LSPPs at a sub-wavelength metal particle

For a spherical metallic particle



_m(



) with its radius a (incoming wavelength) placed in a surrounding medium  , the conduction electrons inside the particle driven by an incoming field

E



E z



 0 move all in phase, leading to the build-up of induced charges on the particle surface. The charges act like an induced dipole p

(see Fig. 2.2.1-1), giving raise to an effective restoring force that allows a

non-propagating resonance (ie localized resonance) at a specific frequency. Due to





a , the spatially varying incoming field around the spherical particle can be treated as a uniform static field, which is also called a quasi-static approximation.

Fig. 2.2.1-1 Localised surface plasmon excitation by a metal nanoparticle in a nearly uniform

quasi-static electric field.

In the electrostatic approach, we start to solve the Laplace equation ²



0 for the potential



of the metal particle. Because of the azimuthal symmetry of the problem, the solution for the potentials inside and outside the spherical particle can be written as

determined by the following boundary conditions at the sphere surfacer a.

Therefore, the solution of the potential for the particle is given by

 

polarizability) experiences a resonant enhancement. By the Drude model

assumption ₂

which is also called Fröhlich frequency.

For the most general smooth metallic particle, its shape is an ellipsoid with principal axes abc, the particle surface specified by

2 1

is in arbitrarily direction, the induced dipole moment p can be written as

) ( ₁

E x

₂

E y

₃

E z

p

 



_m



_O^x



_O^y



_O^z (2.2.1-8)

where

E ,

_O^x

E ,

_O^y

E are the components of

_O^z

E

_O

relative to the principal axes of the ellipsoid. As to the particle polarizability



_i(i=1,2,3), they are given by [42]

) where

L (i=1,2,3) is called geometrical depolarization factor with the relation

_i

3 1

1







i

L

i . The depolarization factors of spherical and spherical particles, for instance, are 3

L

₁ 

L

₂ 

L

₃ 1/ and L₁ L₂ (for oblate spheroids) or

L

₂ 

L

₃ (for prolate

spheroids), respectively. Similarly to the spherical metal particle with ₂

2

1 

_m  ^p ,

the resonant frequency along an axis i is therefore given by



nanoparticle scatters and absorbs light. The scattered field outside the induced dipole (see Fig. 2.2.1-1) from the metal particle at far field (iekr 1) is given by [36]



. The magnetic field therefore is given by ) The corresponding cross section for scattering

C (extinction

_sca

C ) can be calculated

_ext

via the ratio of the total scattering power

W (total extinction power

_sca

W ) to

_ext incident power flux density ₀² ₀²

2

we therefore can obtain [43]:

4 2 The extinction cross section

C presents the sum of the absorption cross section

_ext

C and scattering cross section

abs

C (ie

_sca

C =

_ext

C +

_sca

C ). For a small spherical

_abs

particle with a , the efficiency of extinction (ie

C ), scaling with

_ext

a ,

³ dominates over the scattering efficiency (ie

C ), scaling with

_sca

a . Consequently,

⁶

C is roughly equal to

ext

C [38].

_abs

In scattering problems, the coordinate axes are usually chosen to be fixed relative to the applied filed

E

_inc

. Let

E

_inc

be in such a coordinate system(

x

₁^',

x

₂^',

x

₃^'). From the optical cross-section theorem [44], the scattering and absorption cross sections for the incident field in

x

₁^'-polarized,

x

₂^'-polarized, and

x

₃^'-polarized directions are:

) In most experiments and observations, the quantities of interest are the average cross sections 

C

_Sca(

x

_i^')and

C

_abs(

x

_i^'), which are given by [42] It is interesting to note that when the size of a particle becomes large compared with an incoming wavelength , there is a retardation effect we cannot ignore, which means conduction electrons in the particle will not all move in phase, leading to a poor quasi-static (dipole) approximation. In this case, Mie’s theory [45] is used, where Maxell’s equations are solved analytically without any approximations.

2.2.2 LSPPs at metal/dielectric/metal cavities

We have introduced the SPP metal/dielectric/metal waveguides in chapter 2.1.3.

Based on the metal/dielectric/metal configuration, two kinds of boundaries with one open end and the other closed end capped by metal are concerned (see Figure 2.2.2-1).

When the SPP in the MDM waveguide is excited, the major part of energy is confined in the dielectric core. With the boundaries, the reflection of the SPPs at both metal/dielectric interfaces can occur. Therefore, the forward and backward SPPs will

form a standing wave also called a Fabry–Pérot resonance (ie  0

dk v

_g

d 

) which is independent of the angle of incidence (ie tilting angle of the dispersion relation



(k)).

Fig. 2.2.2-1 Lowest-order TM mode of metal/dielectric/metal (a) open and (b) closed cavities

with a length of L.

Such resonance conditions in the open and closed cavities are as follows [46]:

L

(2

m

1)



_p/4 (2.2.2-1) 2

p /

m

L





(2.2.2-2)

where



_p is the resonant wavelength in a cavity with a length of L . When the

waveguide core is decreased, the effective index of the core for the SPP propagation becomes larger, giving a red-shifted resonant wavelength



_p. The



_p for both types

of cavities is linearly proportional to L . For them th resonance, the resonant wavelength in the closed-end cavity is

) 1 2 (

2



m

m

times larger with respective to that

in the open-ended resonance cavity. Thus, the resonance energy for the closed-end

cavity is much lower than the energy for the open-ended one. Moreover, one of differences between the both cavities is field intensity enhancement on its core entrance. Light in the closed-end cavity is mostly reflected back from the end metal wall, while light in the open cavity is partially transmitted through the other side entrance. As a result, the closed cavity generally produce higher field enhancement.

Fig. 2.2.2-2 Schematic diagram of the investigated MD structure.

For two-dimensional metal/dielectric/metal cavities, one of simple open-end cavity structures is a round-shaped metal disk array based on a dielectric/metal substrate. Figure 2.2.2-2 shows illustrates the geometry of the metallic disk (MD) array structure. An array of a Λ periodic MD with diameter D and thickness tAg is deposited on the top and a silver (Ag) ground plane is on the bottom separated by a thin SiO2 layer with a thickness tSiO2. The bottom layer acts as a mirror to reflect incident light and block light transmittance. Similar to the one-dimensional open-end metal/dielectric/metal cavity as shown in Figure 2.2.2-1 (a), a LSPP mode can occur.

Figure 2.2.2-3(a) and 2.2.2-3(b) show the TM- and TE- polarized reflectance spectra of the structure (D=1 μm, Λ=1.5 μm, tAg=100 nm, and tSiO2=80 nm) simulated by Rigorous Coupled Wave Analysis (RCWA) algorithm [47-50] with photon energy ranging from 0.12 eV to 0.64 eV, and the angle of incidence θi varying from 0° to 90°.

The frequency-dependent complex dielectric constants of silver (Ag) and SiO2 for the RCWA simulation are taken from the reference [51]. As shown in both TM and TE polarized reflectance spectra, a clear angle-independent resonance absorption band occurs at 0.35 eV, corresponding to the LSPP mode. In Figure 2.2.2-3(a), there is an angle dependent straight line with a slope of light speed C, corresponding to the grating-coupled SPPs at the air/Ag interface. The SPP coupling effect becomes much obvious when the period Λ is comparable with its working wavelength. At large incidence angles in both spectra, other absorption peaks also occur due to excitation of horizontal resonance modes. The LSPP mode at 0.35eV is from a strong coupling between the SPP modes of the top MD and bottom silver layers (see Figure 2.2.2-4 (a)). This strong coupling forms a Fabry–Pérot-like resonance in the SiO2 cavity, as displayed in Figure 2.2.2-4 (b).

Fig. 2.2.2-3 (a) TM- and (b) TE- mode stimulated reflectance spectra of the MD structure.

Fig. 2.2.2-4 TM-polarized |H_y|² distributions in one pitch of the MD array at 0.35 eV for

normal incidence in (a) X-Y plane at Z=40 nm and (b) X-Z plane at Y=0 nm.

3. Angle and polarization independent narrow-band thermal emitter made of metallic disk on SiO

₂

Based on the Kirchhoff’s law of thermal radiation [52], good light absorbers are good light emitters when they are heated. We demonstrated an efficient narrow-band thermal emitter as an active plasmonic device. The device is made of the metallic disk (MD) structure as mentioned in the section 2.2.2. The absorption and emittance spectra of such structure were investigated theoretically and experimentally. The structure exhibits one significant LSPP mode for both TM and TE polarizations, leading to an un-polarized narrow peak with a FWHM of 250nm and low sideband emission. The emission peak caused by the mode can be tuned by either varying the disk diameter or the SiO2 spacer.

3.1 Device description

The MD array structure as shown in Figure 2.2.2-2 is based on a silicon substrate.

An array of Λ periodic sliver disks with diameter D and thickness 100nm is depositedon top of a uniform SiO2 layer with thickness t=50nm. Below the SiO2 layer is a 100nm metallic sliver thin film to block the light transmittance. The fabrication of the structure began with e-gun deposition of a 5nm Cr adhesion layer and a 100 nm sliver layer on the top of a silicon (Si) substrate, followed by a thickness of SiO2 thin film deposited by plasma-enhanced chemical vapor deposition (E-gun deposition and PECVD recipes shown in Appendix C). A photoresist layer was then spin-coated on the top of the SiO2 thin-film layer. An array of the round-shaped disks periodically spaced with a lattice constant Λin x and y directionswas defined on the resist by using photolithography. After developing the resist, a 100-nm-thick sliver layer was deposited. Then, a lift-off process was carried out by rinsing the sample in acetone for a few minutes and cleaning it with isopropyl alcohol and de-ionized water, respectively. Finally, the completed structure was dried with nitrogen gas. The size of the array sample was 1cm×1cm. To heat up the sample, a DC current was applied through the molybdenum (Mo) thin film deposited on the backside of the silicon wafer. Due to no transmission for the case, the thermal emittance spectrum of the sample can be predicted by the equation

) Analysis (RCWA) method [47-50].Through the equation, the thermal emittance peaks are mainly dominated by the reflectance spectrum. In the simulation part of the structure, we collaborated with Mr. Mohammed Nadhim Abbas (a PhD student of the Director Yia-Chung Chang in the RCAS at Academia Sinica). We found that both TM- and TE- polarized reflectance spectra show one clear resonant dip at 0.33eV for full incident angles, as shown similarly in Fig. 2.2.2-3(a) and 2.2.2-3(b). The angle and polarization independent peak feature will give an un-polarized thermal emission peak.

The wavelength of the emission peak also can be tuned by varying either disk diameter or SiO2 layer thickness. Figure 3.1-1 shows the absorption spectra

) , , (

1

R   

for various disk diameters when t=50nm. The reduction of the disk diameter results in a blue shift in the resonance wavelength. On the other hand, when thickness of SiO2 layer (spacer) increases, the coupling of top and bottom interface decreases, resulting in a blue shift.

Fig. 3.1-1 Absorption spectra (1−R(λ)) of the MD array structure with different diameters D

for θ=0° when t=50nm. The inset shows resonance wavelength (λ) versus the SiO₂ layer

thickness (t) when D=1000nm.

3.2 Experimental setup and results

To characterize the thermal emission peak, we corroborated with professor Si-Chen Lee’s group. A Perkin Elmer 2000 Fourier transform infrared spectrometer system was adopted to measure the thermal radiation spectra. A 1cm² sample with D=1.15μm and Λ=3μm was fixed across the electrodes in a chamber with a pressure of 3 mTorr (see Figure 3.2-1(a) and 3.2-1(b)). A Dc current was then applied through the Mo film to heat up the sample. The thermal radiation of the sample was collected by a 45^O off-axis mirror with a NA of 0.1 and then reflected into the FTIR system

input port. An external wire-grid polarizer was set up between the sample and the FTIR system for the polarized thermal radiation measurement.

Fig. 3.2-1(a) Side view of thermal emitter chamber [53].

Fig. 3.2-1(b) Top view of thermal emitter chamber [53].

Figure 3.2-2(a) shows the dispersion relation of reflectance spectra of the sample, the gray scale from dark to bright represents the reflectance from low to high. The

measurement was done by varying the incident angle from 12^ο to 65^ο. The dip at 0.29eV (4.27μm) corresponding to the LSPP mode of the metallic disk. Figure 3.2-2(b) shows the measured thermal emission spectrum of the IR emitter when the sample was heated up to 220^o C (blue line) and 300^o C (black line), respectively. The emission peak was observed at 4.27μm with a full-width at half-maximum (FWHM) of 0.25μm. By performing both emittance and reflectance spectra measurements, we found that the emission and resonant peak wavelengths agree well as predicted by the

Kirchhoff’s law of thermal radiation. Because of the TE- (s-) and TM-polarized (p-) spectra are almost identical (see Figure 3.2-2(c)), we can clearly confirm that the thermal radiation peak is un-polarized.

Fig. 3.2-2(a) Measured reflectance spectra of sample with D=1.15μm and Λ=3μm.

Fig. 3.2-2(b) Simulated and measured emission spectrum of the IR emitter at 220 °C (blue

line) and 300 °C (black line), respectively.

Fig. 3.2-2(c) The measured emission spectrum for unpolarized, s-polarized (TE-polarized)

and p-polarized (TM-polarized) for 220 °C.

3.3 Summary

The plasmon-polariton band structures of metallic disk structure for both TM and TE polarizations have been investigated. We show that a narrow band thermal emitter at IR region can reach an emission peak at 4.27μm with a FWHM of 0.25μm. The peak can be tuned by either changing the disk diameter or SiO2 thickness. This kind of emission spectrum with narrow bandwidth, low sideband and high intensity is very useful for the application in IR light sources.

Chapter 4 Wide-angle plasmonic infrared filters/absorbers

One-dimensional plasmonic filter/absorber assisted by LSPPs in a symmetric Ag/SiO2/Ag T-shaped array was theoretically and experimentally investigated. An angle-independent LSPP resonant mode caused by a Fabry-Pérot resonance in the structure was observed in agreement with our RCWA simulation. The resonant wavelength of the mode can also be controlled by modifying the geometry of the T-shaped structure. The LSPP angle-independent feature makes the designed filter more flexible than a guided-mode resonance (GMR) dielectric filter [54-56] and a surface plasmon-polariton (SPP) filter [57] as well as a plasmonic multilayer filter related to our previous work [58]. To further improve the absorption performance and reduce the fabrication difficulty, a two-dimensional round-shaped metal disk array is applied. Different from the previous work [59, 60], the our results clearly revealed that the resonant wavelength of a LSPP angle-independent band is independent of the disk periodicity. Therefore, a broadband thermal emitter made of six distinct disks in one unit cell can be realized. We also first experimentally found that the absorptivity of the disk absorber obeying the Beer Lambert law can be enhanced by increasing the ratio of disk size to the unit cell area. By modifying the area filling ratio, we demonstrated a high-performance, wide-angle, polarization-independent dual band

absorber with two maximal absorptivity peaks greater than 84% over a wide range of incident angles.

4.1 Design and simulation of the Ag/SiO

₂

/Ag T-shaped array

Figure 4.1-1(a) shows the illustration of the proposed Ag/SiO2/Ag T-shaped array with geometric parameters as follows: Λg=3000nm, tAg=100nm, tw=50nm, WT=800nm, and WAg=1100~2000nm. Figure 4.1-1(b) is a schematic sketch of the T-shaped structure as a notch filter when light is reflected back toward a signal detector. In the simulation, the incident light is TM-polarized (i.e. magnetic field parallel to the y-axis) with different incident angles in the x-z plane. The frequency-dependent complex dielectric constants of silver (Ag) and SiO2 are taken from Ref. [61].

Fig. 4.1-1(a) Illustration of the T-shaped array structure. (b) Illustration of the reflection-type

filter with the designed structure

To find the resonant energy and understand the behavior of the resonant mode in the designed T-shaped array, reflectance spectra are calculated. Figure 4.1-2(a) shows the calculated reflectance spectra for WAg = 1500nm and photon energy ranging from 0.12eV to 0.62 eV, while the angle of incidence varies from 0° to 90°. An angle-independent flat band is found at the photon energy of 0.35eV. This flat band indicates the group velocity (ω/Kx) in the x-direction is zero and the mode at the band is highly-localized at the metal-dielectric interface, which is called a LSPP mode.

The reflectance spectra with various incident angles in the y-z plane are also examined as shown on Figure 4.1-2(b). The dispersion curve in Ky is parabolic.

Therefore, a small deviation of Ky from zero will not lead to significant change in resonance energy. The angle-independent mode is due to a strong coupling between the SPP modes of the cap silver layer and bottom layer. This strong coupling will form the Fabry-Pérot type resonance in the closed-end Ag/SiO2/Ag cavities under the cap [62]. The resonance not only can be excited at any incident angle, giving a strong angular tolerance of the structure compared with the GMR and SPP filters [54-57], but also can offer a single flat band in IR region, which is better for single-band rejection applications compared with the 1D plasmonic multilayer filter [58]. Figure 4.1-2(c) shows the |Hy|² distribution of the LSPP mode in one unit cell of the periodic structure when the photon energy is tuned to 0.35eV (ie resonant wavelength 3.54 μm)

with normal incidence. The |Hy|² field has nodes at the open ends (x = ± 750nm) and anti-nodes at the closed ends (x = ± 400nm), showing the spatial response of the first Fabry-Pérot resonance mode. When the SiO2 layer increases, the coupling will be weaker and the LSPP band becomes broad, blur, and blue-shift. For a thicker SiO2

spacer, the effective index of the mode in the resonant cavities will be decreased [63, 64]. Therefore, the resonant wavelength of the band is blue-shifted. One of the advantages of this T-shaped array is that the LSPP resonance wavelength has a strong dependence on the geometrical parameter WAg due to its Fabry-Pérot type resonance.

It can be found that the resonance wavelength increases linearly as WAg varies from 1100nm to 2000nm. The wavelength tuning rate is approximately 3.8 nm per nm in WAg.

Fig. 4.1-2(a) Stimulated reflectance spectra in x-z plane. (b) Stimulated reflectance spectra in

y-z plane

Fig. 4.1-2(c) |Hy|² distribution at 0.35ev in x-z plane.

4.2 Fabrication of the Ag/SiO

₂

/Ag T-shaped array

Fig. 4.2-1 Fabrication process of the T-shaped array.

The Ag/SiO2/Ag T-shaped structure was fabricated on a silica substrate. A 100 nm Ag film and a 50nm SiO2 film were deposited on the substrate by using E-gun

evaporator and RF sputtering system (E-gun deposition and RF supttering recipes shown in Appendix C). A PMMA layer was coated on the SiO2 layer, as shown in Figure 4.2-1. A grating structure with a lattice constant (Λg) of 3μm and a line spacing of 800nm (WT) was defined on the PMMA layer by electron beam lithography. The pattern was transferred to SiO2 layer by reactive ion etching (RIE recipe in Appendix C). The second EB lithography was executed to make another PMMA periodic structure on top of the SiO2 layer with a line width WAg. Finally, a 100nm Ag layer was deposited, and the T-shaped structure was obtained by lifting PMMA layer off.

The size of the structure is 400 μm × 400 μm, which is large enough to obtain clear signals from the structure. Figure 4.2-2(a) is the image of T-shaped array with a tilt angle of 45°. Figure 4.2-2(b) is the cross-sectional image of the structure.

Fig. 4.2-2(a) 45° angle SEM image of the T-shaped array. (b) Cross-sectional SEM image of

the T-shaped structure.

4.3 FTIR measurement setup

Fig. 4.3-1 Experimental setup for measurements.

A Bruker Vertex 70 model Fourier-transform-infrared (FTIR) spectrometer coupled to a Hyperion model microscope system was applied for sample measurements (see Figure 4.3-1). The Hyperion unit includes transmission and reflection modules. In the experiment, a MIR reflection module was used. In this module, a MIR un-polarized light source was focused a sample and reflected back with a 15X objective lens (NA=0.4 and focus length f=24mm). The back-reflected light through a controllable 50μm×50μm slit was collected and detected using a MCT (mercury-cadmium-telluride) photodetector with a spectral resolution of 2 cm^-1. Because of the slit size 50μmx50μm back of the objective lens, the maximum reflected light acceptable angle can be reduced from 23.5° to 0.05°, giving a narrow

range of angles of incidence. Based on the setup, the measured reflectance or absorbance spectra varying with incident angles from 0° to 15° can be observed by using a tilt-angle wedge on which a sample is placed.

4.4 Experimental results of the Ag/SiO

₂

/Ag T-shaped array

To characterize the optical filtering property of the Ag/SiO2/Ag T-shaped array, the reflectance and absorbance spectra (see Figure 4.4-1(a)) of the T-shaped structure at normal incidence were measured. A resonance peak (dip) in the absorbance (reflectance) spectrum is at 3.34μm with a FWHM of 0.29μm, where this bandwidth is much narrow than that of the plasmonic multilayer structure 0.5μm [58]. To increase the contrast of the dip, a TM polarized light can be applied. The location of the resonance peak (or stop-band center wavelength) can also be controlled by varying the top width WAg or the neck width WT. Figure 4.4-1(b) shows the absorbance spectra at normal incidence for WAg = 1300nm, 1540nm and 1910nm and WT =800nm. It is seen that the resonance peaks occur at 2.80μm, 3.48μm and 5.08μm, respectively, while CO2 and water vapor absorptions in the atmosphere are also visible.

Figure 4.4-1(c) shows the measurement and simulation results of the resonant

Figure 4.4-1(c) shows the measurement and simulation results of the resonant

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