On super resolved spots in the near-field regime

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On super resolved spots in the near-ﬁeld

regime

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magniﬁcus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 08 april 2013 om 12:30 uur

door

Alberto DA COSTA ASSAFR ˜AO

Mestre em F´ısica

Universidade Federal de Juiz de Fora, Brazil geboren te Muria´e, Minas Gerais, Brazil

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Dit proefschrift is goedgekeurd door de promotor: Prof. dr. H.P. Urbach

Samenstelling promotiecommissie: Rector Magniﬁcus, voorzitter

Prof. dr. ir. H.P. Urbach, Technische Universiteit Delft, promotor Dr. S.F. Pereira, Technische Universiteit Delft, copromotor Prof. dr. C. Sheppard, Italian Institute of Technology

Prof. dr. P. Chavel, CNRS Palaiseau

Prof. dr. H.P. Herzig , Ecole Polytechnique Federale de Lausanne Prof. dr. J.J.M. Braat, Technische Universiteit Delft

Prof. dr. A. Gisolf, Technische Universiteit Delft

This work was supported by the European Community’s Seventh Framework Programme FPC7-ICT-2007-2, Surpass Project.

ISBN ??-???????-?

Copyright c 2013 by A.C. Assafrao

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the author.

A free electronic version of this thesis can be downloaded from: http://www.library.tudelft.nl/dissertations

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Aan Marieke en Noah Aan mijn Ouders en Zuster

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Cover:

The frontside of the cover shows a collection of measured spots, displayed in a three-dimensional plot, which were taken with a scanning near-field microscope. Under appropriated illumination conditions (that will be explored in this thesis), a ‘super resolved’ spot, i.e., a spot not limited by diffraction, can be generated in the surface of an indium antimonide sample, in a region referred as ‘near-field regime’. The backside shows an important experimental plot where the size of focused spots is plotted as function of the laser power. Below the red line tagged with squares, super resolved spots are observed.

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Introduction

1.1 Three generations of optical discs

After competing and winning the optical disc ‘format war’ against the HD-DVD (High Deﬁnition Digital Versatile Disc) [1], the Blu-Ray technology (BD), introduced in the market in 2006, is gradually replacing the Digital Versatile Disc (DVD). On its ﬁrst format, an optical disc could store a maximum of 74 minutes of music or 650MB of data on a single-sided disc with 12cm of diameter. Those are the well-known Compact Discs (CD). The following generation, the DVD discs, kept the same physical dimensions as the CD but are capable of storing nearly 5GB of data in one single layer. Double layered disc can, naturally, store twice as more. The current BD format can store up to 25GB whereas its defeated contender, the HD-DVD disc, could store 15GB.

Basically, the main diﬀerences among the three generations can be seen in Fig. 1.1. From one generation to another, the numerical aperture (NA) of the objective lens employed, deﬁned as NA = n sin θ (n is the refractive index of the medium and θ is the maximal angle of the marginal rays and the optical axis), was increased whereas the wavelength λ of the light employed was decreased. By doing so, the size of the focused spot, whose diameter is in the order of 1.22λ/NA, decreases, allowing for detection of smaller data marks [2].

Blu-ray Disc DVD CD λ=780 nm NA=0.45 1.2 mm substrate capacity 0.65 GBytes λ=650 nm NA=0.6 0.6 mm substrate capacity 4.7 GBytes λ=405 nm NA=0.85 0.1 mm cover layer capacity 25 GBytes

Figure 1.1: Three generations of optical data storage systems [3]. Higher capacities are achieved by decreasing the wavelength employed and increasing the NA of the objective lens.

From this simpliﬁed analysis, it is straightforward to conclude that one way to read smaller data marks is indeed by decreasing λ and increasing NA, as done up to now. However, a careful examination on the BD parameters reveals that the NA used has been pushed closer to unity (NA = 0.85) and, according to its deﬁnition, the numerical aperture in air has a maximum value

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2 Chapter 1 Introduction of one. Furthermore, the wavelength employed, λ = 405nm, corresponds to an affordable diode laser operating at low wavelength. Thus, it seems that a new generation of optical data storage (ODS) can not be achieved by increasing NA and decreasing λ, which forces the development of alternative techniques for breaking the diffraction limit imposed to the focused spot itself. Hence, super resolved spots (i.e. focused spots that are not limited by diffraction) that occurs in the near-field regime (i.e., in a sub-wavelength region in the vicinity of the focal plane) may represent a feasible solution for improving ODS systems. Before we further explore what these techniques are, few words about the project in which this work was carried out is appropriated to be given here.

1.2 The SURPASS project

The work described in this thesis was carried out within an European project named SUR-PASS (SUper-Resolution Photonics for Advanced Storage Systems). The technical scope of the project, initially proposed in 2008, was to develop a prototype of a high density optical disc by combining key technologies, namely, the Super-REsolution Near-field Structure effect (Super-RENS) [4, 5] and near-field readout with solid immersion lens (SIL) [6]. The objective was to increase the data storage capacity up to 200-400 GB for the next generation of optical disc, in an industrial-based type of research. However, following the withdrawal of the main industrial partner at the end of 2009 and due to the doubts whether there will be a completely new 4th generation of ODS or just an extension of the Blu-Ray format, the objectives of the project have evolved in a large part into a more academic-based type of research.

Hence, this work was done from this academic standpoint, and our main interest was to understand the basic optics behind the Super-RENS effect and micro solid immersion lens, and to be able to apply this knowledge to fields other than optical data storage. Specifically, we are mainly interested in investigating the near-field super resolved spot resulting from each tech-nique. Nevertheless, we will keep ODS as the background motivation, since the difficulties and limitations imposed to optical data storage systems are basically the same in many other optical systems. Diffraction limit is there!

1.3 Current optical data storage market

1.3.1 Video content distribution

High resolution pre-recorded video content distribution is very important in today’s world and this need will remain in the future. It is driven by the trends toward larger displays (high deﬁnition television or HD-TV), by the rapid growth of 3D games (on PlayStation 3 hardware and future generations) and the emergence of 3D video. Usually, video contents are distributed either by physical means or by internet. The distribution by internet of a high-quality video content requires per se a high bandwidth connection. Whereas the average connection speed reaches 10 Mb/s in Japan and 18 Mb/s in South Korea, it is limited to 6 Mb/s in the United States and it is much slower in developing countries. In Europe, the average connection speed is intermediate, up to 5-10 Mb/s in Sweden and in the Netherlands. In 2011, the United States rank only 13th in the world in average internet connection speed and is not making signiﬁcant progress in building a faster network [7]. On the other hand, it appears from a consumer study done by the Future Source Consulting Ltd., published end of 2011 [8], that HD-TV owners familiar with Blu-Ray discs are largely in favour of the format over downloading, because they

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1.4 What could be the 4th generation of optical discs? 3 like to own a physical mean that they can keep. In Fig. 1.2, the global market evolution of video distribution is presented, where a (slow) growth in BD video sales can be seen.

Online video Pay TV Blu-Ray DVD-Video (11%) (18%) (37%) (34%) 0 2000 2009 2010 2011 2012 2013 2014 2015 4000 6000 8000 10000

Retail Value (Euro millions)

Figure 1.2: Blu-Ray supporting the home entertainment industry, 2011 [8].

At the moment, there are mainly two possible physical means to distribute video-content: solid-state memories or optical discs. The cost per GB is clearly much more favourable to optical discs. Moreover, the main advantages of optical discs compared to hard drive discs and solid state are media removability and exchangeability, privacy and security, media longevity and low-cost.

1.3.2 Archiving

In the ﬁeld of archiving personal data, recordable and rewritable optical discs suﬀer from a large competition with portable hard drive disks and solid-state memories, which become more and more popular and present a rapid growth of their capacity. As a consequence, pursuing the work on WORM (write once read many) discs has become irrelevant.

1.4 What could be the

4

th

generation of optical discs?

1.4.1 New proposed technologies

Several technological options are pointed out as potential candidates for the next generation of ODS. Holography [9], data multiplexing [10], two dimensional optical storage [11], and near-ﬁeld recording [12] are among them. Although these techniques can increase the storage density, their drawback are extreme technical complexity, high system costs and lack of backward compatibil-ity. Therefore, the aforementioned drawbacks, combined with the slow growth of the Blu-Ray market, the competition with downloading and the competition with other types of storage de-vices, raise a serious doubt whether there will ever be a brand new 4th generation of optical discs. Those facts explains why most of the industries, including the previous partner in the SURPASS project, have stopped development in the optical data storage ﬁeld.

1.4.2 Towards an extension for the BD format

It is clear from the above analysis that the introduction of a completely new 4th generation is more and more doubtful. However, it is still possible to increase the storage capacity of the Blu-Ray disc without requiring major changes of the optical pick-up itself. One strategy to increase

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4 Chapter 1 Introduction capacity is by piling up multi data levels. It was demonstrated that 500 GB can be reached by piling up 20 semi-transparent 25 GB Blu-Ray data layers on the same disc [13]. However, such impressive numbers come at a cost. For this large number of levels, the industrial feasibility in terms of fabrication process is questionable. Moreover, in a multi-level discs, each level has a very low reﬂectivity, thus requiring extremely advanced signal processing and maybe even a modiﬁcation of the optical pick-up.

In this context, super resolution near-field effect can be very interesting as it increases the storage capacity of a disc by a factor of 2 to 3 without increasing the number of moulding machines and stampers on the disc fabrication process. The only modification required is the deposition of the super-resolution stack comprising up to 5 thin film layers per disc level instead of a single and simple metallic layer in usual single level ROM discs. Thus, it appears that an extension of the current Blu-Ray format for commercialization in 2014-2015 with 100 GB per disc or more could be provided by a combination of multi-level, super-resolution and advanced signal processing.

1.5 Super-RENS eﬀect in optical data storage

The Super-RENS effect is an incremental technology that potentially leads to an increase of the storage capacity of an optical disc by a factor of 2 or 3 [5]. The technique is remarkable since it requires no further modifications of the BD optical set-up but only a specific type of signal processing, named advanced partial response maximum likelihood (PRML) [14, 15].

Indeed, the effect is obtained by modifying the layer stack deposited on the disc medium. One of the materials of the super-resolution stack is an “active” non-linear material. Its optical properties are modified by the incident focused laser beam in a region smaller than the laser spot itself, which in turn influences the incident spot. The result is a super resolved spot that allows for the detection of data marks below the diffraction limit of the optical set-up.

During the last few years, the Super-RENS technique was mostly promoted by Tominaga, although few problems were encountered. The main issue is to ﬁnd a material combining large optical contrast between low and high optical power, fast response and recovery, high power sensitivity and stability after a large number of readings. So far, several materials have been proposed as the Super-RENS layer, where the most common are certainly the phase change materials, such as Antimonide (Sb) [16], GeSbTe (and some of its derivatives) [17] and AgInS-bTe (AIST) [18]. Diﬀerent classes of materials have been also considered, such as, silver ox-ide (AgOx) [19], platinum oxide (PtOx) [20], PbTe (chalcogenide-based thermoelectric

mate-rial) [21], and ZnO (semiconductor) [22]. Naturally, each of these materials responds differently when excited by the incident focused light, being usually classified in two main categories de-pending on how the imaginary part of the refractive index changes: if k decreases from the material initial state to the excited state (low-power to high-power), it is said that the material belongs to an aperture type (A-type) class of Super-RENS. In fact, one can regard this de-creasing of the imaginary part of the refractive index as a localized optical aperture, justifying the name ‘aperture type’. On the other hand, if k increases, it is said that the material is a scatterer type (S-type) of Super-RENS. In this case, a localized opaque structure is generated in the super resolution layer, partially blocking and scattering the incident spot. A summary of the change of the refractive indices (real (n) and imaginary (k) parts) for some Super-RENS ma-terials are displayed in Table 1.1. The two types of Super-RENS effect are illustrated in Fig. 1.3.

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1.5 Super-RENS eﬀect in optical data storage 5

Table 1.1: Variation of the real (n) and imaginary (k) components of the refractive indexes at 405nm.

Material n (low→high power) k (low →high power) Classiﬁcation

AgOx, PtOx, PbTe, ZnO Scatterer type

Sb, AIST, GeSbTe, SbTe Aperture type

Substrate

Dielectric Layers

? ?

Focusing Lens

Aperture type

Scatterer type

Dielectric Layers Super-RENS Layer Substrate rs F FooocccuuusssiinngggggggggggggggLLeeennsss

pe

S

rs er More absorbing region More absorbing region Less absorbing region Less absorbing region

Figure 1.3: Schematic representation of the aperture and scatterer types of Super-RENS eﬀect. Under laser radiation, a sub-wavelength thermally induced region, smaller than the area of the focused spot, is generated in the super resolution layer. Within this region, the sample optical parameters (e.g., the permittivity) are temporarily changed. For certain materials, the induced region (represented in yellow, on the left) becomes less absorbing than the outer region (blue). Therefore, an optical aperture is formed. For other materials, the induced region (represented by green, on the right) becomes more absorbing than the outer region. Therefore, a near-ﬁeld optical scatterer is formed. The dielectric layers are used to protect the super resolution layer from thermal damage. Our task is to measure and/or simulate the super resolved spot as it leaves the Super-RENS stack layer.

During the SURPASS project, the semiconductor Indium Antimonide (InSb) was proposed as an alternative non-linear material [23]. As it happens with AgOx, a reversible sub-wavelength

optical scatterer is generated in the InSb layer upon laser radiation. When compared to super-resolution discs made of different materials, the InSb-based Super-RENS disc showed superior performance. In addition to excellent carrier to noise ratio (CNR) values, a very low bit error rate in the range of 10−5 (much better than the 3× 10−4 criterion holding for Blu-Ray) was measured [24]. With this material, high-definition video playback from a Super-RENS optical disc with 46 GB was demonstrated for the first time in 2010 [25].

From a practical point of view, it is essential to understand the effect of the generated optical aperture/scatterer on the focused laser spot as it is transmitted through the Super-RENS stack. For the aperture-type of Super-RENS materials, the interaction of the optical aperture and the laser beam is expected to result in a local focused spot that is not limited by diffraction. In this way, readout of data marks beyond the diffraction limit could be possible due to a smaller readout spot. On the other hand, for scatterer-type of Super-RENS materials, the effect of the optical scatterer on the focused spot is not so straightforward to interpret. In fact, it has been proposed that surface plasmons enhancement or the strong interaction of the evanescent scat-tered field with the underlying data marks are the main responsible mechanisms for the readout

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6 Chapter 1 Introduction signal beyond the diffraction limit [26–28]. But the actual features of the super resolved spot for both types of Super-RENS effect remains unknown. Hence, there is still an open question on what happens to the focused spot after passing through the activated Super-RENS layer, that allows for readout beyond the diffraction limit. In addition, there is a need for a model that can accurately describe the focused spot characteristics after its interaction with the induced optical aperture/scatterer, which would certainly allow for further improvement of the Super-RENS technique.

In this context, we intend to ﬁnd a solution to these problems by investigating the Super-RENS focused spot itself, both numerically and experimentally, hoping that not only the features of the super resolved spot would be characterized but also that the Super-RENS technique could be applied to ﬁelds other than optical data storage. Moreover, the tools devised for this study is expected to be extended for the investigation of the super resolved spots generated by micro-sized solid immersion lenses. Those are the main objectives of this work.

1.6 Scope of this thesis

As discussed before, we are mainly interested in investigating the Super-RENS focused spot as it leaves an activated super-resolution stack layer. Specifically, we will study theoretically and experimentally the focused spot generated by an scatterer type of Super-RENS effect. Moreover, the tools developed for this study, either experimental and theoretical, will be used to investigate the immersed focused spot generated by micro-sized solid immersion lenses. The remaining of this thesis is organized as follows: Chapter 2 starts with a discussion on the Super-RENS effect, directly applied to the readout of optical discs, using a scalar framework. The scalar diffraction theory of readout systems is presented along with a simplified model for the Super-RENS effect. Then, the readout of an A-type and S-type of Super-RENS focused spots is presented and the results are compared with available published data. At the end of the chapter, a discussion on a possible cause for readout beyond the diffraction limit is presented.

The limitations inherent to the scalar approximation compelled us to develop a more sophis-ticated model for the Super-RENS eﬀect, based on the fully vectorial description of the light interacting with matter. Therefore, the basic theoretical background for such rigorous analysis, together with some examples of interest, are presented in Chapter 3. In Chapter 4, a rigorous threshold model for the Super-RENS eﬀect, based on the theory shown in Chapter 3, is pro-posed. Some predictions of the model are compared with the scalar results.

Since the results of all previous chapters are based upon a threshold-like model, these should be validated by an experimental counterpart. Therefore, Chapter 5 is entirely dedicated to ex-perimental measurements of the super resolved focused spots. Here, direct measurements of the super resolved focused spot in the near ﬁeld regime, as it leaves an active Super-RENS stack layer, are shown. The results are presented along with a detailed explanation of the experimental setup used to obtain them. Moreover, the unexpected outcome of the near-ﬁeld measurements forced a careful comparison between the experimental results and the simulations performed at identical conditions. These results are also included in the chapter.

The rigorous threshold model is used in Chapter 6 to study in details the properties of the Super-RENS focused spot for a wide range of conﬁgurations, such as diﬀerent numerical aper-tures and materials. Chapter 7 is again dedicated to study the readout problem, but this time using the spot computed rigorously as the input for the scalar readout algorithm developed in

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1.6 Scope of this thesis 7 Chapter 2. In the following chapter, the last one dealing with the Super-RENS effect, a different approach to take advantage of the scatterer generated in the active layer is shown. The goal is to achieve focused spots smaller than the diffraction limit at high numerical apertures.

Finally, the tools developed throughout the Chapters 2 to 8 are used to study several other applications of interest, mainly regarding solid immersion lens. The Section 9.1 shows an intro-duction to the solid immersion technique. A rigorous numerical model is presented to simulate the light interacting with tiny SILs. The immersed spot is experimentally measured in the near-ﬁeld regime using the measuring technique described in Chapter 5. A deeper study on the immersed focused spots is presented in Section 9.2. In particular, a detailed experimental and theoretical study on the immersed doughnut spot, generated by focusing an azimuthally polar-ized laser beam onto a 2μm-SIL is presented. In Section 9.3, an interesting analysis of the mis-alignment tolerance of the 2μm-SIL immersing azimuthally polarized laser beam is performed, with surprising results. In Section 9.4, an alternative method for generating a doughnut-like focused spot that does not rely in changing the polarization state of the laser beam is discussed. At last, the conclusions of this work, along with recommendations for future research, are given in Chapter 10.

I have also included five appendices to complement the description of the methods used in the thesis. In Appendix A, the possible mechanisms that lead to the non-linear behaviour of the InSb when exposed to high intensity laser light are briefly discussed based on the available literature. In Appendix B, an analytical model for the scalar super-resolution effect is presented. Next, in Appendix C, near field measurements of the super resolved spots obtained at low nu-merical apertures are shown. In Appendix D, a computationally method to obtain the focused spot for high numerical aperture lenses is described in details. Finally, the Appendix E gives an introduction to the Finite Element Method (FEM) programming, useful to understand the basic concepts of a FEM program.

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Chapter 2

A simpliﬁed model for the

Super-RENS eﬀect

A simplified model for the Super-RENS effect, in the framework of scalar diffraction theory, is given. The model is used to analyse the readout properties of Super-RENS discs based on InSb and AIST material1.

2.1 Introduction

Scalar diffraction analysis has been successfully employed to model and study a variety of prob-lems in optics because of its simplicity and flexibility. As is well known, scalar analysis is essen-tially an approximation (see for instance Ref. [29]), which describes quite well optical systems operating at small numerical aperture lenses in which the light has to interact with structures larger than its wavelength. However, when the light interacts with structures in the order of the wavelength and high numerical apertures are used, vectorial effects cannot be neglected if one wants an accurate description of the phenomena under study. In this case, the scalar approach must be replaced by a rigorous method. Nonetheless, scalar theory has been used to describe systems with high numerical aperture with surprisingly good results [30], which, combined with its already mentioned simplicity and flexibility, results in a fast and educative way to study op-tical problems. We shall profit from these advantages and initiate our study on the Super-RENS effect in the scalar framework.

2.2 Scalar diﬀraction theory of readout systems

In what follows, the scalar theory of readout systems is brieﬂy described. For further details, we refer to Refs. [2, 31, 32].

2.2.1 Hopkins’ analysis

To analyze optical discs readout, the starting point is usually the Hopkins diffraction model [31]. The goal of Hopkins mathematical analysis was to find an expression for the detector signal after the interaction of the light spot with a disc containing a series of pits. Starting with the light amplitude emitted by a source, one first calculates the field distribution of the beam spot in the focal plane of an objective lens. Next, the diffraction of the light by the data structure

1_{The contents of this chapter are based on Ref. [27], A.C.Assafrao, S.F. Pereira, and H.P.Urbach: Scalar}

readout model for Super-RENS focused spot, J. Europ. Opt. Soc. Rap. Public. 6 11056 (2011).

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10 Chapter 2 A simplified model for the Super-RENS effect is considered, where the supposed periodic structure of the disc greatly simplifies the analy-sis. Part of the light diffracted by the disc is captured by the collector lens. The electric field intensity signal is finally integrated over the collector lens area, which gives the final readout intensity I on the detector (see Fig. 2.1). The Hopkins method sets the theoretical background for analysing readout from optical disc, but its implementation in the way that it is presented is not very attractive, since computer programming has evolved from the earlier 80’s (year when the paper was published) up to now. In fact, with the Fast Fourier Transform (FFT) algorithm, a scalar based readout program can be much more efficiently programmed, as we will show in the next sub-section.

2.2.2 Fast Fourier Transform approach

In Fig. 2.1, the lightpath of an optical data storage system is shown (in transmission). The incident light distribution f (x, y) is focused onto the disc by the objective lens. Apart from a scaling factor and a phase term, the ﬁeld in focus is given by,

Objective

f(x,y)

g(x,y)

F(u,v) R(u,v)

Collector

Figure 2.1: Lightpath for a scalar readout program. The input field distribution f (x, y) is focused on the disc plane by means of a Fourier transform resulting in the field distribution F (u, v) that interacts with the disc reflection function R(u, v). The product UT(u, v) = F (u, v)· R(u, v) is back propagated to the collector lens,

resulting in the ﬁeld distribution g(x,y). Here we show a readout system in transmission.

F (u, v) = _+∞

−∞

_+∞

−∞ f (x, y) exp[−2πi(ux + vy)]dxdy (2.1)

where (u, v) are the coordinates in the image plane, normalized by λ/NA, and (x, y) are the coordinates in the pupil plane normalized by the lens diameter. The pupil function f (x, y) of the objective lens is given by,

f (x, y) = exp [− x2 W_x2 + y2 W_y2 ], if (x2+ y2)≤ 1 0, elsewhere (2.2)

where Wx and Wy are parameters that determine the width of the laser beam in the entrance

pupil. If chosen suﬃciently large, the ﬁeld amplitude impinging on the lens becomes evenly distributed, resulting in the well-known Airy function distribution in the focal plane,

F (u, v) = F (ρ) = J₁(2πN A λ ρ)/(

2πN A

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2.3 Scalar threshold model for Super-RENS 11 where, J₁ is the Bessel function of ﬁrst kind and ρ = √u2+ v2 is the radial direction. This particular focused ﬁeld distribution is used throughout this chapter.

Next, the focused field distribution F (u, v) interacts with the data marks, described by a reflection function R(u, v). The main difference between the FFT approach and the Hopkins approach lies in the fact that the reflection function is represented in a mesh grid rather than expressed as a Fourier series. In this way, one has the freedom to design any type of data marks to be readout. The product UT(u, v) = F (u, v)· R(u, v) is propagated to the collector lens

according to

g(x, y) = _+∞

−∞

_+∞

−∞ F (u, v)R(u, v) exp[−2πi(ux + vy)]dudv. (2.4)

Finally, the ﬁeld distribution |g(x, y)|2 is integrated over the pupil area, resulting in the ﬁnal intensity on the detector of a given position. The modulated readout signal is obtained by moving the disc data marks underneath the focused spot and computing Eq. 2.4 for many translated positions.

2.3 Scalar threshold model for Super-RENS

We will now consider the super resolution effect. A schematic view of the scalar threshold model for the Super-RENS effect is shown in the Fig. 2.2(a). As the focused spot passes through the super resolution layer, there will be a local change in the optical properties of the super resolution (SR) material at positions where the laser energy density is enough to trigger the nonlinear effect. For instance, suppose that initially the material is in the crystalline state, having a certain refractive index n₁+ ik₁. When the laser spot is focused onto the super resolution layer, then in the portion of the spot where the electric energy density is above the threshold, the material will melt, leading to a fast change in the refractive index from n₁+ ik₁to n₂+ ik₂. Note that, depending on the type of material used, the complex part k of the refractive index of the molten region may become higher (or lower) than it was in the crystalline state. For this reason, the molten region can be regarded as a scatterer-like structure, if k₂ > k₁, or an aperture like structure, otherwise. In either case, the general name ‘optical near field structure’ (NFS) is given to the molten region. A summary of the refractive indexes values of the two materials considered here, Indium Antimonide (InSb - S-type) and AgInSbTe (AIST - A-type), is given in the Fig. 2.2(b) [33–35].

Laser Intensity (a.u.)

1 1.1

Threshold

Tangential direction

(a) Super resolution eﬀect

Energie density Re Refrac tiv e index Im Refrac tiv e index

Low power regime High power regime n=2.66+3.3i n=2.87+2.94i Threshold n=3+2.37i n=2.1+3.4i AIST InSb

(b) Refractive index of SR materials

Figure 2.2: Schematics of the Super-RENS effect and materials used. a) The focused spot incident on SR layer stack induces an optical aperture/scatterer if the intensity is high enough to trigger the nonlinear effect. b) Refractive index of AIST and InSb materials as function of the field intensity.

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12 Chapter 2 A simpliﬁed model for the Super-RENS eﬀect

Figure 2.3: Diameter of the near-ﬁeld

structure generated by the focused Airy spot as function of the laser power. The

light wavelength is λ = 405nm. 1 1.2 1.4 1.6 1.8 2 0 0.1 0.2 0.3 0.4 0.5

Maximum intensity (a.u.)

NFS diameter (

μ

m)

NA=0.85

NA=0.6

that the near field structure is opened exactly underneath the focused spot. We shall refer to this situation as ‘static regime’. The super resolution effect is then incorporated into the focused beam by a routine that searches the intensity values in the field distribution which are above or below a given threshold. We define this threshold as 1, in an arbitrary unit system. The effect of the super resolution layer is imparting a phase change on the focused field, according to,

ΦSR(u, v) = exp [ikzn(u, v)] (2.5)

where k = 2π/λ, λ the wavelength of the light employed, z is the layer thickness and n is the (usually complex) refractive index, which can be either before (n₁+ ik₁) or after (n₂+ ik₂) the threshold. Thus, if the focused spot intensity (|F (u, v)|2) value in a given position (u₁, v₁) is higher than the threshold, the eﬀect of the super resolution layer will be a phase change in the form of ESR = F (u1, v1)· exp [ikz(n2+ ik2)] at that position.

Based on the algorithm described above, the diameter of the molten region as function of the laser power can be estimated by determining the area of the focused spot which has the energy density above the threshold value. In the Fig. 2.3, the diameter is shown for focusing lenses having NA = 0.85 and NA = 0.6, at wavelength λ = 405nm.

2.3.1 Scalar Super-RENS focused spot in a static regime

We are now in position to compute the Super-RENS focused spot using the scalar static model. In Figs. 2.4(a) to 2.4(c), the normalized amplitude of the focused spots field distribution, computed before and after applying the super resolution algorithm, are shown for a system with λ = 405nm and NA = 0.85. When the super resolution effect is not activated, the focused spot has the typical Airy pattern distribution, as shown in Fig. 2.4(a). When the near field structure is present, its effect is prominent in the central region of the spots, as seen in Figs. 2.4(b) and 2.4(c). In Fig. 2.4(d), the cross-section of the squared field amplitude, to which we will refer as the intensity, is computed for the spots shown in Figs. 2.4(a) to 2.4(c). If the InSb layer is present and activated (laser intensity higher than the threshold), the focused spot distribution presents a sharp structure at the edge of the scatterer. We shall refer to those structures as ‘wings’. In the case of AIST layer, the focused spot becomes slightly narrower at the full width half maximum (FWHM) and the side lobes are smaller in comparison to the other spots. For these calculations, we assumed an optical scatterer of 154nm radius and an optical aperture of 95nm.

2.3.2 Scalar Super-RENS focused spot in a dynamic regime

Now we drop the requirement of having instantaneous phase change on the super resolution layer after laser exposure. In other words, if the optical near field structure is not created instanta-neously and if an optical disc spins at high linear speed, it is plausible to think that the near field structure will be generated at some distance d from the center of the focused spot. We will assume this Super-RENS configuration when computing the readout signal of a Super-RENS

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2.3 Scalar threshold model for Super-RENS 13 0 0.5 1 1 0.5 0 -0.35 0.35 _-0.35 0.35 0 0 x direction (μm) y direction (μ_m) Intensity (a) SR oﬀ 0 0.5 1 1 0.5 0 -0.35 0.35 _-0.35 0.35 0 0 x direction (μm) y direction (μ_m) Intensity (b) InSb 0 0.5 1 1 0.5 0 -0.35 0.35 _-0.35 0.35 0 0 x direction (μm) y direction (μ_m) Intensity (c) AIST f

SR off

InSb

AIST

x-direction (μm) Intensity 0 0.07 0.14 0.21 0.28 0.35 0.42 0.49 1 0 (d) Intensity proﬁle

Figure 2.4: The Super-RENS focused spots computed in the static regime. a) to c) Focused field amplitude without the Super-RENS effect, with the InSb and AIST, respectively. d) Cross-section of the intensity profiles.

disc. In Fig. 2.5(a), an example of the focused field amplitude interacting with a displaced scatterer is shown for an InSb layer, where the scatterer was mismatched by 140nm relative to the focused spot and its radius was 130nm. The cross-section of the normalized intensity profiles of an InSb and an AIST focused spots are shown in Fig. 2.5(b) for a system with λ = 405nm and NA = 0.85. It indicates that the optical scatterer, which in fact has a higher extinction coefficient than the surrounding area, will partially absorb the field intensity from one side of the focused spot. The opposite occurs for the AIST layer. The optical aperture allow for more light to pass through it, resulting in a spot with opposite intensity distribution than that of the scatterer type.

Tangential direction (μm) Moving direction of the disc

Radial direction (μ m) −0.7 −0.35 0 0.35 0.7 0.7 0.35 -0.35 0 -0.7 0 0.5 1 d (a) InSb −1 −0.35 0 0.35 1 0 1

InSb

AIST

Tangential direction (μm) Intensity (b) Intensity proﬁle

Figure 2.5: The Super-RENS focused spot computed in the dynamic regime. a) Focused ﬁeld amplitude with a optical scatterer displaced by 140nm. b) Intensity proﬁle of an InSb and AIST focused spots under a dynamic regime. The amplitude and intensity are normalized.

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14 Chapter 2 A simplified model for the Super-RENS effect 2.3.3 On the computational effort

One of the greatest advantages of using scalar theory is the low computer power required to perform the simulations. For example, the Super-RENS effect is incorporated in the focused spot without any computational effort. For the disc readout, the computation of Equation 2.4, performed via Matlab FFT built-in function, determines how fast the simulations will be. In a typical simulation, one can define a 16 by 16 μm2 computational window, divided into 1024 number of points, which results in a grid with resolution of 15nm. Under these assumptions, the FFT computation, including the time necessary to move the underneath data mask, will take less than 0.1 second on a home computer Intel Core i7, 2.2GHz with 8GB RAM. Thus, scan-ning one period of a periodic data structure with 1000nm length, with resolution of 15nm and considering the Super-RENS effect, will last no longer than 1 minute. Better accuracy can be achieved by increasing the number of points. For the upcoming simulations, we have considered 1800 points, resulting in a mesh grid with resolution of approximately 10nm.

2.4 Readout of a super resolution beam

In the previous section we described the algorithm that incorporates the super resolution eﬀect on the focused spot using the scalar approach. Now we will use the dynamic Super-RENS spot to study its eﬀect on the readout signal of a BD-like system (NA = 0.85 and at wavelength λ = 405nm). We exemplarily assume the spots shown in Fig. 2.5(b).

2.4.1 Signal characteristics of random patterns

To determine the system response under the Super-RENS spot readout, we consider the data mark structure depicted in Fig. 2.6. A set of data marks having the same length is arranged along the scanning track. The reﬂectivity values of the land and of the mark are rL = 0.9

and rM = 0.002, respectively [32]. The readout spot scans over one period, which results in a

modulated signal intensity I. Next, the visibility curve is calculated from the modulated readout signal, according to V = (Imax− Imin)/(Imax+ Imin). From the visibility curve, the carrier to

noise ratio (CNR) is computed by CNR = 20· log₁₀(V /Vref), in decibel (dB). The reference

visibility is computed for the 300nm data mark.

Scan track

Mark period

Super-RENS Readout spot

Ma Markrk p pererioiod d Su Supeper-r-RERENSNS RReaeadodoutut sspopott Mark size Mark width 0.16μm

Figure 2.6: Track layout for simulations. The marks have variable length, width of 160nm and period of twice the length size.

The CNR curves for AIST and InSb are shown in Figs. 2.7(a) and 2.7(b), respectively. Up to the cut-off frequency (which corresponds to data mark with 120nm length), the spectra are typical of a diffraction-limited modulation transfer function at low power. At high power, the InSb material shows an increase in the modulation at all frequencies, when compared to the readout of the spot without Super-RENS effect. The AIST material, on the other hand, showed

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2.4 Readout of a super resolution beam 15 a slightly worse performance at frequencies close to the cut-off frequency. In particular, a dip appears close 130nm data marks. It ultimately indicates that data marks at that frequency may be poorly readout by the Super-RENS spot. This is particularly dangerous for improving the recording density, because the shortest marks in current BD discs are 150nm. Nonetheless, both materials show a significant increase in the CNR at high frequencies, beyond the cut-off frequency. It can be noticed a higher CNR when reading out the data with the InSb spot. The inset in both figures are the experimental results obtained by Gael Pilard et al. at Deutsche Thomson OHG, Germany, published in Ref. [18]. Qualitatively, the predictions of the scalar readout shows a good agreement with the experimental data.

0.1 0.15 0.2 0.25 0.3 −60 −50 −40 −30 −20 −10 0 SR off SR on po w e r (dBm ) 0.8mW 50 40 30 20 10 0 10 0 10 20 30 40 50 60 frequency (MHz) 2.6mW W W 0.8mW 2.6mW

Data marks size (μm)

CNR (dB) (a) AIST po w e r (dBm ) 0.8mW 50 40 30 20 10 0 10 0 10 20 30 40 50 60 frequency (MHz) 2.0mWWWW 0 0.88mmWW 2.0mW 0.1 0.15 0.2 0.25 0.3 −60 −50 −40 −30 −20 −10 0 SR off SR on

Data marks size (μm)

CNR (dB)

(b) InSb

Figure 2.7: Readout signal as function of the data mark for super resolved spots obtained with (a) AIST and (b) InSb. Readout beyond the diﬀraction limit is observed. The inset corresponds to the published experimental data, plotted as function of the data frequency [18]. A qualitative agreement is found.

2.4.2 Eﬀect of the mark length on the high frequency signal

An interesting property of the Super-RENS readout signal was found for a situation where a sequence of 11 pits with size of 100nm, i.e., beyond the diffraction limit, were inserted between a 800nm mark (on the right) and a 800nm land (on the left side). The computed and measured signals are shown in Fig. 2.8. As expected, the amplitude of the readout signal is higher on the 800nm land than on the pit of the same size, regardless the readout spot used. For the data marks of 100nm being readout by the InSb, the same readout signal characteristic was observed, i.e., intensity higher on land and lower on the pits. However, this situation changes for the 100nm data marks being readout by the AIST spot, where the amplitude of the readout signal is higher on the pit. Moreover, only 10 out of 11 data marks could be resolved with AIST spot, whereas all 11 data marks can be seen with the InSb spot. These results are again qualitatively in good agreement with the experimental measurements (see Fig. 2.8 bottom), indicating that this peculiar readout behavior can be understood based on diffraction effects.

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16 Chapter 2 A simpliﬁed model for the Super-RENS eﬀect 0.4 0.2 0.0 InSb -0.2 -0.4 1200 1500 AIST 1800 time (ns)2100 2400 2700 Amplitude (a.u .) 1000 2000 3000 4000 5000 0.2 0.4 0.6 0.8 1 InSb AIST Disc position (nm) Amplitude (a.u .) (a) (b)

Figure 2.8: Readout signal of high frequency data marks by AIST and InSb Super-RENS spots. The pattern is a sequence of 11 data marks of 100nm length surrounded by 800nm mark (right) and land (left). (a) Simulated readout signal. (b) Measured readout signal for 20 data marks surrounded by 800nm mark/land. The AIST readout could resolve 19 out of the 20 data marks. [18]

2.5 An interpretation for the readout signal beyond the

diﬀrac-tion limit.

Although modulated signals beyond the diffraction limit have been experimentally observed during AIST or InSb readout, the general readout mechanism that leads to it has not been fully clarified [17, 36]. Surprisingly, the scalar model gives us an useful interpretation on how the modulated signal at high frequencies is possible. Let us first consider a periodic structure being read by a spot without super resolution effect. By evaluating and plotting Eq. 2.4, we find the intensity distribution of the scattered field on the pupil plane. According to the general scalar readout theory, if part of the ±1st diffracted orders falls inside the zeroth order, there will be modulation in the readout signal. When the period of the marks becomes smaller, the overlap of the 0th and the±1st orders becomes smaller and hence the amplitude of the modu-lated signal diminishes. At the cut-off frequency, there will be no overlap between orders and consequently no modulation in the readout signal. As an illustration, we plot in the Fig. 2.9(a) the intensity distribution in the pupil plane for a periodic disc with periodicity of 80nm (be-yond the cut-off frequency) and duty cycle of 50%. The adjacent tracks are 500nm far from the scanned track. As seen, the first orders are not overlapping with the zeroth one in the tangential direction, and therefore no modulation in the readout signal can be expected. At this point, we remind that the zeroth order (the red circle) corresponds to the collector lens pupil. Next, let us consider a flat disc (without any data marks on it) and a focused spot with Super-RENS effect activated. By computing the intensity distribution in the pupil plane, we will find that the 0th order is enlarged in diameter by a factor of three [see Fig. 2.9(b)]. Please notice that even though the zeroth order is enlarged, the lens pupil size remains unaltered, always in the range −1 to 1, in diffraction units. Finally, we compute the intensity distribution on the pupil plane generated by the InSb Super-RENS spot reading the same periodic structure as before, as shown in the Fig. 2.9(c). Here we can clearly observe interference signals in between the diffracted orders. This suggests, in fact, that not only the 0th order was enlarged, but also the ±1st _{orders. As a result, it becomes possible to have constructive/destructive interference of}

these enlarged±1stdiﬀracted orders within the lens pupil (red circle), even for data marks with frequencies beyond the cut-oﬀ frequency. In this way, super resolution readout signal is achieved.

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2.6 Conclusions 17

Pupil plane (NA/λ)

Pupil plane (NA/

λ ) −3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 (a) SR oﬀ

Pupil plane (NA/

λ ) −3 −3 −2 −1 0 1 2 3

Pupil plane (NA/λ)

−2 −1 0 1 2 3

(b) SR on - Flat disc

Pupil plane (NA/λ)

−2 −1 0 1 2 3

Pupil plane (NA/

λ ) −3 −3 −2 −1 0 1 2 3 (c) SR on - Data disc

Figure 2.9: Diﬀracted orders on the pupil plane. a) Beyond the cut-oﬀ frequency no overlapping of

the±1storders with the 0th order occurs for a focused spot without Super-RENS. b) The Super-RENS

spot reading a disc without any marks on it generates an enlarged 0th order in the lens pupil. c) The

interference patterns between orders suggests that the ±1st diﬀracted orders are also enlarged, which

allows overlapping even beyond the cut-oﬀ frequency. Destructive interference explains the dip in the signal of Fig. 2.7(a).

2.6 Conclusions

In this chapter, we have described a scalar readout model for the super resolution near field structure effect. The Super-RENS effect is incorporated into the scalar focused spot by means of a threshold model. This modified spot, assuming a dynamic situation, is then used to retrieve the readout signal out of some data structures of interest. The results are compared with avail-able literature. It was shown that resolution beyond the diffraction limit is achieved under the displaced Super-RENS readout spot. The main predictions of the model, among others, include the signal losses at low frequencies and inversed modulation for AIST. General readout char-acteristics of the InSb material are also found in good agreement with the experimental data. Moreover, the model helps to understand how the super resolution is achieved, by analysing the diffracted field distribution in the pupil plane. Although not rigorous, this scalar method provides useful insights on the Super-RENS effect, and is an educative tool to understand the basic mechanisms of the Super-RENS readout.

A direct consequence from all that was discussed so far is that the AIST material is less attractive for ODS as the active super resolution layer. Besides the signal losses and the in-verted signal modulation, it was also experimentally veriﬁed that the AIST based optical discs shows poor recyclability [37]. For those reasons, we will mainly concentrate on the InSb super resolution material, which has proven to be superior to AIST in all these aspects.

In spite of the good start with the scalar approach, the presented theory may be too simple to describe such a complex problem involving high numerical apertures and objects that are smaller than the light wavelength used. As a consequence, a more rigorous model should be developed instead. Hence, in the next section, we will present the basic electromagnetic theory that supports a development of such rigorous model.

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Chapter 3

Introduction to diﬀraction and

electromagnetic theories

We present the electromagnetic background theory that is necessary to treat the Super-RENS eﬀect in a rigorous manner.

3.1 Introduction

From the discussion of the previous chapter, it was found that, although the scalar theory can give valuable hints on the basic working mechanisms of the Super-RENS effect, it is proba-bly not sufficient to completely describe the physics. The high numerical apertures involved combined with the small structures that interact with the focused light does require a more sophisticated approach to study it. Therefore, in this chapter, we will briefly introduce the theoretical background that is necessary to develop a more rigorous simulation model.

3.2 The diﬀraction integral

Consider an aplanatic focusing lens, i.e., a lens that obeys Abbe’s sine condition, with rotational symmetry with respect to the optical axis [38]. The lens is considered to focus without wavefront aberration and to have the entrance and exit pupil diameters larger than the wavelength of the light. In addition, we assume that the lens does not absorb or reflect the incident light. Also, the medium on the image side is assumed to be homogeneous, isotropic, nonmagnetic (μ = μ₀) and transparent. The lens is illuminated by a monochromatic time harmonic plane wave, with frequency ω and electric field E (˜ r, t) = Re[ E(r) exp(−iωt)], where r is a position vector in the Cartesian coordinates (x, y, z) and the field amplitude has components E = ( ˜˜ Ex, ˜Ey, ˜Ez).

Moreover, the incident plane wave is assumed to propagate along the positive z-axis. If the medium of the exit pupil and the focal region has refractive index n, then a wave vector in this space is k = nk₀ with components k = (kx, ky, kz) and k0 is the wave number in vacuum. Under

these assumptions, that are by no means restrictive for practical cases, the ﬁeld in focus is given by the well-known diﬀraction integral [39, 40],

E(r₂) =− i 2π Ω1 a(kx, ky) kz exp ik· (r₂− r₁) dkxdky (3.1)

where r₁ and r₂are the position vectors from the lens to the focal point and from the lens to the observation point, respectively, Ω₁ is the cone given by k_x2+ k_y2 ≤ k_o2n2NA2 subtended by the

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20 Chapter 3 Introduction to diﬀraction and electromagnetic theories aperture at the focal point and k is a wave vector. The vector amplitude given by a(kx, ky) is

usually a known quantity in the object space. In Appendix D, a method for solving this integral is described in details for the polarization cases used throughout this thesis.

3.2.1 Focused ﬁeld in the homogeneous focal plane Linear polarization

In Figs. 3.1(a)-3.1(d), the square modulus of the electric field components and the total electric field distribution in the focal plane of an aplanatic focusing lens with NA = 0.85 are shown. The incident beam is linearly polarized along the x-direction and the wavelength employed is λ = 405nm. Each squared field component, i.e., |Ex|2, |Ey|2 and |Ez|2, is normalized to unity

and displayed separately in Figs. 3.1(a)-3.1(c). The total electric ﬁeld energy density (the sum of all squared components, |Et|2 = |Ex|2 +|Ey|2+|Ez|2), which will be referred throughout

this thesis as total electric field, field intensity or simply intensity is shown on Fig. 3.1(d). The plot in Fig. 3.1(a) shows that the x-component of the total electric field is elliptically shaped with its long axis parallel to the direction of the polarization. The y-component, on the other hand, is symmetric along the x and y directions, presenting four lobes (see Fig. 3.1(b)). The z-component, shown in Fig. 3.1(c), exhibits two peaks that contributes to a further broadening of the total electric field in the direction parallel to that of the polarization in the entrance pupil. A similar effect does not occur in the paraxial (scalar) limit, where the focused spot is always circularly symmetric if no aberrations are present. This observation has important consequences: as smaller spots are aimed by increasing the numerical aperture, the vector nature of the light starts to play an important role and therefore must be considered.

−600 −400 −200 0 200 400 600 −600 −400 −200 0 200 400 600 0 1 x direction (nm) y direction (nm) 1 0 0.5 (a)|Ex|2 −600 −400 −200 0 200 400 600 −600 −400 −200 0 200 400 600 0 1 x direction (nm) y direction (nm) 1 0 0.5 (b)|Ey|2 −600 −400 −200 0 200 400 600 −600 −400 −200 0 200 400 600 0 1 x direction (nm) y direction (nm) 1 0 0.5 (c)|Ez|2 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.9 x direction (nm) y direction (nm) −600 −400 −200 0 0 200 400 −600 600 600 −400 −200 200 400 0 0.5 1 (d)|Et|2

Figure 3.1: Computed electric field distribution in the focal plane of an aplanatic focusing lens with NA = 0.85 that is illuminated by a linearly polarized light beam in the x-direction. (a) Squared modulus of the Ex field component, (b) squared modulus of the Ey field component and (c) squared modulus of the Ez field component. The ratio|Ex|2,|Ey|2 and|Ez|2 is 100 : 0.3 : 13.8 (d) Contour plot of the modulus of the electric energy density

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3.2 The diﬀraction integral 21 Circular polarization

In Figs. 3.2(a)-3.2(d), the computed ﬁeld intensity distributions are now shown for a circularly polarized plane wave incident on the focusing lens. It is noticeable that the |Ex|2 and |Ey|2

have the same peak intensity value. Moreover, the summation of|Ex|2+|Ey|2 shows rotational

symmetry around the optical axis. The|Ez|2 is plotted in Fig. 3.2(c), and it also shows

circu-lar symmetry. As a consequence, the total electric energy density|Et|2 in the focal plane of a

focused circularly polarized incident light has circular symmetry, as can be seen in Fig. 3.2(d). For this reason, unless otherwise stated, we will use circularly polarized light throughout the remainder of this thesis, specially when dealing with the Super-RENS eﬀect.

−600 −400 −200 0 200 400 600 −600 −400 −200 0 200 400 600 0 1 x direction (nm) y direction (nm) 1 0 0.5 (a)|Ex|2 −600 −400 −200 0 200 400 600 −600 −400 −200 0 200 400 600 0 1 x direction (nm) y direction (nm) 1 0 0.5 (b)|Ey|2 −600 −400 −200 0 200 400 600 −600 −400 −200 0 200 400 600 0 1 x direction (nm) y direction (nm) 1 0 0.5 (c)|Ez|2 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.9 x direction (nm) y direction (nm) −600 −400 −200 0 200 400 −600 600 600 −400 −200 200 400 0 0 0.5 1 (d)|Et|2

Figure 3.2: Computed electric field distribution in the focal plane of an aplanatic focusing lens with NA = 0.85 that is illuminated by a circularly polarized light beam. (a) Squared Ex field component, (b) squared Ey field component and (c) squared Ez field component. The ratio|Ex|2,|Ey|2and|Ez|2 is 100 : 100 : 13.8. (d) Contour

of the total electric energy density. A circularly symmetric spot is observed. Hence, this particular state of polarization will be used throughout this thesis.

Cross-sections of the intensity proﬁles

In Fig. 3.3(a), the cross-sections along the x and y-directions of the normalized electric energy densities of the spots displayed in Figs. 3.1(d) and 3.2(d) are shown. As can be observed, a clear effect of focusing light with high NA lenses is the lack of a well defined dark region in the first ring of the focused spot. This occurs due to the strong z component present in the focused field. In optical recording systems, a narrow field structure with a well defined first dark Airy ring is desired to reduce difficulties with inter-symbol-interference crosstalk or problems with adjacent tracks crosstalk [41, 42]. In the same figure, we also indicate how to compute the so-called Full Width at Half Maximum (FWHM), which is an useful and often used measure of the spot size. In Fig. 3.3(b), the FWHM is computed as function of the numerical aperture when focusing in air (n = 1). Under the scalar regime, the spot FWHM is equal to 0.51λ/NA, regardless the aperture used. For the vectorial calculations, the results indicates that, at small numerical apertures, the spot FWHM for the linear and circular polarization cases converges towards the scalar solution. However, as the NA increases, a significant difference between scalar and vectorial solution emerges. Considering the BD lens, NA = 0.85, this difference is approximately 4% for circularly polarized light and 20% for x-polarized light in the broadening

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22 Chapter 3 Introduction to diﬀraction and electromagnetic theories direction. For systems with relatively smaller NA, for instance, NA≤ 0.65, the scalar theory can still represent quite well the focused spot whenever circular polarization is used at the entrance pupil. Although even for BD system the focused spot deviates only by 4% from that of the scalar theory, there is still an urge for using vectorial theory rather than scalar, and the reason is that the structures which interact with the focused spot are usually as small as the wavelength em-ployed (or even smaller) so that the fully vectorial nature of the light must be taken into account.

−400 −200 0 200 400 600 -600 Distance (nm) Normalized intensity x pol. − x x pol. − y circular pol. 1 0 0.5 FWHM (a) 0 0.2 0.4 0.6 0.8 1 0.5 0.6 0.7 Numerical Aperture FWHM (λ /NA) x pol. - x direction x pol. - y direction scalar circular polarization (b)

Figure 3.3: (a) Intensity proﬁles of the focused spot generated by a NA = 0.85 objective lens illuminated by an linearly and circularly polarized beams. The deﬁnition of FWHM is indicated by the arrow. (b) The FWHM as function of the numerical aperture of the focusing lens. At small NA, the vectorial predictions converge towards the scalar solution.

3.3 Multilayer transmission and reﬂection for a single plane

wave

Consider a multilayered space, consisting of N linear, isotropic and homogeneous media with (complex) refractive index ni(i = 1· · · N), as depicted in Fig. 3.4(a). The N −1 interfaces extend

inﬁnitely in the x and y-directions. The continuity relations across an interface for the normal components, derived from the Maxwell’s equations (see Section 3.5), are n2_iEi,n = n2i+1Ei+1,n

and Bi,n = Bi+1,n, where E is the electric ﬁeld and B is the magnetic ﬁeld. The continuity

relations of the tangential components are Ei,t = Ei+1,t and Bi,t/μi = Bi+1,t/μi+1. From these

relationships, the Fresnel equations are derived, which allow for computing the reﬂected (rf)

and transmitted coefficients of a wave incident on one of these interfaces. With the Fresnel coefficients, the field in the entire multilayer structure can be found. In particular, the reflected and transmitted fields are the observable quantities. A complete procedure on how to obtain the reflected and transmitted fields is described in Ref. [43].

3.3.1 Optimization of the Super-RENS stack layer

By computing the transmitted and reflected field using the above method1, the Super-RENS stack layer can be designed according to pre-defined criteria. The most common Super-RENS multilayer stack designed for ODS applications are basically made of a thin layer of an active material sandwiched by two dielectric layers, as schematically depicted in Fig. 3.4(b). The ‘active layer’ is in fact the non-linear optical material, whose optical properties vary with the incident laser power. Here we consider only the low band-gap semiconductor Indium Antimonide.

On super resolved spots in the near-field regime

On super resolved spots in the near-ﬁeld

regime

Contents

Chapter 1

Introduction

1.1

Three generations of optical discs

1.2

The SURPASS project

1.3

Current optical data storage market

1.4

What could be the

4

generation of optical discs?

1.5

Super-RENS eﬀect in optical data storage

Aperture type

Scatterer type

pe

S

1.6

Scope of this thesis

Chapter 2

A simpliﬁed model for the

Super-RENS eﬀect

2.1

Introduction

2.2

Scalar diﬀraction theory of readout systems

2.3

Scalar threshold model for Super-RENS

SR off

InSb

AIST

InSb

AIST

2.4

Readout of a super resolution beam

2.5

An interpretation for the readout signal beyond the

diﬀrac-tion limit.

2.6

Conclusions

Chapter 3

Introduction to diﬀraction and

electromagnetic theories

3.1

Introduction

3.2

The diﬀraction integral

3.3

Multilayer transmission and reﬂection for a single plane

wave