Introducing Advanced Freeform Optic Design to Li-Fi Technology

René Kirrbach

1,2

, Benjamin Jakob

1,2

and Alexander Noack

Fraunhofer IPMS, Maria-Reiche-Straße 2, Dresden, Germany

Department of Electrical and Computer Engineering, TU Dresden, Dresden, Germany

Keywords: Composite Ray Mapping, Freeform Optics, Fresnel Lenses, Li-Fi, Optical Wireless Communications, TIR

Optic.

Abstract: The paper considers the potential of freeform optics for Li-Fi technology and presents design approaches for

transmitter and receiver optics using ray mapping methodology and freeform Fresnel lens, respectively.

Simulation results are then presented for models validation.

1 INTRODUCTION

The proceeding digitalization of our environment leads

to continuously increasing mobile data traffic. The

capacity provided by current radio frequency (RF)

based wireless technologies such as Wi-Fi, Bluetooth

will not be sufficient in the future, due to their limited

frequency bands. Inter-channel interference is an

emerging issue that degenerates data rate and latency

of wireless links in crowded areas. The so-called

“spectrum crunch” can be faced by introducing new

technologies with different carrier frequencies. Besides

intensive research in the field of millimeter-wave

based communications (Rappaport et al., 2013), Li-Fi

technology becomes more and more popular. Li-Fi

utilizes visible or invisible optical wireless

communication links that offer high-speed and low

latency data transfer trough spatially well-defined

communication channels. This allows to design

cellular networks and to reduce inter-channel

interference.

In the past decade different aspects of the Li-Fi

technology emerged rapidly. Various modulation

schemes were investigated (Islim et al., 2016), new

emitters were developed (Ferreira et al., 2016) and

integration of Li-Fi into existing networks was studied

(Wu et al., 2017). However, despite investigation

concerning fluorescence concentrators (Collins et al.,

2014), modern optic design methodology for Li-Fi was

not in focus of the scientific discourse. Typically,

simple lenses are used for beam shaping and optical

amplification. But these cannot fully serve current

trends like an ongoing miniaturization of Li-Fi

transceivers in order to allow their integration into

other devices. Scaling down the optics is directly

connected to performance degeneration. This is due to

the extended source problem at transmitter side and

reduced receiver gain. Advanced freeform optics can

compensate the performance degeneration and provide

compact, high-performance solutions precisely

tailored to the application. For example, providing Li-

Fi connectivity within a corridor can effectively be

realized by shaping rectangular spots.

This paper demonstrates the potential of freeform

optics for Li-Fi technology and gives an overview over

suitable optical design methods. The rest of the paper

is organized as follows: in chapter two fundamental

requirements for Li-Fi optic modules are defined and

limitations of standard lenses are shown. Chapter three

provides an overview over different optical design

concepts. In chapter four we present design examples

of freeform transmitter and receiver optics and

characterize them with optical simulations. Finally,

chapter five gives a short summary.

2 FUNDAMENTALS

As Figure 1 illustrates, a Li-Fi module consists of a

transmitter (Tx) and a receiver (Rx). The transmitter

uses light emitting diodes (LEDs) or laser diodes (LDs)

for signal transmission, whereas the receiver

incorporates a photodiode (PD) for signal detection.

Both parts are characterized by their field-of-view

(FOV). Typically, both FOVs are designed equally.

However, in certain application scenarios they may

differ. If Li-Fi connectivity is provided within a

corridor, the fixed transmitter at the ceiling shapes a

248

Kirrbach, R., Jakob, B. and Noack, A.

Introducing Advanced Freeform Optic Design to Li-Fi Technology.

DOI: 10.5220/0007471802480254

In Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2019), pages 248-254

ISBN: 978-989-758-364-3

rectangular spot. The receiver of the mobile device

below has a rotationally symmetric FOV due to the

unknown orientation of both devices to each other.

Figure 1: Li-Fi transceiver consisting of a transmitter (a)

and a receiver (b). Simple systems incorporate spherical

lenses as shown here.

The optical link is further characterized by its

dynamic range which defines the spatial distance

where data transmission is possible. It is limited by a

minimum and a maximum range. Below the minimum

distance the signal is too strong and the receiver runs

into saturation. Above the maximum distance the

signal level is below the sensitivity of the receiver. The

receiver amplifier can use automatic gain control to

improve the dynamic range. However, this approach

has its limits. For a maximization of the dynamic range

the transmitter and receiver must exhibit a

homogenous behavior over their FOV. This can easily

be understood if we assume for instance a strong peak

in the transmitter’s emission profile. The peak raises

the minimum communication distance and

consequently lowers the dynamic range.

2.1 Transmitter Optics Requirements

As already mentioned, LEDs or LDs are used as

emitters. LDs exhibit small emission angles.

Sometimes even standard aspheric lenses allow

sufficient beam shaping. LEDs are isotropic emitters.

Thus, efficient optic design for LEDs is more

sophisticated. Fortunately, Li-Fi technology can profit

from advances in freeform illumination design where

LEDs are omnipresent nowadays. In contrast to

illumination design, efficiency and homogeneity is

even more crucial since it refers directly to range, data

rate and bit error rate. Moreover, the transmitter’s

optical output power might be limited due to

bandwidth requirements or because of the limited

power budget of mobile devices.

The communication spot can be defined as the area,

where the irradiance E is larger than the minimum

irradiance E

min

required for communication. The

transmitter’s efficiency 



is the power that reaches

the FOV divided by the total emitted power. However,





does not pay attention to the power distribution

within the FOV. If the transceiver has a bit-loading

mechanism, it adjusts its data rate to receiver’s current

signal level.

Yet, low-latency transceivers typically have simple

modulation schemes with fixed data rate. They require

a defined minimum receiver signal level and thus a

minimum irradiance E

min

in order to fulfil the

specification, i.e. ensuring a bit error rate. An

irradiance peak within the FOV gives no benefit, since

the specification is already fulfilled with E

min

. In fact

such a peak actually reduces the dynamic range by

increasing the minimum communication distance as

mentioned before. Therefore, it is better to equally

distribute the power within the FOV to raise E

min

order to maximize the range of the link. Hence, for

transceivers with fixed data rate we define a more

powerful figure of merit by combining efficiency and

uniformity: equation (1) defines the effective

transmitter efficiency 



as the ratio of the

minimum irradiance E

min

within the FOV at the

maximum distance produced by the optic to 



This 

 

is the irradiance achieved by an ideal

optic, which concentrates 100 % of the emitted power

homogenously into the FOV and forms a so-called

tophat profile. It is calculated by dividing the emitted

power P

by the illuminated area A













 















(1)

Figure 2 illustrates a numerical example, where the

FOV should have a half-angle of 17°. The LED

SFH4451 (Osram Opto Semiconductors, 2016) has an

angle of half intensity of 17° and thus seems to be well

suited. However, only about 30.7 % of the emitted

power P

is within the FOV and the effective

transmitter efficiency is only 



 . In

contrast, an ideal optic with 



  reaches an

minimum irradiance E

min

which is 5.94 times (7.7 dB)

higher. This corresponds to an increase of the

communication range by a factor of 2.4 if the data rate

is fixed. Simple transmitters use spherical lenses in

order to improve the performance, as shown in

Figure 1a. Table 1 summarizes the measures of all

three emission profiles. Using the lens LA1805.1

(Thorlabs, 2018) nearly doubles the efficiency to





 . It can be seen, that the irradiance profile

is still very inhomogeneous, leading to bad dynamic

range and an effective efficiency of only





 . Aspheric lenses could improve the

performance, but there are still two problems: First, not

all of the emitted power reaches the lens. Second, if

standard lenses are used the design freedom is low and

it is hard or even impossible to find an aspheric lens

that ideally fits.

LED / LD

(a)

(b)

Introducing Advanced Freeform Optic Design to Li-Fi Technology

249

Figure 2: Irradiance along x-axis in 1 m distance for Osram

SFH4451 LED without an additional lens and with the

spherical lens LA1805.1. The distance d between lens and

PD is 9.6 mm (Figure 1a) and the optical power P

55 mW. The tophat represents the ideal irradiance profile.

Table 1: Measures of the emission profiles from Figure 2.

Transmitter













SFH 4451,

no optics

0.307

0.314×10

-5

W/cm²

0.168

SFH 4451 +

LA1805.1

0.595

0.529×10

-5

W/cm²

0.282

Ideal tophat

1.873×10

-5

W/cm²

2.2 Receiver Optics Requirements

The receiver optic introduces an optical gain g by

concentrating the incident signal onto the PD.

It is well known that the optical gain g of classical

optics is Étendue limited. In a 3D system g can be

calculated by using equation (2) (Welford et al., 1989),

where n

denotes the optic’s refractive index and n

the

refractive index of the surrounding medium, which is

typically air. The optic’s half acceptance angle is 







describes the incident angle of the boundary rays

from the optic to the PD chip. The maximum

theoretical optical gain g

max

is reached for 



 

(Welford et al., 1989). Therefore, the optic has to be in

direct contact to the chip. Depending on how close the

receiver’s gain is to g

max

, we can classify the

performance of the optic module. Ideally, the gain

should be constant over the entire FOV in order to

achieve the maximum dynamic range. In practice

however, the gain varies and we choose the angle

within the FOV with the lowest gain g

min

for

classification. In order to reduce inter-channel

inference and noise induced by ambient light the gain

should drop rapidly outside the FOV.

  





















(2)

The design of receiver optics can profit from

advances in optical design for solar concentration

technology. Li-Fi systems typically need a greater

FOV. Half-angles in the range of 5° ≤ 



≤ 60° enable

the required mobility, at the expense of a lower gain. A

lot of Fresnel lenses for solar concentration have been

proposed (Shen et al., 2013; Koshel, 2013: 199) due to

their small volume and low material costs. Fresnel lens

grooves can be designed according to three different

working principles (Wallhead et al. 2012): refracting,

single total internal reflection (TIR) and double TIR.

Combining these three working principles can improve

the efficiency by reducing the Fresnel losses (Wallhead

et al. 2012).

In solar concentration, a lot of secondary optical

elements have been proposed (Koshel, 2013). If

possible, these elements can be applied to Li-Fi

modules. In practice however, the detector’s active

area may be some millimeters within the package and

it may already include a secondary optical element.

The photodetector is typically chosen because of

properties like high modulation bandwidth, large area

and high responsivity rather than its package geometry.

In that case, the designer can tailor the primary optics

precisely to the photodetectors geometry and make use

of included optical elements.

Using a Compound Parabolic Concentrator (CPC)

or one of its derivatives may be the right choice if their

length and the detectors package is suitable. This is

typically the case for large FOVs and flat packages,

where the active chip area is directly below the package

surface.

3 OPTIC DESIGN METHODS

3.1 Classification

Miñano (Miñano et al., 2013) separates optic design

methods into two fundamental categories: numerical

optimization and direct calculation.

Numerical optimization is a straight-forward

method for designing complex optic modules. Modern

optic simulation tools like Optic Studio Zemax, FRED,

LightTools, etc. allow forming and optically simulating

arbitrary shaped optics by overlapping parametric

objects. Optimization algorithms like the

Levenberg-Marquardt algorithm are used for adjusting

parameters of these objects until a sufficiently good

result is achieved. Due to the large amount of variables,

the optimization is typically inefficient, because of

many local minima in the merit function. This makes it

hard to find the global minimum. Moreover, whenever

PHOTOPTICS 2019 - 7th International Conference on Photonics, Optics and Laser Technology

250

the system specifications change, the optimization

process has to be carried out again.

In contrast, direct calculation algorithms follow

well-defined design procedures and yield deterministic

outcomes. This approach yields better results than

numerical optimization methods (Koshel, 2013),

especially if the systems are complex. With the tailored

freeform design method, proposed by Ries and

Muschaweck (Ries et al., 2001), the designer solves a

set of non-linear equations to generate a freeform

surface. However, more often geometrical calculations

are used for surface construction. Various approaches

are known, e.g. composite ray mapping (Ma, 2015),

forming surfaces using Cartesian ovals (Michaelis et

al., 2011), simultaneous multiple surface (SMS)

method in 2D (Winston et al., 2005) and 3D (Benitez

et al., 2004).

The edge-ray principle is used in most of these

design methods. It states, that extreme rays at the input

aperture edge will form the rim of the output aperture

(Welford et al., 1989). We can use this principle by

designing the optic for the extreme rays and assuming

that all other rays lie in-between the output apertures

rim. Although this assumption is not completely true in

3D, this approach still yields good results (Welford et

al., 1989).

Direct calculation methods lead to deterministic

results, but optimization of certain input parameters

can still be a useful tool for compensating unrealistic

assumptions during the calculation, like assuming a

point source. In contrast to numerical optimization, less

but much more effective variables are chosen.

Therefore, the optimization process converges faster.

Most of the direct methods give dedicated points of

the optical surfaces. Non-uniform rational B-splines

(NURBS) are a powerful tool for surface interpolation.

Piegl and Tiller (Piegl et al., 1995) give a detailed

description on how to set up the required algorithms.

NURBS are supported in the most popular CAD

formats such as STEP or IGES. This is beneficial, since

the calculated optic geometry has to be exported into a

CAD format for optical simulation and fabrication.

3.2 Composite Ray Mapping

Composite ray mapping combines an energy mapping

approach with a subsequent geometrical calculation of

the optics shape by assuming a point source. An

optimization step addresses the extended source

problem and other unrealistic assumptions by

modifying the source or target energy map or both in

parallel. The method is used in this work because it is

versatile, easy to understand and it has the potential to

yield very efficient results.

3.2.1 Energy Mapping

Energy mapping allows the designer to transfer the

emission profile of the source into a desired

illumination pattern. We assume a homogenous

illuminated target surface for the following

considerations. Typically, the half-space around the

source is divided into areas in such a way that the same

amount of energy is emitted trough each surface

element. Next, the target surface is divided into parts

of equal size. Each surface element of the source map

is linked to a corresponding element of the target map.

If the optic module is able to provide this link, a

homogenous illuminated spot is formed.

The coordinate system that is used for creation of

the energy maps strongly influences the optics

performance. This is because of a surface error that

appears during the geometrical calculation of the optic

surfaces (Ma, 2015; Wang et al., 2017). The coordinate

system determines the magnitude of this surface error.

For circular spots, we recommend a spherical

coordinate system for the source map and a radial

energy map for the target as Wang et al. described

(Wang et al., 2017). For rectangular spots the author

recommends a double-pole coordinate system for the

source as Ma proposed (Ma, 2015).

3.2.2 Geometrical Calculation

The edge points of the surface elements of the source

and target energy map are used as unit vectors for the

input and the output rays. An initial surface point for

calculation has to be defined. The following point is

calculated by using the surface normal of the previous

point and the next input ray. Thereby an initial curve of

the surface is calculated. For rotationally symmetric

optics, that curve is rotated around the optical axis. For

non-rotationally symmetric optics, multiple curves are

calculated. Typically, a quarter or half of the geometry

is calculated and the rest is generated by mirroring.

Detailed information concerning the calculation

algorithm and about the composite ray mapping

methodology in general can be found in the work of

Ma (Ma, 2015) and Wang (Wang et al., 2017).

3.2.3 Optimization

During the calculation some false assumptions were

made which lead to a surface error that can be corrected

by optimization. These false assumptions may include:

the point source model, a mismatch between the source

and target energy map (Ma, 2015) and monochromatic

light. A purposeful distortion of the source energy map,

the target energy map or both simultaneously can

address these false assumptions. Therefore, the

Introducing Advanced Freeform Optic Design to Li-Fi Technology

251

designer should parametrize the energy maps with a

minimum number of parameters to enable an effective

optimization.

4 DESIGN EXAMPLES

All simulations are based on optical ray tracing using

Optic Studio Zemax 17. The simulations incorporate

realistic simulation models like the corresponding ray

files and spectrum files. No anti-reflection (AR)

coatings are used. For the emitter, the infra-red LED

Osram SFH4451 (Osram Opto Semiconductors, 2016)

is used with 55 mW optical power. The receiver

incorporates a Hamamatsu S10784 (Hamamatsu,

2013) PD. The PD package includes a spherically

shaped lens.

4.1 Transmitter Optics

4.1.1 Design

LED chips are isotropic emitters. In order to maximize

the transmitters efficiency the optic has to surround the

emitter. Illumination systems typically incorporate a

reflector. This approach can provide a homogenous

power distribution at the center of the FOV. But its

efficiency is limited due to absorption losses (Koshel,

R. J., 2013) and the reflectors tend to be large. For

small reflectors on the other hand, the steepness at the

edge of the FOV is poor as we can see in Chaves

example designs (Chaves, J., 2016). The reflector

approach is still an interesting low cost solution:

transmitter and receiver can have separated reflectors,

but both can be placed on the same carrier and

fabricated simultaneously. The reflector can be

calculated by traditional methods (Chaves, 2016) or by

using the composite ray mapping methodology. The

latter can face the extended source issue and can easily

be applied to any kind of source profile.

For high-performance designs, there are two

different design approaches. Figure 3 shows a design

based only on refraction, whereas the design from

Figure 4 has at least one interface with TIR. Both optics

were realized using composite ray mapping

methodology with a spherical coordinate system for

the source map and a radial energy map for the target

plane. The design in Figure 3 is suitable for large FOV.

This is due to the limited deflection of two refractions

and increasing Fresnel losses with large refraction

angles. Moreover, it tends to be thick for relatively

small FOVs. The design in Figure 4 is more complex

and should be used for small and medium FOV. For a

rectangular spot, non-rotationally symmetric versions

of both designs can be derived.

Figure 3: Transmitter optic based on refraction. The body is

formed by rotating the white spline around the optical axis.

It is 22 mm in diameter, 12 mm in height and forms a FOV

with a half-angle of 37°.

Figure 4: Transmitter optic based on refraction and TIR.

The body is formed by rotating the white spline around the

optical axis. It forms a FOV with half-angle of 17°. The

optics diameter is 25 mm and its height is 10 mm.

4.1.2 Results and Discussion

The following considerations stick to the anticipated

FOV with half-angle of 17°. Therefore, only the TIR

optic in Figure 4 is considered. Figure 5 shows the

irradiance at 1 m distance. We get 



  and





   



W/cm² which results in





 . In comparison to the SFH4451 LED

without additional optics this is an improvement by a

factor of 3.98 (5.99 dB). Even compared to the

spherical lens LA1805.1 from Figure 2 E

min

increased 2.36 times (3.73 dB).

The simulation shows, that 10.5 % of the emitted

power is lost due to Fresnel reflections. This could be

reduced by depositing an AR coating. However, the

shape of the optic makes it difficult to deposit

homogenous layers. Another 15.5 % of the power

misses the FOV due to the extended source problem.

By scaling up the optic this loss can be reduced.

Moreover, 5% of the “losses” for 



result from

inhomogeneity. The white circle in Figure 5 marks the

minimum within the FOV. The ray file of the SFH4451

reveals that this minimum is not caused by the optic,

but by the reflector within the LED package, which is

not fully rotational symmetric.

1 mm

PHOTOPTICS 2019 - 7th International Conference on Photonics, Optics and Laser Technology

252

Figure 5: Irradiance in 1 m distance. The black circle marks

the FOV. The white circle highlights minimum.

4.2 Receiver Optics

4.2.1 Design

The Fresnel lens shown in Figure 6 is precisely tailored

to the PD and provides a FOV with a half-angle 





. It is 2.5 mm thick and has a refracting section in

the center surrounded by one TIR groove. The

thickness could be further reduced if both sections are

divided into multiple grooves. For the initial design the

edge-ray principle was applied for all surfaces. Due to

the discontinuity between both sections, the edge-ray

principle is not valid for the complete input aperture.

Therefore, the gain is not constant within the FOV. A

homogenization can be achieved by slightly adjusting

the groove for a range of incident angles rather than

only for the maximum incident angle. The designer has

to be aware of shading effects within the grooves for

rays with large incident angles. Due to non-ideal rays

the actual performance at the edge of the FOV will be

worse than one may expect in the first place. These rays

emerge for example from polychromatic light or they

are simply skew rays. The issue can be addressed by

directing the rays not directly the edge of the PD active

area but slightly next to this edge.

For comparison, a second receiver with the

spherical lens LA1074.1 (Thorlabs, 2018) is designed,

as depicted in Figure 1b. The lens has a diameter of

12.7 mm and the distance d to the PD is 2 mm.

Figure 6: Freeform Fresnel lens tailored to PD S10784. The

lens is 12.5 mm in diameter and 2.5 mm in height. The cross

sectional spline is colored white and the active area yellow.

4.2.2 Results and Discussion

Figure 7 shows the gain over the angle of incidence 



The gain of the Fresnel lens is 15.5. This is 1.8 times

(2.6 dB) higher than the gain of the spherical lens,

which is 8.5. Moreover, the gain of the Fresnel lens

drops much faster the outside FOV. This effectively

reduces inter-channel interference and shot noise

induced by ambient light. According to Figure 7, 15 %

of the power is lost due to Fresnel reflections. These

losses can be reduced by applying an AR coating at

least at the flat top surface of the lens. Despite the

Fresnel losses, the minimum gain g

min

is still about 25

% below the ideal gain g

max

. Three reasons for that can

be derived from the design procedure. First, the

freeform lens directs the rays onto the spherical lens.

The maximum coupling angle 



to the active chip is

only 73.5° instead of the ideal 90°. Second, the rays are

not directed directly on to the chip edge, but slightly

next to it. Therefore, the calculated lens is smaller and

thus its gain is lower than g

max

. Third, due to the

discontinuity, the edge-ray principle is not fully

satisfied and losses occur.

Figure 7: Optical gain g of the Fresnel lens and the spherical

lens LA1074.1 in conjunction with PD S10784 over angle

of incidence 



. The ideal gain was calculated with

equation 2 assuming 



 , 



 , 



 

and 



 .

4.3 Complete Optical Channel

Figure 8 shows the incident optical power onto the PD

active area P

pd opt

over the FOV for transceivers without

optics, with spherical lenses and with the freeform

lenses from section 4. The freeform lenses provide a

homogenous signal level within the FOV. It varies only

about 1.3 dB and never drops below -24.1 dBm. In

contrast, the signal level provided by the spherical

lenses fluctuates by 7.5 dB and drops at the edge to -

30 dBm. This inhomogeneity is caused by the spherical

transmitter lens. The simulation without any optics

show signal levels down to -36.1dBm. This simulation

is noisy, because only a small amount of rays hit the

detector and the initial number of rays is limited by the





1 mm

Introducing Advanced Freeform Optic Design to Li-Fi Technology

253

ray file.

Figure 8: Incident optical power 



onto the PD active

area over FOV for no optics, spherical lenses (LA1805.1,

LA1074.1) and freeform lenses. The angle  corresponds to

a misalignment of both transceivers in the plane over a

distance of 50 cm. The graphs are very noisy in the dotted

region, because only a few rays hit the PD surface.

5 CONCLUSIONS

This paper demonstrates the potential of modern

freeform optics for Li-Fi technology. Design strategies

for transmitter optics are discussed and a TIR based

optic is presented and characterized. The design

example proofs that composite ray mapping is an

efficient tool for shaping homogenous emission

profiles. For the receiver, the designer should tailor the

optic precisely to the PD. A Fresnel lens based on

refraction and TIR is proposed and it is shown that the

optical gain is about 2.6 dB higher compared to a

conventional spherical lens for the considered PD.

We show that the proposed freeform optics provide

a minimum signal level which is 5.9 dB higher than a

optic setup with spherical lenses. The signal level has

an excellent homogeneity within the FOV and

fluctuates only by 1.3 dB. This is about 6.2 dB less

compared to the proposed spherical lenses. This high

homogeneity maximizes the dynamic range and the

sharp cut-off at the edge of the FOV effectively reduces

inter-channel interference and noise.

Our next steps will include the fabrication and

experimental characterization of the designs. Finally,

transmitter and receiver optics should be combined to

one hybrid optic module for size and cost reduction.

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