waveguides report

7/31/2019 Waveguides Report

1/32

1

Metal clad symmetric waveguides: properties and their use forthe determination of dc Kerr coefficients of organic films.

Jonathan Cornish

Project report 2011-2012Supervisors: Marek Szablewski and Graham Cross.


2/32

2

Abstract

The properties of fabricated metal clad symmetric waveguides are examined in termsof the variance of structure, cover layer thickness, film thickness and film thicknessuniformity. The materials used as film layers are PMMA (polymethylmethacrylate) dopedwith MOR 2 and IPDI (polydicyanovinyl isophoronediisocyanate). Silver is used as the coverand cladding layers. Glass is used as the base layer and for coupling light from in onestructure type (base coupled), whilst air is used for coupling light from in the other structuretype (free space coupled). Analysis of their ATR spectra at 632.8nm is carried out, allowingthe achievement of up to 83.40.1% light coupling, single mode waveguiding, film heightuniformity analysis, and dc Kerr effect analysis. Free space coupled structures with silvercover layers of ~24nm are found to be of most use for dc Kerr anaylsis.

Microscopic flaws in film layer quality restrict dc Kerr analysis to only one of many

fabricated waveguides. Upper bounds for to and and therefore a range for the dc Kerrcoefficient are found for 0.8050.006% w/w doped MOR 2 in isotropic PMMA. These boundsare and for and respectively, leadingto a range for the dc Kerr coefficient of . This range implies thatdoping MOR 2 into isotropic PMMA at 0.8050.006% w/w does not significantly change thedc Kerr coefficient compared to undoped isotropic PMMA.

Acknowledgements

I would very much like to thank Dr. Szablewski for being always supportive and

helpful with regard to carrying out the project, but more so for just being easy to talk to andhaving a good sense of humour. I would like to thank Dr. Cross for always being availablefor discussion with regard to the operation of waveguides, and again for having a good senseof humour. I thank the lab technicians as they always made borrowing equipment easy, andespecially Duncan McCallum, for his constant help with regard to making my experimentssafe. My housemates were supportive as always, and were always open to letting me talk indetail about how my project was going, while even at points seeming genuinely interested,for these reasons and more, I thank them.


3/32

3

Contents

1 Introduction

2 Theory

2.1 Waveguide theory2.1.1 Ray optics model

2.1.2 Effective refractive index and propagation constant

2.1.3 EM field model

2.2 Waveguide coupling techniques

2.3 NLO origins and effects

2.4 Organic NLO materials

3 Experimental3.1 Fabrication

3.1.1 Preparation of solutions

3.1.2 Waveguide structures and cleaning

3.1.3 Deposition of silver layers

3.1.4 Formation of thin films

3.2 ATR technique

3.3 Film thickness measurements3.4 Absorbance spectra

3.5 dc Kerr effect measurements

4 Results and discussion

4.1 Absorbance spectra

4.2 Unsuccessful waveguides

4.3 Successful waveguides

4.4 Film thickness measurements and code generated ATRs4.5 Variance of structure type

4.6 Variance of cover layer thickness

4.7 Single mode waveguides


5 Conclusion


4/32

4

1. Introduction

Telecommunications sees the widespread commercial use of waveguides. This is dueto the low loss with which optical light can transfer information over long distancescompared to electronic signals in copper wire [1]. Developments into increasing bandwidthfor fibre-optic communication were needed and were continuously being made up untilrelatively recently [2]. Electro-optics has taken over research with regard to waveguides as itfound its home in the advent of laser technology. Being able to modulate the frequencyand/or phase of laser light is essential for mode locking and Q-switching in lasers, which isbought about with a NLO (non linear optical) material, with a waveguide used to couple thelaser light to it[3,4]. Due to the high sensitivity of metal clad waveguide mode angles andintensities to anomalies in the film or cover layer quality, single mode waveguides can alsobe used as biosensing devices [5].

Waveguides trap light to propagate along one direction within the guiding layer.Ways to couple light to a waveguide include end fire coupling[6], tapered film coupling[7],grating coupling[8] and prism coupling[9]. However in 2003 using metal clad symmetricwaveguides, a new method to couple light to a waveguide from free space wasinvestigated[10]. This report looks to experimentally explore the coupling of such metal cladwaveguides whilst also briefly investigating the theory that allows them to operate.

The experimental procedure for analysing waveguides will be to obtain theirAttenuated-Total-Reflectance spectra (ATR) [ adam ], as this method allows a very sensitivemeasure of the mode angles of the waveguides. ATR spectra allow experimental analysis for

coupling by varying different properties of the waveguides. This report will analyse thevariance cover layer thickness, film layer thickness and structure type on the ATR spectra thewaveguides. Through the variance of these different parameters, a single mode waveguidewill be attempted to be fabricated and coupling efficiency will be optimised. ATR spectra canfurther be used for sensitive thickness measurements of the film layer [ balthazar ], but aremostly for the investigation of NLO effects [ chrome ].

Once the ATR spectra of fabricated waveguides have been obtained, they will be usedfor the measurement of the NLO properties of the guiding materials. The materials used willbe organics as these types of materials have typically large NLO susceptibilities, fast NLOresponse times and can be spin-coated allowing ease of fabrication [11]. In the literatureorganic materials used in conjunction with waveguiding can be seen in electro-optic devices[dandilion ], but also in other devices such as for lighting [ excelsior ] and for photovoltaic cells[flutter ].

The NLO effect investigated in this project will be the dc Kerr effect, a third orderNLO effect. Although typically third order effects are of little importance for consideration of materials for integration into devices, an appreciation of the third order polarisability of amaterial allows a more discerning approach to appropriate material choice [ tyrant ].

2. Theory


5/32

5

2.1 Waveguide theory

The different types of waveguide differ mostly on how they couple light to the filmlayer; not in the fundamentals of how they operate[11]. Waveguides confine visible (and nearvisible) electromagnetic waves to propagate in one direction, with the electric and magneticfields confined to oscillate inside the film layer of the waveguide. EM waves propagatingwith no magnetic field in the propagation direction are labelled transverse magnetic (TM)modes, whilst those that propagate with no electric field in the propagation direction arecalled transverse electric (TE) modes. This project is concerned with general slab waveguides,and as such will discuss the guiding theory behind these waveguides but it should be notedthat this theory can be applied, without much deviation, to any other waveguide type.

Slab waveguides consist of three layers, a cover layer, a film layer and a substratelayer. The light is coupled by a number of methods from outside the waveguide through thecover layer and into the film layer, which then guides the light along it.

There are two ways to mathematically analyse the process of waveguiding. One is totreat light as rays and to solve the problem in terms of optical geometry. The second is toconsider light as EM fields and therefore solve Maxwells equations ins ide the waveguide.

2.1.1 Ray optics model

Slab waveguides, as can be seen in Fig. 1, operate by repeated total internalreflection at the film-cover and film-substrate layer boundaries respectively. Exceeding thecritical angle is not the only requirement for waveguiding to occur. Only waves that

constructively interfere with their repeated reflections can waveguide. Only certain angles of incidence allow this constructive interference; these are called the waveguide modes. Fig. 2shows constructively interfering waves being guided without loss.

From Fig. 2 it can be seen that is subject to certain conditions if it is to be anallowed mode of the waveguide. After two reflections, i.e. from the point to in figure 2, itis clear that the two rays must be in phase with one another so that constructive interferencecan occur. This implies:

where is the mode order , is the phase change between the ray

travelling from points a and b, and is given by [12]:


6/32

6

Figure 2.1.11: A diagram to show the basic symmetric slab waveguide, showing repeatedtotal internal reflection at both film layer boundaries, with i having to be greater than C forthis to occur. The waveguide is symmetric, meaning that the cover layer and the substratelayer have the same value for permittivity. The coordinate system used throughout this reportis that quoted here; propagation along , waveguide thickness along and width of devicealong . This diagram was self-made.

Figure 2.1.12 [5]: A diagram showing a ray optics model of the operation of a waveguide.Only rays that constructively interfere along the waveguide are allowed modes of thewaveguide. and are the phase changes induced in the ray at reflection. This project

only considers symmetric waveguides, such that .

where is the thickness of the film, and is the refractive index of the film.

The phase shift, , can be found to be [12]: [() ] with being the refractive index of the cover layer and being an indicator for whether T Eor TM modes are being considered, with =0 for TE and =1 for TM.

Subbing in 2.1.13 and 2.1.12 into 2.1.11 leads to the full transcendental equation:


7/32

7

[() ] from which it can now readily be seen how the mode angle, depends only on , , ,

, and .

2.1.2 Effective refractive index and propagation constant

The discrete angular modes of a waveguide govern the phase velocity at which thelight within the waveguide travels. This can be seen in equation 1.4, as the term actsas a refractive index that is dependent on mode angle. This term is called the effectiverefractive index of a mode, , and is defined thus:

where is the propagation constant assigned to each mode, and is defined as:

where is the phase velocity of the light guided by a particular mode.

2.1.3 EM field model

The problem of a waveguide can be approached using Maxwells equations.Assuming no free charges exist within the waveguide system, one can use Maxwellsequations to arrive at the wave equations for the electric field and magnetic field of lightpropagating through the waveguide:

where

and is assumed to be unity for these materials as they are not

appreciably magnetic. Using the same coordinate system seen in figure 2.1.11, it can besafely assumed that for in a slab waveguide, when the electric field (equation 2.1.31) ormagnetic field (equation 2.1.32) is polarised along , then:

Equations 2.1.33 and 2.1.34 lead to Maxwells equations being divided into two sets;

one in which there is only an E-field along and H-fields along and (TE), and one inwhich there is only an H-field along and E-fields along and (TM).


8/32

8

Figure 2.1.31 [5] (modified): The E field profile for the TE modes m=0 and m=1 of ametal clad waveguide configuration. TM modes exhibit similar behaviour, only that the H

field has a larger field in the substrate and cover layers, and thus have a slightly differentshape to the E field profile.

Substituting in a plane wave solution to solve the wave equations under theseconditions yields sinusoidal solutions for (TE) or (TM) along in the film layer andexponentially decaying functions for the field in the cover and substrate layers, as seen infigure 2.1.31. Applying the boundary conditions that phase, amplitude and the gradient of thefield are conserved across the boundaries between layers leads to eigenvalue equations forsymmetric and anti-symmetric TE and TM modes.

Applying the condition that the wave propagates in phase between two total internalreflections leads to allowing the rearrangement of any of the eigenvalues equations to be of the form [ jackhammer ]:

() where and . Note that this equation is exactlythe same as equation (2.1.14).

2.2 Waveguide coupling techniques

As mentioned previously, there are several ways to couple light to a waveguide. Theprism coupling technique is most similar to the coupling techniques investigated in this report,so it is useful to investigate for analogies to be drawn, and for the power of the free spacecoupling technique to be seen. The technique setup can be seen in figure 2.21.

The prism coupling method relies on the evanescent wave created in the air gap at thepoint where the incident light ray hits the edge of the prism. This wave allows the light to betransferred to the guiding layer and thus be coupled to the waveguide. The air gap then acts asa cover layer of the guiding layer where total internal reflection can repeatedly occur. Careful


9/32

9

Figure 2.21 [10]: A diagram of the prism coupling method, where n 3 is the refractive index of the prism and 3 is the incident angle of the light to the guiding layer of the waveguide.

control of the air gap thickness allows for maximum light coupling from prism to guidinglayer to be achieved.

From solving Maxwells equations for this system, it is seen that o nly modes witheffective refractive index less than the refractive index of the prism are allowed:

Another limit is that the effective refractive index of modes is that they must lead to

solutions of Maxwells equations where the light propagates in the film layer but isevanescent in the air gap and substrate layer [12], with the allowed range being:

In analogy to the prism coupling layout we can see the metal clad symmetricwaveguide setup in figure 2.22.

When discussing light propagation properties of the various layers of the metal cladsymmetric waveguide, it is necessary for theory relating to the refractive index of a materialto be examined further. From equations 2.1.31 or 2.1.32 it can be seen that

However, equation 2.1.35 contains , not , so considering with regard topropagation properties instead of allows a more thorough approach. When considering itmust be noted that it has a real and complex part, and therefore so does the refractive index:

where is the real part and is the complex part of the relative permittivity, and isthe real part of the refractive index and is the extinction coefficient. The complex parts of and must be considered in this project due to metals tending to have

| |>

| |.


10/32

10

Figure 2.22: This diagram shows the free space coupling arrangement with the permittivity of each layer shown. It is analogous to figure 2.21, apart from instead of an actual prism, air actsas the prism layer. The silver cover layer is analogous to the air gap layer in figure 2.21, withthe guiding and substrate layers being identical, other than that the substrate and the guidinglayer have the same permittivity 2. This diagram was self made.

Although the real and complex part of are functions of the wavelength of thepropagating wave, the only wavelength considered in this project is that of a HeNe laser(632.8nm). For silver at the HeNe wavelength, and [micheal ].Substituting in these values into equation 2.24 yields and .

Numerically solving equation 2.1.35 for as negative for the cover and substratelayers leads to a much broader range of allowed [10]:

This result is significant because it allows the refractive index of the film investigatedto be arbitrarily small. It also allows the study of modes where the effective refractive indexis less than 1. F or the free space coupling setup the prism used is air, thus only modes withan effective index less than that of air are allowed, as the condition seen in equation 2.21 stillholds [ jackhammer ].

2.3 NLO origins and effects

When an electromagnetic field is incident onto any material, the bound charges thatmake up that material respond to it. For most materials, these bound charges are chargesfound in atoms. The Electric part of the EM field is absorbed by these charges and they thenare displaced. The relationship between the applied field and the charge displacementinduced in the material is the polarisation of the material, . For optically linear materials therelationship between and the applied E-field is linear, related simply by the permittivity of free space and the linear susceptibility of the material, (1). The energy absorbed is thenemitted radiatively or non-radiatively.

If the material emits on radiative modes, and is homogeneous and isotropic, the fieldthen travels through the material in the same direction it entered. However the wave travels


11/32

11

slower through the medium than through a vacuum, due to the time spent through absorptionand re-emission. The ratio of the speed of light in a vacuum to that of the speed of light in amaterial is that materials refractive index, .

If the charges in the material emit on non-radiative modes, through heat dissipation,then some energy from the travelling EM wave is absorbed in the material. The absorption of the material is then the ratio of light exiting the material to the amount that entered it, divided

by the materials thickness.

The refractive index and absorption of a material are linear properties, but can beinfluenced by higher order effects. Non-linear properties of a material come about when theresponse of the charges within a material respond to an applied field is higher than first order.This occurs for any material if either the incident light field strength or an applied potential ishigh enough, but for some materials NLO effects can be seen due to the nature of its boundcharge, not only due to field strength. The polarization of a bound charge in a material can beexpressed as a Taylor expansion to see the whole range of response orders:

where is the permanent dipole moment of the bound charge, is its linear polarisabilityand and are the second and third order polarisability (also called first and second orderhyperpolarisability). Macroscopic polarisation of the material can be written in a similarmanner:

where is the permanent polarisation of the material, , , and are the linear,second order and third order susceptibilities respectively. These E-fields can oscillate or beconstant, so different kinds of second and third order effects exist depending on thefrequencies of the fields.

The dc Kerr effect, investigated in this project, is the variance of the refractive indexof a material proportionate to the square of an applied electric field. In order to measure thiseffect, any second order effects must be taken into account as they are typically far strongerthan third order effects [ George ]. However, ensuring that samples used are centrosymmetric

prohibits second order effects from manifesting as only non-centrosymmetric materials willshow even orders of susceptibility[13], whereas all materials show odd orders of susceptibility.

The dc Kerr effect ma kes a material birefringent if it otherwise wouldnt have beensuch that the change in refractive index between incident light perpendicular and parallel toan applied field is given by:

where is the difference between the refractive indices, is the Kerr coefficient for amaterial and is the magnitude of an applied dc electric field.


12/32

12

The change in refractive index in the direction of the film layer of a waveguidewhen subjected to a dc electric field is given by [ marvellous ] (for full derivation seeappendix):

where for TM modes and for TE modes. The quadratic electro-optic coefficientrelates, under isotropic conditions, to the third order susceptibility :

The dc Kerr coefficient for a material can be gained from and from:

The Kerr effect can be observed using the ATR spectra obtained from this project, asthey are sensitive to small changes in refractive index of the film layer [14]. Once a mode dipin an ATR spectrum has been found, choosing an angle, , at which the gradient of the dipin reflectance is approximately linear, it can be shown (see appendix for full proof) that achange in refractive index in the film constitutes a measurable change in reflectance[marvellous ]:

where is the change in reflectance, the linear gradient is given by and isthe change in the refractive index of the film.2.4 Organic NLO materials

In non organic crystal structures there is a rigorous approach as to the crystal groupsthat are non-centrosymmetric and which are not, from analysis on the lattice groups and theirstructures [13].

With organic materials however, there is not such a rigorous approach. Using guest-host organic systems allows one to investigate the effects of altering the Kerr coefficient of amaterial by doping it with small molecules. The guest-host system of PMMA (poly(methylmethacrylate)) doped with the chromophore MOR 2 is chosen for this project for this reason.The other organic material chosen for this experiment is the side-chain polymer IPDI(polydicyanovinyl isophoronediisocyanate).


13/32

13

Figure 2.41: The three organic materials used in this project. a) Is the side-chain polymerIPDI (polydicyanovinyl isophoronediisocyanate). b) Is the host polymer PMMA(polymethylmethacrylate). c) Is the guest small molecule MOR 2.

From figure 2.41 it can be seen that IPDI and MOR 2 have a section of their molecularbuild that is connected by conjugated bonds and section that is not. This change in mobilityof the electrons within the bonds is what leads to these materials having highhyperpolarisabilities [ reference here would be nice ] and is harder to achieve in inorganicmaterial structures [ all day mate ]. It should also be noted that as the electrons that oscillatesubject to incident light are mobile through conjugated bonds, they are a lot more free to

move than in the inorganic case and thus allows them a faster response time [ all bloody day ].

3. Experimental

3.1 Fabrication

All of the following procedures for fabrication were conducted in a clean room withfull clean room equipment worn: goggles, gloves, full body suit, clean shoes and a clean hat.

Due to the very sensitive nature of waveguides to contaminates, two waveguides weremade of every different type listed in this section.

3.1.1 Preparation of solutions

The two different waveguiding organic systems had to be prepared in solution suchthat they could be spin-coated to form the film layer of the waveguides. The glass vials thatthe solutions were made in were first extensively cleaned. This entailed washing indicholoromethane (DCM) and wiping with dust free dry medical wipes, then washing inisopropanol (IPA), then washing and sonicating in deionised water for 20 minutes, beforefinally blow drying with dry oxygen free nitrogen. The solutions, once made, were stirredmagnetically over night and covered in tin toil to avoid photo degradation [ probably ].


14/32

14

Name of soln.

MOR2mass

(0.0001)g

PMMAmass

(0.0001)g

Amountof solvent(0.1)ml

Solutionconc.

% w/wDoping conc.

% w/wPMMA1 0.0240 2.0102 10.0 21.5(0.2) 1.194(0.005)PMMA2 0.0134 1.6642 7.0 25.4(0.3) 0.805(0.006)PMMA3a 0.0084 1.9010 7.0 28.9(0.3) 0.442(0.005)PMMA3b 0.0090 2.0401 10.0 21.7(0.2) 0.441(0.005)PMMA4 0.0050 2.2900 7.0 34.7(0.3) 0.218(0.004)PMMA5 0.0000 2.1454 10.0 22.7(0.2) 0

Figure 3.1.11: A table showing all appropriate characteristics and their errors of the solutionsmade for the guest-host system of MOR 2 doped in PMMA. The solvent used was DMF.

Name of

soln.PDCV-IPDI

mass (0.0001)gAmount of

solvent (0.1)mlSolution

conc. % w/wIPDI1 0.5820 4.0 29.20.7IPDI2 0.4222 2.5 17.90.7

Figure 3.1.12: A table showing the appropriate characteristics and their errors of the solutionsmade for the side-chain polymer PDCV-IPDI. The solvents used were cyclohexanone forIPDI1 and DMF for IPDI2.

To investigate the effect of varying different parameters of the film layer of thewaveguides, several solutions were made comprising of the two organic systems used in thisproject. The solutions relating to the guest-host system of MOR 2 doped in PMMA can beseen in figure 3.1.11, while the solutions relating to the side-chain polymer PDCV-IPDI canbe seen in figure 3.1.12.

3.1.2 Waveguide structures and cleaning

ISO 8037 glass slides were cut into thirds using a glass cutter and a straight edge toform the base for which the waveguides were constructed. The slides were cleaned in thesame manner that the glass vials were cleaned in section 3.1.1. All washing and drying wasconducted by holding the edge of the slides with fingers with nitrile gloves on. The surfacesof the slides were never touched except when wiping.

Two different structures were fabricated for these waveguides. The free space coupled

method [10], and a base coupled structure that is similar to prism coupled structures seen inthe literature [9]. The specific layouts of these structures can be seen in figure 3.1.21.

In order for the metal cladding layers to act as electrodes they had to be deposited in apattern such that they overlapped in the centre of the slide but nowhere else, as shown infigure 3.1.22. For a contact to be made with the first deposited silver layer, the film layer hadto be removed. This was done by carefully soaking the edge of the structure in chloroform forapproximately 10 seconds, then gently wiping away the film with a lint free dry medical wipe.


15/32

15

Figure 3.1.21: Free space coupled and base coupled structures are shown, with the arrowsbeing the incident light to the waveguides. The nature of the various layers is discussed in fullin this section. Right at the end, put in some labels for the cover layers .

Figure 3.1.22: The specific structure of the waveguides in order for the substrate and coverlayers to act as electrodes. The film layer on the left edge would have to be removed for aconducting contact to be made.

3.1.3 Deposition of silver layers

The initial layers of silver were deposited on the centre of the glass slides using aBOC Edwards evaporator. This evaporator achieved a pressure around 10 -5 Torr (1 Torr =1/760 Atm), by utilising first a mechanical backing pump to achieve around 10 -1 Torr, then anoil diffusion pump to raise the vacuum higher. Silver was thermally evaporated by use of acurrent of 25(1)A being passed through a molybdenum boat containing a silver coil. For 5seconds the covering baffle was closed to allow imperfections to be cooked off. It was thenopened to allow deposition of silver onto the glass slide.

Deposition thicknesses used for fabrication were 11.2, 18.0 and 24.0 (0.1)nm for thecover layer, whilst thicknesses mostly of more than 200nm were used for the substrate layer.A quartz crystal vibration detector was utilised to measure the thickness of the depositedlayer. Controlling the thickness accurately was challenging due to there being a delaybetween the baffle being closed and the thickness meter showing an invariant value, thusseveral thicknesses evaporated differed slightly to these cover layer values.

The deposition rate of the silver is proportional to the magnitude of the currentflowing through the molybdenum boat [reference mother fuckeerrrrr] . At a current of 25(1)A


16/32

16

the deposition rate was observed to be approximately 0.1nms -1. This was the slowestdeposition speed that could be obtained, as below this rate the amount of current flowingthrough the boat fluctuated too wildly. The slowest and most steady deposition rate arepreferential because this ensures a common density of silver perpendicular and parallel to

deposition does it? . A slight flaw of vapour deposition is that the deposition will always be atits highest rate at the shortest distance between the boat and the sample [reference that shitagain, yo] . This is anticipated in the design of the evaporator, with the distance between thesample and the boat large compared to the size of either.

3.1.4 Formation of thin films

The thin polymer films formed in this project were spin coated. To ensure as littlecontamination as possible, the slides were immediately placed from the evaporator to the spincoater after the first silver layer was deposited. The spin coater had an environment of nitrogen gas constantly pumped through it to further prevent contamination to the waveguide.The slide was held in place by vacuum.

Millipore 0.50m hydrophilic PTFE membrane with 1.0m APFB glass fibre pre-filter filters were used when depositing around 0.5ml of the solutions through syringes ontothe thin silver cover layers for spin coating. The drops were deposited directly onto themiddle of the slide, with the pre-programmed spin session started immediately after the dropsfell to ensure even consistency of solution after spinning. The spin coater used was the LaurelWS-400 Lite series spin processor. Final spin speed and solution concentration have beenshown to be the most important factors for thin film thickness [15], so the exact amount of

solution deposited each time did not need to be carefully measured. 0.5ml seemedapproximately enough to give a full coverage whilst not being too much to waste the solution.

It was found that 1300rpm for 15.0s seemed appropriate for allowing the variance of film thickness by solution strength, apart for when attempting to fabricate a single modewaveguide, where 1600rpm was used.

Post spin coating the slides were immediately placed in an oven at 80(10) Co whichwas then immediately placed under vacuum for at least two hours. This ensured the solventwas evaporated, leaving only the organic material. The last few steps were done as quickly as

possible such that there was as little contamination as possible amongst the waveguide layers.All moving of the glass slides at their various stages of housing the waveguides were

done delicately but quickly with tweezers at the very edge, making sure not to touch thecentral part where the overlapping of the silver cladding was located. After completingfabrication, the waveguides were stored in small slide containers and then wrapped inaluminium foil to avoid photo degradation.

3.2 ATR technique

As explained in the theory section, modes of the waveguide will be excited only if thelight incident is at the correct angle. The method to find these angles was the ATR method.


17/32

17

Figure 3.21: The experimental set up used to obtain angular reflectance spectra.

From figure 3.21, the arrangement of rotating the sample degrees and rotatingthe photodiode degrees can be seen. The laser used was a polarized HeNe 632.8nm 5mwlaser. The polariser used that was calibrated such that at 0 the E-field of light passingthrough it is along . Thus rotating the laser until a maximum intensity was found when thepolariser was set to gives TM mode propagation in the waveguide. Setting the polariser to

and finding the maximum intensity ensures that the H-field is along and therefore gives

TE mode propagation in the waveguide.The laser was initially set up so that the beam was directly normal to the polarizer and

waveguide. This was accomplished by observing the reflected beam returning to the lasercavity exactly. A set square was used to measure the height at which the laser beam was withregard to the optical bench at various points along the lasers path to ensure that there was nopitch angle between the laser and the sample, and that the beam would always be, as much aspossible, incident on the same part of the waveguide.

The mount on which the sample was placed allowed for initial easy manoeuvrabilityand screws to tighten such that the sample could be firmly held in place at any pitch orperpendicular displacement with respect to the beam. This was necessary as probing thewaveguides for the best areas was common, where often some parts of the waveguides wouldshow light coupling while others would not, due to film quality variations.

The beam was positioned so that it passed exactly though the axis of rotation of thestage, and the photodiode was rotated around the same axis of rotation as the sample by beingattached to the goniometer, which for sim plicitys sake is not shown in figure 3.21. Theangular range measured for was from to .

To investigate deviation in measured current from the photodiode across the angularrange used for the ATR spectra, a waveguide was placed in the mount backward, acting as a


18/32

18

mirror. Once proper alignment had been achieved, it was found that the very slight variancesin measured photodiode current were only due to blemishes in the substrate layer of thewaveguide.

Noting the reading on the multimeter attached to the photodiode every half a degreeallowed angular spectra of current recorded by the photodiode to be constructed. To obtainthe reflectance spectra from the current spectra, the current readings were simply divided bythe highest current reading obtained, as this then amounted to unity reflection.

The laser had to be left on for several hours to reach and stabilize a maximum power.The light was on in the lab during all sessions to ensure t hat a persons pupils were small incase of accidental direct viewing on the laser, but as the class of laser was 3B the damagecaused by direct viewing is extremely low [ reference this surely ].

3.3 Film thickness measurements

A Taylor-Hodson tally step machine was used to measure the thicknesses of the filmsof the waveguides. This was carried out by carefully scratching off a small section of thepolymer film at a point on the waveguide, then subjecting that small section to the tally stepto measure the thickness of the film.

The spin coating technique for polymer solutions is known to give approximatelyuniform film height [reference it] but the edges of the slides were appreciably different inconsistency and thickness due to build up there, so the edges were avoided for tally stepmeasurements.

3.4 Absorption spectra

To ensure no absorption processes involved with the organic materials interfered withthe angular reflectance spectra, two samples were prepared as above but with no silver layers.The solutions used for these samples were PMMA3a and IPDI2. Absorption spectra werefound for both samples using a Shimadzu UV/VIS spectrometer.


As the Kerr effect is a very weak and quadratically dependant on an applied dcvoltage, a power generator producing voltages up to was used. As such highvoltages were used, the mount had to be completely shrouded.

The mount on top of the rotating stage was enveloped in a shrouded environmentconsisting of insulating plastic. The front was transparent and had a horizontal slit cut out asto not interfere with the incident and reflected laser beam. The plastic shroud had connectionsto crocodile clips inside the environment which were then attached to the electrodes of thewaveguides. The transparent front part was also removable to allow positioning of the sampleon the mount, but safety switches ensured a break in the circuit if the lid was off.

From equation 2.35, to maximise for a specific , needs to be maximised, andneeds to be minimised. Minimising is achieved by using the lowest


19/32

19

order mode available, while is maximised by finding the steepest mode dip in the ATRspectra. Thus specific modes from each ATR spectra will give the most sensitivemeasurement of the change in refractive index of a film layer, and these were found for eachwaveguide.

As commercial grade slabs of PMMA are known to have a low Kerr coefficient of ~ at 632.8nm [ tout ], too low to be seen with the setup in this report, analysiscan be carried out by varying the doping of MOR 2 in PMMA, to see if the Kerr coefficientcan be bought up to detectable levels of ~ . The Kerr coefficient of isotropic IPDIat 632.8nm can also be found if it is larger than ~ , as it is currently unknown. and can also be analysed for these systems to an accuracy of ~ , and giventhat other polymers such as polyimide have and of ~ [marvellous ], itdoes not seem unreasonable that analysis can be carried out.

4. Results and Discussion4.1 Absorbance spectra

To ensure no absorption effects altered the ATR spectra such that reflectivity could bealtered without light being coupled to the waveguide, the absorbance spectra of solutionsPMMA3a and IPDI2 were obtained.

Figure 4.11: The absorbance spectra of PMMA3a and IPDI2. There is no appreciableabsorption at 632.8nm.

The HeNe laser used operated at 632.8nm, and from figure 4.11 it can be seen there isnegligible absorption at this waveglength for the host, dopant and side-chain materials. Thusabsorption effects can be ignored with regard to the ATR spectra.

4.2 Unsuccessful waveguides

Many waveguides initially fabricated did not show ATR spectra with reflectivity dips,indicating that no light was being coupled to the guiding layer.

0

0.4

0.8

1.2

1.6

2

300 350 400 450 500 550 600 650 700

Absorbance

Wavelength (nm)

PMMA3a

IPDI2


20/32

20

The first few waveguides were constructed with a cover layer of around 50nm. This isclearly thicker than the skin depth of silver at 632.8nm for this environment, as no couplingoccurred at all. It seemed prudent to investigate the effect varying the cover layer thicknesshad on the ATR spectra following from this, as the literature typically only uses thicknesses

of ~24nm [ ref ].More often the failure of waveguides was down to the quality of the film layer. In

some cases it could be seen that the film layer was inhomogeneous in thickness to anunacceptable extent, indeed for IPDI despite many waveguides being made whencyclohexanone was used as a solvent for its solution, none showed light coupling. Once DMFwas used as the solvent for it however, a smoother film could be seen as the comparison infigure 4.21 shows. Subsequently light coupling was observed for an IPDI film layer.

Figure 4.21: Photos of a waveguide using IPDI2 (left) and one made with IPDI1 (right). Itcan be seen that in the waveguiding section of the samples (where the silver layers overlap),that the IPDI2 film is a lot smoother than the IPDI1 film.

4.3 Successful waveguides

Although many fabricated waveguides were unsuccessful in producing ATR spectrathat correspond to waveguiding, enough were successful such that suitable analysis can bemade. The successful waveguides fabricated can be seen in figure 4.31.

Waveguidename

Solution Structure type Cover layerthickness(0.1nm)

Substratethickness(0.1nm)

WG1 PMMA3a Base coupled 11.2 208.5WG2 PMMA3a Base coupled 18.0 208.5WG3 PMMA3a Base coupled 24.0 211.2WG4 PMMA3b Free space coupled 11.2 320.0WG5 PMMA3b Free space coupled 24.1 217.9WG6 PMMA1 Free space coupled 23.9 209.4WG7 PMMA1 Free space coupled 24.1 204.4WG8 PMMA2 Free space coupled 23 239.4

WG9 PMMA4 Free space coupled 23.8 218.1WG10 PMMA5 Free space coupled 24.4 236.6


21/32

21

WG12 IPDI2 Free space coupled 11.4 211.1Figure 4.31: A table showing the successful fabricated waveguides. For film thicknessapproximations see section 4.31.

The substrate thickness for each waveguide fabricated varies considerably, however

as seen in section 4.2 that silver seemed to act as a mirror even when only 50nm thick , so toensure no substrate effects interfered with the investigation, only a minimum thickness of 200nm seemed necessary for the silver substrate layer.

4.4 Film thickness measurements and code generated ATRs

Only one film thickness measurement was made for each waveguide measured, but asfrom section 3.3 it is seen that as long as edge is not used to measure the thickness, thethickness measured and the thickness of the film at the waveguiding section should beapproximately equal.

As the TE modes and TM modes ATR spectra of the waveguides were not collectedat the exact same point on each waveguide, it can be seen whether the films areapproximately uniform in height. In all experimentally achieved waveguide ATR spectra,there was never a difference in the number of modes seen for the TE and TM spectra, exceptfor WG10. The TM modes were mostly seen at slightly higher angles than TE modes, whichis in line with theory [ reference ]. Thus although there are slight variations in film thicknessacross the waveguide, these variations are not enough to distort the shape of a dip in an ATRspectrum enough such that the equations seen in section 2.3 would not hold.

Analysing the spectrum of WG10 allows more specific analysis, as the permittivity of PMMA is known to be 2.217 at 632.8nm [ 4.42 ], and Taylor-Hodson tally step machine wasused to measure the film thickness at a point on the film layer, giving a thickness value of 3.250.01m.

The TM and TE mode dips from the experimental ATR spectra are very closetogether, implying a good uniformity of the film layer for WG10. However, for high anglesof incidence the laser beam was spread over a much larger area of the waveguide, andtherefore is subject to more changes in thickness. Thus the dip after 70 seen in the theorisedplot is barely seen in the experimental plot.

The theorised dips in figure 4.41 are not exactly in the same place as they arein the experimental dips, but they are very close. Comparing the angular difference for eachmode from theory and experiment allows a corresponding difference in film thickness to befound from equation 2.1.35, as tabulated in figure 4.42.

The average difference in film height from figure 4.42 is calculated as 0.64 m with astandard deviation of 0.62 m. This value and its associated error seem rather high given thatspin coated polymer layers are categorised to be approximately uniform in height seen insome section or paper . This can be accounted for by recognising that the experimental ATR


22/32

22

Figure 4.41: A plot of the experimental and theoretical ATR spectra for WG10. Filmthickness of 3.25m was used for the theoretical plots. The experimental TE and TM ATRspectra were obtained from different points on the waveguide. The error bars are shown, butare all smaller that the shape that contains them.

Mode number Absolute differencein mode angle ()

Correspondingdifference in film

height (m)

TE3 6.40 0.54TM3 5.34 0.16

TE2 1.30 1.57TM2 2.03 0.18TE1 1.34 1.22TM1 0.89 0.15

Figure 4.42: A table showing the difference in coupling mode angle for the theoretical ATRspectra for WG10 using the film layer thickness as 3.25m. The equation 2.1.35 was used togenerate the corresponding film thicknesses for each angular mode separation. The errorsassociated with the mode angle difference and therefore film height difference are very smallcompared differences amongst the film height differences themselves, so they have not beendisplayed.

spectra are distorted by the film height changing across the spectra due to the spread of theincident laser light increasing for higher angles as previously mentioned, which cannot bemodelled by the code. This difficulty is overcome by using a laser with as small a beam widthas possible. Thus while it is definitely fair to say that there is an observed non uniformity infilm height across the waveguide, the value of 0.64m is an overestimate.

4.5 Variance of structure type

The glass base had to be extremely clean for the based coupled waveguides otherwisethe incident laser light would be unacceptably dispersed. It was thought that the base coupledstructure would have an advantage over free space coupled structure in that the thin silverlayer would not be exposed, and so would be less susceptible to degradation, however over

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70

Reflectance

Angle of incidence ()

Theory TE

Theory TM

Expt. TM

Expt. TE


23/32

23

Solutionstrength %

w/w

Normalisedsolution strength

(0.01)

Number of modes between

0 and 40

Structure type

TE TM21.5 0.2 0.62 1 1 free space21.7 0.2 0.63 1 1 free space22.7 0.2 0.65 2 2 free space25.4 0.3 0.73 2 2 free space28.9 0.3 0.83 8 8 base coupled

34.7 0.3 1.00 5 5 free spaceFigure 4.51: A table showing the difference in the number of modes seen in waveguides forincreasing strength of film solution with reference to their structure type. For simplicity of analysis the solution strengths were normalised with respect to the highest value.

the time frame of this project of approximately 20 weeks, the free space coupled structuresshowed no signs of degradation when exposed to air and being carefully moved around.

Total internal reflection within the glass base layer reduced the incident laser power tothe waveguide by around a half, so this led to the error on reflectance being doubled.Doubling the error on reflectance halves the sensitivity of waveguide to dc Kerrmeasurements and thus the base coupled structures are disadvantaged to the free spacecoupled structures from this standpoint.

Due to the refraction of the laser light through the glass base layer, the base coupledATR spectra angle of incidence to the waveguide only reaches a maximum of around 40 ,owhereas the free space coupled ATR spectra reach the full 73 obtainable with this setup. Asthe same amount of angular steps was taken for each, the base coupled structure allows betterangular resolution for the lower order modes. From equation 2.37 it is seen that higher ordermodes are more sensitive to changes in refractive index of the film layer, so these are of moreuse for Kerr shift measurements.

The largest difference between the structure types is the amount of allowed modesthat can be supported. As the refractive index of glass is higher than air, there should be alarger mode density for the base coupled structure than from the free space structure, as there

is a larger allowed mode range, which can be seen from equation 2.21.Given that all waveguide film layers were spin coated at 1300rpm, the strength of the

solution used for a waveguide is approximately proportional to the film thickness for thatwaveguide [ yep ]. In figure 4.51 it is seen that there are more modes over the same angularrange for the base coupled structure than for any of the other structures, regardless of solutionstrength. Even despite small discrepancies in the relation between solution strength and filmthickness, it is clear that the base coupled structure has a higher mode density than the freespace structure, as predicted from the restriction shown in equation 2.21.

From a theoretical standpoint the base coupled structure has some qualitiesconvenient for the observation of dc Kerr shifts, as they have a higher mode density which


24/32

24

leads to steeper mode dips and they also have better angular resolution. However, minimisingis important as seen from 3.5, so the limit of 40 of the ATR spectra observable

for the base coupled structure renders them not as useful as the free space coupled structure.In practise it was also more difficult to achieve deeper, more uniform mode dips from the

base coupled structures. Many base coupled structured waveguides fabricated showedcoupling of less than 10%, and usually only a few modes were seen rather than the amountexpected. These problems were due to the glass base layer needing to be extremely clean anduniform on both surfaces, which although was sometimes achieved, no difference in cleaningtechnique seemed to have a direct influence on the quality of the waveguides.

Free space coupled waveguides showed deeper, if not slightly less steep, angularmode dips, consistently achieving coupling of 40% or more. Indeed 83.40.1% coupling forthe 11.2(0.1)nm cover layer seen in figure 4.61 is surprisingly high given how easilycoupling is affected by contaminants leading to deviations in a smooth waveguide surface.

4.6 Variance of cover layer thickness

Silver cover layers of 50(0.1)nm were determined to be too thick to allow the lightthrough, as several waveguides were fabricated with both structures but no mode dips wereseen in their ATR spectra.

Varying the silver cover layer from 11.2 to 24.1(0.1)nm shows a largedifference in the shape of the mode dips seen in the ATR spectra, as can be seen in figure4.61. Although the TE mode dips have not been shown for clarity, their shapes were almostidentical to those seen in figure 4.61. The width of the mode dips for WG4 are clearly muchlarger than those of WG5, even to the extent that there is very close to a linear plot from thebottom of the dip to the beginning of the next.

The different shapes of the dips can be explained by the nature of how the lightcouples to the film layer from free space. When the metal cover layer is thick such that thereis only a small field tunnelled through to the film layer, propagation through the film layerbecomes very lossy even for small deviations away from a mode angle. If the cover layer isthinner and there is a larger field in the film layer, then more lossy modes can be sustainedfor longer, such that the mode dip shape is wider. There is a critical value for cover thickness

where the coupling is largest, where after which the dip will still continue to become widerbut will not get any deeper [ ref ]. This critical cover thickness value varies depending on thethickness and refractive index for each particular waveguide, and is clearly closer to 11.2nmthan 24.1nm from figure 4.61.

Although this is not shown in figure 4.61 due to slight variations in film thicknessoccurring even when the same solutions are used at the same spin speed, changing the coverlayer thickness should not alter the position of the mode angles [ ref ].

Varying the cover layer thickness for the base structured waveguides seemed to haveless of an obvious effect to that of the free space coupled structures. Figure 4.62 shows thatalthough the WG1 ATR spectra, with the thinnest cover layer of 11.20.1nm, had the deeper


25/32

25

Figure 4.61: The ATR spectra of WG4 and WG5 for TM modes only.

Figure 4.62: The TE ATR spectra of WGs 1, 2 and 3 between 11 and 24 .o Although themode dips were not perfectly aligned in the experimental data, they have been shifted here forease of mode dip shape analysis. These implemented shifts were no more than by 2 .o

mode dips as expected, there was little variance between the shapes of the dips for WG2 andWG3. WG1 is also seen to have the sharper dips of the three, which is unexpected. Areasonable explanation for these differences from expectation is that of non uniformity of theglass base layer, cover layer and/or film layer.

4.7 Single mode waveguides

Several waveguides were fabricated at 1600rpm with the most dilute solutions shownin figures 3.1.11 and 3.1.12 to try and achieve a film layer thin enough that would support

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80

Reflectance

Incident angle ()

WG4 TM

WG5 TM

0

0.2

0.4

0.6

0.8

1

10 12 14 16 18 20 22 24

Reflectance

Incident angle ()

WG1 TEWG2 TEWG3 TE


26/32

26

only a single mode. These very thin film layer waveguides did not show any mode dips intheir ATR spectra except for WG12.

Figure 4.71: The single TE mode and TM mode ATR spectra for WG12.

Although it is possible that there could be other modes in figure 4.71 that are notbeing seen by the experiment due to contamination, this seems very unlikely due to howsmooth the spectra are until the dip is seen for both the TE and TM case. Also the dips seenare wide as expected due to the cover layer for WG12 being only 11.4(0.1)nm. Thus it is

fair to say that WG12 is a single mode waveguide, and that the material IPDI can be madeinto a successful waveguide, just requiring DMF as the solvent and not cyclohexanone.


Unfortunately only one fabricated waveguide could be investigated for theobservation of the dc Kerr effect. This was due to their being a current flowing from thecover layer to the substrate layer of all other waveguides, such that no voltage could beapplied across the film layer of the waveguide. This seems to have been caused by very slightdeformations in the film layer of the waveguides, not noticeable when looked at by eye. As

this problem was unanticipated and due to the time constraints on this project, it was notpossible to fabricate more waveguides with thicker films in order to overcome this setback.Thicker film layers were not initially investigated due to them having many more modes, thusmaking their ATR spectra a lot harder to investigate or even to see at all, due to the angularresolution of the goniometer being 0.25 .o

WG8 however did allow a voltage of up to 200.0(0.1)V across it. The most suitablemodes were located and their gradients were found, as can be seen in figure 4.81.

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70

Reflectance

Incident angle ()

WG12 TE

WG12 TM


27/32

27

Figure 4.81: The TE and TM mode dips with the lowest values for in the ATRspectra for WG8. The places where the absolute value for are highest are where aretaken, and they are marked with vertical lines. These values are and

.

No change in intensity was measured at the angles seen in figure 4.81 from 0.00.1V

all the way up to 200.00.1V for TE or TM modes. This allows an upper bound of the dcKerr coefficient for this material and its associated error to be calculated. Taking inequation 2.35 to be the error on the photodiode leads to the upper bound on to be

and to be . From equation 2.36, thesetwo bounds give a range for for this film as . It seems fair to saythat this level of MOR 2 doping has not substantially changed the Kerr constant for isotropicPMMA, even despite there being possible density differences between the film layer in WG8and the commercial grade PMMA it is being compared to in section 3.5.

Calculating these bounds carried the assumption that the refractive index of the film

layer was the same as that of PMMA, just that it was given a 2% error. Given the doping wasonly 0.8050.006% w/w it seems reasonable that the refractive index of the film layerwouldnt change b y more than 2% of its value undoped [ the last one prob ]. The film height,

, was that obtained from the Tally-step method, and was given an error of inlight of section 4.4. The errors on and are very high, but would be reduced if betterangular resolution could be achieved.

5. Conclusion

The properties of metal clad symmetric waveguides were examined in terms of the

variance of structure, cover layer thickness, film thickness and film thickness uniformity.Varying these parameters allowed optimisation of the devices for several different uses. The

0

0.2

0.4

0.6

0.8

1

55 57 59 61 63 65 67 69

Reflectance

Incident angle ()

WG8 TM

WG8 TE


28/32

28

uses achieved/analysed in this report were; the successful fabrication and demonstration of asingle mode waveguide, achievement of a maximum coupling efficiency of 83.40.1%,insight into the film thickness nonuniformity associated with spin coating, and analysis of thedc Kerr coefficients for the organic materials used. Film layer quality often hampered

waveguide analysis; coupling efficiency is greatly reduced by contaminates and voltagescould not be sustained across the electrodes of all fabricated waveguides except one.

Upper bounds for to and and therefore a range for the dc Kerr coefficientwere found for 0.8050.006% w/w doped MOR 2 in isotropic PMMA. These bounds were

and for and respectively, leading toa range for the dc Kerr coefficient of . This range implies thatdoping MOR 2 into isotropic PMMA at 0.8050.006% w/w does not significantly change thedc Kerr coefficient compared to undoped isotropic PMMA. Greater angular resolution wouldhave allowed thicker films to be analysed with regard to the dc Kerr effect, increasing the

probability that film quality would be sufficient to sustain voltages across the metal cladelectrodes, whilst also allowing higher sensitivity of the waveguides to changes in refractiveindex, allowing more refined electro optic measurements of the film layers.

References

[1] Kapron et al., Radiation losses in glass optical waveguides , Applied Physics Letters 17 ,423 (1970)

[2] K. Satzke et al., Ultrahigh-bandwidth (42 GHz) polarisation-independent ridgewaveguide electroabsorption modulator based on tensile strained InGaAsP MQW, IEEEElectronics Letters 31 (23), 2030 (1995)

[3] J. J. Degnan, Optimization of passively Q-switched lasers , IEEE Journal QuantumElectronics 31 (11), 1890 (1995)

[4] L. E. Hargrove, R. L. Fork, and M. A. Pollack, Locking of He Ne laser modes induced bysynchronous intracavity modulation , Applied Physics Letters 5, 4 (1964)

[5] N. Skivesen, Metal-clad waveguide sensors, PhD Thesis, Riso National Laboratory(2005)

[6] D. Marcuse and E. A. J. Marcatili, Excitation of Waveguides for Integrated Optics with Laser Beams, Bell System Technical Journal 50 , 43 (1971)

[7] M. L. Dakss et al., Grating coupler for efficient excitation of optical guided waves in thin films, Applied Physics Letters 16 , 523 (1970)

[8] P. K. Tien and R. J. Martin, Experiments on light waves in a thin tapered film and a newlight wave coupler, Applied Physics Letters 18 , 398 (1971)

[9] D. Sarid, P. J. Cressman and R. L. Holman, High efficiency prism coupler for optical

waveguides, Applied Physics Letters 33 , 514 (1978)


29/32

29

[10] H. Li et al., Free-space coupling of a light beam into a symmetrical metal-claddingoptical waveguide, Applied Physics Letters 83 , 2757 (2003)

[adam ] S. B. Mendes et al., Broad-band attenuated total reflection spectroscopy of ahydrated protein film on a single mode planar waveguide , Langmuir 12 , 3374 (1996)

[Balthazar ] L. Lvesque et al., Precise thickness and refractive index determination of polyimide films using attenuated total reflection , Applied Optics 33 , 8036 (1994)

[chrome ] Y. Jiang et al., Low voltage electro-optic polymer light modulator using attenuated total internal reflection , Optics & Laser Technology 33 , 417 (2001)

[dandelion ] G. F. Lipscomb et al., Poled electro-optic waveguide formation in thin-filmorganic media , Applied Physics Letters 52 , 1031 (1988)

[excelsior ] H. Y. Lin et al., Improvement of the outcoupling efficiency of an organic light-emitting device by attaching microstructured films , Optics Communications 275 , 464 (2007)

[flutter ] S. Rhle et al., Optical waveguide enhanced photovoltaics , Optics Express 16 , 21801(2008)

[tyrant ] P. N. Prasad and D. J. Williams, Introduction to nonlinear optical effects inmolecules and polymers, Wiley, New York (1991)

[11] H. S. Nalwa, Organic Materials for Third-Order Nonlinear Optics , Advanced Materials5, 341 (1993)

[12] P. K. Tien, Intergrated optics and new wave phenomena in optical waveguides, Rev.Mod. Phys 49 , 361 (1977)

[ jackhammer ] H. Lu et al., Study of ultrahigh-order modes in a symmetrical metal-claddingoptical waveguide , Applied Physics Letters 85 , 4579 (2004)

[micheal ] P. B. Johnson and R. W. Christy, Optical constants of the noble metals, PhysicalReview B 6, 4370 (1972)

[13] M. Melnichuk and L. T. Wood, Direct Kerr electro-optic effect in non-centrosymmetric

materials, Physical Review A 82 , 13821 (2010)

[Probably ] Y. Ren, M. Szablewski and G. H. Cross, Waveguide photodegradation of nonlinear optical organic chromophores in polymeric films , Applied Optics 39 , 2499 (2000)

[George ] J. M. Hales and J. W. Perry, Organic and polymeric 3rd order nonlinear opticalmaterials and device applications , in S.-S. Sun and L. Dalton (eds.), Introduction to Organic

Electronic and Optoelectronic Materials and Devices , CRC Press, Orlando, FL (2008).

[marvellous ] J. Zhou et al., Determination of dc Kerr coefficients of polymer films with

prism-optical waveguide configuration , Applied Physics Letters 88 , 21106 (2006)


30/32

30

[14] Y. Jiang et al., Improved attenuated-total- reection technique for measuring the electro -optic coefcients of nonlinear optical polymers, J. Opt. Soc. Am. 17, 805 (2000)

[15] C. J. Lawrence, The mechanics of spin coating of polymer films, Phys. Fluids 31 , 2786(1988)

[4.41] J. P. Cresswell, Waveguiding in electrooptic Langmuir-Blodgett films, PhD thesis,University of Durham (1992)

[4.42] S. N. Kasarova et al., Analysis of the dispersion of optical plastic materials , OpticalMaterials 29 , 1481 (2007)

[tout ] K. S. Kim et al., Kerr effect in solid polymethylmethacrylate and polyethene , Journal of Applied Physics 54 , 449 (1983)

[last one prob ] N. A. Hackman, Nonlinear optical characterisation of organic chromophoresand aspects of molecular aggregation , PhD thesis, University of Durham (2001)


31/32

31

Appendix

How you worked out errors in section 4.4 lol I mean

Error propagation on theta:

The angular error used for the free spaced coupled method is 0.25 . This is due to 2having an accuracy of 0.5 ,o and so therefore the error on has half this value. This followsfrom error propagation analysis such that if

then,

where is the error on and is the error on and is a constant.

The angular error for the base coupled method requires more calculation. Given thatthe incident angle on the glass, , is related to the incident angle of the light on the

waveguide by

where is the refractive index of the glass and is assumed to be unity , then the error

on , , will be given as

where

and is the error on .

The error on and are propagated from the above error analysis rule seen in theabove section, but also the analysis such that if is a function of and that

then


32/32

Errors for upper limits on s 11 and s 12

The equation used to calculate the upper limit on s 11 and s 12 is as follows:

where all the variables have been previously defined, except is the chosen angle to use foreither the TM or TE mode, and is used as the error on the photodiode.

All the variables in this equation have associated errors except for . The methodsused to propagate these errors are the same as those used as those for propagating the errorsfor theta in the above section.

waveguides report

Documents