performance analysis of a multimode waveguide-based optical disk readout system

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erformance analysis of a multimodeaveguide-based optical disk readout system

rederik Fransoo, Dries Van Thourhout, and Roel Baets

We propose a method to improve the optical resolution to read out optical disks, without making the spotsize on the disk smaller than the diffraction limit. The idea is to reconstruct the bit pattern from thecomplete field profile �including amplitude and phase� of the light reflected from the disk. We measurethe phase and amplitude information by picking up the wave front into different modes of a bimodalwaveguide. Once picked up, these modes can be split by a photonic integrated circuit to be measured byseparate detectors. By combining the information from the responses from the different modes, we canimprove the bit error rate substantially. © 2004 Optical Society of America

OCIS codes: 210.0210, 110.0110, 100.5010, 100.5070.

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. Introduction

ptical data storage tries to cope with the strongeed for exchangeable super-high-density, high-data-ate storage memories. Applications include largetorage devices for backup and miniaturized versionsn mobile devices. In the search for higher informa-ion density, different approaches are being investi-ated to make readout and writing of smaller marksossible.1,2 It is well known that the smallest fea-ure distinguishable in the far field is given by��2NA�.3 Therefore the most obvious way to in-rease resolution is to decrease the wavelength � andncrease the numerical aperture �NA�. However,urther improvement of these parameters is increas-ngly difficult. Therefore new techniques that canvercome the diffraction limit are being investigated.xamples include magneto-optical recording basedn magnetic domain expansion4 and near-field read-ut by aperture probes or solid immersion lenses.5ther approaches try to enhance the resolution in the

ar field, with phase masks placed in the pupil ormage plane6 or with interference microscopy to de-ect the phase of the optical field.7

In this paper we present a new way of reading out

The authors are with the Department of Information Technol-gy, Interuniversity MicroElectronics Center, Ghent University,int-Pietersnieuwstratt 41, Ghent 9000, Belgium. The e-mail ad-ress for F. Fransoo is [email protected] 14 November 2003; revised manuscript received 12arch 2004; accepted 25 March 2004.0003-6935�04�173480-09$15.00�0© 2004 Optical Society of America

480 APPLIED OPTICS � Vol. 43, No. 17 � 10 June 2004

ptical disks. The idea is to use an integrated pho-onic chip with a multimodal waveguide to pick uphe optical field coming from the disk. Such aaveguide supports multiple optical modes, and the

elative amplitude by which these modes are excitedill depend on both the amplitude and the phaserofile of the field coming back from the disk. If wean split up the respective waveguide modes and de-ect the power in each of them separately, we may beble to reconstruct the data written on the disk withhigher resolution than in the case of a conventional

ystem. The concept to increase the resolution inhe far field is similar to other approaches that usehase information such as interference microscopy.7he disk can be illuminated by a single mode or by a

inear combination of multiple modes. A second ra-ionale behind the approach of the scanningaveguide readout system is the potential integra-

ion of all optical elements, including the laser andetectors on a single chip, thereby reducing the size ofhe pickup head by an order of magnitude and even-ually leading to a much more compact optical diskrive. Furthermore the disk is illuminated with theame multimodal waveguide as used for the detec-ion, which simplifies the design further and makeshe alignment much less sensitive than, for example,n a confocal microscope.

. Overview of the Scanning Waveguide System

. Description of the Optical System

igure 1 shows a schematic view of the scanningaveguide. The total system can be divided into twoarts. The upper part comprises the photonic inte-

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rated circuit �PIC�, which forms the gateway fromhe laser source and detectors to the modes of theultimodal waveguide; the lower part describes the

nteraction between the modes of the multimodalaveguide and the disk at both ends of the imaging

ystem. The PIC guides the input light from a laserource into the modes of the multimodal waveguidend guides the reflected modes back to the detectors.n general it should be designed to excite the desiredinear combination of modes needed to illuminatehe disk and to separate all modes reflected backrom the disk to the different detectors. A PICeparating the zeroth- and first-order modes has al-eady been described in the literature.8,9 Our focusn this paper is on the lower part of Fig. 1: theropagation of the modes inside the waveguide to-ard the disk and the coupling of the reflected light

rom the disk into the backward-propagating modesf the waveguide. An imaging system images theight between the waveguide–air facet from the disknd back to the waveguide. In this first approach,imilar optics as in a common digital versatile diskDVD� pickup system could be used. The waveguides placed in the far field, which means that no specialffort is needed to keep the pickup head close to theisk as in near-field methods; also, it is not necessaryo use immersion fluids as with a solid immersionens.5 In an alternative design, the waveguide

oves directly over the disk with a small air gap inetween. This also means that evanescent wavesre picked up, but at the cost of a more complicatedechanical design. As we describe in Subsection

.B, the second approach has advantages if the gapetween the waveguide and the disk is smaller than

ig. 1. Schematic view of the PIC, waveguide, and disk. Theifferent subparts are not drawn to scale.

he wavelength. Therefore the main focus of thisaper is on the far-field approach.To describe the optical properties of the waveguide

canning system, the detector response as a functionf the patterns on the disk are calculated below.his response represents the power of the lighticked up by each of the modes in the multimodalaveguide and are derived by the calculation of theptical field along the optical light path from the lasero the detectors as shown in Fig. 2, which is an un-olded picture of the lower part of Fig. 1. The x axisies along the tracks and the waveguide facet, the yxis is orthogonal to the waveguide chip, and the zxis lies along the propagation direction. We used acalar theory to calculate the optical fields �. Thispproximation is in principle valid only for small NAsut does not change the final results.Assume that the multimodal waveguide has N

uided eigenmodes. Because the disk is illuminatedy a linear combinations of the modes, the field insidehe waveguide at the air interface is given by

�1� x1, y1, z � 0�� i�1

N

�imwgi� x1, y1�. (1)

ecause of the linearity of the optical system, it isufficient to determine the excitation coefficients forach mode separately to calculate the response mea-ured by the detectors. If we define mair

i�x, y, z �� as the field resulting from the transmission ofwg

i�x, y, z � 0�� through the waveguide–air inter-ace, we find, for the field at the disk interface,

�2ai� x2, y2� �

y1

x1

mairi� x1, y1�psfopt� x2 � x1�M, y2

� y1�M�dx1dy1. (2)

n this formula psfopt�x, y� represents the point-pread function of the imaging system, or of the airap, when propagating from the waveguide to theisk; and M is the demagnification factor.10 Theisk reflectivity, which is modulated by the bit pat-ern, is approximated by a local function bp�x, y�, andhe scanning position of the disk along the x axis is x .

ig. 2. Schematic view of the light path from the waveguide to theisk and back to the waveguide. The illumination and detectionides are unfolded.

s

10 June 2004 � Vol. 43, No. 17 � APPLIED OPTICS 3481

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he field �2bi, reflected from the disk, can then be

alculated from the incident field �2ai by

�2bi� x2, xs, y2� � �2a

i� x2, y2�bp� x2 � xs, y2�. (3)

he reflected field �2bi is imaged back onto the

aveguide in the same way as for the illumination:

�3i� x3, xs, y3� �

y2

x2

�2b� x2, xs, y2�psfopt�� x3

� Mx2, y3 � My2�dx2dy2. (4)

sfopt��x, y� now represents the point-spread functionor the imaging system when propagating from theisk to the waveguide10 and is given by

psfopt�� x, y� � psfopt� x�M, y�M�. (5)

t the air–waveguide interface, �3i excites the differ-

nt modes in the multimodal waveguide. From theeciprocity theorem, it can be shown that the complexxcitation coefficients �i, j�xs� of the detected modesan be calculated by the overlap integral of the inci-ent field and the different mode profiles outside theaveguide:

�i, j� xs� � y3

x3

�3i� x3, xs, y3�mair

j� x3, y3�dx3dy3. (6)

ombining Eqs. �2�–�6� results in

�i, j� xs� � [( �� mairi� x1, y1�psflens� x2

� x1�M, y2 � y1�M�dx1dy1�bp� x2

� xs, y2��psflens�� x3 � Mx2, y3

� My2�dx2dy2)mairj� x3, y3�]dx3dy3. (7)

y changing the integration order and replacing psf�sing Eq. �5�, we can simplify Eq. �7� to

�i, j� xs� � �bp� x2 � xs, y2�

� mairi�Mx1, My1�psfopt� x2 � x1, y2

� y1�dx1dy1 mairj�Mx3, My3�psfopt

� � x � x , y � y �dx dy dx dy . (8)
2 3 2 3 3 3� 2 2

sing the two-dimensional convolution operator Rnd the definitions

psfdetectj� x, y� � psfopt� x, y� � mair

j�Mx, My�,

psfillumi� x, y� � psfopt� x, y� � mair

i�Mx, My�,

psftoti, j� x, y� � psfillum

i� x, y�psfdetectj� x, y�, (9)

q. �9� can be rewritten as

�i, j� xs� � y

x

bp� x � xs, y�psftoti, j� x, y�dxdy

� bp � psftoti, j. (10)

he response measured at the detector is propor-ional to the power in the excited modes and can beritten as

Pj� xs� � ��i�1

N

�i�i, j�2

� �bp � �i�1

N

�ipsftoti, j�2

� �bp � psftotj�2, (11)

here psftotj � ¥i�1

N �ipsftoti, j, �i is the coefficients of

he linear combination of the illumination modes asn Eq. �1� and is a proportionality coefficient depen-ent on the detector characteristics. The effectiveoint-spread function psftot

j is a measure for the ef-ective resolution of the signals captured at eachetector and depends heavily on the characteristicsf the imaging system as well as on the effectiverofile of the different waveguide modes. An alter-ative formula to describe the resolution of an op-ical system is the modulation transfer functionMTF�, defined as the amplitude of the Fourier trans-orm of the point-spread function: MTFj� fx, fy� ��psftot

j�x, y��. MTFj� fx, fy� is a good measure forow well the spatial frequencies on a disk can beesolved at the detector side, and MTFj�0, 0� is aeasure for the overall light throughput when noodulation is present.It is interesting to take a close look at a system by

se of only the zeroth-order mode for illumination�0 � 1, �i � 0�. In this case there is a close analogyetween the response P0 and the response of a con-ocal microscope. Whereas a confocal microscopeas a pinhole at the illumination and detector side,he field profile of the zeroth-order mode mair

0�Mx,y� forms the effective aperture in the scanningaveguide system. A higher magnification impliesnarrower effective aperture. For high magnifica-

ions or small waveguides, the zeroth-order mode canoughly be seen as the equivalent of the pinhole in aonfocal microscope. The additional losses in the op-ical path of the scanning waveguide system over thatn a confocal microscope are limited to the losses athe waveguide–air interface. At this interface, partf the light may be reflected due to the difference inefractive index. However, this can be avoided by auitable antireflection coating. Similarly there is annalogy between the response P1 and a push–pullignal from a split photodiode �with the split between

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he two detector halves orthogonal to the track�.11

he relationship, however, is not as straightforwards for the response P0. Figure 3 shows that therst-order waveguide mode is approximately propor-ional to the first derivative of the zeroth-orderaveguide mode: mair

1�Mx, My� � ��d�dx�mair0�Mx,

y� where � is a proportionality coefficient. Fromqs. �9� and �10� one easily finds

�0,1� xs� ��

2d

dxs�0,0� xs�. (12)

f one writes �0,0�xs� as A�xs�exp� j��xs��, with A andthe amplitude and phase of �0,0, respectively, Eq.

11� yields

P0� xs� � � A� xs��2,

P1� xs� � �2

4 �dA� xs�

dxs� A� xs�

d�� xs�

dxs�2

. (13)

quations �13� show that the response P0 is relatednly to the amplitude A of the reflected field, and P1s also a function of the phase �. This means thathe responses P0 and P1 contain partially indepen-ent information from the bit pattern on the disk.t first sight one could compare the first-order signal1 with the push–pull signal �with the split between

he detector halves perpendicular to the track�.11

oth approaches boost the higher frequencies be-ause they take a differential response. The big dif-erence is that the waveguide detection is a coherent

ethod, which means that the right and left part ofhe complex reflected field are subtracted from eachther, whereas in the push–pull signal the intensitys subtracted. A full comparison between the two

ethods is beyond the scope of this paper, but theost striking difference can be shown for the exam-

le of a pure amplitude grating: The push–pull sig-al subtracts the power of the left and right halves ofhe plane of the Fourier transform of the reflected

ig. 3. Normalized modes of a waveguide �width is 0.5�, ncore �.5, nclad � 3.0�. The dotted curve shows the zeroth-order mode,he dashed curve shows the first-order mode, and the solid curvehows the spatial derivative of the zeroth-order mode.

eld from the disk, which means it subtracts theower in, respectively, the positive and the negativerequencies. For a real function, the power in theegative and positive frequencies, however, is alwaysqual, which means that the push–pull signal muste zero for such a grating. As shown in Eqs. �13�,his is not the case for the P1 response of theaveguide system. In conclusion, the split detector

n a DVD system and the first-order mode in theaveguide system behave differently. Whether one

s better than the other depends on the specific diskharacteristics.

. Simulation Method

he simulation of the scanning waveguide can beivided into three parts: the waveguide with theaveguide–air interface, the imaging system or airap, and finally the reflection of the disk. We re-tricted ourselves to two-dimensional calculations,mitting the dimension along the y axis. The opticalroperties along the y axis are identical to those de-cribed along the x axis, but as the waveguides areonomodal along this axis, there is only the P0 re-

ponse. We used TE-polarized light, i.e., the electriceld is parallel to the x axis in Fig. 2, and all dimen-ions were scaled by ��NA with � the wavelength ofhe light and NA the numerical aperture of the illu-ination system �NA equals 1 in the case in which

he waveguide moves at a small air gap over the diskithout the imaging system�.For the modeling of the waveguide and theaveguide–air interface, a full-vectorial eigenmodexpansion tool, the Cavity Modelling Framework�,12

as employed. This tool rigorously solves the Max-ell equations in two dimensions and was used to

alculate the field profile of the waveguide modesnd their transmission at the waveguide–air inter-ace. The propagation from the waveguide inter-ace to the disk is most easily described in thepatial Fourier domain. The optical field is decom-osed into propagating and evanescent plane waves.n our simulations we investigated two differentesigns: The first is an aberration-free lens �NA ishe numerical aperture toward the disk�. In suchcase the imaging system acts as a low-pass filter

n the Fourier domain. In the spatial domain thiss equivalent to a convolution with psfopt�x� �inc�2�NAx�� or psfopt��x� � sinc�2�NAx��M��hen looking from the disk or the waveguide, re-

pectively. In an alternative design the waveguides scanned over the disk with a narrow gap wgap inetween. The propagating plane waves undergo ahase shift, and the evanescent plane waves de-rease in amplitude; the point-spread function isiven by psfopt�x� � ��exp��j�� f �wgap��.In this equation �� f � is defined as

�� f � � 2� 1�2 � f 21�2for �f� �

1� ,

�� f � � �j2�f 2 �1�21�2for �f� �

1� .


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Finally, the three-dimensional disk structure wasodeled by a one-dimensional amplitude response.

n a real disk system the laser spot covers the holesnd parts of the surrounding lands. The reflectionf these holes and lands is different in phase andmplitude. The interference of these results is aodulation of the reflection, which can be modeled bycomplex function bp�x�. The simulation results inubsection 2.C are based on a strong amplitude mod-lation: bp�x� � 1 for ones and bp�x� � 0 for zeros.esults for other modulation functions, however, areimilar.

. Simulations

n our simulations we focused on the following case:he zeroth-order mode is used to illuminate the disk

�0 � 1, �i � 0 in Eq. �1�� and the reflected light isaptured by the zeroth- and the first-order modes,hich result, respectively, in the responses P0 and P1t the detector. Figure 4 shows results for threeonfigurations. In all three configurations the mul-imodal waveguide has a core and cladding refractivendex of 3.5 and 3.0, respectively. These values areomewhat arbitrary and were chosen because ourxperimental research is based on the gallium ar-enide material system.9 In principle any multimo-al waveguide can be used as long as one also selects

ig. 4. Left column shows the MTF for the P0 and P1 response inolid and dashed curves, respectively. The dotted curves give thehape of the MTF of a confocal microscope. On the right side, theespective effective detection apertures mair

0�Mx� and mair1�Mx�

re shown by the solid and dashed curves, respectively. A, widths 1.5, M � 1; B, width is 0.5, M � 1; C, width is 1.5, M � 3.


n appropriate magnification factor in the lens sys-em. In practice a silica- or polymer-basedaveguide would be an appropriate choice because

ransparency for blue light is needed. The lens sys-em in between the waveguide and the disk has a NA.or configurations A and C the waveguide width is.5��NA, for configuration B it is 0.5��NA. Theagnification factor M is 1 in configurations A and B

nd equals 3 in configuration C. On the left theTF of responses P0 and P1 are shown as solid and

ashed curves, respectively. The dotted curves rep-esent the shape of the MTF of a confocal micro-cope.13,14 The right column of Fig. 4 shows theffective detection apertures m0

detect�Mx� and1

detect�Mx�. The illumination aperture is given by0

illum�Mx� and equals m0detect�Mx�. As the proper-

ies of the imaging system are identical in all threeonfigurations, the MTF depends solely on these ef-ective apertures. The effective apertures them-elves depend on the width of the waveguide, thendex contrast between the core and cladding layer,nd the magnification of the imaging system.A comparison of the three configurations in Fig. 4

ndicates that a system with a large effective aper-ure, as in configuration A, has a worse MTF at largerpatial frequencies than those with smaller effectivepertures, as in configurations B and C. In theseast two cases the shape of the MTF for P0 is nearlydentical to that of a confocal microscope. Comparedith configuration A, however, there is a significant

ower overall light throughput given by the valueTF�0�. Taking into account the trade-off between

he resolution at high spatial frequencies and theverall light throughput, the optimal width for theffective apertures lies around ��2 NA�, as in config-ration B or C. Compared with the MTF of the P0esponse, the MTF of the P1 response has a lowerverage light throughput and favors the higher spa-ial frequencies.

Figure 5 shows the MTF for the case in which theaveguide detector is scanned directly over the diskith only a small air gap in between them instead oflens system. For this simulation the waveguide

onfiguration B in Fig. 4 is used. For an air gap ofidth ��4, the waveguide picks up parts of the eva-

ig. 5. MTF of the waveguide scanning system with theaveguide sliding over the disk at a flying height of ��4 and �,

espectively.

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escent waves and the MTF extends beyond the dif-raction limit 2�� note that in this case, NA � 1�.or an air gap of � �B in Fig. 4�, this increase hasecome negligible whereas the overall light through-ut decreased considerably. Therefore this solutions viable only if the distance between the waveguideetector and the disk can be kept below ��4, and inhe remainder of this paper we focus on the case withhe imaging system in between the disk and theaveguide detector. As described above, the re-

ponse P0 of the waveguide scanning system is essen-ially the same as for a confocal system. With thecanning waveguide readout system, however, it isossible to retrieve in parallel information from thether responses Pj. In Section 3 we describe how thenformation of the response P0 and the other re-ponses Pj can be combined to result in a lower bitrror rate �BER�.

. Extracting the Recorded Information from theeasured Responses

. Description of the Bit Pattern Extraction Method

n a conventional compact disk or DVD system, theero and one values from the bit sequence are ex-racted from the signal at the detector when the sig-al is sampled at specific points. A zero crossingarks a change from a one to a zero and vice versa.12

his method is fast and reliable, but a large part ofhe information contained in the detected signal isropped. Enhanced methods for reading out bitsake it possible to increase the data density as in, for

xample, multilevel modulation methods.15 In prin-iple it is even possible to resolve features smallerhan the cutoff frequency of the MTF, ��2NA�.3here exist methods based on inverse filtering andnalytic continuation of the image spectrum that caneconstruct the information outside the MTF band.hese methods, however, are sensitive to small errors

n the measured signal, which means it is eventuallyoise that limits the effective resolution.In this paper we do not look into the details of theseethods, but, starting from a simple parameter fit-

ing algorithm, we prove that the waveguide scan-ing system can read out bits at a lower BER than aonventional system would do in an equivalent situ-tion. The results in Subsection 2.C show that theesponse P0 of the waveguide detector is essentiallyhe same as that of a confocal system. The secondesponse, P1, is detected simultaneously without aecrease in the power of P0. In addition measure-ents have shown that reading out bits from a DVDith a confocal system results in the same jitter val-es as a conventional DVD system.16 Hence we canhow the potential of the scanning waveguide systemy demonstrating that a combination of multiple re-ponses, Pj� j � 0 . . . N � 1�, reduces the BER com-ared with a system that uses only the response P0.As the broad range of coding schemes makes it

arder to compare the different results, we intendedo use a method independent of the possible codingchemes and chose a simple least-squares parameter

tting method to extract the bits from the measure-ents in groups of n consecutive bits. For each of

he modes a response Pj is captured at the detectors.ecause of noise, cross talk, and errors in the track-

ng of the servo system, these responses will be aistorted version of the theoretical response as calcu-ated in Section 2. In the left part of Fig. 6 a sampleit pattern is shown with the corresponding P0 and P1esponses. The dashed curve gives the theoreticalesponse; the solid curve shows the distorted signals.he aim is to recover the n bits inside the dashedectangle from the distorted signal. For n bits, therere 2n possible bit pattern candidates. For each ofhese, the theoretically expected responses are calcu-ated and are written as Cj

k �where k � 1 . . . 2n de-otes the 2n bit patterns and j � 0 . . . N � 1 describeshe order of the mode used to capture the response�.hese candidate bit patterns and their respective cal-ulated responses are shown on the right side of Fig.. To improve the fitting of the distorted responses,ot only knowledge of the parameters of the opticalystem but also knowledge of the bit sequence ex-racted in previous steps are used to calculate theesponses Cj

k from the candidate bit patterns.To select the correct bit pattern �denoted by the

ndex kcorrect� from the 2n candidate bit patterns, aeast-squares fitting algorithm is used: The squaredifferences of each calculated response Cj

k with theetector responses Pj are integrated over a certainange of s, the scanning position along the disk, andorm the overlap matrix S. This matrix has N rowsnd 2n columns, and the individual elements areiven by

Sjk � � Pj�s� � Cj

k�s��2ds

�k � 1 . . . 2n, j � 0 . . . N � 1�. (14)

ig. 6. Distorted signal at detectors 2 � 2n calculated responses.eft column shows the original bit pattern and the distorted sig-als P0 and P1. The right side shows the candidate bit patternsnd the calculated superimposed responses C0

k and C1k.


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or each response j we define kj as the k for which Sjk

as the lowest value, i.e.,

Sjkj � min

k�1. . .2nSj

k. (15)

s long as the distortion on the signals Pj is low, anyf the responses can be used to find a correct bitattern, which means @j:kj � kcorrect. For larger dis-ortion this may no longer be true, and we may havej � ki for some i, j. In such a case it is no longertraightforward to decide which one of the responsesredicts the correct bit pattern. Therefore we haveo construct a decision-making algorithm, whichaximizes the probability of our selecting the correct

it pattern. We propose to do this by taking a well-hosen �linear� combination of the individual re-ponses:

STk � �

j�1

N

�jSjk, (16)

hich is subsequently minimized. The index k cor-esponding with the lowest value of ST

k is called kTnd is used to select the most probable bit pattern.igure 7 explains the principle behind this method

or the case N � 2: The couples �S0k, S1

k� for all k �. . . 2n are plotted on a grid with S0

k and S1k as the

orizontal and vertical coordinates, respectively.he point k that is located the closest to the horizon-

al axis, i.e., with the smallest value S0k, defines the

ndex k0 and, in the same way, the point located thelosest to the vertical axis defines k1. For low dis-ortion values, as explained above, these points willoincide, which means that k0 � k1 and representshe most probable candidate for the correct bit pat-ern kcorrect. For increasing distortion, however, it isossible that k0 � k1, and such a selection is notossible anymore. Instead we chose kT, the minimalalue of ST

k as defined in Eq. �14�, which is the couplehat lies at the bottom left corner along the grayiagonal line ¥j�1

N �jSjk � constant. Note that the

ngle of this line is determined by the relative weight

ig. 7. Graph of the couples �S0k, S1

k� for k � 1 . . . 2n. S0k is

long the horizontal axis, and S1k is along the vertical axis.


j given to each response Sjk and is a parameter to be

ptimized. Simulations in Subsection 3.B show thathis method results in a better chance of our findinghe correct bit pattern then when we take into ac-ount only one of the separate modes.

. Simulations

or the actual simulations we concentrate again onhe case in which the disk is illuminated with theeroth-order mode and is read out by the zeroth- andrst-order modes. For the waveguide and the imag-

ng system, the configuration as shown as B in Fig. 4as used. The BERs for the responses P0 and P1ere simulated for different types of noise. In anctual system, noise can originate from several sourc-s: cross talk from neighboring tracks, intersymbolnterference between the bits within one track, inac-uracies on the disk itself, noise induced by the track-ng servo, or detector noise. In the currentimulations only noise independent of the light poweras implemented. The power of the P0 response isot lower than the signal from a confocal microscopeith a similar aperture, which means that the P0

esponse and the confocal microscope will have a sim-

ig. 8. BER in the case of white noise �upper graph� and inter-rack cross talk �lower graph�. The dashed curves show BER0, theotted curves show BER1, and the solid curves show the BER of theptimum combination. In each graph the upper three curves de-cribe a higher noise level than in the lower three curves.

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lar signal-to-noise ratio. The P1 response, however,s relatively weak and the noise effect may be heavier.n Figs. 8 and 9 the influence of noise on the BER forwo types of noise is shown: white noise, which isandom noise added to the bit patterns, and inter-rack cross talk, which is modeled by the addition ofhe response from random bit patterns to the originalignal. BER0 �dashed curves� and BER1 �dottedurves� are, respectively, the bit error rate from the0 and the P1 response separately. Figure 8 showsERs for two simulations with a different noise levels a function of the minimal bit size in the bit pat-erns. To calculate the BER, 104 bit patterns wereested. This means that BERs below 10�4 are notetected and explains the cutoff of the curves in Fig.. The BER increases rapidly with smaller bit sizes.epending on the type and the amount of noise, the

eroth-order mode can outperform the first-orderode or vice versa.Figure 9 shows how use of a combination of the

esponses P0 and P1 can lead to a lower BER than usef the two responses separately. The curves repre-ent the BER as a function of the ratio between the

ig. 9. BER in the case of white noise �upper graph� and inter-rack cross talk �lower graph� plotted as a function of the linearombination. The different curves represent simulations with de-reasing noise levels. The curves start at the left with the valuef BER1, go through an optimum, and end at the right with thealue of BER0. The simulated bit patterns have minimum bitizes of 0.25��NA.

oefficients �0��1 defined by Eq. �15�. For the whiteoise as well as for the intertrack cross talk, there iscombination ST

k � ¥j�1N �jSj

k that results in a min-mum BER �BERopt� that is lower than the BERchieved with the separate responses BER0 andER1. The gain of the combination in the case ofhite noise, however, is much bigger than in the casef intertrack cross talk. Moreover, the values of theoefficients for an optimum linear combination areot identical for the two types of noise. This meanshat a trade-off in the choice of the linear combinations necessary. Using these results we calculated theERs as a function of bit size and noise. The solidurves in Fig. 8 show the BER of this combination,ERopt, as a function of minimum bit size. For both

ypes of noise the BERopt is much lower than theER0. The optimal ratio of �0��1 is smaller than 1,hich is logical as the response P1 is weaker than the0 response and has to be amplified. This last pointight still be an important drawback as it poses

trong constraints on the mode splitter. Mode split-ers as described in Refs. 8 and 9 have a theoreticalfficiency of 100% for the zeroth-order mode and 50%fficiency for the first-order mode. Also, the crossalk can in principle be made negligible. Practically,owever, it might be hard to split off the weak first-rder signal from the strong zeroth-order signal with-ut adding cross talk on the first-order signal.

. Conclusions

he scanning waveguide approach is a new methodor the readout of optical disks. By illuminating theisk and picking up the reflected light with aaveguide with a few guided modes, we can extract

he phase as well as the amplitude information fromhe field reflected from the disk. The response fromhe zeroth-order mode is equivalent to that of a con-ocal microscope, which itself has similar results ashe conventional readout DVD system. As the dif-erent modes are measured in parallel, the results ofhe different modes can be combined. A well-choseninear combination leads to a BER that outperformshe results from the different modes separately.his means that, for a given BER, the scanningaveguide system can read out bit patterns with

maller bit sizes and allow for an increase of the dataensity on the disk. In this respect the waveguidecanner is a potential candidate for use in futureeadout systems for optical disks.

Part of this research is supported by the Europeannion in the context of the European project IST-000-26479-SLAM.

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performance analysis of a multimode waveguide-based optical disk readout system

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