# Simulated focal separation as a function of the taper length LT for the three-mode demultiplexer. Calculations are performed at the wavelength of λ0=1550 nm x_1 (Length, µm) x_2 (Length, µm) y_1 (Separation TE1-TE2, µm) y_2 (Separation TE0-TE1, µm) 5 5 2.55853402165519 1.95281860290147 5.1 5.1 2.57639502261065 1.99082284215029 5.2 5.2 2.59438445945913 2.02880422861473 5.3 5.3 2.61250204080675 2.06676283101339 5.4 5.4 2.63074747525964 2.10469871806488 5.5 5.5 2.64912047142388 2.14261195848781 5.6 5.6 2.66762073790561 2.18050262100079 5.7 5.7 2.68624798331094 2.21837077432244 5.8 5.8 2.70500191624597 2.25621648717136 5.9 5.9 2.72388224531681 2.29403982826616 6 6 2.74288867912959 2.33184086632545 6.1 6.1 2.76202092629041 2.36961967006784 6.2 6.2 2.78127869540539 2.40737630821194 6.3 6.3 2.80066169508064 2.44511084947636 6.4 6.4 2.82016963392227 2.4828233625797 6.5 6.5 2.8398022205364 2.52051391624059 6.6 6.6 2.85955916352912 2.55818257917762 6.7 6.7 2.87944017150657 2.59582942010941 6.8 6.8 2.89944495307486 2.63345450775457 6.9 6.9 2.91957321684008 2.67105791083171 7 7 2.93982467140837 2.70863969805943 7.1 7.1 2.96019902538582 2.74619993815635 7.2 7.2 2.98069598737856 2.78373869984108 7.3 7.3 3.00131526599269 2.82125605183222 7.4 7.4 3.02205656983433 2.85875206284838 7.5 7.5 3.04291960750959 2.89622680160818 7.6 7.6 3.06390408762458 2.93368033683023 7.7 7.7 3.08500971878542 2.97111273723313 7.8 7.8 3.10623620959822 3.00852407153549 7.9 7.9 3.12758326866909 3.04591440845592 8 8 3.14905060460414 3.08328381671304 8.1 8.1 3.17063792600948 3.12063236502545 8.2 8.2 3.19234494149124 3.15796012211176 8.3 8.3 3.21417135965552 3.19526715669058 8.4 8.4 3.23611688910843 3.23255353748053 8.5 8.5 3.25818123845609 3.2698193332002 8.6 8.6 3.28036411630461 3.30706461256822 8.7 8.7 3.3026652312601 3.34428944430319 8.8 8.8 3.32508429192867 3.38149389712371 8.9 8.9 3.34762100691644 3.41867803974841 9 9 3.37027508482952 3.45584194089588 9.1 9.1 3.39304623427403 3.49298566928474 9.2 9.2 3.41593416385606 3.5301092936336 9.3 9.3 3.43893858218175 3.56721288266107 9.4 9.4 3.4620591978572 3.60429650508576 9.5 9.5 3.48529571948852 3.64136022962627 9.6 9.6 3.50864785568182 3.67840412500122 9.7 9.7 3.53211531504322 3.71542825992921 9.8 9.8 3.55569780617884 3.75243270312886 9.9 9.9 3.57939503769477 3.78941752331877 10 10 3.60320671819715 3.82638278921757 10.1 10.1 3.62713255629207 3.86332856954384 10.2 10.2 3.65117226058565 3.90025493301621 10.3 10.3 3.67532553968401 3.93716194835328 10.4 10.4 3.69959210219325 3.97404968427367 10.5 10.5 3.72397165671949 4.01091820949598 10.6 10.6 3.74846391186884 4.04776759273882 10.7 10.7 3.77306857624742 4.0845979027208 10.8 10.8 3.79778535846134 4.12140920816054 10.9 10.9 3.8226139671167 4.15820157777664 11 11 3.84755411081963 4.19497508028771 11.1 11.1 3.87260549817623 4.23172978441236 11.2 11.2 3.89776783779262 4.26846575886919 11.3 11.3 3.9230408382749 4.30518307237683 11.4 11.4 3.94842420822921 4.34188179365388 11.5 11.5 3.97391765626163 4.37856199141895 11.6 11.6 3.9995208909783 4.41522373439065 11.7 11.7 4.02523362098531 4.45186709128758 11.8 11.8 4.05105555488879 4.48849213082837 11.9 11.9 4.07698640129485 4.52509892173161 12 12 4.10302586880959 4.56168753271592 12.1 12.1 4.12917366603913 4.5982580324999 12.2 12.2 4.15542950158959 4.63481048980217 12.3 12.3 4.18179308406707 4.67134497334134 12.4 12.4 4.20826412207769 4.70786155183601 12.5 12.5 4.23484232422757 4.7443602940048 12.6 12.6 4.2615273991228 4.78084126856631 12.7 12.7 4.28831905536952 4.81730454423916 12.8 12.8 4.31521700157382 4.85375018974195 12.9 12.9 4.34222094634183 4.8901782737933 13 13 4.36933059827965 4.9265888651118 13.1 13.1 4.39654566599339 4.96298203241608 13.2 13.2 4.42386585808918 4.99935784442475 13.3 13.3 4.45129088317312 5.0357163698564 13.4 13.4 4.47882044985133 5.07205767742966 13.5 13.5 4.50645426672991 5.10838183586313 13.6 13.6 4.53419204241498 5.14468891387542 13.7 13.7 4.56203348551266 5.18097898018514 13.8 13.8 4.58997830462905 5.2172521035109 13.9 13.9 4.61802620837027 5.25350835257131 14 14 4.64617690534243 5.28974779608498 14.1 14.1 4.67443010415164 5.32597050277052 14.2 14.2 4.70278551340402 5.36217654134654 14.3 14.3 4.73124284170568 5.39836598053165 14.4 14.4 4.75980179766273 5.43453888904445 14.5 14.5 4.78846208988128 5.47069533560356 14.6 14.6 4.81722342696745 5.50683538892759 14.7 14.7 4.84608551752735 5.54295911773514 14.8 14.8 4.87504807016709 5.57906659074483 14.9 14.9 4.90411079349279 5.61515787667527 15 15 4.93327339611055 5.65123304424506 15.1 15.1 4.96253558662649 5.68729216217282 15.2 15.2 4.99189707364673 5.72333529917715 15.3 15.3 5.02135756577736 5.75936252397667 15.4 15.4 5.05091677162452 5.79537390528998 15.5 15.5 5.08057439979431 5.8313695118357 15.6 15.6 5.11033015889284 5.86734941233242 15.7 15.7 5.14018375752622 5.90331367549877 15.8 15.8 5.17013490430057 5.93926237005336 15.9 15.9 5.20018330782201 5.97519556471478 16 16 5.23032867669663 6.01111332820166 16.1 16.1 5.26057071953057 6.0470157292326 16.2 16.2 5.29090914492992 6.0829028365262 16.3 16.3 5.3213436615008 6.11877471880109 16.4 16.4 5.35187397784933 6.15463144477587 16.5 16.5 5.38249980258161 6.19047308316915 16.6 16.6 5.41322084430376 6.22629970269954 16.7 16.7 5.44403681162189 6.26211137208565 16.8 16.8 5.47494741314212 6.29790816004608 16.9 16.9 5.50595235747055 6.33369013529946 17 17 5.5370513532133 6.36945736656438 17.1 17.1 5.56824410897649 6.40520992255946 17.2 17.2 5.59953033336622 6.4409478720033 17.3 17.3 5.63090973498861 6.47667128361452 17.4 17.4 5.66238202244976 6.51238022611173 17.5 17.5 5.6939469043558 6.54807476821354 17.6 17.6 5.72560408931284 6.58375497863855 17.7 17.7 5.75735328592698 6.61942092610537 17.8 17.8 5.78919420280434 6.65507267933262 17.9 17.9 5.82112654855103 6.6907103070389 18 18 5.85315003177318 6.72633387794283 18.1 18.1 5.88526436107688 6.76194346076301 18.2 18.2 5.91746924506825 6.79753912421806 18.3 18.3 5.9497643923534 6.83312093702657 18.4 18.4 5.98214951153845 6.86868896790717 18.5 18.5 6.01462431122951 6.90424328557847 18.6 18.6 6.04718850003269 6.93978395875906 18.7 18.7 6.0798417865541 6.97531105616756 18.8 18.8 6.11258387939986 7.01082464652259 18.9 18.9 6.14541448717608 7.04632479854274 19 19 6.17833331848887 7.08181158094664 19.1 19.1 6.21134008194435 7.11728506245288 19.2 19.2 6.24443448614862 7.15274531178008 19.3 19.3 6.27761623970781 7.18819239764686 19.4 19.4 6.31088505122801 7.22362638877181 19.5 19.5 6.34424062931535 7.25904735387355 19.6 19.6 6.37768268257594 7.29445536167068 19.7 19.7 6.41121091961589 7.32985048088183 19.8 19.8 6.44482504904131 7.36523278022559 19.9 19.9 6.47852477945831 7.40060232842057 20 20 6.51230981947302 7.4359591941854 20.1 20.1 6.54617987769153 7.47130344623867 20.2 20.2 6.58013466271997 7.50663515329899 20.3 20.3 6.61417388316445 7.54195438408498 20.4 20.4 6.64829724763107 7.57726120731525 20.5 20.5 6.68250446472595 7.61255569170839 20.6 20.6 6.71679524305521 7.64783790598304 20.7 20.7 6.75116929122496 7.68310791885778 20.8 20.8 6.7856263178413 7.71836579905124 20.9 20.9 6.82016603151035 7.75361161528202 21 21 6.85478814083823 7.78884543626873 21.1 21.1 6.88949235443105 7.82406733072999 21.2 21.2 6.92427838089491 7.85927736738439 21.3 21.3 6.95914592883594 7.89447561495056 21.4 21.4 6.99409470686024 7.9296621421471 21.5 21.5 7.02912442357393 7.96483701769262 21.6 21.6 7.06423478758312 8.00000031030573 21.7 21.7 7.09942550749392 8.03515208870503 21.8 21.8 7.13469629191245 8.07029242160915 21.9 21.9 7.17004684944482 8.10542137773668 22 22 7.20547688869713 8.14053902580625 22.1 22.1 7.24098611827551 8.17564543453645 22.2 22.2 7.27657424678606 8.2107406726459 22.3 22.3 7.31224098283491 8.24582480885321 22.4 22.4 7.34798603502815 8.28089791187698 22.5 22.5 7.38380911197191 8.31596005043583 22.6 22.6 7.41970992227229 8.35101129324836 22.7 22.7 7.45568817453541 8.3860517090332 22.8 22.8 7.49174357736739 8.42108136650893 22.9 22.9 7.52787583937433 8.45610033439418 23 23 7.56408466916234 8.49110868140756 23.1 23.1 7.60036977533755 8.52610647626767 23.2 23.2 7.63673086650605 8.56109378769312 23.3 23.3 7.67316765127397 8.59607068440253 23.4 23.4 7.70967983824742 8.6310372351145 23.5 23.5 7.7462671360325 8.66599350854764 23.6 23.6 7.78292925323534 8.70093957342056 23.7 23.7 7.81966589846205 8.73587549845188 23.8 23.8 7.85647678031873 8.77080135236019 23.9 23.9 7.8933616074115 8.80571720386413 24 24 7.93032008834648 8.84062312168227 24.1 24.1 7.96735193172977 8.87551917453325 24.2 24.2 8.00445684616749 8.91040543113567 24.3 24.3 8.04163454026575 8.94528196020814 24.4 24.4 8.07888472263066 8.98014883046927 24.5 24.5 8.11620710186834 9.01500611063766 24.6 24.6 8.1536013865849 9.04985386943194 24.7 24.7 8.19106728538645 9.0846921755707 24.8 24.8 8.2286045068791 9.11952109777256 24.9 24.9 8.26621275966897 9.15434070475612 25 25 8.30389175236217 9.18915106524 25.1 25.1 8.34164119356481 9.22395224794281 25.2 25.2 8.37946079188301 9.25874432158316 25.3 25.3 8.41735025592286 9.29352735487965 25.4 25.4 8.45530929429051 9.32830141655089 25.5 25.5 8.49333761559204 9.3630665753155 25.6 25.6 8.53143492843358 9.39782289989209 25.7 25.7 8.56960094142123 9.43257045899926 25.8 25.8 8.60783536316112 9.46730932135562 25.9 25.9 8.64613790225935 9.50203955567978 26 26 8.68450826732203 9.53676123069036 26.1 26.1 8.72294616695528 9.57147441510596 26.2 26.2 8.76145130976522 9.6061791776452 26.3 26.3 8.80002340435794 9.64087558702667 26.4 26.4 8.83866215933957 9.675563711969 26.5 26.5 8.87736728331622 9.71024362119078 26.6 26.6 8.916138484894 9.74491538341064 26.7 26.7 8.95497547267903 9.77957906734718 26.8 26.8 8.99387795527741 9.814234741719 26.9 26.9 9.03284564129526 9.84888247524473 27 27 9.07187823933869 9.88352233664296 27.1 27.1 9.11097545801381 9.91815439463232 27.2 27.2 9.15013700592674 9.9527787179314 27.3 27.3 9.18936259168359 9.98739537525881 27.4 27.4 9.22865192389048 10.0220044353332 27.5 27.5 9.2680047111535 10.0566059668731 27.6 27.6 9.30742066207879 10.0912000385972 27.7 27.7 9.34689948527244 10.1257867192241 27.8 27.8 9.38644088934058 10.1603660774723 27.9 27.9 9.42604458288931 10.1949381820606 28 28 9.46571027452475 10.2295031017074 28.1 28.1 9.50543767285301 10.2640609051315 28.2 28.2 9.54522648648021 10.2986116610514 28.3 28.3 9.58507642401245 10.3331554381857 28.4 28.4 9.62498719405584 10.3676923052531 28.5 28.5 9.66495850521651 10.4022223309721 28.6 28.6 9.70499006610056 10.4367455840614 28.7 28.7 9.74508158531411 10.4712621332395 28.8 28.8 9.78523277146327 10.5057720472252 28.9 28.9 9.82544333315415 10.5402753947369 29 29 9.86571297899286 10.5747722444933 29.1 29.1 9.90604141758551 10.6092626652131 29.2 29.2 9.94642835753823 10.6437467256147 29.3 29.3 9.98687350745712 10.6782244944169 29.4 29.4 10.0273765759483 10.7126960403382 29.5 29.5 10.0679372716179 10.7471614320973 29.6 29.6 10.1085553030719 10.7816207384128 29.7 29.7 10.1492303789166 10.8160740280032 29.8 29.8 10.1899622077581 10.8505213695872 29.9 29.9 10.2307504982024 10.8849628318833 30 30 10.2715949588556 10.9193984836103 30.1 30.1 10.3124952983239 10.9538283934867 30.2 30.2 10.3534512252134 10.9882526302311 30.3 30.3 10.3944624481302 11.0226712625621 30.4 30.4 10.4355286756804 11.0570843591984 30.5 30.5 10.4766496164702 11.0914919888585 30.6 30.6 10.5178249791056 11.125894220261 30.7 30.7 10.5590544721927 11.1602911221246 30.8 30.8 10.6003378043377 11.1946827631679 30.9 30.9 10.6416746841466 11.2290692121095 31 31 10.6830648202256 11.263450537668 31.1 31.1 10.7245079211809 11.297826808562 31.2 31.2 10.7660036956184 11.33219809351 31.3 31.3 10.8075518521444 11.3665644612309 31.4 31.4 10.8491520993649 11.400925980443 31.5 31.5 10.8908041458861 11.4352827198651 31.6 31.6 10.932507700314 11.4696347482157 31.7 31.7 10.9742624712548 11.5039821342135 31.8 31.8 11.0160681673146 11.5383249465771 31.9 31.9 11.0579244970995 11.572663254025 32 32 11.0998311692156 11.6069971252759 32.1 32.1 11.141787892269 11.6413266290485 32.2 32.2 11.1837943748659 11.6756518340612 32.3 32.3 11.2258503256123 11.7099728090328 32.4 32.4 11.2679554531144 11.7442896226818 32.5 32.5 11.3101094659782 11.7786023437268 32.6 32.6 11.3523120728099 11.8129110408865 32.7 32.7 11.3945629822157 11.8472157828794 32.8 32.8 11.4368619028015 11.8815166384242 32.9 32.9 11.4792085431736 11.9158136762395 33 33 11.521602611938 11.9501069650438 33.1 33.1 11.5640438177009 11.9843965735559 33.2 33.2 11.6065318690683 12.0186825704942 33.3 33.3 11.6490664746464 12.0529650245775 33.4 33.4 11.6916473430413 12.0872440045243 33.5 33.5 11.7342741828591 12.1215195790532 33.6 33.6 11.776946702706 12.1557918168829 33.7 33.7 11.8196646111879 12.1900607867319 33.8 33.8 11.8624276169111 12.2243265573189 33.9 33.9 11.9052354284816 12.2585891973625 34 34 11.9480877545056 12.2928487755812 34.1 34.1 11.9909843035892 12.3271053606938 34.2 34.2 12.0339247843385 12.3613590214187 34.3 34.3 12.0769089053595 12.3956098264746 34.4 34.4 12.1199363752585 12.4298578445802 34.5 34.5 12.1630069026415 12.464103144454 34.6 34.6 12.2061201961147 12.4983457948146 34.7 34.7 12.2492759642841 12.5325858643807 34.8 34.8 12.2924739157559 12.5668234218708 34.9 34.9 12.3357137591361 12.6010585360037 35 35 12.378995203031 12.6352912754977 35.1 35.1 12.4223179560465 12.6695217090717 35.2 35.2 12.4656817267889 12.7037499054442 35.3 35.3 12.5090862238642 12.7379759333338 35.4 35.4 12.5525311558785 12.7721998614591 35.5 35.5 12.596016231438 12.8064217585387 35.6 35.6 12.6395411591488 12.8406416932912 35.7 35.7 12.6831056476169 12.8748597344353 35.8 35.8 12.7267094054485 12.9090759506896 35.9 35.9 12.7703521412498 12.9432904107726 36 36 12.8140335636267 12.977503183403 36.1 36.1 12.8577533811855 13.0117143372994 36.2 36.2 12.9015113025322 13.0459239411804 36.3 36.3 12.945307036273 13.0801320637645 36.4 36.4 12.9891402910139 13.1143387737705 36.5 36.5 13.0330107753612 13.1485441399169 36.6 36.6 13.0769181979208 13.1827482309224 36.7 36.7 13.1208622672989 13.2169511155055 36.8 36.8 13.1648426921016 13.2511528623848 36.9 36.9 13.2088591809351 13.285353540279 37 37 13.2529114424054 13.3195532179066 37.1 37.1 13.2969991851187 13.3537519639864 37.2 37.2 13.3411221176811 13.3879498472368 37.3 37.3 13.3852799486986 13.4221469363765 37.4 37.4 13.4294723867774 13.4563433001242 37.5 37.5 13.4736991405236 13.4905390071983 37.6 37.6 13.5179599185434 13.5247341263176 37.7 37.7 13.5622544294427 13.5589287262006 37.8 37.8 13.6065823818279 13.593122875566 37.9 37.9 13.6509434843048 13.6273166431323 38 38 13.6953374454798 13.6615100976182 38.1 38.1 13.7397639739588 13.6957033077423 38.2 38.2 13.7842227783481 13.7298963422231 38.3 38.3 13.8287135672536 13.7640892697794 38.4 38.4 13.8732360492815 13.7982821591296 38.5 38.5 13.917789933038 13.8324750789925 38.6 38.6 13.9623749271292 13.8666680980866 38.7 38.7 14.006990740161 13.9008612851305 38.8 38.8 14.0516370807398 13.9350547088429 38.9 38.9 14.0963136574716 13.9692484379423 39 39 14.1410201789624 14.0034425411474 39.1 39.1 14.1857563538184 14.0376370871767 39.2 39.2 14.2305218906458 14.071832144749 39.3 39.3 14.2753164980506 14.1060277825827 39.4 39.4 14.320139884639 14.1402240693965 39.5 39.5 14.364991759017 14.1744210739091 39.6 39.6 14.4098718297908 14.2086188648389 39.7 39.7 14.4547798055664 14.2428175109047 39.8 39.8 14.4997153949501 14.277017080825 39.9 39.9 14.5446783065479 14.3112176433185 40 40 14.5896682489659 14.3454192671037 40.1 40.1 14.6346849308102 14.3796220208993 40.2 40.2 14.679728060687 14.4138259734239 40.3 40.3 14.7247973472023 14.4480311933961 40.4 40.4 14.7698924989623 14.4822377495344 40.5 40.5 14.8150132245731 14.5164457105576 40.6 40.6 14.8601592326408 14.5506551451842 40.7 40.7 14.9053302317715 14.5848661221328 40.8 40.8 14.9505259305713 14.6190787101221 40.9 40.9 14.9957460376464 14.6532929778705 41 41 15.0409902616028 14.6875089940969 41.1 41.1 15.0862583110467 14.7217268275197 41.2 41.2 15.1315498945841 14.7559465468576 41.3 41.3 15.1768647208213 14.7901682208291 41.4 41.4 15.2222024983642 14.824391918153 41.5 41.5 15.267562935819 14.8586177075478 41.6 41.6 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