsymbol \lambda } = 850{\textrm{ nm}}$, ${{\boldsymbol C}_4} = 1.995$, ${\boldsymbol r} = 100{\boldsymbol \; }{\textrm{ mm}}$, ${\boldsymbol f} = 75{\boldsymbol \; }{\textrm{ mm}}$, ${{\boldsymbol \alpha }_{\textrm{ min}}} = 1.5{\boldsymbol \; }{\textrm{ mrad}}$.
The measurement of the LD without the MPL shows a very small apparent source. It is treated as a point source with a very low MPE. ${\Phi _\textrm{m}}$ exceeds the MPE by 10.3 dB. For laser class 1 operation, the laser output power ${\Phi _{\textrm{TX}}}$ must be reduced from 190 mW to 17.7 mW.
The measurement with the MPL is divided into the measurement of the envelope of all peaks and of the most powerful single peak.
The observation of the peak envelope shows, that the MPL enlarges the apparent source size and increases MPE by 10 dB. Additionally, the larger output aperture reduces the measured power $ {\Phi _\textrm{m}}$ due to the Ø7 mm aperture. Both effects improve the eye safety margin by 13 dB. Thereby, the LD with MPL is 2.7 dB below MPE. In theory, this would allow for an increase of ${\Phi _{\textrm{TX}}}$ to 354 mW. The observation of the single peaks shows a drastic reduction of the power per peak. The peak with the highest power exhibits $ {\Phi _\textrm{m}} = 0.22\; \textrm{mW}$, which corresponds to an improvement by 15.8 dB compared to the LD without MPL.
5. Discussion
5.1. Methodology and performance
The simulation results from Fig. 4 and the measurement results from Fig. 7 prove the suitability of ray mapping methodology for MPL design. The lens successfully transforms the elliptical emission profile of the LD into a FOV with a rectangular cross-section. Especially the sharp FOV edges in Fig. 4 show the high performance of this approach. The MPL performs slightly worse in the measurement due to production imperfections. The fabrication procedure is discussed in section 5.3. The lens exhibits high transmission efficiency, which is only limited by Fresnel reflections. Consequently, an AR coating might be used to improve the performance even further.
The alignment of the LD and the MPL was carried out by hand without active alignment. Therefore, the required alignment precision of the MPL is in the sub-millimeter range and can be rated as moderate. A modern assembly process should easily achieve sufficient positioning tolerances.
The freeform multi-path design approach comes with a very high degree of design freedom. Apart from the refracting lens different concepts are possible. For instance, including total internal reflection or multiple refractions could be used to fold the optical design to reduce the source lens distance $ {z_\textrm{l}}$. Moreover, a discrete monitor photodiode could be utilized by designing one of the facets as a back-reflecting mirror.
Although the MPL was designed for a certain LD with a specific wavelength, it is still possible to use other sources with different emission spectra. Different wavelengths result in a slightly different refraction angle. However, this influence is weak compared to production imperfections. By increasing the number of facets per solid angle, the MPL becomes more compatible with sources with different emission profiles. This is because an increasing amount of facets per solid angle reduces the change in intensity over the ray bundle of a single facet.
The general solution of an MPL requires every facet to illuminate the full FOV homogenously. Interestingly, the design can be simplified by dropping this condition if the source emission pattern and the FOV exhibit axial symmetry for both axes. If a facet is illuminating the full FOV but does not achieve a full homogenous irradiance pattern, the corresponding mirrored facets produce an inversely inhomogeneous pattern. The superposition of all four patterns may result in an acceptable homogeneity of the power distribution. However, the robustness of this approach is low. It only works for the ideal laser to MPL alignment and dirt on some of the facets will degrade the homogeneity.
5.2 Eye safety
The measurements prove the feasibility of using a freeform MPL to increase the MPE. Thereby, a higher transmission power can be used to improve the range of a communication link.
Increasing ${\Phi _{\textrm{TX}}}$ from 17.7 mW to 354 mW improves the link range ${z_{\textrm{max}}}$ by a factor of 4.5 if we assume a simple paraxial approximation where $ {z_{\textrm{max}}}\sim \sqrt {{\Phi _{\textrm{TX}}}}$. Of course, there should always be a certain safety margin for addressing 1st order errors. This margin should be in the range of 3 dB. Therefore, ${\Phi _{\textrm{TX}}}$ = 190 mW seems to be a good choice.
The results in Table 3 show that the envelope of all peaks is currently the limiting factor concerning eye safety. Therefore, ${\Phi _{\textrm{TX}}}$ can be further increased by scaling up the MPL size and the FOV. Increasing the MPL size means an upscaling of the distance between LD and MPL. Currently it is equal to $ \; {z_\textrm{l}} = 25\; \textrm{mm}$, but this might cause issues if miniaturization is important. As soon as the single peaks become the limiting factor, the number of facets has to be increased. Since the center peaks carry the highest power, it might be sufficient to increase the facet density in the center of the MPL.
The MPE can be further increased by combining the MPL with a source with a larger size, like for instance an LD array instead of a single laser source. In this case, every single peak within the image of the apparent source is blurred out and can be treated as an extended source with the angular subtense $ \alpha$.
In general, increasing the size of the MPL increases the MPE as long as $\alpha$ is smaller than ${\alpha _{\textrm{max}}} = 100\; \textrm{mrad}$. Further upscaling does not increase the MPE anymore, but the measured power ${\Phi _\textrm{m}}$ decreases since less power passes through the Ø7 mm aperture due to the larger beam diameter.
The eye-safety evaluation is generally wavelength-dependent. The faceted structure of the MPL provides a benefit as long as $\alpha$ influences the MPE. This is typically the case for $400{\textrm nm} < \lambda < 1400{\textrm {nm}}$. Therefore, the equations from Table 1 are only a subset of the definitions given by IEC 60825-1 [11]. The cornea absorbs radiation above 1400 nm and corneal damage is likely. For corneal damages, the size apparent source is of less concern. Instead, the irradiance at the cornea and therefore the beam diameter is of interest.
5.3. Fabrication
Most of the differences between simulation and measurement are caused by lens fabrication. It is well-known from literature, that the fabrication of discontinuous lenses is more challenging compared to the production of continuous surfaces [24,31,34,35,49,50]. The limiting factor during the production of the lens is the rounding radius of the milling tip. Due to the discontinuity between the facets, their edges and corners are rounded. In contrast, the facet centers can be produced with high accuracy. Since all facets of the proposed prototype illuminate the full FOV, the center of each facet directs most of the light into the center of the FOV. Accordingly, the edges concentrate the light to the edge of the FOV. Thus, the rounding effect influences the FOV edge performance. For our prototype, the edges of the FOV are blurred.
In general, the result can be improved by using finer milling tips. Fabrication is possible with mill tip radii down to 100 µm or even below. Domhardt [51] states something similar concerning mill tip radii. A drawback of a smaller tip is a longer processing time.
The non-ideal bottom lens shape from Fig. 6 (b) is caused by a different effect. The cool-down phase of the injection molding process causes stress and shrinkage. Since the effect scales with the material thickness, it is most significant at the center of the MPL. A center thickness of 3.9 mm can be rated as relatively large compared to a Fresnel lens [52]. The lens can be thinned by designing it in a Fresnel lens fashion with larger steps between the facets. However, this increases the production complexity. Alternatively, some process parameters can be optimized, for instance the speed of the cooling down. Since the aspect ratio of the profile in Fig. 7 (c) is nearly equal to 1, we assume that the influence of the non-ideal shape is weak.
6. Conclusions
This article considers the use of MPLs for OWC. The MPL increases the MPE and allows for an increase in transmission power of small-sized emitters like LDs. A prototype of a freeform MPL was fabricated and characterized. By using the prototype, the optical transmission power ${\Phi _{\textrm{TX}}}$ can be increased by 13 dB, which corresponds to a range improvement by a factor of approximately 4.5. The lens transforms the elliptical emission pattern of an edge-emitting LD into a FOV with a rectangular cross-section and homogenous power distribution. The MPL captures 96.5% of the emitted LD light. It exhibits a high transmission efficiency of 0.905, which is only limited by Fresnel reflections. The comparison between simulation and experiments shows the influence of fabrication non-idealities, which mainly affect the edge of the FOV. The improvement concerning eye safety increases with MPL size, FOV, and the size of the source. Consequently, even higher transmission powers are possible by combining the MPL with larger sources like VCSEL arrays.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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