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I Simulated Surface Plasmon Polaritons with COMSOL — Transcript

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0:00hello everyone I hope you are doing
0:02great in this tutorial video uh I want
0:05to talk about surface plasman
0:08polaritons and uh we will do the
0:12simulation with the console multi
0:14physics I hope you subscribe to my
0:17Channel Please share my channel leave
0:19your comments in this tutorial video and
0:24like this video Let's
0:27started uh at first uh
0:31the electromagnetic waves that are
0:34confined to propagate along the surface
0:38such as surface plasma
0:40polarian are great of research
0:43interest and because they are uh
0:48interested in the NCAP manipulation of
0:52light uh in this model we want to
0:54discuss about the simulation and
0:57visualization of the prop
1:00propagation as uh well as frequency
1:05versus propagation constant disp
1:07dispersal relation of
1:11SPS um for the physics
1:15background it's better to know about
1:17propagating electromagnetic wave that is
1:20consist in a variety of form such as
1:24plane waves spherical waves Gan beams
1:27and so on there are also propagating
1:31electromagnetic waves that are
1:33confined in a space such as wave guides
1:39and wave guide modes propagating in
1:41metallic or dialectric wave guide in
1:44addition there is another special type
1:49of electromagnetic wave that is confined
1:52to a plan or
1:53Surface uh this type of wave propagates
1:57uh tangentially to the surface with a
1:59exponentially decaying fields in
2:04PR perpendicular
2:06Direction its wavelength is often uh
2:10smaller than the free space wavelength
2:13at the same frequency does this type of
2:15wave provides promises for NCAP control
2:18and manipulation of photons which is
2:21desirable in many application ranging
2:24from Optical
2:26communication and information processing
2:29to solar energy harvesting and digital
2:34displays the existence of this wave type
2:38was found at metal de electric
2:40interfaces and is known as surface
2:43plason polari the term plasmon refers to
2:47the collective oscillation of charge in
2:52metal whereas the term polari generally
2:55refers to a CA particle that is the
2:58result of the coupling between a photon
3:00with a polar exiton in a material the
3:04SPs are the result of coupling of
3:07surface plasmas at light here uh as you
3:11can see the this geometry we have
3:16uh two different material de electric
3:20and
3:21metal that we want to demonstrate the
3:25SPs in the simplest
3:28system that uh we can call it the bulk
3:32metal dialectric
3:34interface uh we can image that the metal
3:37dialectric interface is
3:39represented by
3:42the XZ plan at y equal to Z the D
3:48electri region is above
3:52this y zero and uh the metal region the
3:57below of this plane
4:02and uh here we must consider
4:07the
4:09equation that uh it is our interest that
4:14study
4:15the TM mode surface wave that the
4:19experion for the electric and magnetic
4:21field in the the electric and metal are
4:26given by equation one to equation
4:29equation four this
4:32equation and uh where D is
4:38the denote the D Electric and M is
4:43denote the metallic
4:45domains beta is the
4:48complex SP propagation
4:52constant
4:53and GMA D
4:56and GMA M represent the posi real
5:01numbers that uh describe the decay of
5:04the field away from the metal dialectric
5:10interfaces okay for the equation 5 to
5:147 uh we can see uh the tangential
5:19components of the electric and magnetic
5:22fields and the normal component of the
5:24electric displacement field that are
5:27continuous across the D Electric
5:30boundary therefore we see this uh
5:39equation for equation 8 and nine uh as
5:44we know there is no external charge here
5:47and the permitivity is constant inside
5:50the respective metallic and the electric
5:53domains it means the Divergence of
5:58electric field is equal to Z must hold
6:02inside the two region combining this
6:05condition with equation two and four
6:08gives the following two equation which
6:11means 8 and
6:13n and subsequently if those two equation
6:18are
6:19combined we can get the simple
6:22relation we can see GMA D is per square
6:27uh per Epsilon D is = to minus GMA
6:32m / Epsilon
6:37M from this from 8 to 10 uh it can be
6:43clear that y SPS only exists between a
6:47de electric having a positive real part
6:50of the permitivity and a metal having a
6:53negative real part of the permitivity to
6:57have the field decay in the wide
7:00Direction both GMA D and GMA M must be
7:05positive which means that the
7:07permitivity Epsilon D and Epsilon M must
7:09be must have opposite
7:12sign to
7:15derivate to dve the expression for the
7:18propagation constant we can uh write the
7:22helm HS
7:25equation as you can see equation 11 and
7:29the propagation constant by the related
7:36equations
7:37okay here uh we can see
7:41the the L SP which is mean
7:46the wavelength of surface plasman
7:50polarian which is related to real of
7:54beta that considered in equation 1224
8:01okay uh we can start the
8:04simulation uh for the
8:06simulation I choose console uh
8:146.2 in the model builder I go to
8:22the model
8:25wizard in model wizard I choose the 2D
8:32then I I go to
8:36Optics and wave
8:39Optics in wave Optics I choose
8:42electromagnetic waves frequency
8:45domain
8:47ewf and I add
8:50it then I click on the
8:56study and I choose the
9:03present study for selected
9:08physics and you can see
9:12the study here I choose the boundary
9:18mode
9:22analysis and I click done
9:32okay and here uh in
9:37the global definition I go to
9:40parameters I Define some parameters for
9:44example
9:47L uh equal to 2
9:54micrometer which means the simulation
9:56domain lens and Ed
10:01is equal to 3
10:11micrometer and LDA
10:16Zer which mean the
10:19wavelength
10:25400 nanometer
10:34and
10:36uh
10:40F0 that is uh equal to C
10:46const divided by LDA
10:520 the LDA Z it mean the wavelength of
10:56the operation and the F0 is it's mean
10:59the
11:01frequency okay
11:04uh in the
11:06geometry I go to Geometry part I click
11:11right on
11:12it I choose
11:16rectangle in rectangle
11:20I in the v text I type the
11:26L and in the height
11:30I type the
11:40Ed and uh I go to layers I expand
11:45it and then uh for layer one
11:49I
11:53write half of
11:58H and and I F all
12:06object we can uh choose it as
12:11[Music]
12:15the maybe as the
12:18center or maybe as Corner uh it depends
12:22on
12:24ourself uh I choose a corner here
12:29and I choose form Union to build all
12:35okay in the following I go to
12:41material and
12:46I choose the material from the
12:53library I go to
12:57Optical in optic
13:01uh in or inorganic
13:05material I choose AG
13:08silver in ag silver I choose
13:11experimental
13:14data
13:19bulk and uh in the experimental data I
13:24choose Johnson and
13:25Christi from
13:30uh the first one I choose this I double
13:35click on
13:38it okay then
13:41[Music]
13:44I go
13:48to a blank
13:57material for ch using
14:02air I go
14:04to blank
14:06material and I write I type it as
14:12air
14:14okay and for AG region I choose the
14:20bottom and for a I choose the top as we
14:25can see the refractive index real and
14:30imaginary
14:31part is selected from the material
14:34library of the console and for air we
14:38must Type n and K as we know the N is
14:43one for the air and the K is
14:48zero
14:54okay in the electromagnetic part uh uh I
15:01click right on it and and first I group
15:05by a space
15:09Dimension I click right on the
15:12boundaries I choose the
15:16port into
15:19Port I choose
15:26the left side
15:30and I choose the default values
15:37one wat per
15:41meter and for the type of Port I choose
15:47the
15:49numeric and the mo phase I choose the 0
15:55degree or zero
15:57Radian for the mod phase
16:05and and I double click I click on
16:09boundaries and I choose another Port
16:11Port as a port
16:13two in Port to I choose the numeric
16:23and import two I choose a numeric for
16:27the right side
16:31and I off the vave
16:35exitation and the numeric port and also
16:39as the same the mode phase is equal to
16:51zero
16:53okay
16:56uh in the continue I go
17:02to the study step
17:08one the study step
17:11one uh we can see the bond mode
17:21analysis and in this study uh setting we
17:25can see the transform
17:29and other uh properties that we can
17:32change
17:33it and in the mode analysis frequency I
17:38type
17:40F0 which we defined in the
17:49parameter and for mode search
17:54method uh I
17:57choose I can type
18:03the around shift maybe or
18:08rectangle I choose round shift
18:11here and desired number of modes also
18:15can be
18:17changed I I can uh choose a different
18:27values and and also for the Search for
18:33Mod around the shift I can choose
18:37another different values for example I
18:39choose a five and also the search method
18:44around shift I choose the closest in the
18:47absolute
18:53value okay
19:11for boundary mode uh we can choose
19:14another boundary mode as a boundary mode
19:17two and uh
19:20to study different
19:23analysis let me
19:30add
19:33it by right click on this and
19:39duplicating uh we have a two
19:44step step one boundary mode analysis
19:47step two boundary mode analysis of
19:51one in this one I choose the port
19:57name uh
20:01two which means we have uh analysis on
20:06Port two and for the first we have
20:08analysis on Port
20:12one and
20:15uh the mode analysis is frequency is
20:20equal to F0 air pack round shift and the
20:26five and
20:31the values of
20:34linearization uh point is better to be
20:37physics
20:41controlled okay in frequency domain I
20:46can choose the
20:51F0 in the frequencies and terz as the
20:56unit
21:02okay in also we could
21:05uh we can add the parametric sweep in
21:09the parametric sweep I can add the LDA Z
21:15and I can change the
21:19range
21:21from
21:27340 to to
21:30600
21:35nanometer
21:38okay and it's better to check
21:44the mesh also
22:16okay uh we choose the frequency domain
22:20for the stud simulation also I add the
22:24parametric
22:26s and in uh I can go to analytic to
22:32type let me check this I can go to
22:37definition and in the
22:41analytics in
22:43analytics I can uh write
22:48the function for analytic
22:51one
22:56for Epsilon r
23:05in the
23:06exerion I write
23:09the
23:11math
23:14one.
23:19RFI
23:21n RX
23:32minus 1 I which means the imaginary
23:37part multiplied to matth
23:421 do
23:47RFI
23:51ni X
24:08two
24:11and we can uh choose a lower limit for
24:17the lower and upper limit for
24:22the
24:26X here let me check
24:31the function you
24:36need uh after running it will be
24:41uh show us
24:44um let me check the
24:49code n RX Min - 1
24:56I mat one
25:07RFI
25:09okay uh this code
25:13uh was given
25:16uh from the material let
25:20me show the equation
25:23view we must add the equation view from
25:26this
25:30and we can see
25:33the equation are available
25:40here
25:43and now we can check the
25:48mesh for the mesh
25:52I choose the
25:55size I right click on it I choose the
26:00size and in the size I choose General
26:04Physics and I choose
26:07custom
26:15for costume and I choose uh
26:2550 nanometer
26:34[Music]
26:40and
26:41[Music]
26:44nanometer
26:461.3 0.3 and
26:49one and for size
26:55one I choose the boundary
27:01of 13 6
27:057 1
27:093 6
27:11[Music]
27:137 and I choose the
27:17custom for the maximum and minimum
27:21element side I choose uh 25
27:32nanometer and for minimum element size I
27:37choose as
27:43075 the maximum element gr rate
27:491.3 and the curvature factor is 0.3 and
27:55resolution is one
27:59and for size two I add another
28:06size for size two I can choose the
28:10boundary
28:164
28:22[Music]
28:25and I can choose costume
28:32and in the maximum element size I choose
28:37the I write this
28:41code
28:45ld0 divided
28:49by
28:54real sqrt
29:06Epsilon
29:10R LDA
29:17Z
29:21one meter
29:32divided
29:36by
29:381
29:40plus Epsilon
29:44R
29:45Epsilon
29:48R LDA
29:53Z multi uh divided by one
30:04meter and we must
30:11add five
30:16parentheses divided by
30:2012 it is okay you can see the black box
30:24which means the code is okay
30:28and uh let me also
30:33uh use the nanometer unit for
30:37the
30:40all geometry it's better
30:43and we can uh add another option for
30:48geometry I choose free
30:52trangular
30:53triangular in fre free triangular I
30:59use the remaining scale geometry V one
31:03one in X and Y and the control enti is 4
31:08and four desolation is automatic
31:12and I can build
31:15all
31:17okay and now we
31:21can run the
31:25simulation we can compute the
31:28[Music]
31:34simulation and the convergence plot we
31:37can see
31:39the
31:41convergence of the error bar versus
31:45iteration number
32:14after the uh running this
32:17simulation we can plot the transmittance
32:20and absorbance the electric mode field
32:23on Port one and two and also s s PP
32:30dispersion that gives us
32:35the good information about the surface
32:38polyon
32:42plasma of this
32:51material okay we can see the electric
32:55field
33:01in the electric field uh we
33:08can we can add
33:12the surface as we can see and in the
33:16surface I can choose uh the
33:19electromagnetic field
33:22in in the y direction
33:30eyy I can plot it and also I can choose
33:35Arrow
33:38surface and in Arrow surface I can
33:43choose e x and ey
33:51Y and also
33:55the number of 50 and 50
34:06with the scale factor
34:18of the arrow type and proportional
34:23tail 1 E minus 3
34:28and
34:30the color is for example
34:36black and we can plot
34:48it
34:50okay and uh we can
34:55also uh check the
34:59parametric solution we can choose a
35:02different wavelength for
35:05example this
35:07value and also
35:11the the color
35:15of the surface we can choose uh for
35:20example Wave light let me check the
35:30for example Wave light you can see the
35:32Wave light
35:35here and uh in the reflectant and
35:39transmittance we can see
35:46the this
35:49figure
35:51the Cen is related to absorbance and the
35:55red is related
35:58to
36:00transmittance total reflectance and
36:03transmittance and
36:09uh and we can uh remove for
36:15example R
36:17[Music]
36:22and R total and R port to see battery
36:27result T Port 2 and 8 total it's
36:32better and you can see the absorbance
36:35and transmitt the reflectance is very uh
36:39low that can be
36:42neglected and also you can see the
36:45electric mode
36:48field
36:51in two
36:55different condition
36:58for the port one
37:01and Port
37:04two also we have we can have
37:09the SP dispersion for this I can go to
37:14result I right click on it I choose
37:181D then I click
37:22right and I choose Global in global I
37:25can choose uh
37:28freak which means the
37:34frequency and multiply
37:38to H
37:42count
37:44then uh it can be as electron
37:51volt I can plot it
38:00for
38:01all maybe we can
38:03choose all frequency or we can choose a
38:08parametric it's
38:10better to send uh
38:13[Music]
38:15all I can turn off the legend to see
38:19better
38:24resolution and also I can uh
38:30check this
38:35as the all solution and the
38:40experion as the beta I can e choose e
38:47wfd excuse me ew FD
38:54do beta
38:59one radian per meter it's
39:04better and you can see
39:09the analytic
39:11SP
39:14dispersion we can call it let me
39:24uh title it as
39:34and also we can use a color expression
39:38[Music]
39:41for doing a better model in the color
39:46expression I can write the
39:51minus
39:55real ewf F
40:00d. beta
40:06one divided
40:10by imaginary
40:14of e
40:17wfd
40:19dot
40:21beta
40:25one and the AL the range of color I can
40:30choose
40:32from for example
40:36zero to
40:39800 and
40:46also choose the different color for
40:50example let me
40:55check color table
40:59for example with this you can see the
41:02different color for the for this plot
41:06and also
41:12uh I can plot it as
41:16the let me duplicate
41:24it and I remove the color
41:35and we can plot it as the ew f.
41:45k0 and we can see
41:49the light
41:51Line This is light line because we have
41:54k z which means the
41:58uh wave number in the free
42:04space equal to 2p ided by LDA or
42:12L and for the global
42:18three also we we can add
42:25the we can add the Global
42:32three and in the color experion we can
42:36add
42:37the different equation to see
42:45the different properties okay uh the
42:50simulation is
42:52done and here we we choose uh AG you can
42:58search the other material
43:03I suggest you choose of optical
43:06inorganic material for example it's
43:10better choose
43:11a
43:13aluminium
43:16maybe
43:18platin iron and other material and also
43:24gold and see what will happen for the
43:29result of electric field electric field
43:32mode and also the transmittance
43:38and
43:41absorbance uh these are will these will
43:46uh
43:48different and also for
43:52the SP dispersion you can add the
43:57frequency multipli
44:01to
44:04hedge uh versus beta which means you
44:07have
44:09the dispersion of
44:12bulk for your material here is
44:15silver here we have uh
44:20simulate light line we have a simulated
44:24SP and we can add un I that you can see
44:28the both of them are the
44:32same okay uh I hope you enjoy this video
44:38please subscribe to my
44:40channel uh share my challeng channel to
44:43your friends leave your comments like my
44:47videos uh thank you for carrying my
44:52advices have a good time take care
44:55goodbye

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