WAVEGUIDES BY3D-PRINTING

Vladislav Ananyev

MSc Thesis

June 2020

Department of Physics and Mathematics

University of Eastern Finland

Vladislav Ananyev Waveguides by 3D-printing, 35 pages

University of Eastern Finland

Master’s Degree Programme in Photonics

Supervisors Prof. Jyrki Saarinen

Prof. Matthieu Roussey

Abstract

In this work, optical properties of 3D-printed slab waveguide were studied both

numerically and experimentally. Besides the 3D-printing process of fabrication of

optical components is well described in scientific papers, there are not enough specific

studies on the optical properties of the obtained structures. 10 waveguides designs

with 2 different substrates: PMMA and fused silica, and 5 various thicknesses of the

core layer: 5µm, 10µm, 15µm, 20µm and 30µm, have been printed using LUXeXceL

3D-printing technology. Prism coupler device was used to study the propagation

of the electromagnetic waves at three wavelengths: 532nm, 635nm, and 1550nm.

Experimental data has shown that higher wavelengths lead to the lower effective

index in all 10 samples, which is in good agreement with simulations. A number

of modes values show the linear dependency from the thickness of the core and

grows faster with thickness in fused silica samples. Lower wavelengths contribute

to the highest rate of the number of modes value growth. This data will help to

understand the suitability of LUXeXceL 3D-printing technology for manufacturing

working waveguide structures, which can be used in integrated optics, and to spot

the weak points of this process to be improved in the future.

Keywords: 3D-printing; slab waveguides; prism coupler

Preface

Writing this thesis was a great challenge and an enjoyable experience that brought

me the opportunity to gain a myriad of valuable skills and a lot of knowledge. I would

like to thank Noora Heikkila for guidance along the whole studying journey. I would

also like to extend my deepest gratitude to my supervisor Jyrki Saarinen for giving

the opportunity to participate in 3D printing meetings. I’d like to acknowledge the

assistance of Markku Pekkarinen in manufacturing the samples and giving valuable

information on the 3D printing process itself. Finally, I wish to give special thanks

to Matthieu Roussey for invaluable support, constructive criticism, and patience

that cannot be underestimated.

Joensuu, the 11th of May 2020 Vladislav Ananyev

iii

Contents

1 Introduction 1

2 Waveguide theory 4

2.1 Refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Snell’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Total internal reflection . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4 Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.5 Waves inside the core . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.6 Cut-off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 3D-printing 12

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Inkjet printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 LUXeXceL optical 3D printing technology . . . . . . . . . . . . . . . 14

4 Prism coupler 16

4.1 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Film properties estimation . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Simulations and measurements 19

5.1 General work description . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

iv

5.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Conclusions 29

References 32

v

Chapter I

Introduction

3D-printing technology was invented by Charles Hull in 1984. It was a simple process

called ”stereolithography”. The idea behind this concept was to add a layer of

photosensitive liquid polymer and then cure it with ultraviolet light, starting the

reaction, which solidifies the obtained layer. By adding material layer by layer an

object of a certain shape can be formed. This idea is still used to these days in some

models of 3D-printers but the quality of printing along with accuracy and material

spectrum available for the printing process has changed dramatically [1]. These days

myriad of different objects are being printed including technical parts and electronics

for various applications from medicine to cosmology [2] [3]. Photonics and optical

devices are not an exception.

Recently it became possible to use transparent materials in 3D printing that

after a long way of development found its application in optics [4]. One of the

most influential companies dealing with 3D-printing of the optical components is

LUXeXceL. LUXeXceL is a company, based in the Netherlands, which has adapted

3D-printing for making optical parts. One of the most common optical parts printed

using transparent materials is the lens. Meanwhile, the quality of printed optics is

similar to the conventional manufactured lens, there are some strong points of using

3D-printing instead [5].

The main advantage of the 3D-printing optics over conventional manufacturing is

an avoidance of the additional steps such as polishing and taping during the process.

Not even this saves time but also leads to less material wastage. In addition, optical

3D printing may be used for producing goods with custom design: LUXeXceL has

experience of producing lens for VR headsets. That all makes LUXeXceL the most

1

advanced 3D-printing company so far. However, this technology has its flaws. It is

not reasonable to apply it on a large scale for now, mainly because of the cost. That

is why it is rather important to develop this technology further to make it more

affordable [5].

Lenses are only a small part of the whole range of various objects which are

possible to manufacture by optical 3D-printing technology. Optical components

production for photonics devices is a promising application for additive manufac-

turing. It can be used for imaging fiber optics purposes such as printing on-fiber

multilens assembly for medical application in endoscope [6], micro-optics for optical

coherence tomography fibre probes [7] as well as diffractive optical elements [8], and

guiding structures such as simple slab waveguides [9] or even optical fibers drawn

from 3D-printed preforms [10]. There have already been written some papers about

3D-printed waveguides [11] [12]. However, usually, the main attention is paid to the

process of manufacturing, not to the properties of obtained structures.

The aim of this work is to study the properties of the optical slab waveguide

fabricated using LUXeXceL 3D-printing technology. This includes 4 main objectives.

Firstly, the waveguide design should be made. This includes choosing the right

substrates for printing along with the thickness, satisfying 3D-printer’s capabilities.

Mode behavior simulations should be performed to check the possibility of the chosen

design to guide waves. The simulation process should take into consideration such

waveguide parameters as effective indices of the fundamental mode and number

of modes for each sample at three different wavelengths (532 nm, 636 nm, and

1050 nm). Secondly, 10 different slab waveguides need to be made by additive

manufacturing using LUXeXceL printer: 5 waveguides with 5 various thicknesses of

the core layer on the PMMA substrate and the other 5 using a fused silica substrate

with a similar variety of thicknesses. The next goal is to measure properties of

obtained structures, compare them to the simulations and find how the wavelength

of the incident beam, the thickness of the core layers, chosen substrate affect the

mode the effective indices and number of modes. In addition, values of the film

thicknesses and refractive indices of all material have to be measured and then

compared to the simulations.

This data will help to understand the suitability of the LUXeXceL 3D-printing

technology for manufacturing slab waveguides applied in integrated optics. Additive

manufacturing is now the most advanced method in manufacturing, and it is hard to

2

overestimate its importance since more and more details, as well as entire working

devices, are been printed using a 3D-printer [13]. This fact means the future of the

optical component fabrication can depend on how we advance 3D-printing technol-

ogy further, improve its speed, accuracy and make optical properties of materials

used for printing more suitable for particular purposes.

In the first chapter of this work general information about waveguides and physics

behind them is discussed. In the second chapter 3D-printing technology and LUX-

eXceL optical printing are stressed in a comprehensive way. In the next chapter

device used for measurement and it’s working principals are discussed. After that

measurements and simulations results related to the manufactured waveguides are

elaborated. In the last chapter, conclusions are made.

3

Chapter II

Waveguide theory

2.1 Refractive index

When an electromagnetic wave propagates through the free space it does not interact

with any matter and its speed remains constant, c = 299 792 458 m/s. But at the

moment the wave faces the medium it impacts some of its properties including phase

velocity, wavelength, and direction of propagation. This change of light path after

entering a more optically dense medium is called refraction. The representation of

this phenomenon is shown in Fig. 2.1.

Figure 2.1: Refraction of the light wave

To estimate the ability of the material to inhibit electromagnetic wave propa-

gation refractive index was introduced. It shows the ratio between the speed of an

electromagnetic wave in a vacuum to its speed in the particular medium.

4

n =c

v(2.1)

where n is the refractive index of the medium, c is the speed of the electro-

magnetic wave in free space, v is the speed of the electromagnetic wave in the

medium [14].

2.2 Snell’s law

Let us assume having two mediums with different refractive indices, as shown on

Fig. 2.1, where n2 > n1. In this case, the incident wave will change its path after

crossing the boundary between two materials. Correlation between incident and

refracted angles is given by Snell’s law as follows:

n1

n2

=sin θ2sin θ1

(2.2)

where n1 and n2 are refractive indices of the two materials, θ1 is an angle between

normal to the boundary of the two materials and incident wave propagation, θ2 is

an angle between normal to the boundary of the two materials and refracted wave

propagation [15].

2.3 Total internal reflection

When the light wave propagates through the medium with a higher refractive index

to the medium with a lower refractive index, the behavior of the radiation depends

on the incident angle. Fig. 2.2 shows three scenarios of a wave’s propagation. If

the incident angle θ1 is lower than a certain angle, called “critical angle”, θc, the

wave will be partially reflected from the border and refracted at the angle θ2 = θ1

as shown in Fig. 2.2a. This angle can be found using the following formula:

θc = sin−1(n2/n1) (2.3)

If the incident angle is equal to the critical angle, the wave will follow along the

path of the border (Fig. 2.2b). If the incident angle is higher than the critical angle,

the incident wave will be fully reflected from the border (Fig. 2.2c) [16].

5

Figure 2.2: Representation of the total internal reflection. a – incident angle

is higher than critical, b – incident angle is equal to critical, c –incident angle

is higher than critical.

2.4 Waveguide

A waveguide is a structure that works on the principle of total internal reflection

to guide waves. A simple waveguide consists of three layers with different refractive

indices as shown in Fig. 2.3.

Figure 2.3: A waveguide with three layers.

The core layer with the highest refractive index n2 is located in between two

materials with lower refractive indices (n1 and n3) to establish repeating reflection

6

from the borders of the materials in order to localize the radiation inside the core.

There are different types of waveguides. 2D slab waveguide is the waveguide

where the wave can only one dimension (Fig. 2.4a). 3D or channel waveguide is a

structure that allows the wave to propagate in the 2-dimensional space (Fig. 2.4b).

Figure 2.4: a – slab waveguide, b – channel waveguide.

Let us have a closer look at the 1-dimensional waveguide as this work is devoted

to this particular type of dielectric guiding structure [17].

2.5 Waves inside the core

Only waves which in phase are allowed to be guided, thus to establish wave propaga-

tion inside the core of the structure constructive interference is needed. The waves

out of phase inhibit propagation of each other until they completely vanish. Suppose

electromagnetic wave with wavelength λ and phase constant k traveling through the

slab waveguide core with refractive index n2, experiencing total internal reflection

from the cladding with refractive index n1 at the angle to the cladding’s normal θ

as shown on the Fig. 2.5.

7

Figure 2.5: Visual representation of the wave propagation inside the slab

waveguide

β and κ here are propagation constants along longitudinal and transverse direc-

tions responsively:

β = ksinθ

κ = kcosθ(2.4)

The wavelength of the propagating radiation inside the core as well as its phase

constant can be described as:

λ =λ0

n2

k = k0n2

k0 =2π

λ0

(2.5)

where λ0 is the wavelength in free space, n2 is a refractive index of the core and

k0 is a phase constant in a free space.

Wave changes its phase each time it reflects from the boundaries of the core. To

interfere with each reflection constructively, phase difference should be even to 2π.

Thus the phase change between the wave at point A and point C should be:

∆ϕ = 2πm (2.6)

where m = 0, 1, 2, 3, ...

8

On the other hand, we can rewrite phase change in terms of total length wave

has to traverse:

∆ϕ = k(AB +BC)− 2ϕ (2.7)

Paths BC and AB can be described as:

BC =d

cos θ

AB = BC cos(2θ)(2.8)

Taking into account equations 5.1, 5.2, and 5.3:(2πn2d

λ0

)cos θm − ϕm = mπ (2.9)

This equation is a waveguide condition. It shows which waves are allowed to

propagate in the waveguide. These waves are called waveguide modes. Its number

is defined by the integer number m and its spatial distribution within a core change

with its increment. Typical modes are shown on Fig. 2.6. Green arrows show an

exponential decay of the evanescent waves within a cladding [18].

Figure 2.6: Mode distribution inside the slab waveguide

9

Every mode propagating within the waveguide structure is characterized by a

certain number which defines the relation of the phase delay per unit length in a

waveguide to the phase shift in a vacuum. This number is called ”effective index”[19]:

neff =∆ϕw

∆ϕ0

(2.10)

Where ∆ϕw is the phase delay in the waveguide and ∆ϕ0 is the phase delay in

a vacuum. Sometimes the effective index is mentioned as a ”modal index” because

it depends not only on the wavelength but also on the mode number. That makes

an effective index is a parameter that is useful in designing waveguides to predict

light behavior within it. The effective index is also important to estimate already

manufactured films using prism coupler, which will be discussed in detail in the next

chapters [18].

Two different types of wave polarization are possible within a slab waveguide:

TE and TM modes. TE stands for transverse electric, which means that the electric

field is transverse to the direction of propagation and TM stands respectively for

the case when the magnetic field is transverse to the direction of radiation as shown

in Fig. 2.7.

Figure 2.7: Two modes polarizations

10

2.6 Cut-off

It is not only the reflection angle that defines the number of propagating modes

within a core of the waveguide. The higher the wavelength of the mode the harder

it gets to it to fit in the core. There is the critical frequency that corresponds to the

mode with the highest wavelength which can exist within the core. It is called ”cut

off wavelength”:

λc =2n2d

m(2.11)

where n2 is the refractive index of the core.

V - Number is a parameter which shows the number of modes which can exist

inside the core, and it is defined as follows:

V =2πa

λ(n2

2 − n21)

1/2 (2.12)

If V < π/2 only one mode can propagate through the core of the waveguide [20].

11

Chapter III

3D-printing

3.1 Introduction

Additive manufacturing or 3D-printing is a technology allowing to fabricate differ-

ent objects of various shapes and materials from plastic figures to optical parts by

converting digital 3D-model into the real material ware. There are myriad different

types of 3D-printing technology each designed for specific purposes. Some of them

work by melting a powder material using a laser (selective laser melting) or electron

beam (electron beam melting) to fuse particle into solid form while other designs

create an object by adding special ink and then curing it with ultraviolet light to

solidify obtained layer (Inkjet printing) [21].

3.2 Inkjet printing

Let us focus on the latter method. Inkjet printing deposition method is designed to

use liquid substances known as inks. Inks are made by neither solution or dispersion

in a solvent. There are two existing ways of carrying out the process. The first one

is called Continuous Inkjet (CIJ) printing (Fig. 3.1a). This technique is based on

creating Rayleigh instability to make a sustained flow of ink droplets falling onto

the substrate. Applying a voltage to the nozzle, which ejects the ink, allows control

over a droplet spacing. At the moment printing is not going on, ink droplets are

turned to the collecting tank needed for further recycling material [22].

12

Figure 3.1: Schematic representation of (a) continuous inkjet (CIJ) and Drop

on demand (DOD) inkjet printing systems using (b) thermal and (c) piezo-

electric technology.

The second process is called Drop on Demand (DOD). This method implies

creating a pressure in the printhead with the ink to induce its drop onto the target

through a nozzle. The surface tension within a liquid allows it to stay inside the

printhead unless printing is needed. The aforementioned pressure can be caused by

heat created in the printhead to generate bubbles, which separate ink into single

droplets falling onto the target substrate through the nozzle (Fig. 3.1b). There

is a different way of ink separation within the printhead. This technique is based

on voltage-induced deformation (Fig. 3.1a). It implies using piezoelectric element

instead of a heating element to generate a so-called “shockwaves” which separate

a certain amount of ink similarly to the technique mentioned above. This method

is more reliable in comparison with a bubble creation due to its accuracy in the

timing of droplet making. Besides, it dwindles the droplet size to typically tens of

micrometers.

The printhead usually comprises a glass capillary with a supply channel to feed

the structure with ink on one side and a nozzle for liquid material output on the

other. Piezoelectric element with electrodes installed on both of its sides is placed

13

around the capillary’s outer walls (Fig. 3.2a). The voltage vs time graph commonly

has a trapezoidal shape as can be seen from Fig. 3.2b. The voltage rises dramatically

from zero to V0 during the time period trise. Then it holds on this level for amount

of time tdwell and further come back to zero during time tfall [23].

Figure 3.2: (a) Detailed schematic structure of a piezoelectric single nozzle

printhead and (b) trapezoidal voltage piezoelectric excitation.

3.3 LUXeXceL optical 3D printing technology

LUXeXceL is a 3D printing company, founded in the Netherlands in 2009, known

to be the only company in the world which can manufacture optical components for

eyeglasses, virtual reality (VR) headset, industrial and many other types of a lens

by use of their own unique printers which perform printing using special-designed

material for printing, named “LUX-Opticlear” [24] [25]. This technology along with

the “LUX-Opticlear”material properties and printing process itself are strictly con-

fidential due to its outstanding effectiveness and possibilities it provides [26]. The

general picture of this process is shown in Fig. 3.3. Firstly droplets are ejected from

the nozzles onto the substrate material using a drop on demand technique described

above. This process is called ”deposition”. Substrates are usually made of PMMA

or fused silica. Then droplets are cured by a UV light source to establish polymer-

ization of the deposited dots and make them solid [27] [28]. The polymerization

process is based on radical fragments generation by monomer exposure to the elec-

tromagnetic wave with a certain wavelength. These radical reactive species induce

polymer chain growth [29].

14

Figure 3.3: Representation of LUXeXceL 3D-printing process.

In order to make smooth lines while printing, the capillary bridges technique is

utilized. The idea is to print two dots, stabilize them, and then deposit the third

droplet so capillary forces connect the first two dots as shown in Fig. 3.4. The third

dot in which volume is distributed between main dots is called the capillary bridge.

This technology is not limited by the two dots. It can be applied to making different

complicated structures [30].

Figure 3.4: Capillary bridges shown in blue color connect the main dots.

15

Chapter IV

Prism coupler

4.1 General description

Prism coupler is a device that is used for measuring the refractive index and thickness

of the sample. It is capable of working both with bulk materials and thin films.

Besides the refractive index and thickness high precision measurements it is also

utilized for mode analysis within the waveguides which makes it a perfect choice

for comparing printed samples in this work. With certain modifications, it is also

possible to estimate waveguide losses, but it usually makes sense only with long or

very lossy samples as prism coupler can only measure losses above 0.1 dB/cm, which

is not the case in this particular work [31].

4.2 Principle of operation

The device is a prism with a certain refractive index that is placed close to the film

or bulk material to be measured so there is a small air gap as shown in Fig. 4.1.

Analyzed material is pushed by the coupling head to keep its position stable during

measurements. All this system is placed on the rotatory table. Laser outside the

table generates light that hits the prism at a certain angle. The beam is partially

reflected from the base of the prism so the other part of its energy is conveyed through

the film. This process of transferring modes from one material to another is called

coupling. It is crucial for the measurement process to ensure appropriate coupling

to perform experiment. Light reflected from the base of the prism is analyzed by

the detector, which is also connected with the rotatory table. By rotating the table,

it is possible to iterate over the whole range of modes that can be coupled [31].

16

Figure 4.1: Schematic representation of the prism coupler

4.3 Film properties estimation

The effective index of each mode can be found from the angle of the incident beam

in relation to the prism face and angle between this face and the film.

Nm = sin θm cos θm +√

n2p − sin2 θm sin ϵ (4.1)

Here Nm is the effective index of the mode, θm is the angle between normal to

the film and refracted incident laser beam, ϵ is the angle between the film and face

of the prism, m is the mode number and np is the refractive index of the prism.

To find the thickness of the filmW and its refractive index of the film n eigenvalue

equation is used.

kW√

n2 −N2m = Ψ(n,Nm) (4.2)

Where

Ψ(n,Nm) = mπ + ϕ0(n,Nm) + ϕ2(n,Nm) (4.3)

17

Here subscripts 0 and 2 correspond to the substrate and top layer respectfully.

ϕj = arctan

[(n

nj

)2ρ(N2m − n2

j

n2 −N2m

)]1/2

(4.4)

Where j = 0, 2 and ρ is polarization of the incident beam (ρ = 0 for TE and

ρ = 1 for TM).

To estimate thickness and refractive index of the film effective indices of two

modes are used. Let us define these two effective indices as Nα and Nβ. Let us

combine equations 4.2 - 4.4 and then insert Nα and Nβ.

n2 = F (n2) (4.5)

Where

F (n2) =N2

αΨ2β −N2

βΨ2α

Ψ2β −Ψ2

α

(4.6)

Equation 4.5 can not be solved analytically for n2. However, a solution can be

found by iterating values. The way to perform it is to use recursion formula

n2[q] = F (n2

[q−1]) (4.7)

where q = 1, 2, 3, ...

n2 = limq→∞

n2[q] (4.8)

|∂F/∂(n2)| < 1 (4.9)

This inequality also can not be solved analytically, but it was found that 4.8

converges in all cases that are practically reasonable since n2[0] > N2

α and n2[0] > N2

β .

With known refractive index of the film n it is easy to find its thickness W using

formula 4.2 [32] [33].

18

Chapter V

Simulations and measurements

5.1 General work description

In this work, a study was conducted on 10 different slab waveguides made using

3D printing technology in order to evaluate the ability of the LUXeXceL 3D printer

to manufacture working waveguide structures which can be further used as optical

components for integrated optics. Firstly, the ability of the obtained waveguide to

actually guide the electromagnetic waves was investigated. The second goal was to

evaluate mode behavior by simulating effective indices and the number of modes of

each propagating mode for two polarizations at three different wavelengths for each

sample. It was also important to figure out how mode propagation is affected by the

wavelength of the incident light, thickness of the core layer, and substrate choice.

The next objective was to measure the same parameters and to compare obtained

data with simulations. After that, real thicknesses of the samples along with the

refractive indices of each material were compared to the expected ones.

The printing process was performed by jetting unique LUXeXceL ink material

onto the substrate layer by layer. During the printing process, the capillary bridges

technique was used. Due to specific printing technology limitations, the thickness

of the single ink layer could not be less than 4 micrometers. Thus, the minimal

thickness of the sample was decided to be 5 micrometers as it could be achieved

without serious noticeable defects. The next 4 thicknesses were considered to be

10, 15, 20, and 30 microns in order to analyze the tendency of changing guidance

properties in relation to the gradual thickness increase. Those 5 various in thick-

ness layers of LUXeXceL ink were jetted onto two different substrates, Poly(methyl

19

methacrylate) (PMMA), and fused silica to compare the difference in the efficiency

of the waveguide structures with particular substrate layers.

5.2 Simulations

To analyze light behavior and mode propagation within a structure, simulations were

prepared via online “1-D mode solver for dielectric multilayer slab waveguides” [34],

which calculates a number of modes, mode’s profile and effective index of each

mode using wavelength, refractive indices of the core, substrate layers and core layer

thickness as an input data. Expected substrate refractive index values were taken

from the open-source refractive index database [35], while ink refractive index was

calculated by the formula given by LUXeXceL:

n2 − 1 =A+ λ2

λ2 − λ20

(5.1)

where A = 1.2576, λ0 = 116.4 nm.

Mode distribution was analyzed at three wavelengths: 635nm, 538 nm, and 1550

nm, which corresponds to the operating wavelengths of three lasers of the prism

coupler, used for measurements. Fig. 5.1 shows how sample thickness and incident

wavelength influence the effective index of the fundamental modes for two polariza-

tions and two different substrate material. As can be seen from the curves, samples

printed on the PMMA substrate has a higher effective index of the fundamental

modes of both TM and TE polarizations, which can be explained by the lower dif-

ference between refractive indices of the substrate and core region of the waveguide.

It becomes more obvious with the increment of the incoming wavelength. The effec-

tive index also highly depends on the thickness of the core layer. After 15 micrometer

point, the thickness of the ink layer almost stops to influence the guidance, due to

the closeness of the effective index to the refractive index of the ink. On the other

hand, the difference between 2.5-micrometer thickness and 5-micrometer thickness

makes the abrupt change in the effective index. Simulations confirm the possibil-

ity of a 3D-printed structure to guide electromagnetic waves. From the effective

index data, it can be concluded that the fused silica substrate is more suitable for

making waveguide structures using optical 3D-printing technology since it has the

lower effective index, which means higher energy of the fundamental mode and lower

competition between fundamental and high-order modes.

20

Figure 5.1: Effective indices of the fundamental modes with different polar-

izations at three wavelength. a) TE polarization, PMMA substrate, b) TM

polarization, PMMA substrate, c) TE polarization, fused silica substrate, d)

TM polarization, fused silica substrate.

A number of modes was also analyzed to underline the difference between two

substrates and to evaluate the dependence of this value on the wavelength and core

layer thickness. As can be seen from Fig 5.2 samples printed on fused silica substrate

have a greater number of modes as a result of higher refractive index difference of

waveguide layers in this case. A number of modes tends to increase with the thickness

and decrease with the incident wavelength, which correlates well with the previous

plots, representing effective index change.

21

Figure 5.2: Number of modes of samples for different polarizations at three

wavelength. a) TE polarization, PMMA substrate, b) TM polarization,

PMMA substrate, c) TE polarization, fused silica substrate, d) TM polar-

ization, fused silica substrate.

5.3 Measurements

Properties of manufactured waveguides were studied using Metricon 2010M prism

coupler. The mode observation process consisted of coupling laser light into the

film by using a prism and changing the angle of the rotation table to catch the

propagating modes. Fig. 5.3 shows the photo, made during the measurement process

22

at two different wavelengths of the visible spectrum. Light tracks on the sample are

the propagating modes, which appears at the certain position of the rotation table.

Figure 5.3: Photo of the sample during the measurements at 636 nm (left)

and 532 nm (right).

As the detector catches the light, propagating through the film, intensity dips

appear at some points, each of which corresponds to the effective index of the partic-

ular mode as shown on Fig. 5.4 below. The first deep shows the fundamental mode.

In some cases, it appeared impossible to distinguish modes between each other, due

to superimposition. It becomes more common when measuring samples with a high

number of modes, for instance, samples with high thicknesses at a lower wavelength

of the incident light. A typical case of mode superimposition is shown on the Fig.

5.4. A knee after deeps shows the refractive index of the substrate.

23

Figure 5.4: Observation of the modes using prism coupler.

As expected, the increment of the incident light’s wavelength leads to decreasing

of the fundamental mode’s effective index as shown in Fig. 5.5. Substrate material

impact also matches the simulation. Waveguides, based on PMMA material tend

to have higher effective indices due to the smaller difference between its refractive

index and the ink than in silica-based waveguide. The thickness of the ink layer and

effective index measured values correlation is uncertain and does not fully meet the

expectations shown in Fig. 5.5. This can be explained by small changes in laser

position during measurement process because of not perfect table rotations that

affect coupling and therefore overall mode distribution picture. The second reason

is thickness fluctuations a mismatch between the real thickness of the samples and

simulated.

24

Figure 5.5: Measured effective indices of the fundamental modes with differ-

ent polarizations at three wavelength. a) TE polarization, PMMA substrate,

b) TM polarization, PMMA substrate, c) TE polarization, fused silica sub-

strate, d) TM polarization, fused silica substrate.

A number of modes of all ten different samples at three wavelengths were ana-

lyzed to get a better understanding of the difference between two substrates. Fig.

5.6 below represents how a number of modes changes with the thickness and wave-

length. Despite the fact measured data curves do not give an almost linear tendency

of a number of mode increment like in simulated data, it clearly shows that the larger

core layer gives a greater quantity of modes propagating through the printed waveg-

25

uides. Wavelength makes visible changes in the number of modes within a structure

which correlates with the simulations. The small difference from the expected data

and some fluctuations are the cause of the expected and real thickness mismatch as

well as the aforementioned laser position error.

Figure 5.6: Measured number of modes for different polarizations at three

wavelength. a) TE polarization, PMMA substrate, b) TM polarization,

PMMA substrate, c) TE polarization, fused silica substrate, d) TM polar-

ization, fused silica substrate.

During mode observation thickness values of all ten samples were calculated by

the software comparing two adjacent modes. The mean value of the data obtained

26

at various wavelengths for two different polarizations for each sample was then com-

pared with the expected data. The results are represented in Fig. 5.7. As can be

seen at some points measured data does not meet the expectations. This mismatch

is determined mostly by the mode observation error discussed above. However, the

overall picture correlates well with the supposed thickness of the films.

Figure 5.7: Measured and simulated thickness comparison.

The refractive index of the ink was measured in a similar way, using two adjacent

modes and then compared with the data, calculated by the given formula 5.1 given

by LUXeXceL. Fig. 5.8 represents the difference between measured and simulated

data as well as the Cauchy model. Colored dots show a mean value of measurement

result for each sample at all three incident wavelengths with standard deviation

included shown as error bars. The Refractive indices of the substrates were also

measured and compared to the database values, which is represented in Fig. 5.8 (b,

c). Measured data is close to the simulations and table values as well as plotted the

Cauchy model. Fluctuations of ink refractive index can be explained by the effect of

oxygen inhibition caused by the UV curing process was incomplete in some samples,

but prism coupler measurement errors are considered to have a higher effect on the

final refractive index curve.

27

Figure 5.8: Measured and expected refractive indices of the ink material (a),

fused silica (b), and PMMA (c).

28

Chapter VI

Conclusions

As expected waveguides manufactured using LUXeXceL 3D-printing technology are

the working optical components that are experimentally proved to guide electromag-

netic waves at three wavelengths 532 nm, 635 nm, and 1550 nm as shown on the

Fig. 5.3, 5.5 and 5.6. Samples based on fused silica substrate tend to have smaller

effective indices and a higher number of modes what is caused by the lower refrac-

tive index of this substrate. Despite the measurement data does not fully meet the

simulations in both mode quantity and effective index studies, the overall picture

shows a tendency of effective index and number of modes increment with increasing

of the core thickness and decreasing of the wavelength. The main error comes from

prism coupler laser small disposition with the time as well as the difference between

expected data of the thickness and refractive indices of all three materials used in

simulations with the real ones, what is shown in the Fig. 5.7 and 5.8. The minor

errors may also come from the 3D printing process during UV curing, which could

not be fully performed on some samples causing oxygen inhibition and therefore

thickness fluctuations. Mode and material analysis done in the work as well as real

photos of the obtained waveguide structures (Fig. 5.3) show the possibility of LUX-

eXceL 3D-printing technology to manufacture working components for integrated

optics.

In this work 10 different waveguide samples fabricated using Luxexcel 3D-printing

technology were experimentally and numerically studied to test the ability of addi-

tive manufacturing to produce working optical components for integrated optics .

2 different materials, PMMA, and fused silica were used as a substrate to print 5

samples with a wide range of core layer thicknesses (10, 15, 20 and 30 micrometers)

29

on each substrate.

Simulations were performed using 1-d mode solver software. Numerical analysis

has shown a clear influence of the thickness of the film layer of the printed waveg-

uides, a substrate on which this layer was printed, and incident wavelength of the

conveyed light on the mode behavior of the structure. The effective index grows

with the increment of the core thickness. The growth becomes more explicit as the

wavelength increases. Thickness affects the effective index only before 10 microme-

ters. After that point core layer thickness does not make any significant change to

the mode behavior. Samples printed on the PMMA substrate tend to have slightly

higher effective indices than fused silica samples. It is more prominent for higher

wavelengths. A number of modes values depend linearly on the thickness and the

slope of this line becomes larger with a higher wavelength. This slope is even higher

for the fused silica samples. Although, the lower thicknesses substrate does not make

a significant impact.

Waveguides were printed layer by layer using capillary bridges technique. Each

printed layer had a thickness of 5 micrometers. A visible track of laser light of

wavelengths 636 nm and 532 nm could be observed on obtained samples which

serves as an indicator of electromagnetic wave confinement within slab waveguides.

This underlines the capability of Luxexcel 3D-printing technology in making working

devices.

To evaluate the exact properties of obtained structures such as effective indices, a

number of propagating modes, refractive indices of the substrates, and core layers, as

well as core layer thicknesses prism coupler device, was used. Experimental results

have shown that a higher wavelength always leads to the lower effective index in

all 10 samples. This is related to the inverse correlation between the propagation

constant and therefore effective index with incident wavelength. The relationship

between thickness and effective index obtained experimentally is not clear. It was

caused by several factors. Firstly, the thicknesses of the resulted layers differ from the

simulated ones. Secondly, there is a certain error during effective indices observation

related to the precision of the laser light that affects coupling into the film since the

laser points in slightly different points of the prism every. Data has shown that this

error has the most impact on the measurements at the lower wavelengths, 532 nm,

and 635 nm. This is related to the less abrupt change of effective indices of the

fundamental modes in relation to the thickness change at these wavelengths.

30

Despite the printer showed the consistency of the results, there are some fluctua-

tions between the experimental and expected thicknesses of the structures, although

dependency is linear as expected. Experimental thicknesses tend to be less than

expected in all 10 samples regardless of their thickness of substrate material. This

problem is related to the aforementioned issue with laser position as thickness and

refractive index values are calculated using effective index data. Every small change

in the laser beam direction led to little changes in the overall mode distribution

picture. Thus, considering the number of rotations this continuously increased the

error. This error also continues to grow with the addition of each new layer what

can be an important factor to consider while printing multimode waveguides with

a large thickness of the core. The error tends to reach 4 um which is close to the

thickness of 1 printed layer. Refractive index values do not deviate much from the

table values in case of substrate materials and theoretically calculated values in case

of the core.

Results show the ability of LUXeXceL 3D-printing technology to manufacture

working slab waveguides. Both substrates, PMMA, and fused silica are suitable for

manufacturing. Although there are still issues with the accuracy of the thickness

of each printed layer, such technology can be used for fabricating waveguides for

integrated optics.

31

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35