Baesd on the Kirchhoff’s law of thermal radiation, we demonstrated an angle and polarization independent narrow-band thermal emitter as an active plasmonic device.
The device is made of metallic disks with D=1.15μm and Λ=3μm on a SiO2/Ag
substrate. The emission peak was found at 4.27μm with a FWHM of of 0.25μm for both TE and TM polarization. The resonance peak also can be tuned by either changing the disk diameter or SiO2 thickness. This kind of emission property with narrow bandwidth, low sideband and high intensity is very useful for the application in IR light sources.
Regarding to passive plasmonic devices, a one-dimensional angle-independent IR filter/absorber with Λg=3000nm, tAg=100nm, tw=50nm, WT=800nm, and WAg=1100~2000nm was investigated and characterized in chapter 4. The optical filtering/absorbing property is caused by a Fabry-Pérot resonance corresponding to an angle-independent LSPP mode. By adjusting the WAg from 1910nm to 1300nm, the LSPP resonance wavelength can be linearly tuned with a rate of 3.8 nm per nm in WAg, in agreement with our RCWA simulation. The T-shaped structure with the LSPP resonance therefore has a strong advantage for single-band rejection applications.
To further improve the absorption performance of the T-shaped structure, two-dimensional round-shaped metallic disk arrays on a SiO2/Ag/Si substrate was
peoposed. We found that the metallic disk exhibits a LSPP mode independent of the disk periodicities. Therefore, a broadband emitter composed of the sublattices with six different disks from 800nm to 1.35μm can be realized. The emission bandwidth could achieve 2000nm centered at the wavelength 4.32μm. In addition, by controlling the disk sizes and disk area-fill factor, the absorptivity of the 2D array absorber can be tuned. With the ideal, we demonstrated an angle and polarization independent dual-band absorber with two maximal peak absorptivities over 84%. The angle of incidence for the absorber can achieve nearly 90° in the operating mid-infrared region from 2.85 μm to 3.65 μm. The approach is applicable for thermal photovoltaic, sensor, and camouflage applications.
In chapter 5, by tuning the aspect ratio of the round-shaped disk structure, we found both angle-independent TE- and TM- polarized resonant peaks can be separated.
Based of the strong absorption resonant bands and its low-cost building materials, a cheap omni-directional mid-IR polarizer made of an elliptical disk array withΛ
g=2000nm, a=1500nm, and b=1000nm was demastrated. In the experiment, both TM- and TE- resonant wavelengths were observed respectively at 5.2μm with a degree of polarization 99%, and 4.1μm with a degree of polarization 91%. The extinction ratios for both TM and TE modes are 15dB and 20dB, all of which can be further improved by tailoring the b/a axial ratio.
In additional to the TE and TM separation property of the oval-shaped disk array structure, we found that the TM-mode |Hy|2 field of the oval structure shows more leaky field to the atmosphere compared with the round-shaped structure, giving rise to an increase in the sensitivity to the environment. To further improve the sensitivity, an Au/SiO2 elliptical shaped structure with a=283nm and b=146nm was proposed. The sensitivity 691nm/RIU and FOM 2.5 can be achieved to be the highest record up to now in the NIR region. The improvement of the sensitivity is caused by increasing leakage field distribution out of the disk structure into ambiance. Furtermore, the Au/SiO2 disk resonant cavity is able to be against the FWHM broadening, giving an increase in FOM. The structure therefore can be a good candidate as a highly performance angle-independent plasmonic index sensor. In the future work, we will cooperate with Professor Yi-Chung Tung at Academic Sinica to produce target cells on such device for the cell detection.
Appendix A
Characterization of the surface plasmon polariton band gap in an Ag/SiO
2/Ag T-shaped periodical structure
We investigated the localized surface plasmon polariton band gap based on an Ag/SiO2/Ag asymmetric T-shaped structure [70]. The band gap will appear with an index contrast modification without additional periodic grating. The phenomenon to control the surface plasmon polariton band gap was simulated by RCWA and directly observed using a FTIR spectrometer. The T-shaped plasmonic periodical structure not only provides a new method for generating the band gap, but also provides a strategy to tune the LSPP band-gap with the geometry. Such a T-shaped structure with a LSPP band gap can be widely exploited in various applications, such as band gap waveguides, defect cavity lasers/emitters, and a study of nonlinear plasmonics.
Design and simulation
Figure A-1 shows the proposed Ag/SiO2/Ag asymmetric T-shaped array with the geometric parameters as follows: Λg= 1 μm, Wtop= 550 nm, ttop= 200 nm, Wpost= 200 nm, tpost= 0~320 nm, d= 50 nm, Gt = 320 to 0 nm, and tSiO2= 320 nm.
Fig. A-1 Schematic diagram of the T-shaped array structure
To understand the resonant behavior of the structure, its reflectance spectra and resonant mode profiles are calculated by RCWA simulation. In the simulation, because of no resonant response in the proposed structure for the TE-polarized light applied in our designed photon energy region, TM-polarized incident light (the magnetic field parallel to the y-axis) is used with different incident angles in the x-z plane. Figure A-2(a) shows the calculated reflectance spectra of the Ag/SiO2/Ag multilayer structure (tpost=0nm and Gt=320nm) with the photon energy ranging from 0.5 eV to 1.2 eV, while the angle of incidence θi varies from 0° to 90°. The crossings are from the grating coupling at the SiO2/Ag interfaces and associated with the first Brillouin zone folding. The crossings all lies on the Bragg planes, and kx = m π/Λg
where m is an integer. The slope of the dispersion indicates the group velocity (vg =
ω/kx) of the SPP propagation at the SiO2/Ag interface. Due to less interaction between the two branches, the crossing point is found to be 0.87 ev at normal incidence, showing no energy gap in the dispersion relation. To form an energy gap,
additional periodic grating with a period of Λg/2 is commonly used [55, 71, 72]. The periodicityΛg/2 is designed to couple an energy gap region with photons inside the light line.
Fig. A-2 (a) Stimulated reflectance spectra of the multilayer structure with design parameters
of Λg=1 μm, Wtop =550 nm, ttop=200 nm, Wpost=200 nm, d=0 nm, tpost=0 nm, and Gt=320 nm.
(b) Stimulated reflectance spectra of the T-shaped structure when d=50 nm, tpost=170 nm, and
Gt=150 nm.
However, this study found that without using extra periodic grating, an energy gap can be opened when tpost is introduced, as shown in Figure A-2(b). The slope of the bent dispersion curves provides the group velocity in the x-direction as a function of the resonance wavelength and incident angle. At small values of kx, we also found that a momentum band gap will occur in the first branch if the T-shaped structure becomes symmetric (d=0nm). The momentum gap is due to the non-coupling strength in the first branch and determined by the relative phase between the top grating strip
and the post structure [71, 73]. Regarding the |Hy|2 distributions at normal incidence for the two branches of the designed structures, Figure A-3(a) shows the free-propagation-like field distribution at the bottom SiO2/Ag interface along the x-direction in one pitch of the multilayer structure. Figures A-3(b) and A-3(c) are the field distributions for the two standing wave solutions at the first and second branches when the tpost =170 nm. Most of the field intensity is concentrated in the corners between the post and the grating on the top layer for the first branch. Regarding the second branch, the intensity distribution reveals a periodicity equal to half the pitch period, with the strong field in the SiO2 spacer below the post.
Fig A-3 |Hy|2 distribution at normal incidence in one period of (a) the Ag/SiO2/Ag multilayer
structure at the crossing point 0.87 eV, and (b) the first and (c) second branches of the
T-shaped structure when d=50 nm, tpost=170 nm, and Gt=150 nm.
The mechanism of the dispersion-relation modification arises from the impedance mismatch [74] between the metal-metal and single metal regions of the T-shaped structure, where the impedances of the metal-metal regions strongly depend on the geometric parameters t and W , and when the t and W are fixed. As
the tpost increases, the band gap progressively opens and is linearly proportional to the post height (tpost) when 0 ＜tpost ≦270 nm, as shown in Figure A-4(a). Because tpost＞ 270 nm (Gt＜50 nm), the band gap increase rate becomes nonlinear (not shown) due to the resonant mode of the second branch beginning to form Fabry–Perot resonance in the gap (Gt) between the post and the bottom layer. When Gt is decreased, the effective index of the mode will increase [63, 64]; hence, the resonant wavelength of the second branch is red-shifted. This study also observes that the resonance wavelength shift in the first branch of the energy gap is extremely sensitive to variations of tpost compared to the second branch because the field distribution in the first branch is significantly perturbed by the post. The post plays an important role in perturbing the propagation of SPP modes (a change in the group index for the SPP propagations), leading to a modification of the grating-induced line shape in the dispersion relation and energy-gap opening. This study also explores the energy-gap behavior in the varied Wpost, as shown in Figure A-4(b). When the Wpost increases, the first band is shifted upwards to high energy, whereas the second band is moved downwards. Eventually, both branches meet at approximately 0.80 ev when Wpost
=450 nm. We expect that when the Wpost isadjusted, both resonance modes of the two branches (see Figures A-3(b) and A-3(c)) are modified along the x-axis, shifting all their resonance energies. In comparison to the results shown in Figures 4.1-4(a) and
A-4(b), the band gap’s tunability with the post is clearly much greater and simpler regarding the Wpost and our previously proposed structure [73]. The band gap tuning rate is approximately 1 meV per nm in the tpost. In addition to the tunability, varying post lengths in the T-shaped structure are easier fabricated.
Fig. A-4. (a) Energy gap of the T-shaped structure varying with tpost when the Wpost is fixed at
200 nm. (b) Energy gap versus Wpost when the tpost =170 nm.
Fabrication of the asymmetric T-shaped array
The fabrication processes of the structures are described as follows (see Figure A-5(a)). A 100 nm Ag film and a 320 nm SiO2 layer were deposited on a silicon substrate using an electron gun evaporator and RF sputtering system. Then a PMMA layer as an e-beam resist was spin coated on the SiO2 layer. The grating pattern with a lattice constant Λg and line spacing Wpost was exposed with electron beam lithography, followed by a dry etching step with a mixture gas of CHF3/O2/Ar in an inductively coupled plasma (ICP) system. (ICP recipe shown in Appendix C) After etching a
depth of tpost, an O2 plasma ashing process in Appendix C was used for 6 seconds. A sliver film was then evaporated on the surface with a thickness of tpost. After removing the residual PMMA, another PMMA periodic structure with a period Λg, line spacing WTop, and displacement d was formed by the alignment in the second EBL. Finally, a 200-nm-thick silver film (ttop) was deposited, and the T-shaped structure was completed via a PMMA lift-off process.
Fig. A-5 (a) The fabrication process of the T-shaped Ag/SiO2/Ag structure. (b) SEM view of the T-shaped array with a displacement of d=50 nm. The inset shows the details of the structure with a tilt angle of 25° at the ends of the grating slabs on the Ag posts. (c) AFM image profile of the T-shaped grating.
Figure A-5(b) is the scanning electron microscope (SEM) image of the fabricated structure with a tilt angle of 25°, where a bump structure is on the top of the silver grating due to the imperfect nature of the fabrication process. Figure A-5(c) is the atomic force microscopy (AFM) image profile of the fabricated T-shaped grating.
Experimental results and discussion
To characterize the band structures varying with the tpost, the absorbance spectra under oblique incidence in x-z plane was measured using a FTIR spectrometer. The light source was focused on the sample that was placed on wedges with tilt angles θi
during the FTIR measurements. The back-reflected light from the sample through a 50μm×50μm slit was collected and detected using a MCT (mercury-cadmium-telluride) photodetector with a spectral resolution of 2 cm-1. In order to verify the bandstrucutre of the T-shaped grating from TM mode response (see Fig. A-2(b)), a near-infrared polarizer was used to select input light polarization.
Figure A-6 exhibits the absorbance spectra for TE-, TM-, and un-polarized incident light. As can be seen, two pronounced absorption peaks occurs at λ=1.41μm and λ=1.85μm for both TM- and un-polarized cases, corresponding to the LSPP band gap, while there is no peak for the TE mode. The evidence clearly shows the band-gap feature originates from TM polarization. Due to the limitation of our current setup
with the polarizer, the absorbance spectra of the structures with two different tpost and incidence angles from 0° to 10° were also measured under un-polarized illumination.
Fig. A-6 Experimental absorbance spectra of the T-shaped grating (Λg=1 μm, Wtop =620 nm,
ttop=200 nm, Wpost=200 nm, tpost=170 nm, and Gt=150 nm) at normal incidence under TE-,
TM-, and un-polarized illumination.
Figure A-7(a) shows the absorbance spectra of the proposed structure when tpost
= 0 nm, and its simulation result. The results show that as θi increases, the resonance peak at λ=1.43 μm at normal incidence is split into two, one peak is red-shifted and the other is blue-shifted, corresponding to the grating-coupled SPP at the bottom SiO2/Ag interface. The distance difference between the two split peaks is linearly increased with an increasing incidence angle in the presence of a 3 % measurement error. The measured absorbance spectra of the T-shaped structure with d=50 nm and tpost=170 nm was also observed in Figure A-7(b). Two clear resonance peaks at
normal incidence are found at λ=1.83μm for the first band and λ=1.41μm for the second band, demonstrating an energy gap between them in accordance with our simulation. The width of the band gap is up to 420 nm, much larger than the 188 nm created by the silicon-loaded bihamonic metallic grating [72]. Because of the wider band gap occurring on the Bragg plane kx =0 (incident angle θi = 0°), the structure is feasible for band gap defect cavities and band gap defect mode laser applications.
Moreover, if the post tpost reaches 320 nm (Gt=0 nm), an angle-independent band-stop reflective filter can be realized [75]. When the incident angle increases, both resonance peaks of the T-shaped structure are moved away, and the wavelength difference between the two peaks is not linearly proportional to the incident angle.
This indicates a change in the first and second band curves. Therefore, the band curve feature implies the possibility of controlling the SPPs for dielectric-loaded SPP waveguides. The propagation loss for the SPPs is mainly from the roughness of dielectric/metal interfaces and ohmic heating loss in the metal. To reduce the loss and extend the propagation length, much energy concentrated in the dielectric medium and smaller values of group velocity dispersion should be taken into account [76].
Fig. A-7 Experimental absorbance spectra of (a) the multilayer structure (Λg=1 μm, Wtop =570
nm, ttop=200 nm, Wpost=200 nm, tpost=0 nm, and Gt=320 nm) and (b) the T-shaped structure
(Λg=1 μm, Wtop =620 nm, ttop=200 nm, Wpost=200 nm, tpost=170 nm, and Gt=150 nm) for the
different incident angles θi = 0°, 5°, and 10°. In both (a) and (b), the simulated absorbance
spectra are represented by black solid curves.
Because most of the field intensity of the SPP propagation is on the bottom SiO2/Ag interface (see Figure A-3(a)), and the SPP effective index can be modified by different metallic slit widths, this study proposes a simple 1D photonic crystal slab to
qualitatively interpret the SPP band gap behavior. Figure A-8 shows the dispersion relation of the 1D photonic slab with a periodicity of 1 μm and a SiO2 thickness of 320 nm, where n1 is the SiO2 index and n2 is a high-index in the Wpost region. An energy gap at kx=0 caused by the index contrast between the constituent dielectrics can be found in its dispersion relation, which behaves similarly to that shown in Figure A-2(b). Overall, these results substantially prove that the band curves and the band gap between the first and second bands can be engineered by varying the post depth. The unique properties of the T-shaped configuration can be applied to control the light localization and propagation at the dielectric/metalinterface.
Fig. A-8 1D photonic dispersion curve of the slab with the constituent dielectrics n1=1.414
and n2=2.236, when Λg=1 μm, tSiO2=320 nm, and Wpost=200 nm.
Summary
In summary, this study demonstrated the localized surface plasmon-polariton band gap based on an Ag/SiO2/Ag asymmetric T-shaped structure. The localized
surface plasmonic band gap was characterized with a measured absorbance spectra from the FTIR system. This band gap is attributed to the index contrast between the metal-metal and single metal regions, and is linearly proportional to the increased tpost
(tpost ≦270 nm). When the band gap opens, the shift of the first branch is much greater than that of the second branch because of the perturbed SPP mode of the first branch caused by the post. The plasmonic band gap structure suggests applications for plasmonic devices with LSPP band gap manipulations, such as band gap waveguides, and defect cavity lasers/emitters, and a study of nonlinear plasmonics.
Appendix B
Hydrodynamic modeling of surface plasmon enhanced photon induced current in a gold grating
We cooperated with professor Wan Kuang’s group at Boise State University to study photon induced voltage on an Au grating slab [77]. A semi-classical electrodynamic model is developed for the Au grating slab under the weak nonlinearity approximation. The electrons in the conduction band are treated as an electron gas in the presence of the self-consistent electromagnetic field. The model was solved by finite element method and compared with our measurements. The calculated photon induced voltage as a function of incident angles and wavelengths was found to be in qualitatively agreement with the experimental measurements. The results show that increasing surface plasmon spatial variation enhances photon induced current.
Fundamental study of semi-classical electrodynamic model
Enhancement of optical properties by plasmon resonances in metallic materials has attracted much attention over the past two decades. Strong local fields from plasmon resonances are particularly important for nonlinear optical processes which scale with a high power of electromagnetic fields strength. A light beam with a frequency of ω can produce the photon induced current on metallic structures. The
overall shapes of the metallic structures play a significant role in determining the induced current response [78, 79]. In the chapter, we will introduce the hydrodynamic theory developed by Goff and Schaich [80] to qualitatively explain the response.
Based on the model using the finite element method (FEM), the photon included current on an Au grating slab is also investigated numerically.
The photon induced current can be treated by the Maxwell’s equation with an explicit current density
J
,
is the current density due to electron transport in metal. The electric field
E
and polarization P
in Eq. (1) are written out separately because of numerical convenience. In the absence of interband transitions, the electrons in the conduction band can be treated as an electron gas with an effective mass m*in the presence of the self-consistent fields E
and H
[81]. The hydrodynamic equation of motion for the average velocity
v
( tr
, )is electron flux density which related to electron number density n multiplied by the average velocity (ie
j n v
), and pressure p is attributed to quantum mechanical Coulomb correlations and exchange contribution. A
phenomenological decay time
m is employed to describe other Coulomb scattering.To simplify and calculate the nonlinear current density j(r,t)
, we ignore the
influence of the magnetic field B
and expand the variables in Eq. (2) as a series of
and expand the variables in Eq. (2) as a series of