Vlnovody s velkým kontrastem indexu lomu

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Ladislav Mašek
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1 Vlnovody s velkým kontrastem indexu lomu Fotonický drát (vlnovod s velkým kontrastem indexu lomu) Rozložení elektromagnetického pole základního vidu TE E x H y 1

Vazba do nanofotonických vlnovodů 1mm SOI wire Problémy: Účinná

konvertor velikosti vidového pole: v horizontální rovině ve

fiber core Adiabatický přechod mezi vlnovody velmi různých

2 Vazba do nanofotonických vlnovodů 1mm SOI wire Problémy: Účinná vazba mezi submikrometrovým vlnovodem a vláknem Je nutný konvertor velikosti vidového pole: v horizontální rovině ve vertikální rovině (obtížnější) Polarizační problém Single mode fiber core Adiabatický přechod mezi vlnovody velmi různých profilů / kontrastů SOI drát.mm.4mm polymerní vlnovod invertovaný klínový přechod 5 mm 8nm

Křemíkové vlnovody se subvlnovými strukturami (subwavelength grating waveguide, SWG) Schematic picture of (a) a strip channel waveguide and (b) SWG waveguide considered in this contribution.

$- SWG waveguide - a new type of microphotonic waveguide - Practical implementations to fiber-chip coupling, waveguide crossing and refractive index engineering Scanning electron microscope (SEM)$ images of fabricated structures including: a) SWG straight waveguide with Λ = 3 nm, w = 5 nm and a duty cycle of 33%. b) Detail of two SWG segments. P. J. Bock, Optics Express, 18(19), 51 (1).

images of fabricated structures including: a) SWG straight waveguide with Λ = 3 nm, w = 5 nm and a duty cycle of 33%. b) Detail of two SWG segments. P. J. Bock, Optics Express, 18(19), 51 (1).

3 Křemíkové vlnovody se subvlnovými strukturami (subwavelength grating waveguide, SWG) Schematic picture of (a) a strip channel waveguide and (b) SWG waveguide considered in this contribution. In both cases, Si guide (either continuous or segmented) on SiO substrate, embedded in SU8 polymer (or, alternatively in SiO cladding) are considered; h represents the guide thickness, w guide width, L is the SWG period (with Si groove dimension a, and gap g). - SWG waveguide - a new type of microphotonic waveguide - Practical implementations to fiber-chip coupling, waveguide crossing and refractive index engineering Scanning electron microscope (SEM) images of fabricated structures including: a) SWG straight waveguide with Λ = 3 nm, w = 5 nm and a duty cycle of 33%. b) Detail of two SWG segments. P. J. Bock, Optics Express, 18(19), 51 (1). ELEMENTÁRNÍ TEORIE EFEKTIVNÍHO PROSTŘEDÍ (Effective medium theory, EMT) Vrstevnaté prostředí s parametry e, d a e, d, d1, d l 1 f Střední hodnota elektrické indukce pro elektrické pole rovnoběžné s vrstvami : Dx1d1+ Dxd e1d1 + ed d1 Ex1 Ex E, Dx = = E = e E f d1 + d d1 + d d d d =, = 1 - f, f 1. Tedy e = fe1 + ( 1 - f) e, d d d d Střední hodnota intenzity elektrického pole pro elektrickou indukci kolmou k vrstvám : z Dz1d1 + Dzd d1 e1 + d e 1 Dz1 Dz D, Ez = = Dz = Dz, d1 + d d1 + d e^ d1, e1 d ee, e Tedy = =, e e e e e J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films, Philosophical Transaction of the Royal Society London 3, (194). 6 ^ 1 f ( f), e^ 1 f + ( 1 - f) 1 x Efektivní prostředí je anizotropní, jednoosé, s tenzorem permitivity eff æe ö = e ç è e^ ø 3

51.6 Složitější subvlnové vlnovodné struktury Vazební člen - vidový transformátor a) b) c) d) Křížení

a) SEM image of the coupler, b) low - confinement section near the chip edge, c) high-confinement section near the

1, Beijing Scanning electron microscope images of SWG crossings: A) multiple SWG crossings, B) one SWG crossing, C)

4 Složitější subvlnové vlnovodné struktury Vazební člen - vidový transformátor a) b) c) d) Křížení segmentovaných vlnovodů Subwavelength grating mode transformer. a) SEM image of the coupler, b) low - confinement section near the chip edge, c) high-confinement section near the strip waveguide, d) Intermediate section. P. J. Bock et al., 7th IEEE Conference on Group IV Photonics, Sept. 1, Beijing Scanning electron microscope images of SWG crossings: A) multiple SWG crossings, B) one SWG crossing, C) detail of the crossing region with square center segment, D) SWG straight waveguide. P. J. Bock et al., Optics Express, 18(15), (1). Disperzní vlastnosti SWG vlnovodů Standard SWGW, w = 35 nm, Λ = 4 nm, g = nm, TE polarization 11bandgap region = /( ), g 6 4 g 6 nm Si g = nm 6 nm Si n s n s g = nm phase and group effective indices, g phase effective index 4

1..61.4.351.44551.51.61..61.4.351.44551.51.6 BLOCH MODE FIELD PROPAGATION Vertical component of the magnetic field intensity @ λ = 15 nm 1 8 8, g 6 4 g g = nm 1 6 nm Si 6 nm Si 1n s 1.35 1.4 1.45 1.

5 BLOCH MODE FIELD PROPAGATION Vertical component of the magnetic field λ = 15 nm 1 8 8, g 6 4 g g = nm 1 6 nm Si 6 nm Si 1n s n s 1.g = nm 1. H, λ= 1.5 μm character quite similar to a uniform waveguide BLOCH MODE FIELD PROPAGATION Vertical component of the magnetic field λ = 14 nm 1 8 8, g 6 4 g g = nm 1 6 nm Si 6 nm Si 1n s n s 1.g = nm 1. H H, λ= 1.4 μm backward propagating waves are becoming important 5

1..61.4.351.44551.51.61..61.4.351.44551.51.6 BLOCH MODE FIELD PROPAGATION Vertical component of the magnetic field intensity @ λ = 1375 nm 1 8 8, g 6 4 g g = nm 1 6 nm Si 6 nm Si 1n s 1.35 1.4 1.45 1.

6 BLOCH MODE FIELD PROPAGATION Vertical component of the magnetic field λ = 1375 nm 1 8 8, g 6 4 g g = nm 1 6 nm Si 6 nm Si 1n s n s 1.g = nm 1. H H, λ= μm markedly resonant character BLOCH MODE FIELD PROPAGATION Vertical component of the magnetic field λ = 135 nm 1 8 8, g 6 4 g g = nm 1 6 nm Si 6 nm Si 1n s n s 1.g = nm 1. H H, λ= 1.35 μm evanescent Bloch mode within the bandgap 6

7 416nm,=35nm;SiSiU8 VAZBA MEZI SWG VLNOVODEM A NANODRÁTEM Total length L = 5 m Bridged section ~13.5 µm, 58 periods z Unbridged section ~36.5 µm, 18 w=45nmzw= periods 1, 1 wdetail of bridged section z z v 1 L ws zboth wide and narrow bridged segments are linearly tapered; w L ns w 1 the period length is also linearly tapered, from nm to 7 nm in the bridged section and from 7 nm to 4 nm in the unbridged section Version (L/) Similar (linearly tapered) but twice shorter: total length ~ 5 µm Bridged section ~ 6.75 µm, 9 periods, unbridged section ~ 18.5 µm, 54 periods Version 3 (L/4) Similar (linearly tapered) but four-times shorter: total length ~ 1.5 µm Bridged section ~ 3.38 µm, 15 periods, unbridged section ~ 9.13 µm, 7 periods Version 4 (L/8) Similar (linearly tapered) but eight-times shorter: total length ~ 6.5 µm Bridged section ~ 1.69 µm, 7 periods, unbridged section ~ 4.6 µm, 13 periods SO6 nm TRANSMITTANCE AND REFLECTANCE OF THE NANOWIRE TO SWGW COUPLER P,in P T P Bout,, P R P, refl, in, in Transmittance, Reflectance P,refl P P, P modal input and reflected power power of the fundamental forward Bloch mode, in, refl Bout, Transmittance Long Long/ Long/4 Long/8 Edge of Brillouin zone No taper (wire-air-si-air...) No taper (wire-si-air-si...) Reflectance Transmittance P B, out TE polarization Transmittance Long Long/ Long/4 Long/

db H x TE MODE FIELD DISTRIBUTION IN THE L/4 COUPLER: HORIZONTAL PLANE (upper

8 nanowire TE MODE FIELD DISTRIBUTION IN THE L/4 COUPLER: VERTICAL PLANE coupler SWGW normal mode Bloch mode E y Reflectance: 36 db Transmittance:. db H x TE MODE FIELD DISTRIBUTION IN THE L/4 COUPLER: HORIZONTAL PLANE (upper half) nanowire coupler SWGW normal mode Bloch mode E y Reflectance: 36 db Transmittance:. db H x 8

5 nm = 5 nm realizations - SWG waveguide with random fluctuations 1.4 1.5 1.6 1.7 1.8 1.

9 INFLUENCE OF RANDOM FLUCTUATIONS ON SWGW PERFORMANCE Positions and dimensions of Si segments fluctuate with normal distribution and standard deviation σ Loss (db/mm) = =.5 nm = 5 nm = =.5 nm = 5 nm realizations - SWG waveguide with random fluctuations Wavelength ( m) Aplikace subvlnových segmentovaných vlnovodů na směrovou odbočnici Vložný útlum v obou větvích Optimalizace parametrů umožňuje využít větší šířku pásma: Vazební délka 9

Aplikace subvlnových segmentovaných vlnovodů na vazební člen s mnohovidovou interferencí P. Cheben et al., Wavelength-Independent Multimode Interference Coupler, Opt.

Optimization of MMI section for broadband operation. Check of imaging properties of the MMI section 3. Verification of taper function 4.

10 Aplikace subvlnových segmentovaných vlnovodů na vazební člen s mnohovidovou interferencí P. Cheben et al., Wavelength-Independent Multimode Interference Coupler, Opt. Express 1 NRC, Ottawa, Canada, and University of Malaga, Spain Optimalizace parametrů umožňuje širokopásmové použití BROADBAND SWGW MMI COUPLER 1. Optimization of MMI section for broadband operation. Check of imaging properties of the MMI section 3. Verification of taper function 4. Analysis of possible mutual coupling between tapers 5. Field distribution and scattering matrix of the complete coupler A. Maese Novo, R. Halir, S. Romero García, D. Pérez Galacho, L. Zavargo Peche, A. Ortega Moñux, I. Molina Fernández, J. G.Wangüemert Pérez, and P. Cheben, Opt. Express vol 1, (13) 1

BLOCH MODES IN THE SWG MULTIMODE REGION Ey ( x, y), 1.55 µm 18 nm x y TE 9 mode is weakly guided and for 1.55 µm is cut - off N TE m.4.. 1.8 1.

width = 6 μm Eff. indices = 17 nm "ideal" beat length: m = 9 8 1.4 1. 1.3 1.4 1.5 1.6 1.7 (µm) Beat lengths 1 3 4 5 6 7 L m N TE m.4.. 1.8 1.6 1.4 ( m 1) 1 mm ( ), m 1,,, 8 3( ) 6( N N ) = 19 nm m m 1.

11 BLOCH MODES IN THE SWG MULTIMODE REGION Ey ( x, y), 1.55 µm 18 nm x y TE 9 mode is weakly guided and for 1.55 µm is cut - off N TE m OPTIMIZATION OF MMI SECTION FOR BROADBAND OPERATION Minimize wavelength dependence of the beat length between several lowest order lateral Bloch modes by optimization of period length; MMI section width = 6 μm Eff. indices = 17 nm "ideal" beat length: m = (µm) Beat lengths L m N TE m ( m 1) 1 mm ( ), m 1,,, 8 3( ) 6( N N ) = 19 nm m m (µm) 9 m = 8 N TE m = 1 nm (µm) L 9 L m µm) = 17 nm L 9 L 1 L m (µm) = 19 nm L 9 L 1 L m µm) L 1 L 8 = 1 nm 3 L 8 31 L ( m) (µm) (µm) 11

OPTIMIZATION OF THE MMI SECTION FOR 1.3 1.7 µm WAVELENGTH RANGE Average beat lengths Standard deviations of the beat lengths Beat length L (µm) 38 36 34 3 3 Averaged over spectral range 1.3 1.7 µm TE - TE 8 TE - TE 1 8 15 16 17 18 19 1 Period length (nm) Averaging over wavelengths and modes: Std.

196 15 16 17 18 19 1 Period length (nm) 1 1 1 1 1 opt L NoP L opt 196 nm, 3.85 µm, ( ) 84 periods, 8 8 8 8 8 opt L NoP L opt = nm, 3.13 µm, ( ) 8 periods.

12 OPTIMIZATION OF THE MMI SECTION FOR µm WAVELENGTH RANGE Average beat lengths Standard deviations of the beat lengths Beat length L (µm) Averaged over spectral range µm TE - TE 8 TE - TE Period length (nm) Averaging over wavelengths and modes: Std. deviation of L (µm) Averaged over spectral range µm TE - TE 8 TE - TE Our choice: 1. 8 periods,.5 = nm L = 3.85 µm L = 3.13 µm 84 periods 8 periods Period length (nm) opt L NoP L opt 196 nm, 3.85 µm, ( ) 84 periods, opt L NoP L opt = nm, 3.13 µm, ( ) 8 periods. IMAGING PROPERTIES OF THE SWG MMI SECTION Excitation of the SWG MMI section with SWG ports by the superposition of symmetric and antisymmetric Bloch modes MMI: 8 periods, Λ = nm E y 1

PROPERTIES OF INPUT AND OUTPUT COUPLERS Estimated SWG period Λ = nm E y

conversion efficiency difficult to reliably calculate (loss <=.

1.3 µm, 1.5 µm, and 1.7 µm. Shorter taper could probably work well, too.

λ(µm) S 11 S 31 S 41 Loss 1.7.34 1 5.995 4.963 1 3 1.561 1 5 1.5.84 1 5.

13 PROPERTIES OF INPUT AND OUTPUT COUPLERS Estimated SWG period Λ = nm E y Conversion from photonic wire into Bloch mode of the SWG output: Very high conversion efficiency difficult to reliably calculate (loss <=.1 db), very small return loss reflected power <= 45 db for all wavelengths 1.3 µm, 1.5 µm, and 1.7 µm. Shorter taper could probably work well, too. CHECK OF MUTUAL COUPLING IN THE TAPERS Calculated scattering parameters: λ(µm) S 11 S 31 S 41 Loss Mutual coupling in tapers is unimportant 13

14 FIELD DISTRIBUTION IN THE SWG MMI COUPLER S-PARAMETERS OF THE COMPLETE MMI DEVICE S 11 (db), S 31 / S 41 (db), S 31 + S 41 (db) Complete device, = 1 nm, 75 MMI periods, taper aperture 1.7 µm 1 = nm power unbalance total insertion loss phase error return loss arg(s 31 ) arg(s 41 ) - 9 (deg) µm) 14

15 INFLUENCE OF RANDOM FLUCTUATIONS S 11 (db), S 31 / S 41 (db), S 31 + S 41 (db) Complete device, = 1 nm, 75 MMI periods, taper aperture 1.7 µm 1 = 1 nm power unbalance insertion loss -1 phase error - - return loss arg(s 31 ) arg(s 41 ) - 9 (deg) µm) INFLUENCE OF RANDOM FLUCTUATIONS Complete device, = 1 nm, 75 MMI periods, taper aperture 1.7 µm S 11 (db), S 31 / S 41 (db), S 31 + S 41 (db) = 5 nm power unbalance total insertion loss phase error return loss arg(s 31 ) arg(s 41 ) - 9 (deg) µm) 15

16 SWG BASED BRAGG FILTERS fundamental limitation of this approach!!!.5d komerční FDTD software NUMERICKÉ SIMULACE 3D Fourierovská modální metoda (FJFI, ÚFE) 16

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