Page 1

Thermal emission and design in

2D-periodic metallic photonic crystal

slabs

David L. C. Chan, Marin Soljaˇ ci´ c and J. D. Joannopoulos

Department of Physics and Center for Materials Science and Engineering,

Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

dlcchan@mit.edu

Abstract:

derstand some of the physical phenomena that drive thermal emission in

2D-periodic metallic photonic crystal slabs, emphasizing phenomenology

and physical intuition. Through detailed numerical calculations for these

systems, we find that periodicity plays a key role in determining the types

of physical phenomena that can be excited. We identify two structures

as good candidates for thermal design, and conclude with a discussion

of how the emissive properties of these systems can be tailored to our needs.

We present a useful framework within which we can un-

© 2006 Optical Society of America

OCIS codes: (000.6800) Theoretical physics; (160.4670) Optical properties; (350.5610) Radi-

ation.

References and links

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inverted-opal photonic crystals,” Phys. Rev. A 72, 033821–033829 (2005).

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(1985).

1. Introduction

A blackbody is defined as an object of perfect absorption. Its entropy is maximized, and

in that sense it exemplifies utter disorder. The physics of blackbodies has both fascinated

and intrigued scientists for well over a century now [1]. In practice, most objects have only

finite absorption, and are thus referred to as ‘graybodies’. However, graybodies are of in-

terest because their thermal emission spectra can be changed by altering the geometry of

the system or the materials used. The ability to modify or tailor the thermal emission pro-

file of an object is of great importance and interest in many areas of applied physics and

engineering. It has been noted that periodic sub-wavelength scale patterning of metallo-

dielectric systems, i.e. photonic crystals, can modify their emission spectra in interesting

ways [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Thermal radiation from 2D-

periodic photonic crystals has been studied within the contexts of spectral and directional con-

trol [19, 8, 20, 21, 22], guided resonances [23], thermophotovoltaic generation [13], resonant

scattering [24, 25], laser action [26], Kirchhoff’s law [15], coherence [9, 22], and spontaneous

emission enhancement [5, 7, 20].

In this article, we focus on some of the most important physical phenomena that give rise

to many of the features observed in thermal emission spectra of 2D-periodic metallic photonic

crystal slabs, with the intention of developing physical intuition and understanding of features

of emission spectra. We demonstrate through detailed numerical studies the key role played by

periodicity in determining the types of physical phenomena that can be thermally excited in 2D-

periodic metallic photonic crystals. We develop understanding and physical insight using two

illustrative examples, before applying them to hybrid structures. Such structures exhibit strong

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thermal emission peaks which can be used as building blocks in thermal design. We show how

one can tailor the emissive properties of these structures to one’s design needs by changing two

simple physical parameters.

2.Description of numerical methods

Kirchhoff’s law states that for an object in thermal equilibrium with the surrounding radiation

field, its absorptivity and emissivity are equal, for every frequency, direction, and polarization.

Thus, to study thermal emission of an object, we need simply calculate its absorptivity spec-

trum, knowing that the object’s absorptivity and emissivity spectra are identical. Moreover, for

the purposes of developing an intuitive understanding of the physics behind thermal emission,

it is often more helpful to think in terms of absorption rather than emission, and it is on this

basis that we will proceed.

Fig. 1. Schematic illustrating the geometry of a typical system. The x- and y-axes are de-

fined in the plane of the slab, with the z-direction coming out of the slab. We study the

thermal radiation being emitted in the perpendicular direction.

Figure 1 is a schematic illustrating the geometry of a typical system under investigation. It

is important to note that because of the mirror symmetry of the system in a plane perpendic-

ular to x and y, the modes of the system can be separated into transverse electric (TE) and

transverse magnetic (TM) modes with respect to the mirror plane. As a result of this symme-

try, x-polarized modes do not mix with y-polarized modes. Thus, we can analyze these two

polarizations completely separately, and this is what we do in all our calculations.

Numerical simulations in our work are performed using a finite-difference time-domain

(FDTD) algorithm [27]. These are exact (apart from discretization) 3D solutions of Maxwell’s

equations, including material dispersion and absorption. We choose a computational cell with

dimensions 40×40×240 grid points, corresponding to 40 grid points per lattice constant a.

The faces of the cell normal to the x and y axes are chosen to have periodic boundary conditions,

while the faces normal to the z-axis (i.e. the top and bottom ones) have perfectly matched layers

(PML)topreventreflection.Inotherwords,thisisa3Dsimulationofa2D-periodicsystem.The

PhC slab is in the middle, and flux planes are placed on either side of it at least 2a away. We run

the simulation for a total of 40,000 time steps, chosen to be sufficiently large to allow resolution

of peaks with quality factors (Q) up to 250. We illuminate the photonic crystal slab with a nor-

mally incident, temporally Gaussian pulse. We record the fields going through flux planes on ei-

ther side of the slab and perform a discrete Fourier-transform on the time-series of fields, which

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we use to calculate fluxes as functions of frequency, Φ(ω) =1

We run the simulation once with the slab in place, and again with vacuum only, such that

Eslab= Evac+Eref, with Erefbeing the field due to reflection. The reflectance is given by

2Re{?E∗(r,ω)×H(r,ω)·dS}.

R(ω) ≡Φref

Φvac

=−1

2Re{?

A1[Eslab(r,ω)−Evac(r,ω)]∗×[Hslab(r,ω)−Hvac(r,ω)]·dS}

1

2Re{?

where A1is the flux plane corresponding to ‘1’, and the minus sign in the numerator is there

to make the reflected flux positive. This expression can be shown to simplify to R(ω) =

[Φvac

1

(ω)]/Φvac

flux plane further from the light source is ‘2’. (One can show that the numerator becomes

Φvac

1

for incoming and outgoing plane waves in vacuum, for which E and H are proportional.) Sim-

ilarly, the transmittance is given by T(ω) = Φslab

A(ω)=1−R(ω)−T(ω). This way, we obtain reflectance, transmittance and absorbance spec-

tra for PhC slabs. We incorporate absorption into our simulations by means of the Drude model,

according to the following equation:

A1E∗

vac(r,ω)×Hvac(r,ω)·dS}

(1)

1(ω)−Φslab

1(ω) where the flux plane closer to the light source is ‘1’, and the

1(ω)−Φslab

(ω)+1

2Re{?

A1(E∗

vac×Href−Hvac×E∗

ref)·dS} but the cross term vanishes

(ω)/Φvac

2

2(ω) and the absorbance is simply

ε(ω) = ε∞+

σ

(ω2

0−ω2−iγω)

(2)

where ε∞, γ, ω0and σ are input parameters. In our case, we are concerned with metals, for

which ω0= 0. By Kirchhoff’s law, the absorbance spectra so calculated are identical to the

emittance spectra of these objects, for each polarization, frequency and observation angle.

3.Holes and dips

Let us now turn our attention to real systems and the physical effects that are manifested therein.

The goal is to develop an understanding of the physical processes that drive emittance in these

systems. The first structure we will examine is a simple metal slab with holes (see Fig. 2). If we

illuminate the structure with light incident from the top of the cell, the light propagates down

the holes which act as metallic waveguides. Waveguide cut-offs arise from the requirement that

the parallel component of the electric field be continuous across a boundary. Inside a perfect

metal, the electric field is strictly zero. For such a material, E?is constrained to vanish at the

surface, and this leads to the well-known cut-off frequency corresponding to a half-wavelength

oscillation. Below this frequency, no propagating mode can be supported within the waveg-

uide, because the boundary condition cannot be satisfied. For a realistic metal (i.e. one that

permits some penetration of fields), the fields are not required to exactly vanish at the surface,

but must decay away rapidly and exponentially once inside the material. Such boundary con-

dition matching leads to a similar cut-off as in the case of the perfect metal, except that the

penetration of field into the metal produces a cut-off with a slightly lower frequency, because

the effective width of the waveguide is slightly larger. Cut-off frequencies depend on the width

of the waveguide. The wider the waveguide, the lower the cut-off frequency.

We present emittance and transmittance spectra for this system. Figure 2(a) shows how the

spectrachangewithholeradius.Thepeaksbelow1.0(indicatedbyblackarrows)arewaveguide

cut-offs arising from propagation of light through the holes. These peaks decrease in frequency

with increasing radius, a clear signature of waveguide cut-offs. They correspond to modes that

fit approximately half a wavelength across the hole in the x-direction. As we discussed, the

electric field has to be continuous as we cross media boundaries in the x-direction (because Eyis

paralleltothemediaboundary)butnotinthey-direction.Thus,thesemodeshaveone‘hump’as

we cross the holes in the x-direction, and decay exponentially inside the metallic bulk between

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01234

Frequency (c/a)

0

0.2

0.4

0.6

0.8

1

Emittance/Transmittance

t = 1.0a

t = 2.0a

0

0.2

0.4

0.6

0.8

1

Emittance/Transmittance

r = 0.1a

r = 0.2a

r = 0.3a

r = 0.4a

?

?

?

?

???

???

?

?

?

?

Fig. 2. (Color) Here we show emittance (solid lines) and transmittance (dotted lines)

spectra for a 2D-periodic metal slab with circular holes, viewed at normal incidence

and for y-polarized light. The Drude parameters used for the metal are ε∞= 1, ω0= 0,

γ = 0.3(2πc/a) and ωp=√10(2πc/a). In Panel (a), we fix the thickness of the slab at

1.0a (where a is the lattice constant of the slab) and vary the radius of the holes. The black

arrows indicate the peaks produced by the waveguide cut-off in the x-direction. In Panel

(b), we keep the hole radius constant at 0.4a and vary the thickness of the slab. Here, we

use arrows to indicate the peaks produced by diffraction.

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holes such that the field profile within the metal is of the form of a hyperbolic sine/cosine

curve (a combination of a decaying and growing exponential), depending on parity. We can see

immediately that as we increase the radius of such a hole, the profile relaxes in the x-direction

in such a way as to make the hump wider. This leads to a larger effective x-wavelength for the

mode, and thus a lower frequency cut-off. (The wavelength in the y-direction is unaffected by

the radius of the hole, since Eyis not required to be continuous in the y-direction.)

Diffraction peaks occur when we consider the slab system at a macroscopic level, in terms of

incoming and outgoing radiation modes. This effect is not unique to metallic PhCs, and can be

observed in non-metallic PhCs as well. In terms of absorption, the incident light, being normal,

can couple into outgoing radiation modes (in transmission or reflection) that conserve the wave

vector up to a reciprocal lattice vector in a direction of discrete periodicity. Because the incident

light has no ktransversecomponent, it can couple into outgoing modes with ktransverseequal to an

integer multiple of 2π/a (i.e. 1 in our units). This means that as we increase the frequency of

the incoming radiation, a new diffraction direction will be coupled into at ω = 1,√2,2,√5...,

corresponding to (kx,ky) = (1,0),(1,1),(2,0),(2,1)... At the threshold frequency for a new

diffraction mode, the wave vector has no kzcomponent, and so k is parallel to the surface of the

slab. Such ‘grazing’ modes have maximum interaction with the slab because they travel close

to the surface of the metal, and as such are strongly absorbed by the material. These absorption

peaks translate into emission peaks, via Kirchhoff’s law, so we would expect to see emission

peaks for modes corresponding to ω = |k| = 1,√2,2,√5...

Figure 2(b) shows how emittance and transmittance change with the thickness of the metal

slab. First, we notice that transmittance is greater for the thinner slab, as one would expect.

Second, we see the emergence of diffraction peaks at 1,√2,2 and√5 (we indicate these with

red and black arrows). Not only do they occur at precisely those frequencies that correspond

to the root of the sum of two squares (their wave vectors being permutations of (1, 0), (1, 1),

(2, 0) and (2, 1), respectively), they are also the same for both black and red curves, lending

further weight to the argument that they are diffraction peaks. Their magnitudes are clearly

quite variable; indeed, they wash out at higher frequencies. Such diffraction peaks can be seen

in Fig. 2(a), too.

What happens if we take the same metal slab, but do not drill holes in the slab that go all

the way through? What happens if, instead of having circular holes, we have circular dips?

We present emittance and transmittance for this structure in Fig. 3 as a function of dip radius.

Again, we see peaks below 1.0 which correspond to cut-offs, except in this case they are not

waveguide cut-offs but a kind of ‘cavity’ cut-off, where kxis such that there is approximately

half a wavelength in the x-direction. We see diffraction peaks at 1,√2,2 and√5. Above ωp=

√10 ≈ 3.16, the plasmon frequency of the metal, transmittance becomes significant, because

above that frequency, the metal becomes transparent and light can pass through it as though it

were a dielectric material (while still being subject to some absorptive loss).

4. Hybrid structures

Let us now turn our attention to hybrid structures which involve both metal and dielectric. We

consider a metal slab with a circular dielectric puck on top. This puck is intended to be a small

perturbation to the system that introduces discrete periodicity in both the x- and y-directions by

means of a piece of dielectric. We observe emitted light at normal incidence and polarized in

the y-direction.

Figure 4(a) shows how emittance and transmittance vary with the dielectric constant of the

perturbation (ε). First, we observe many peaks in the emittance spectra, and we note that the

positions of some these peaks (particularly the ones at frequencies less than 2.0) decrease with

increasing ε. Second, we see zero transmittance in the system for frequencies below ωp≈

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01234

Frequency (c/a)

0

0.2

0.4

0.6

0.8

1

Emittance/Transmittance

r = 0.2a

r = 0.4a

?

?

?

?

Fig. 3. (Color) We show emittance (solid lines) and transmittance (dotted lines) spectra for

a 2D-periodic metal slab of thickness 1.0a with circular dips, observed at normal incidence

and y-polarization. The dips have a depth of 0.5a. The Drude parameters used are ε∞= 1,

ω0= 0, γ = 0.3(2πc/a) and ωp=√10(2πc/a). We show spectra for two different radii of

dips, keeping the slab thickness constant.

3.16, as we expect, because the metal is opaque at frequencies below the plasmon frequency.

Third, we see also an entire series of diffraction peaks, at frequencies 1,√2, 2,√5, 2√2 and

3, corresponding to modes with wave vectors (1, 0), (1, 1), (2, 0), (2, 1) and permutations

thereof. These are especially clearly seen on the black curve. We know they are diffraction

peaks because they not only fit the above sequence, but also have the same frequencies on

the red and green curves. (Diffraction peaks do not change with the dielectric constants of the

structure.) Fourth, we demonstrate that most of the emittance peaks with frequencies below 2.0

that we see in Fig. 4(a) are in fact produced by surface plasmons.

Surface plasmons (SPs) are excitations that exist on the interface between a plane-metal and

a dielectric. They are confined to the surface, but can propagate freely within that surface. They

have a relatively simple dispersion relation that is approximately linear at low wave vectors and

bends over toward a flat cut-off at higher wave vectors (ωp/√ε +1 is the cut-off frequency,

where ωpis the plasmon frequency and ε is the dielectric constant). If the direction of prop-

agation is x (i.e. k is in the x-direction), then the SP will have field components Ex, Ezand

Hy(the z-direction is normal to the interface). The SP is unusual in that it has an electric field

component in the direction of propagation. Normally incident light (for which ktransverse= 0)

cannot couple into SP modes with non-zero k because of conservation of wave vector; however,

it can couple into such modes if the wave vector of the SP is along a direction of discrete trans-

lational symmetry, because in such a direction, wave vector is conserved only up to an integer

multiple of the reciprocal lattice vector. These correspond to k = (m,n)(2π/a) where m and n

are integers.

To show that the emittance peaks with frequencies below 2.0 are indeed SPs, we record the

frequencies of the peaks (up to ωp/√ε +1, the SP cut-off) for each curve in Fig. 4(a), and

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0123

Wavelength (µm)

456789 10

0

0.2

0.4

0.6

0.8

1

1.2

Power ( W / (cm2 * µm) )

Blackbody

W slab

W PhC

?????

???????????????

?

???

???

???

???

?

???????????????????????

?????????

???????

???????

????? ???? ????

????????????µ??

?

???

?

???

?????????????????? µ????

?????????

???????????

?

???

?

???

?

???

? ???? ???? ????

??????????????????????

???????????????

?????????

???????

???????

?????

?????????

???????

?????

?

?

?

?

?

?

???

???

???

?

?

?

???

Fig. 4. (Color) Panel (a) shows emittance (solid lines) and transmittance (dotted lines) spec-

tra for a 2D-periodic metal slab of thickness 1.0a with circular dielectric pucks for normal

incidence and light polarized in the y-direction. The pucks have a radius of 0.4a and a thick-

ness of 0.2a. The Drude parameters used for the metal are ε∞= 1, ω0= 0, γ = 0.3(2πc/a)

and ωp=√10(2πc/a). We show spectra for three different dielectric constants for the cir-

cular puck. In Panel (b), we took the peaks labeled by arrows in Panel (a), and plotted them

on a dispersion curve. (Note that the third red peak in Panel (a) coincides with a diffrac-

tion peak at frequency

circles) lies between the metal-air dispersion and the metal-dielectric dispersion, for the

corresponding dielectric constant. Therefore, it is quite plausible that these peaks are pro-

duced by surface plasmon modes. In Panel (c), we show the thermal emission spectrum for

the same metal slab with pucks of dielectric constant ε =5 at temperature 1000K (we call it

“PhC (model)”). We also show the blackbody spectrum at that temperature for comparison.

The lattice constant was chosen to be a = 2.94µm. Panel (d) shows the thermal emission

spectrum for the same system except that the “model” metal has been replaced by tungsten.

We modeled tungsten with Drude parameters[28] ε∞=1, ω0=0, γ/(2πc)=487cm−1and

ωp/(2πc) = 51700cm−1, and we chose a = 2.94µm. We show the emission spectra for a

uniform tungsten slab of thickness a (without pucks) and a blackbody for comparison.

√2 ≈ 1.41.) We see that the dispersion of the peaks (lines with

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plot them as circles in Fig. 4(b) against wave vector magnitude, making the assumption that

the first peak has a wave vector of (0, 1), the second a wave vector of (1, 1), and the third a

wave vector of (0, 2) (all in units of 2π/a). We make this assumption because this sequence

of (kx,ky) = (m,n) produces a sequence of frequencies in ascending order. In addition, we plot

SP dispersion curves for metal-air and metal-dielectric structures where both media are semi-

infinite in extent (dotted lines). SP modes in the structure under consideration would therefore

be expected to have a dispersion relation that lies between the metal-air and the metal-dielectric

dispersions, since the average dielectric constant of the dielectric strip/air lies between that of

theairand thedielectric.Thus, wewould expect theblack circlestoliebetween thedotted black

and blue curves, the red circles to lie between the dotted red and blue curves, and so on. Indeed,

this is exactly what we see. Furthermore, the fact that the circles, when joined together by solid

lines, form a dispersion relation that clearly bends over toward a cut-off, gives us confidence in

identifying these modes as SPs.

We can obtain the emissive power of these structures by taking the emittance spectra that

we have calculated and multiplying them by the blackbody emission spectrum (which is also

known as the Planck distribution). This is what we did in Fig. 4(c). We chose a = 2.94µm and

plotted thermal emission of the PhC slab as a function of wavelength. We show the emission

spectrum of a blackbody for comparison. We can immediately see an emission peak near 4.7µm

that has as high emission as a blackbody; this peak corresponds to the first SP peak in Fig. 4(a).

The two emission peaks at approximately 2.1µm and 3.2µm are diffraction and SP peaks,

respectively.

In Fig. 4(d), we consider the same structure except that the “model” metal slab is now re-

placed by a tungsten slab. We did this by doing the calculation using the Drude parameters of

tungsten. We also plot the equivalent tungsten slab emittance (dashed red curve) for compari-

son. In keeping with Kirchhoff’s law, at no point does the emission of the PhC structure exceed

that of a blackbody. The qualitative similarities between this emission spectrum and that shown

in Fig. 4(c) can be traced quite easily: the three major peaks remain; the tall central peak and the

peak to its right are SPs, while the sharp peak to the left (around 2µm) comes from diffraction

into (1, 1) modes. Overall, the background emission of the tungsten PhC slab is lower than that

for the “model” metal that we have hitherto been studying, because the background emittance

of a slab[15] goes as 2γ/ωp(in regime γ < ω < ωp), and ωpis much higher for tungsten than

for the Drude metal in Fig. 4(c). Notice that the PhC tungsten slab has higher emission at all

frequencies than the uniform tungsten slab. Thus, we have excellent enhancement of emissive

power through the use of a PhC.

As we have already remarked, the dominant feature of the emission characteristics of this

structure is the central peak at 3.06µm, which achieves 80% of the emission of a blackbody.

As we will show in Fig. 5, it is possible to shift this peak by changing the lattice constant

of the structure. By so doing, we can place a strong emission peak at whatever frequency we

choose. If we combine copies of this structure with different lattice constants, we can place

strong emission peaks at multiple frequencies. This is the beginning of thermal design using

2D-periodic metallic PhC slabs.

5. Thermal design

In order to facilitate our discussion of thermal design in 2D-periodic metallic photonic crystals,

we turn our attention to another variation on the theme of a hybrid structure, and show how the

emission spectrum of this structure can be tailored to our needs. We study a tungsten slab on

top of which sits a dielectric slab with circular holes. One can think of the dielectric portion

of this structure as being the ‘inverse’ of the circular puck. Such a structure exhibits discrete

periodicity in both the x- and y-directions.

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Page 10

0

1

2

3

Power ( W / (cm2 * µm) )

Blackbody (1000K)

W slab (1000K)

W PhC (1000K)

Blackbody (1200K)

W slab (1200K)

W PhC (1200K)

02468 10

Wavelength (µm)

0

1

2

3

Power ( W / (cm2 * µm) )

Blackbody (1200K)

W slab (a = 2.00 µm)

W PhC (a = 2.00 µm)

W slab (a = 3.23 µm)

W PhC (a = 3.23 µm)

???

???

?

?

?

??????

?

?

?

?

Fig. 5. (Color) Here we show the thermal emission spectrum for a hybrid 2D-periodic

structure consisting of a tungsten slab and a dielectric slab with holes. The metal slab is

1.0a thick while the dielectric slab (ε = 5) is 0.2a thick with holes of radius 0.4a. We

show emission of light polarized in the y-direction. In Panel (a), we display emission at two

different temperatures. We chose a lattice constant of a = 2.00µm. In Panel (b), we show

how the emissive power changes with lattice constant. In both panels, we show emission

spectra for a uniform tungsten slab of thickness a without dielectric, and a blackbody, for

comparison.

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We show the emission spectrum for such a structure in Fig. 5. In Panel (a), we choose a =

2.00µm and vary the temperature of operation. We plot thermal emission for the PhC slab,

the unadorned tungsten slab, and a blackbody. Again, the PhC emission far exceeds that of a

uniform tungsten slab. We see three prominent groups of peaks, the smallest of which has fairly

complicated substructure. First, we notice that the positions of the peaks do not change with

temperature. Second, increasing temperature increases emission at all wavelengths. Emissive

power goes as T4(Stefan’s law), so that, going from 1000K to 1200K, emission increases by

a factor of (1.2)4≈ 2.07 (provided the weighting does not change significantly). Third, the

relative weighting given to different wavelengths changes with temperature, because the peak

of the Planck distribution shifts toward lower wavelengths with increasing temperature. In our

case, the group of small peaks between 1 and 2µm were insignificant features at 1000K, but

became more prominent at 1200K, because the blackbody spectrum shifted in such a way as

to give those peaks much more weight than before (thus, they were enhanced by more than

a factor of 2.07). Fourth, the emission of the PhC slab exceeds that of the uniform slab at all

wavelengths and at all temperatures. In fact, the enhancement is impressive: we see a 20-fold

increase in emissive power (over that of a slab) at the major peak at around 2.9µm. Of course,

emissivity never exceeds unity, because that would violate the Second Law of Thermodynamics

(the large peak in question attains 66% emissivity). The important lesson we learn from this

is that we can emphasize different parts of the emission spectrum of a PhC by changing the

temperature at which we operate the thermal structure.

In Fig. 5(b), instead of changing the temperature, we keep temperature fixed and vary the

lattice constant of the PhC. The blackbody envelope and the emission spectrum of a uniform

slab of this same metal are shown for comparison. We see that increasing the lattice constant

shifts the emission peaks in the PhC towards a higher wavelength. In our case, for a = 2.00µm,

the large peak is already close to the point of maximum blackbody emission, so that increasing

thelatticeconstanttoa=3.23µmonlyservedtodecreasethetotalemissionfromthatexcitation

(incidentally, it is a surface plasmon). However, the change in a also brought some small peaks

from the lower wavelengths into the picture. The point of this exercise is to illustrate the degree

of control we have over the position of the peaks, and by these simple techniques, we can

shift emissive power around to different parts of the spectrum. It is useful to note that for both

choices of a, there is significant enhancement of emission over that of a uniform slab because

thebreakingofcontinuoustranslationalsymmetryallowsmorewavevectormodestobeexcited

and coupled into.

The two hybrid structures we considered in this and the previous sections would be suitable

candidates for applications that require narrow band emission in one or more frequencies. Both

structures have a dominant peak that can be shifted in wavelength by changing the lattice con-

stant. If we want three emission bands separated by 1-2µm, the structure in Fig. 5 would be a

good choice. There are two different ways to amplify an emission peak relative to background

emission. We can choose to operate the structure at different temperatures, or we could change

the lattice constant. These are simply two different ways of making the emission peak co-

incide with the wavelength of maximum blackbody emission. By combining many such hybrid

structures, each with its own lattice constant, we can place strong emission peaks at whichever

wavelengths we choose. We therefore have a means of tailoring the thermal emission properties

of a hybrid structure to our needs.

6.Conclusion

We presented a physical and intuitive framework within which we can understand some of

the physical phenomena that drive thermal emission in 2D-periodic metallic photonic crystal

slabs. We performed detailed numerical calculations for these systems, and found that period-

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icity played a key role in determining the types of physical phenomena that can be excited.

In particular, we saw how periodicity gave rise to waveguide cut-offs, waveguide resonances,

diffraction peaks and surface plasmon modes. Using hybrid structures composed of metal and

dielectric components, we obtained sharp emission enhancement over and above that of a metal

slab. In the case of tungsten, we created strong emission peaks with 80% and 66% emissivity,

far exceeding that of a uniform tungsten slab, which plateaus at about 3-4%. These peaks could

be shifted at will by changing the lattice constant of the structure or by changing the tempera-

ture at which the structure is operated. We can design materials with multiple emission peaks

by combining hybrid structures, each with its own lattice constant. Thus, we have a powerful

set of tools with which to develop physical intuition and understanding for thermal design.

The ability to design thermal emission could well find uses in thermophotovoltaic systems and

defense applications, where many targeting systems rely on the detection of thermal emission

from projectiles.

Acknowledgments

We thank our colleagues Peter Bermel and Steven Johnson at the Massachusetts Institute of

Technology for helpful discussions. This work was supported in part by the Croucher Founda-

tion (Hong Kong) and the MRSEC program of the NSF under Grant No. DMR-0213282.

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