Performance Analysis of a multi-mode waveguide based. optical disc readout system.

Transcription

1 Performance Analy of a mult-mode wavegude baed optcal dc readout ytem. Freder Franoo, Dre Van Thourhout, and Roel Baet Ghent Unverty Interunverty McroElectronc Center (IMEC), Department of Informaton Technology, Snt-Peterneuwtraat 4, Ghent, Belgum In th paper we propoe a method to mprove the optcal reoluton for readng out optcal dc, wthout mang the pot ze on the dc maller than the dffracton lmt. The dea to recontruct the bt pattern from the complete feld profle (ncludng ampltude and phae) of the lght reflected from the dc. Phae and ampltude nformaton are meaured by pcng up the wave front nto dfferent mode of a bmodal wavegude. Once pced up, thee mode can be plt by a photonc ntegrated crcut to be meaured by eparate detector. By combnng the nformaton from the repone from the dfferent mode, the bt error rate can be mproved ubtantally. Copyrght 0.00 Optcal data torage 0.00 Imagng ytem Pattern recognton and feature extracton Phae retreval

2 Introducton Optcal data torage tre to cope wth the trong need for exchangeable uper hghdenty, hgh-data rate torage memore. Applcaton nclude large torage devce for bac-up and mnaturzed veron n moble devce. In the earch for hgher nformaton denty, dfferent approache are beng nvetgated to mae read-out and wrtng of maller mar poble., It well nown that the mallet feature dtnguhable n the far feld gven by λ ( NA). 3 Therefore the mot obvou way to ncreae reoluton decreang the wavelength λ and ncreang the numercal aperture (NA). However further mprovement of thee parameter ncreangly dffcult. Therefore new technque that can overcome the dffracton lmt are beng nvetgated. Example nclude magneto-optcal recordng baed on magnetc doman expanon 4 and near feld read-out ung aperture probe or old mmeron lene (SIL). 5 Other approache try to enhance the reoluton n the far feld, ung phae ma placed n the pupl or mage plane 6, or ung nterference mcrocopy to detect the phae of the optcal feld. 7 In th paper a new way of readng out optcal dc preented. The dea to ue an ntegrated photonc chp wth multmodal wavegude to pc up the optcal feld comng from the dc. Such a wavegude upport multple optcal mode and the relatve ampltude by whch thee mode are excted wll depend on both the ampltude and the phae profle of the feld comng bac from the dc. If we can plt up the repectve wavegude mode and detect the power n each of them eparately, we may be able to recontruct the data wrtten on the dc wth a hgher reoluton than n the cae of a conventonal ytem. The concept to ncreae the reoluton n the far feld mlar to other approache ung phae nformaton uch a nterference mcrocopy. 7 The dc can be llumnated by a ngle mode or by a lnear

3 combnaton of multple mode. A econd ratonale behnd the approach of the cannng wavegude read-out ytem the potental ntegraton of all optcal element, ncludng the laer and detector on a ngle chp, thereby reducng the ze of the pc-up head by an order of magntude, eventually leadng to a much more compact optcal dc drve. Furthermore dc llumnated wth the ame multmodal wavegude a ued for the detecton, whch mplfe the degn further and mae the algnment much le entve than for ntance n a confocal mcrocope. Overvew of the cannng wavegude ytem Decrpton of the optcal ytem Fg. how a chematc pcture of the cannng wavegude. The total ytem can be dvded nto two part. The upper part compre the photonc ntegrated crcut (PIC), whch form the gateway from laer ource and detector to the mode of the multmodal wavegude; the lower part decrbe the nteracton between the mode of the multmodal wavegude and the dc at both end of the magng ytem. The PIC gude the nput lght from a laer ource nto the mode of the multmodal wavegude and gude the reflected mode bac to the detector. In general t hould be degned to excte the dered lnear combnaton of mode needed to llumnate the dc and to eparate all mode reflected bac from the dc to the dfferent detector. A PIC eparatng the zeroth and the frt order mode ha already been decrbed n the lterature 8,9. The focu of the remander of the current paper on the lower part of Fg. : the propagaton of the mode nde the wavegude toward the dc and the couplng of the reflected lght from the dc nto the bacward propagatng mode of the wavegude. An magng ytem mage the lght between the wavegude-ar facet and the dc, and bac. In th frt approach 3

4 mlar optc a n a common DVD pc-up ytem could be ued. The wavegude placed n the far feld, whch mean no pecal effort needed to eep the pc-up head very cloe to the dc a n near feld method, t nether needed to ue mmeron flud a wth a old mmeron len 5. In an alternatve degn, the wavegude move drectly over the dc wth a mall ar gap n between. Th mean alo evanecent wave are pced up, but at the cot of a more complcated mechancal degn. A wll be decrbed n the next ecton, the econd approach ha only advantage for a very mall gap between the wavegude and the dc. Therefore the man focu of th paper wll be on the far-feld approach. To decrbe the optcal properte of the wavegude cannng ytem, the detector repone a a functon of the pattern on the dc wll be calculated n the next paragraph. Th repone repreent the power of the lght pced up by each of the mode n the multmodal wavegude and wll be derved by calculatng the optcal feld along the optcal lght path from laer to detector a hown on Fg., whch an unfolded pcture of the lower part of Fg.. The x-ax le along the trac and the wavegude facet, the y-ax orthogonally to the wavegude chp, and the z-ax le along the propagaton drecton. We ued a calar theory to calculate the optcal feld ψ. Th approxmaton n prncple only vald for mall numercal aperture but doe not change the fnal reult. Aume the multmodal wavegude ha N guded egenmode. Snce the dc llumnated by a lnear combnaton of the mode, the feld nde the wavegude at the ar nterface gven by N ( x, y,z = 0 ) = α mwg ( x, ) ψ. () y = Due to the lnearty of the optcal ytem t uffcent to determne the exctaton coeffcent for each mode eparately for calculatng the repone meaured by the detector. If we defne 4

5 + m ar ( x, y,z = 0 ) a the feld reultng from the tranmon of ( x, y,z = 0 ) wavegude-ar nterface, we fnd, for the feld at the dc nterface: m wg through the ψ ( x, ) = mar ( x, y ) pf opt ( x x M, y y M ) dxdy a y In th formula ( x, y) y x () pf opt repreent the pont pread functon of the magng ytem, or of the ar gap, when propagatng from the wavegude to the dc; M the demagnfcaton factor. 0 The dc reflectvty, whch modulated by the bt pattern, approxmated by a local functon ( x, y) bp and the cannng poton of the dc along the x-ax x. The feld the dc, can then be calculated from the ncdent feld ψ a by: ψ b, reflected from ψ ( x,x, ) = ( x, y ) bp( x x, ) b y ψ (3) a y The reflected feld llumnaton: ψ b maged bac onto the wavegude n the ame way a for the ( x, y) ψ ( x,x, ) = b ( x,x, y ) pf opt ( x3 M x, y3 M y ) dxdy 3 3 y3 y x ψ (4) pf opt now repreent the pont pread functon for the magng ytem when propagatng from the dc to the wavegude 0 and gven by: pf opt ( x, y) = ( x M, y M ) pf opt (5) At the ar-wavegude nterface, ψ 3 excte the dfferent mode n the multmodal wavegude. From the recprocty theorem, t can be hown that the complex exctaton coeffcent χ, ( x ) 5

6 of the detected mode can be calculated by the overlap ntegral of the ncdent feld and the dfferent mode profle outde the wavegude., χ ( x ) = 3 ( x3,x, y3 ) mar ( x3, y3 ) dx3dy3 ψ (6) y x 3 3 Combnng equaton ( 6) th reult n: χ, ( x ) = m ( x, y ) pf ( x x M, y y M ) ar dx dy len ( x ) ( ) x, y pf len x3 M x, y3 M y dxdy bp mar ( x3, y3 ) dx3dy3 (7) By changng the ntegraton order and replacng p f ung (5), equaton (7) can be mplfed to: m ar χ, ( x ) = bp ( x x, ) y ( M x,m y ) pf opt ( x x, y y ) dxdy mar ( M x3,m y3 ) pf opt ( x x3, y y3 ) dx3dy 3 dxdy (8) Ung the two dmenonal convoluton operator and the defnton: 6

7 det ( x, y) = pf ( x, y) mar ( M x,m y) pf ect pf opt, llum ( x, y) = pf ( x, y) m ( M x,m y) opt ar, and pf, tot ( x, y) = pf ( x, y) pf det ect ( x, y) llum (9) equaton (9) can be rewrtten a:, ( x ) bp( x x, y) pf, ( x, y) dxdy = bp pf = χ, tot tot (0) y x The repone meaured at the detector proportonal to the power n the excted mode and can be wrtten a: N P ( x )= χ, γ α = γ bp α pf, = = N = tot γ bp pf tot () wth N pf tot = = α, pf tot, α the coeffcent of the lnear combnaton of the llumnaton mode a n equaton () and γ a proportonalty coeffcent dependent on the detector charactertc. The effectve pont pread functon pf tot a meaure for the effectve reoluton of the gnal captured at each detector and depend heavly on the charactertc of the magng ytem a well a on the effectve profle of the dfferent wavegude mode. An alternatve formula to decrbe the reoluton of an optcal ytem the modulaton tranfer functon (MTF), defned a the ampltude of the Fourer tranform of the pont pread functon: MTF ( f, f ) F ( pf ( x, y )) x y =. ( f, f ) tot MTF a good meaure for how well the patal x y frequence on a dc can be reolved at the detector de and MTF ( 0,0 ), a meaure for the overall lght throughput when no modulaton preent. 7

8 It nteretng to have a cloe loo at a ytem ung only the zeroth order mode for llumnaton (α 0 =, α =0). In th cae there a cloe analogy between the repone P 0 and the repone of a confocal mcrocope. Whle a confocal mcrocope ha a pnhole at the llumnaton and detector de, the feld profle of the zeroth order mode m 0 ar ( M x,m y) form the effectve aperture n the cannng wavegude ytem. A hgher magnfcaton mple a narrower effectve aperture. For hgh magnfcaton and/or mall wavegude, the zeroth order mode can roughly be een a the equvalent of the pnhole n a confocal mcrocope. The addtonal loe n the optcal path of the cannng wavegude ytem over that n a confocal mcrocope are lmted to the loe at the wavegude-ar nterface. At th nterface part of the lght may be reflected due to the dfference n refractve ndex. Th can however be avoded by a utable ant-reflecton coatng. Smlarly there an analogy between the repone P and a puh-pull gnal from a plt photodode (wth the plt between the two detector halve orthogonally to the trac). The relatonhp however not a traghtforward a for the repone P 0. Fg. 3 how the frt order wavegude mode approxmately proportonal to the frt dervatve of the zeroth order wavegude mode: m ar d ar wth η a proportonalty coeffcent. From equaton (9) and dx 0 ( M x,m y) η m ( M x,m y) (0) one ealy fnd: 0,0 If one wrte χ ( x ) a ( x ) exp( ( )) repectvely, equaton () gve: η d 0,0 ( x ) χ ( x ) 0, χ. () dx A ϕ, wth A and ϕ the ampltude and phae of χ 0,0 x 8

9 P ( x ) = γ A( ) and P ( x ) 0 x γη da ( x ) dϕ ( x ) + A( x ) (3) 4 dx dx Equaton (3) how that the repone P 0 only related to the ampltude A of the reflected feld, whle P alo a functon of the phae ϕ. Th mean the repone P 0 and P contan partally ndependent nformaton from the bt pattern on the d. At frt ght one could compare the frt order gnal P wth the puh-pull gnal (wth plt between the detector halve perpendcular to the trac). Both approache boot the hgher frequence, by tang a nd of dfferental repone. The bg dfference that the wavegude detecton a coherent method, whch mean the rght and left part of the complex reflected feld are ubtracted from each other, whle n the puh-pull gnal the ntenty ubtracted. A full comparon between the two method beyond the cope of th paper, but the mot trng dfference can be hown for the example of a pure ampltude gratng: The puh-pull gnal ubtract the power of the left and rght halve plane of the Fourer tranform of the reflected feld form the dc, whch mean t ubtract the power n repectvely the potve and the negatve frequence. For a real functon the power n the negatve and potve frequence however alway equal, whch mean the puh-pull gnal mut be zero for uch a gratng. A hown n equaton (3), th not the cae for the P repone of the wavegude ytem. In concluon: the plt detector n a DVD ytem and the frt order mode n the wavegude ytem behave dfferently. Whether one better than the other depend on the pecfc dc charactertc. Smulaton Method The mulaton of the cannng wavegude can be dvded nto three part: the wavegude wth the wavegude-ar nterface, the magng ytem or ar gap and fnally the reflecton of the 9

10 dc. We retrcted ourelve to D calculaton, omttng the dmenon along the y-ax. The optcal properte along the y-ax are dentcal to thoe decrbed along the x-ax, but a the wavegude are monomodal along th ax, there only the P 0 repone. We ued TE-polarzed lght,.e. the electrc feld parallel to the x-ax n Fg., and all dmenon have been caled by λ/na wth λ the wavelength of the lght and NA the numercal aperture of the llumnaton ytem (NA= n the cae where the wavegude move at a mall ar gap over the dc wthout magng ytem). For the modelng of the wavegude and the wavegude-ar nterface, a full-vectoral egenmode expanon tool, CAMFR (CAvty Modellng FRamewor), wa employed. Th tool rgorouly olve the Maxwell equaton n two dmenon and wa ued to calculate the feld profle of the wavegude mode and ther tranmon at the wavegude-ar nterface. The propagaton from the wavegude nterface to the dc mot ealy decrbed n the patal Fourer doman. The optcal feld decompoed nto propagatng and evanecent plane wave. In our mulaton we nvetgated two dfferent degn: the frt an aberraton free len wth numercal aperture equal to NA (een from the dc). In uch a cae the magng ytem act a a low pa flter n the Fourer doman. In the patal doman th equvalent wth a convoluton wth pf opt ( x) = nc ( π NA x λ) or f ( x) = nc ( π NA x ( M λ) ) p opt, when loong from the dc or the wavegude repectvely. In an alternatve degn the wavegude canned over the dc wth a narrow gap w gap n between. The propagatng plane wave undergo a phae hft and the evanecent plane wave a decreae n ampltude and the pont pread functon gven by ( ) ( f ) w gap pf opt ( x)= F e β. In th equaton β ( f ) defned a: 0

11 β λ ( f ) = π f for f and β ( f ) = π f λ for f λ λ Fnally, the 3D dc tructure ha been modeled by a D ampltude repone. In a real dc ytem the laer pot cover the hole and part of the urroundng land. The reflecton of thee hole and land dfferent n phae and/or ampltude. The nterference of thee reult n a modulaton of the reflecton, whch can be modeled by a complex functon bp ( x). The mulaton reult n the next paragraph are baed on a trong ampltude modulaton: bp ( x) = for one and bp ( x) = 0 for zero. Reult for other modulaton functon are however very mlar. Smulaton In our mulaton we focued on the followng cae: the zeroth order mode ued to llumnate the dc (α 0 =, α =0 n equaton ()) and the reflected lght captured by the zeroth and the frt order mode, whch reult repectvely nto the repone P 0 and P at the detector. Fg. 4 how reult for three confguraton. In all three confguraton the multmodal wavegude ha a core and claddng refractve ndex of 3.5 and 3.0 repectvely. Thee value are omewhat arbtrary and were choen becaue our expermental wor baed on the gallum arende materal ytem. 9 In prncple any multmodal wavegude can be ued, a long a one alo elect an approprate magnfcaton factor n the len ytem. In practce a lca or polymer baed wavegude would be an approprate choce, becaue tranparency for blue lght needed. The len ytem n between the wavegude and the dc ha a numercal aperture NA. For confguraton A and confguraton C the wavegude wdth.5λ/na, for confguraton B t 0.5λ/NA. The magnfcaton factor M n confguraton A and B, and equal 3 n confguraton

12 C. On the left the MTF of repone P 0 and P hown n old and dahed lne repectvely. The dotted lne repreent the hape of the MTF of a confocal mcrocope. 3,4 The rght column of Fg. 4 how the effectve detecton aperture m det ect 0 ( M x) and m det ect ( M x) aperture gven by m llum 0 ( M x) and equal m det ect ( M x). The llumnaton 0. A the properte of the magng ytem are dentcal n all three confguraton, the MTF depend olely on thee effectve aperture. The effectve aperture themelve depend on the wdth of the wavegude, the ndex contrat between core and claddng layer and the magnfcaton of the magng ytem. A comparon of the three confguraton n Fg. 4 ndcate that a ytem wth a large effectve aperture, a n confguraton A, ha a wore MTF at larger patal frequence than thoe wth maller effectve aperture, a n confguraton B and C. In thee lat two cae the hape of the MTF for P 0 nearly dentcal to that of a confocal mcrocope. Compared to confguraton A, there however a gnfcant lower overall lght throughput gven by the value MTF ( 0). Tang nto account the trade-off between the reoluton at hgh patal frequence and the overall lght throughput, the optmal wdth for the effectve aperture le around λ/( NA), a n confguraton B or C. Compared to the MTF of the P 0 repone the MTF of the P repone ha a lower average lght throughput and favor the hgher patal frequence. Fg. 5 how the MTF for the cae where the wavegude detector canned drectly over the dc wth only a mall ar gap n between them ntead of a len ytem. For th mulaton the wavegude confguraton of Fg. 4B ued. For an ar gap of wdth λ/4, the wavegude pc up part of the evanecent wave and the MTF extend beyond the dffracton lmt /λ (note that n th cae NA=). For an ar gap of λ (Fgure 4B), th ncreae ha become neglgble whle the overall lght throughput decreaed conderably. Therefore th oluton only vable f the

13 dtance between wavegude detector and dc can be ept below λ/4 and n the remander of th text we wll focu on the cae wth the magng ytem n between dc and wavegude detector. A decrbed above the repone P 0 of the wavegude cannng ytem eentally the ame a for a confocal ytem. Wth the cannng wavegude read out ytem t however poble to retreve n parallel nformaton from the other repone P. In the next ecton we wll decrbe how the nformaton of the repone P 0 and the other repone P can be combned to reult n a lower bt error rate. Extractng the recorded nformaton from the meaured repone Decrpton of the bt pattern extracton method In a conventonal CD- or DVD-ytem, the zero and one value from the bt equence are extracted from the gnal at the detector by amplng the gnal at pecfc pont. A zerocrong mar a change from a one to a zero and vce vera. Th method fat and relable, but a large part of the nformaton contaned n the detected gnal dropped. Enhanced method for readng out bt mae t poble to ncreae the data denty a for ntance n multlevel modulaton method. 5 In prncple t even poble to reolve feature maller than the cut off frequency of the MTF, λ ( NA). 3 There ext method baed on nvere flterng and analytc contnuaton of the mage pectrum that can recontruct the nformaton outde the MTF-band. Thee method are however very entve to mall error n the meaured gnal, whch mean t eventually noe that lmt the effectve reoluton. In th paper we wll not loo nto the detal of thee method but tartng from a mple parameter fttng algorthm we wll prove that the wavegude cannng ytem can read out bt at a lower bt error rate than a conventonal ytem would do n an equvalent tuaton. The 3

14 reult n the prevou ecton how that the repone P 0 of the wavegude detector eentally the ame a that of a confocal ytem. The econd repone, P, detected multaneouly wthout decreang the power of P 0. In addton meaurement have hown that readng out bt from a DVD wth a confocal ytem reult n the ame tter value a a conventonal DVD ytem. 6 Hence the potental of the cannng wavegude ytem can be hown by demontratng that a combnaton of multple repone, P (=0 N-), reduce the bt error rate compared to a ytem ung only the repone P 0. A the broad range of codng cheme mae t harder to compare the dfferent reult, we ntended to ue a method ndependent of the poble codng cheme and choe a mple leat quare parameter fttng method to extract the bt from the meaurement n group of n conecutve bt. For each of the mode a repone P captured at the detector. Becaue of noe, crotal and error n the tracng of the ervo ytem thee repone wll be a dtorted veron of the theoretcal repone a calculated n the prevou ecton. In the left part of Fg. 6 a ample bt pattern hown wth the correpondng P 0 and P repone. The dahed lne gve the theoretcal repone; the old lne how the dtorted gnal. The am to recover the n bt nde the dahed rectangle from the dtorted gnal. For n bt, there are n poble bt pattern canddate. For each of thee, the theoretcally expected repone are calculated and wll be wrtten a C (where = n denote the n bt pattern and =0 N- decrbe the order of the mode ued to capture the repone). Thee canddate bt pattern and ther repectve calculated repone are hown n the rght part of Fg. 6. To mprove the fttng of the dtorted repone, not only nowledge of the parameter of the optcal ytem but alo nowledge of the bt equence extracted n prevou tep ued to calculate the repone bt pattern. C from the canddate 4

15 To elect the correct bt pattern (denoted by the ndex correct ) from the n canddate bt pattern, a leat quare fttng algorthm ued: the quared dfference of each calculated reponec wth the detector repone P are ntegrated over a certan range of, the cannng poton along the dc and form the overlap matrx S. Th matrx ha N row and n column and the ndvdual element are gven by: S = P () C ()d (= n, =0 N-) (4) For each repone we defne a the for whch S ha the lowet value,.e.: S = mn S (5) n =.. A long a the dtorton on the gnal P low, any of the repone can be ued to fnd correct bt pattern, whch mean : = correct. For larger dtorton th may no longer be true and we may have for ome,. In uch a cae t no longer traghtforward to decde whch one of the repone predct the correct bt pattern. Therefore a decon-mang algorthm, maxmzng the probablty of electng the correct bt pattern, ha to be contructed. We propoe to do th by tang a well-choen (lnear) combnaton of the ndvdual repone: N S = β S (6) T = whch ubequently mnmzed. The ndex correpondng wth the lowet value of S T, wll be called T and wll be ued to elect the mot probable bt pattern. Fg. 7 explan the prncple behnd th method for the cae N=: the couple (, ) S for all = n are plotted on a grd 0 S 5

16 wth S 0 and S a the horzontal and vertcal coordnate repectvely. The pont whch located the cloet to the horzontal ax.e. wth the mallet value S 0 then defne the ndex 0, and n the ame way, the pont located the cloet to the vertcal ax wll defne. For low dtorton value, a explaned above, thee pont wll concde, whch mean 0 = and repreent the mot probable canddate for the correct bt pattern correct. For ncreang dtorton however, t poble that 0 and uch a electon not poble anymore. Intead we choe T, the mnmal value of ST a defned n equaton (4), whch the couple that le at the bottom left corner along the gray dagonal lne N = β S = con tant. Note that the angle of th lne determned by the relatve weght β gven to each repone S and a parameter to be optmzed. Smulaton n the next paragraph how that th method reult n a better chance of fndng the correct bt pattern then tang nto account only one of the eparate mode. Smulaton For the actual mulaton we concentrate agan on the cae where the dc llumnated wth the zeroth order mode and read out by the zeroth and frt order mode. For the wavegude and the magng ytem the confguraton a hown n Fg. 4B wa ued. The bt error rate for the repone P 0 and P have been mulated for dfferent type of noe. In an actual ytem, noe may orgnate from everal ource: crotal from neghborng trac, nter ymbol nterference between the bt wthn one trac, naccurace on the dc telf, noe nduced by the tracng ervo, or detector noe. In the current mulaton only noe ndependent of the lght power ha been mplemented. The power of the P 0 repone not lower than the gnal from a confocal mcrocope wth a mlar aperture, whch mean the P 0 repone and the 6

17 confocal mcrocope wll have mlar gnal to noe rato. The P repone however relatvely wea and the noe mpact may be heaver. the On Fg. 8 and Fg. 9 the nfluence of noe on the BER for two type of noe hown: whte noe, whch random noe added to the bt pattern and nter trac crotal, whch modeled by addng the repone from random bt pattern to the orgnal gnal. BER 0 (dahed lne) and BER (dotted lne) are repectvely the bt error rate from the P 0 and the P repone eparately. Fg. 8 how bt error rate for two mulaton wth a dfferent noe level, a a functon of the mnmal bt ze n the bt pattern. For calculatng the bt error rate, 0 4 bt pattern have been teted. Th mean bt error rate below 0-4 are not detected and explan the cut off of the curve on Fg. 8. The bt error rate ncreae rapdly wth maller bt ze. Dependng on the type and the amount of noe the zeroth order mode can outperform the frt order mode or vce vera. Fg. 9 how how ung a combnaton of the repone P 0 and P can lead to a lower bt error rate than by ung the two repone eparately. The curve repreent the bt error rate a a functon of the rato between the coeffcent β 0 /β defned by equaton (5). For the whte noe a well a for the nter trac crotal, there a combnaton N S = β S that reult n a T = mnmum bt error rate (BER opt ), lower than the bt error rate acheved wth the eparate repone, BER 0 and BER. The gan of the combnaton n cae of whte noe however much bgger than n the cae of nter trac crotal. Moreover the value of the coeffcent for optmum lnear combnaton are not dentcal for the two type of noe. Th mean a trade-off for choong the lnear combnaton neceary. Ung thee reult we calculated the bt error rate a a functon of bt ze and noe. The old lne on Fg. 8 how the bt error rate of th combnaton, BER opt, a a functon of mnmum bt ze. For both type of noe the BER opt 7

18 much lower than the BER 0. The optmal rato of β 0 β maller than, whch logcal a the repone P weaer than the P 0 repone and ha to be amplfed. Th lat pont mght tll be an mportant drawbac a t poe trong contrant on the mode pltter. Mode pltter a n decrbed n ref. 8 and ref. 9 have a theoretcal effcency of 00% for the zeroth order mode and 50% effcency for the frt order mode. Alo the crotal can n prncple be made neglgble. Practcally, t mght however be hard to plt off the wea frt order gnal from the trong zeroth order gnal wthout addng crotal on the frt order gnal. Concluon The cannng wavegude approach a new method for read-out of optcal dc. By llumnatng the dc and pcng up the reflected lght wth a wavegude wth a few guded mode, phae a well a ampltude nformaton can be extracted from the feld reflected from the dc. The repone from the zeroth order mode equvalent to that of a confocal mcrocope, whch telf ha mlar reult a the conventonal read-out DVD ytem. A the dfferent mode are meaured n parallel, the reult of the dfferent mode can be combned. A well-choen lnear combnaton lead to a bt error rate that outperform the reult from the dfferent mode eparately. Th mean that for a gven bt error rate the cannng wavegude ytem can read out bt pattern wth maller bt ze and allow for an ncreae of the data denty on the dc. In th repect the wavegude canner a potental canddate for ue n future read-out ytem for optcal dc. Acnowledgement Part of th wor upported by the European Unon n the context of the European proect IST SLAM. 8

19 9

20 Reference. G. Bouwhu, J. Braat, A. Huer, J. Paman, G. van Romalen, K. Schouhamer Immn, Prncple of Optcal Dc Sytem (Adam Hlger, Brtol, 985).. M. Manurpur and G. Sncerbox, Prncple and Technque of Optcal Data Storage, Proceedng of the IEEE 85, (997). 3. A. J. den Deer and A. van den Bo, "Reoluton: a urvey", J. Opt. Soc. Am. A 4, (997). 4. H. Awano, N. Ohta, Magnetooptcal Recordng Technology Toward 00 Gb/n, IEEE Journal of Selected Topc n quantum Electronc 4, (998) 5. T.D. Mlter, Near-feld optc: A new tool for data torage, Proceedng of the IEEE 88, (000) 6. U. Brand, G. Heter, J. Grochmalc, R. Pe, Super-reoluton n optcal data torage, Journal of Optc A-Pure and appled Optc, (999) 7. M. Eberler, R. Dorn, B.Münzer, S. Quab, G. Leuch, Characterzaton of ub-wavelength tructure ung phae-ngularte, n Proceedng of the World Conference on Sytematc, Cybernetc and Informatc, (IIIS, Orlando, 00) 8. J. Leuthold, R. He, J. Ecner, P.A. Bee and H. Melchor, "Spatal mode flter realzed wth multmode nterference coupler", Optc Letter, (996.) 9. F. Franoo, D. Van Thourhout, L. Van Landchoot, A. Verbet, W. Van Pary, P. Van Daele, R. Baet, "A method for detectng ub-wavelength feature by mean of a multmode wavegude and a mode plttng photonc IC," n Proceedng of the LEOS annual meetng (Inttute of Electrcal and Electronc Engneer, Glagow, 00), pp

21 0. B.E.S. Saleh, M.C. Tech, n Fundamental of Photonc, (John Wley and Son, New Yor, 99), pp A. Korpel, Smplfed dffracton theory of the vdeo d, Appled Optc 7, (978).. P. Bentman, R. Baet, "Advanced boundary condton for egenmode expanon model", Optcal and Quantum Electronc 34, (00). 3. R.H.Webb, "Confocal optcal mcrocopy ", Report on Progre n Phyc 59, (996). 4. M. Gu, D. Day, "Three-dmenonal coherent tranfer functon for reflecton confocal mcrocopy n the preence of refractve-ndex mmatch", Journal of the Optcal Socety of Amerca A 6, (00) 5. T. Zhou, C. Tan, C. Le, I. Harvey, G. Lew, T. Wong, M. O Nell, "Multlevel ampltudemodulaton ytem for optcal data torage," n Advanced Optcal Storage Technology, Proc. SPIE 4930, 7-0 (00). 6. S. Stallnga, Confocal detecton and pupl ma for data torage on optcal dc n Proceedng of EOS Topcal Meetng on Advanced Imagng Technque, (European Optcal Socety, Delft, 003), pp

22 Lt of Fgure capton Fg.. Schematc vew of the PIC, wavegude and dc. The dfferent ubpart have not been drawn to cale. Fg.. Schematc vew of lght path from wavegude to dc and bac to wave-gude. The llumnaton and detecton de have been unfolded. Fg. 3. Normalzed mode of a wavegude (wdth=0.5λ, n core =3.5 n clad =3.0). The dotted lne how the zeroth order mode, the dahed lne gve the frt order mode and the old lne how the patal dervatve of the zeroth order mode. Fg. 4. The left column how the modulaton tranfer functon for P0 and P repone, n old and dahed lne repectvely. The dotted lne gve the hape of the MTF of a confocal mcrocope. On the rght de, the repectve effectve detecton aperture m 0 ar ( M x) and m ar ( M x) are hown n old and dahed lne. (A: wdth=.5, M= B: wdth=0.5, M= C: wdth=.5, M=3) Fg. 5. Modulaton tranfer functon of the wavegude cannng ytem wth the wavegude ldng over the dc at a flyng heght of λ/4 and λ repectvely. Fg. 6. The left column how the orgnal bt pattern and the dtorted gnal P 0 and P. The rght part of the fgure how the canddate bt pattern and the calculated upermpoed reponec and 0 C. Fg. 7. A graph of the couple (, ) the vertcal ax. S for = n : S along the horzontal ax, and 0 S 0 S along Fg. 8. Bt error rate n cae of whte noe (upper graph) and nter trac crotal (lower graph). The dahed lne how the BER 0, dotted lne how the BER, old lne gve the BER of

23 the optmum combnaton. In each graph the upper three curve decrbe a hgher noe level than n the lower three curve. Fg. 9. Bt error rate n cae of whte noe (upper graph) and nter trac crotal (lower graph), plotted a a functon of the lnear combnaton. The dfferent curve repreent mulaton wth decreang noe level. The curve tart at the left wth the value of BER go through an optmum and end at the rght wth the value of BER 0. The mulated bt pattern have a mnmum bt ze of 0.5λ/NA. 3