Presented at the COMSOL Conference 2010 China Simulations of nanophotonic waveguides and devices using COMSOL Multiphysics Zheng Zheng Beihang University 37 Xueyuan Road, Beijing 100191, China
Acknowledgement Yusheng Bian Lin An Xin Zhao Muddassir Iqbal Ya Liu Wei Li Tao Zhou (NJIT) Jiangtao Cheng (Penn State Univ.)
Simulation of dielectric waveguides and optic fibers using COMSOL Simulation of surface plasmon polariton (SPP) waveguides and devices using COMSOL
Simulation of dielectric waveguides and optic fibers using COMSOL Simulation of surface plasmon polariton (SPP) waveguides and devices using COMSOL
Motivation - Nanophotonics Development of Integrated Circuits Conventional photonic device Moore's law Substrate Low-index contrast waveguide High-contrast planar waveguide Photonic crystal fiber and waveguide Channel waveguide Slot waveguide ~ Diffraction limit
Dielectric slot waveguides and applications Slot waveguide Ring resonator Optical biosensing Field distribution Optical modulator Optical manipulation *V. R. Almeida et. al, Optics Letters 29, 1209-1211 (2004).
Dispersion analysis of dielectric slot waveguides Group velocity dispersion (GVD) Sellmeier s equation for silicon and silica refractive indices COMSOL settings Perpendicular waves of RF module- mode analysis Scattering boundary condition *Z. Zheng, M. Iqbal, Optics Communications 281, 5151-5155 (2008).
Dispersion analysis of dielectric slot waveguides Slot waveguide: In the normal dispersion regime near the 1550 nm wavelengths Channel silicon waveguide: In the abnormal dispersion regime GVD ( slot ) > GVD ( channel ) Higher order dispersion behavior depending strongly on the geometric parameters of the slot waveguides (e.g. slot & slab width, material filled in the slot region) *Z. Zheng, M. Iqbal, Optics Communications 281, 5151-5155 (2008).
Photonic Crystal Fibers (PCF) A B C A: Standard optical fiber (Total external reflection) B: Index-guiding photonic crystal fiber (Total internal reflection) C: Hollow core photonic bandgap fiber (Photonic bandgap) Various kinds of PCF Merits and Potential of PCFs Lower transmission loss than conventional fibers Substantially higher damage thresholds than conventional fibers Promising for various linear and nonlinear optical processes *J. C. Knight, Nature 424, 847-851 (2003).
Design of ultrahigh birefringent, ultralow loss PCF PCF structure d L a b L 1 Intensity distributions with different elliptic ratio of the air hole y x A core region with a rectangular array of four air holes (to provide the birefringence) A conventional circular-air-hole cladding (to reduce the confinement loss). L 2 COMSOL settings x-polarization y-polarization Perpendicular waves of RF module- mode analysis PML boundary condition *L. An, Z. Zheng. Journal of Lightwave Technology 27, 3175-3180 (2009)
Design of ultrahigh birefringent, ultralow loss PCF Intensity distribution PCF with circular air holes PCF with elliptical air holes x-polarization y-polarization x-polarization y-polarization -120 Ultrahigh single-mode birefringence (~10-2 ) Ultralow confinement losses (<0.002 db/km) Relatively flat dispersion Easy to fabricate GVD (ps/(nm*km)) -150-180 -210-240 -270-300 -330 x polarization y polarization 1.48 1.50 1.52 1.54 1.56 1.58 1.60 Wavelength ( m) *L. An, Z. Zheng. Journal of Lightwave Technology 27, 3175-3180 (2009)
Design of single-polarization, single-mode PCF PCF geometry Intensity distribution y-polarization Single-mode and singlepolarization propagation can be realized by tuning geometry of the air holes, with low confinement loss and small mode area *L. An, Z. Zheng, Optics Communications 282, 3266-3269 (2009)
Design of single-polarization, single-mode PCF Dispersion optimization Intensity distribution Dispersion & confinement loss GVD GVD Near-zero, dispersion-flattened Small mode area Low confinement loss(<0.25 db/km) Ultra-wide band (0.3 1.84 μm) COMSOL settings Perpendicular waves of RF module- mode analysis PML boundary condition *L. An, Z. Zheng, Optics Communications 282, 3266-3269 (2009)
Highly nonlinear holey fiber with a high index slot core Proposed structure COMSOL settings Perpendicular waves of RF module- mode analysis PML boundary condition *L. An, Z. Zheng, Journal of Optics, 115502 (2010).
Highly nonlinear holey fiber with a high index slot core Fiber with a slot core Intensity distribution Modal behavior Group velocity dispersion Group velocity dispersion (ps/nm/km) -3000-3500 -4000-4500 -5000-5500 -6000 GVD -6500 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 Wavelength ( m) Quasi-TE mode well confined in the slot region Single-mode propagation with ultra-small mode area ( < 0.3 μm 2 ) A large negative GVD and large GVD slope *L. An, Z. Zheng, Journal of Optics, 115502 (2010).
Highly nonlinear holey fiber with a high index slot core Fiber with a slot core and a two-air-hole cladding Group velocity dispersion (ps/nm/km) Group velocity dispersion (ps/nm/km) -2800-2900 -3000-3100 -3200-1700 -1750-1800 -1850-1900 -1950-2000 -2050 GVD Telecom C-Band d/l = 0.58 d/l = 0.62 d/l = 0.6 d/l = 0.64 d/l = 0.66 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 Wavelength ( m) Fiber with a slot core and a four-air-hole cladding GVD 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 Wavelength ( m) Modification of GVD Much lower GVD than that without air-hole Different dispersion slope at various air-hole parameters Enhancement of the field confinement Even lower absolute GVD values Further enhancement of the field confinement *L. An, Z. Zheng, Journal of Optics, 115502 (2010).
Simulation of dielectric waveguides and optic fibers using COMSOL Simulation of surface plasmon polariton (SPP) waveguides and devices using COMSOL
Introduction-Surface Plasmons *W. L. Barnes, Nature 424, 824-830 (2003). Surface plasmons (SPs) Light guiding Diffraction limit Sensing Coherent electron oscillations at the metal/dielectric interface Field decays exponentially into both neighboring media Lasing Nanolithography
Introduction-SPP waveguides Surface plasmon polariton (SPP) waveguide Insulator/Metal/Insulator (IMI) Metal/Insulator/Metal (MIM) Dielectric n d Metal n m hm y Wm z x Long-range SPP waveguide Advantages Low propagation loss (a few db/cm) Disadvantages Weak confinement (mode size~λ) CPP waveguides metal slot waveguide Advantages Tight field confinement (subwavelength scale) Disadvantages Huge loss (propagation length ~ several μm) Loss Tradeoff Confinement
Hybrid plasmonic waveguide *R. F. Oulton, Nature Photonics, 2008. 2(8): p. 496-500. Subwavelength mode confinement λ 2 /400 ~λ 2 /40 Long-range propagation distance 40 ~ 150 μm
Design of symmetric hybrid plasmonic waveguide y Metal W d Slab n d Slab n d h d h g n m Cladding n b h m Normalized Ey 1.0 0.5 (a) Normalized Ey 1.0 0.5 0.0-0.5 (b) z x 0.5 W m Substrate n b 0.0-1.0-0.5 0.0 0.5 1.0 y ( m ) 0.5 0.5 (a) (b) (c) -1.0-1.0-0.5 0.0 0.5 1.0 y ( m ) 1 y ( m ) 0.0 y ( m ) -0.5-0.5-1.0-0.5 0.0 0.5 1.0 x ( m ) -1.0-0.5 0.0 0.5My 1.0 Y 0.5 0.0 x ( m ) y ( m ) 0.0 y ( m ) 0.0-0.5-0.5-1.0-0.5 0.0 0.5 1.0 x ( m ) -1.0-0.5 0.0 0.5 1.0 x ( m ) 0 Subwavelength confinement (1~2 orders of magnitude higher than insulator/metal/insulator waveguides) Low loss ( propagation length~ hundreds of microns) *Y. S. Bian, Z. Zheng, Optics Express 17, 21320-21325 (2009).
Design of symmetric hybrid plasmonic waveguide Normalized coupling length 12 10 8 6 4 2 0 (a) h g =10nm h g =30nm S x h g =50nm 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Sx ( m ) Normalized coupling length 12 (b) h g =10nm 10 S y h g =30nm h g =50nm 8 6 4 2 0 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Sy ( m ) High-density 3D photonic integration( packing density increased by nearly 60 times over insulator/metal/insulator waveguides) Finite dimensions in both directions, enabling multilayer, 3-dimensional (3D) integrated circuits COMSOL settings Sub-wavelength field confinement Perpendicular 1~2 orders waves of magnitude of RF module- higher than mode long-range analysis SPP waveguides Scattering boundary condition *Y. S. Bian, Z. Zheng, Optics Express 17, 21320-21325 (2009).
Dielectric-loaded SPP waveguides Relatively tight confinement of light (subwavelength scale) Relatively long propagation distance ( tens of microns) Low-index DLSPP waveguides Low-index polymer (n~1.5) Low loss Relatively large geometry size (e.g.600nm 600nm) Not suitable for high integration High-index DLSPP waveguides High-index dielectric (n~2 & n~3.5) Stronger confinement Compact, Si fab process compatible, suitable for integration Huge loss
Design of DLSPP waveguide with a holey ridge (a) (b) ε d ε c ε c w h ε h a d ε m w ε m w h a z y x Geometry (a) SiO2 Ag Si (b) SiO2 Ag Si Air (c) SiO2 SiO2 Si Air 1 0 Field distribution Strong field enhancement in the nanohole due to the slot effect COMSOL settings Perpendicular waves of RF module- mode analysis Scattering boundary condition *Y. S. Bian, Z. Zheng, Optics Express, To be published.
Design of dielectric-loaded waveguide with a holey ridge Field distributions at different nanohole widths (a) ha=10nm (b) ha=30nm (c) ha=50nm (d) ha=100nm 1 1.0 (e) 1.0 (f) 1.0 (g) 1.0 (h) 0 Ey 0.5 Ey 0.5 Ey 0.5 Ey 0.5 Ey 0.0-1.0-0.5 0.0 x( m) 0.5 1.0 1.0 0.5 (i) Ey 0.0-1.0-0.5 0.0 0.5 1.0 x ( m) 1.0 0.5 (j) Ey 0.0-1.0-0.5 0.0 0.5 1.0 x( m) 1.0 0.5 (k) Ey 0.0-1.0-0.5 0.0 x ( m) 0.5 1.0 1.0 0.5 (l) 0.0-0.2 0.0 0.2 y ( m) 0.4 0.6 0.0-0.2 0.0 0.2 0.4 0.6 y( m) 0.0-0.2 0.0 0.2 0.4 0.6 y ( m) 0.0-0.2 0.0 0.2 0.4 0.6 y ( m) Even stronger field enhancement with a shallow and wide, low-index nanohole *Y. S. Bian, Z. Zheng, Optics Express, to be published.
Design of dielectric-loaded waveguide with a holey ridge NOP 0.5 0.4 0.3 0.2 (a) wa=10nm wa=30nm wa=50nm wa=100nm wa=150nm NAOI 10 1 10 0 (b) 0.1 10-1 0.0 0 30 60 90 120 150 ha (nm) 0 30 60 90 120 150 ha (nm) High optical power and strong optical intensity in the nanohole Neff 2.8 2.4 2.0 1.6 (a) 200 150 100 50 Lp( m) Aeff /A0 1.0 0.5 (b) ha=10nm ha=30nm ha=50nm ha=100nm ha=150nm DLSPP FOM 200 150 100 (c) 0 0 30 60 90 120 150 wa (nm) 0.0 0 30 60 90 120 150 wa (nm) High optical power and strong optical intensity in the nanohole Loss reduction achieved with small sacrifice in the mode area 50 0 30 60 90 120 150 wa (nm) Improved figure of merit (FOM) with a shallow and wide air nanohole *Y. S. Bian, Z. Zheng, Optics Express, To be published.
Nanolasers The first laser (1960) Dielectric nanowire lasers [1] ~ diffraction limit Nanotechology [1] Nature 421, 241-245 (2003). Plasmon nanolasers << diffraction limit Directional emissions similar to the FP lasers High field confinement in the gain media region Low-threshold operation 2D [2] 3D [3] [2] Nature 461, 629-632 (2009). [3] Nature 460, 1110-1112 (2009).
2D plasmon nanolasers Plasmon nanolaser Hybrid plasmonic waveguides Low loss propagation Subwavelength confinement r h r CdS MgF 2 Ag n=2.4 n=1.4 n=-9.2+0.3i A lower index buffer (e.g. air) helps to further enhance the field enhancement in that region An air gap is impossible to fabricate
Design of coplanar plasmon nanolaser 1 Air gap 10 1 Ag t m h r CdS MgF 2 z y x r λ=490nm, t m =2r, h:2~30nm r 0 Threshold ( m) 10 0 0 5 10 15 20 25 30 h (nm) Based on an edge-coupled hybrid plasmonic waveguide Strong field enhancement and low loss caused by the air gap Easy to fabricate Edge plasmonic mode Low pump threshold *Y. S. Bian, Z. Zheng, 2010 Frontiers in Optics
Round corner effect for the plasmon laser 1 3.0 tm r c h r A strong field enhancement occurs in the gap region The enhancement is further strengthened in the center of the gap The pump threshold shows a monotonical reduction with increased radius Compared to the case with sharp corners, the threshold could be lowered by 50% at appropriate corner radius 0 Threshold ( m) 2.5 2.0 1.5 1.0 0.5 0 10 20 30 40 50 60 r c (nm) COMSOL settings Perpendicular waves of RF module- mode analysis Scattering boundary condition *Y. S. Bian, Z. Zheng, 2010 Frontiers in Optics
Integrated plasmonic sensors w/ nanostructure Conventional plasmonic sensing device On-chip SPR sensor based on nanohole array and microfluidic Colinear optical detection Denser integration Smaller footprint Multiplexing biosensing High sensitivity Nature Biotech 26, 417-426 (2008) Mass transport limitation Target molecular diffusion rate <<Binding or reaction rate Target depletion zone
Plasmonic lens Plasmonic microzone plate lens Plasmonic slits array lens Appl. Phy. Lett. 91, 061124 (2007) Nano Lett. 9, 235-238 (2009) Focused beam or evanescent field Optical field gradient Subwavelength focusing High field intensity Large field gradient Optical force Large optical force Trapping and manipulating targets
Proposed plasmonic nano-slit array Focused beam or evanescent field Optical field gradient Optical force Trapping and manipulating targets Optimized nano-slit structure for trapping in micro-fluidic H z of TM mode w 1 = 250 nm w 1,w 2 = 50, 62 nm w 1,w 2, w 3 = 50, 62,160 nm Divergent beam focused beam Focal length f ~ 0.6 m *X. Zhao, Z. Zheng, 2010 Frontiers in Optics
Optical gradient force of nano-slit lens Time average optical force Maxwell stress tensor ij t F h i t T n ij j A t j ds r, t E j r, t h Hi r, t H j r t t 0 t T E, 0 i 1 ij 2 h r, t E r, t H r, t H r t Ei' i' t h 0 0 i' i', i' i' Sensing object: nanorods with a diameter of 50 nm 8.0x10-14 t Input power density=1.28mw/mm 2 Optical force (N/m) 6.0x10-14 4.0x10-14 2.0x10-14 0.0-2.0x10-14 -4.0x10-14 -6.0x10-14 repulsive force x=0 x=0.3 x=0.6 attractive force 0.2 0.6 1.0 1.4 1.8 2.2 Y position of the nanorod ( m) When X=0, Y> f attractive force Y<f repulsive force
Impact and effect of slit in micro-fluidic Optical force could increase target concentration near focal point More target molecular diffused to the sensing surface Alleviate mass transport limit
Conclusions Design and optimization of the nanophotonic devices are critical in realizing advanced photonic integrations in the future. Comsol can be used for simulating various types of nanophotonic devices involving different materials and dimensions. Increased functionalities of the nanophotonic devices also demand simulators capable of handling complex multiphysics simulations.
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