## Abstract

Developing controllable radiation sources in the mid-infrared spectral region is significant in photonics technology because of rare available resources. Based on the thermal emission from a one-dimensional shallow tungsten grating, we propose a two-dimensional orthogonally-crossed shallow grating to produce an orthogonally-polarized dual-wavelength radiation with the emissivity as high as 78% and 91% from a single surface. The simulation shows that the field is intensively concentrated in vicinity of the air-tungsten interface when surface plasmon polaritons are excited. In addition, by optimizing the geometric parameters of the grating, the field is found to be more concentrated which leads to higher emissivity. The two wavelengths can be produced independently or simultaneously, depending on the polarization of the picking-up polarizer. Our investigations can help us developing controllable multi-wavelength thermal radiation sources from a single surface.

© 2013 Optical Society of America

## 1. Introduction

Spatially and spectrally controllable light sources are key components in the application of photonics technology. In the mid-infrared spectral region, utilizing light emitting diodes or quantum cascade lasers as radiating sources is limited because of their high cost and low energy, it is thus very important to find cost-effective and efficient alternatives [1].

One of the conventional ways to obtain spectrally and spatially quasi-coherent mid-infrared light sources is to introduce filters and polarizers to pick narrow-band wavelength regions from the thermal emission of a black body and control its polarization. However, only a very small portion of the energy is picked out from a very wide wavelength range and most of the radiation has been wasted. Several other routes such as utilizing microcavity resonance [2–4], multilayer systems [5, 6], photonic crystals [7–10], excitation of surface phonon polaritons [2, 11] and surface plasmon polaritons (SPPs) [12–14] etc. have been developed to control the wavelength and polarization of the thermal radiation. Three-dimensional (3D) metallic (such as tungsten) photonic crystals are capable to provide a large photonic bandgap (PBG) and simultaneously enhance the absorption at the photonic band edge thereby can be used to design highly selective narrow-band thermal emitters [9, 10]. However, the complicated fabrication procedure limits their applications. One-dimensional (1D) and two-dimensional (2D) photonic crystals can also be utilized to control the thermal emission, either through the excitation of the microcavity effect (when the depth of the holes or grooves is ~λ/2) or SPPs (the depth is much smaller than λ/2). 1D or 2D photonic crystals composed of grooves with a depth much smaller than λ/2 can also be called as shallow gratings when the application is not related with their PBG properties. Because of easy and simple fabrication, a shallow grating is one of the promising structures to obtain wavelength- and polarization-controllable light sources in the mid-infrared region [12, 14].

In nondispersive infrared analysis, the concentration of a specific chemical compound in liquids or gases is determined by comparing the absorption difference at two wavelengths (one as the characteristic wavelength and the other as the reference) [15, 16]. It is thus very important to obtain arbitrarily selectable dual-wavelength emission in the mid-infrared spectral region. Nonetheless, only a few articles have focused on designing applicable architecture for this purpose [16].

When the depth of the grating is comparable to λ/2, the resonance will be induced by microcavity effects, in which the emission wavelength is determined by the resonance of the cavity [2–4]. It is impossible to obtain more than one resonant wavelength by simply arranging one type of microcavities [13]. On the other hand, the thermal emission is highly polarized for 1D microcavity arrays [4], while that for 2D ones is randomly polarized [3]. By arranging two types of 1D microcavities, in which vertical and horizontal resonances are combined, into a checkboard-like structure, Miyazaki et al [14] has observed orthogonally polarized two-wavelength infrared waves thermally emitted from deep Au gratings. It is a simple and useful design. However, only half of the light source (50%) is valid for one polarization in order to obtain orthogonally polarized dual-wavelength emission from the microcavities in their design.

If the depth of the grating is shallow (much smaller than λ/2), the resonance can be induced by the excitation of SPPs [12–14]. As the microcavity effect cannot be formed in this case, it is possible to control the polarization at different wavelength independently if we combine different shallow gratings (azimuthally arranged) to compensate the extra moments required for excitation of SPPs at different directions.

In the present work, we propose a 2D orthogonally-crossed shallow grating to produce dual-wavelength emission with orthogonally polarizations from a single surface. Tungsten is chosen as the materials because it can sustain high temperature (more than 2000K) with good corrosion resistance and can support SPPs in the infrared wavelength range [12]. It had been widely used as thermal source. Both the grating and its supporting substrate are made of tungsten for easy fabrication.

We mainly focus on the wave numbers between 2500 cm^{−1} and 4000 cm^{−1} (corresponding to the wavelength range 4-2.5 μm) as they are in the stretching vibration frequency range of O-H, N-H and C-H. However, the principal can be easily extended to other frequency range.

The simulation in the present paper is based on the rigorous coupled-wave analysis (RCWA) method (from Rsoft Design Group) and the COMSOL Multiphysics finite element analysis (FEA) software. RCWA is used to compute emittance spectra and FEA the corresponding electromagnetic (EM) field distributions in vicinity of the tungsten-air interface. We apply 2D/3D simulations for 1D/2D gratings respectively. A Perfectly Matched Layer (PML) boundary condition is applied for the top/bottom area and Periodic Boundary Condition (PBC) for the four walls. As the wavelength we are discussing in this paper is in the range of 2.5-4 μm, the grid size 10 nm which corresponds to ~λ/250 ensures the convergence of the results both for 2D and 3D simulations. The frequency-dependent complex relative dielectric constant of the tungsten used in our simulations is characterized by a Lorentz-Drude model [17]

*ω*is the plasma frequency. k is the number of oscillators with frequency

_{p}*ω*, strength

_{I}*f*and lifetime

_{I}*1/Γ*. ${\Omega}_{p}=\sqrt{{f}_{0}{\omega}_{p}}$ is the plasma frequency associated with intra-band transitions, in which

_{I}*f*

_{0}is the strength of the oscillator and

*Γ*

_{0}the damping constant. The values of all these parameters were taken from the reference [18].

## 2. Simulations for 1D grating

We start by considering a simple 1D shallow grating to understand the evolution of the
emissivity with geometric parameters. The shallow grating has a depth much smaller than the
wavelength but still sufficiently deep to couple to the incident light strongly. As shown in
Fig. 1(a) , the simple 1D shallow grating is defined by
its period *Λ*, width *d* of the ridge and height
*h*. The filling ratio *f* =
*d*/*Λ*. The thickness *t* of the substrate
is fixed at 500 nm, which is much thicker than the typical skin depth (~20nm) of metals, thus
allowing no light to penetrate it. According to Kirchhoff’s law, the spectral emissivity
(at a wavelength of *λ*)
*ε*(*λ*) is equal to its spectral absorbance
*A*(*λ*) at thermal equilibrium. The validity of
Kirchhoff’s law for textured surfaces has been confirmed by Luo et al. [19]. The absorptivity for each *λ* is
given by *A* (*λ*) = 1 - *R*
(*λ*) -*T* (*λ*), where
*R* (*λ*) and *T*
(*λ*) are the reflectivity and transmittivity of an incident wave. In our
simulations, *T* (*λ*) = 0 because the thickness of the
substrate is much larger than its skin depth. Therefore, the emissivity can be directly related
to the reflectivity by *ε* (*λ*) =
*A* (*λ*) = 1 - *R*
(*λ*). The emission direction is the reverse of the incidence and their
polarizations are identical. The plane of incidence is defined by the incidence and the surface
normal.

SPP is a coupled, localized EM wave that propagates along the interface between two different media due to charge density oscillation [20,21]. At the resonant wavelength, the EM field can be greatly enhanced near the interface, yielding a strong absorption and a sharp reduction in the reflectance within a narrow spectral band [10]. In other words, the emissivity increase steeply since it equals to the absorbance according to Kirchhoff’s law. As the momentum of the SPP mode is greater than that of a free-space photon, the excitation of SPPs requires an electric-field component perpendicular to the grating to provide the extra moment [20]. Generally, such an electric field component exists in both transverse electric (TE) waves and transverse magnetic (TM) waves when the incident plane is not perpendicular to the grooves [22]. Here, without loss of generality, we consider the situation with the incident plane being perpendicular to the groove. In this case, only the TM wave can excite SPPs to enhance the emissivity.

For a flat air-material interface, the surface plasmon wavevector propagating along the *x* direction, *k _{sp,x}*, is determined by the dielectric constant of the metal (

*ε*) and the wavevector in vacuum (

_{m}*k*

_{0}) [23]:

SPPs can be excited between the metal and air if a 1D grating is modulated in the *x* direction. The wavevector of SPP is then given by [13]:

*K*

_{x}denotes the grating vector perpendicular to the grating grooves. Integer

*j*represent the diffraction order while “+” and “-” signs correspond to

*j*>0 and

*j*<0 respectively.

*θ*is the resonant angle of the incidence and

*ϕ*is the azimuthal angle, as defined in Fig. 1(a). When the light incident vertically onto the grating,

*θ*= 0°. Without loss of generality, we fix

*θ*= 0° in the whole paper. The dielectric constant of tungsten, |

*ε*|>>

_{w}*ε*= 1 when λ > 2 μm [24]. When

_{0}*θ*= 0°, the resonant wavelength of SPP,

*λ*, is given by,

_{res}Figure 1(b) illustrates the spectral emissivity of two independent 1D shallow gratings with *Λ* = 3.2 μm and 4 μm respectively. The higher emittance at short wavelength (*λ* <1.6 μm) is due to the intrinsic absorption of tungsten [24]. Very sharp emittance peaks can be obviously seen at *λ* = 3.29/4.10 μm for *Λ* = 3.2/4 μm. The E-field distribution at different wavelengths are shown in Fig. 1(c) for *Λ* = 4 μm. At the wavelength of *λ _{3}* = 4.10 μm, the field is observed to be strongly localized near to the grating showing surface wave characteristic, revealing that the incident light is coupled to surface waves. At other wavelengths (

*λ*), the E-field is much weaker. Therefore, the strong emittance at the wavelength of 4.1 μm is due to the excitation of SPPs and their coupling to free space photons at the metal-air interface [25]. The peaks in the relatively short wavelength range (

_{1}, λ_{2}, λ_{4}*λ*<2.5 μm) correspond to higher orders of SPPs as marked in the Fig. 1(b). As their emittance is obviously lower than that from the first order (

*j*= 1), we will mainly concentrate on discussing the emission at

*j*= 1 in the following of the paper.

Based on the results demonstrated in references [12,14], we started the simulation at *h* = 0.1
μm. Figures 2(a)-2(h) show how the emittance vary with the filling factor and depth of the grating for
*Λ* = 4 and 3.2 μm.
Table 1 summarizes the value and position of the
resonant peak with respect to *h* and *f*. There are several
similar trends for both periods: (1) we can see an emittance climax with a change of
*f* (<0.8) which is accompanied with a slowly red shift of the resonant
wavelength when *h* is relatively small (such as 0.1 μm); (2) for
*h* = 0.2-0.4 μm, the emittance rises and drops twice with an increase of
*f*, revealing that there are two emittance climaxes. The resonant peak is
obviously broadened especially when *f* is in the range of 0.35-0.9; (3) when the
filling factor is small, the resonant wavelength *λ _{res}* =

*Λ*, confirming the validity of Eq. (4) when |

*ε*| >> 1. With an increase of

_{w}*f*, the resonant wavelength red shifts slowly. This change cannot be explained by Eq. (4). As Eq. (2) is derived for a plane surface, it may not be applicable in the presence of a grating for some filling factors. For example, when

*f*is in the range of 0.4-0.9, the grating would cause a modification of the resonant condition. The effective dielectric constant of tungsten (

*ε*) close to air may be changed. We can define the resonant wavelength as in the following alternatively,

_{w}^{eff}With an increase of *f*, *λ _{res}* can be inferred to be red-shifted, which is consistent with the simulation results shown in Fig. 2 and Table 1. It is worth to note that the resonant wavelength blue shifts when the filling factor is very large. It may be due to a smaller influence from air since tungsten materials occupy most of the space in that case.

On the other hand, there are some differences between the effects of geometric parameters on the emittance for two different periods. For instance, in the case of 3.2 μm, the emittance approaches 1 for a large range of *f* (0.35-0.6) when *h* = 0.1 μm, suggesting that it is not significantly sensitive to *f* in this range. This characteristic provides a large fabrication tolerance for devices. In the case of 4 μm, the highest emittance is produced at *h* = 0.2 μm with *f* = 0.75-0.8. This is thought to be ascribed to the complicated effective filling factor which includes the effect from *h* and *f* as also analyzed in reference [14].

As the field distribution can help us to understand the underlying physics of the influence from
the filling factor, we chose *Λ* = 4 μm as an example to analyze
the trend. In Fig. 2(e), we can see two climaxes in the
emittance spectrum which corresponds to *f* = 0.4 and 0.85 respectively. The
corresponding E-field distributions at resonant are displayed in Fig. 3(a) in which a strong confinement of the field can be observed due to the
excitation of SPPs. The specific E-field distribution for *f* = 0.85 and
*f* = 0.4 is however different. We plot the field intensity along the magenta
dotted straight line away from the air-tungsten interface in Fig. 3(b). As shown, the field intensity drops to *1/e* at a distance of
3.8 μm/9.9 μm for *f* = 0.85/*f* = 0.4. The faster
decaying away from the interface for *f* = 0.85 reveals that the field is more
concentrated in vicinity of the air-tungsten interface, which results in a higher emittance
since more photons can be absorbed.

From Eq. (3), the azimuthal angle
*ϕ* would influence the wavelength of SPP when *θ*
≠ 0°. As we only consider *θ* = 0° in this paper, the
effect of the azimuthal angle on the resonant wavelength is eliminated. Under this condition,
different *ϕ* only means different incident polarization. As shown in
Fig. 4, the resonant wavelength remains unchanged but
the emissivity decreases from 1 to 0 with an increase of the angle *ϕ*,
which can be attributed to the weakened coupling between the incident electric field and the
grating.

## 3. Simulations for orthogonally-crossed 2D grating

From the results in Section 2, the emission wavelength is mainly determined by the period
of the grating via the excitation of SPPs in a 1D shallow grating. It is straightforward to try
if the thermal emission containing two independent resonant wavelengths with perpendicular
polarizations can be produced by an orthogonally-crossed grating from a single surface. Figure 5(a) displays the schematic of an orthogonally-crossed
grating with *f _{x}* =

*d*/

_{x}*Λ*and

_{x}*f*=

_{y}*d*/

_{y}*Λ*defining the filling ratio for

_{y}*x*and

*y*directions respectively. By extending Eq. (5), the resonant wavelengths along the

*x*and

*y*directions for an orthogonally-crossed grating are given by,

*j*/

_{x}*i*represents the diffraction order and

_{y}*ε*/

_{w}^{eff,x}*ε*the effective dielectric constant along

_{w}^{eff,y}*x*/

*y*direction respectively. Obviously, in an orthogonally-crossed 2D grating, the emission wavelength is also mainly determined by the period of the grating. However, its emittance spectrum would show a more complicated behavior because more vectorial combination between the grating vectors exists to fulfill the condition for the excitation of SPPs [26]. We started the simulation by setting

*Λ*=

_{x}*Λ*= 3.2 μm, as illustrated in Fig. 5(b). Comparing to the results in Fig. 1(b), we can see an additional plasmon excitation at the diffraction order of (

_{y}*j*,

_{x}*i*) = (1,1), as we expect.

_{y}From the discussions in Section 2, it is known that the coupling efficiency between the incident light and SPPs shows strong dependence on the filling ratio and depth of the grating. We investigate the effect of the grating depth at first. For easy fabrication, *h* is defined to be the same for *x* and *y* directions. As the 3D simulation is time-consuming, we scanned only the wavelength range we are interested, i.e. around the resonant peak corresponding to (*j _{x}*,

*i*) = (1,0) and (0,1). From Fig. 5(c) we can observe that an emittance as high as 1 can be produced when

_{y}*h*= 0.3 μm.

The filling factor from orthogonal directions would influence each other. The effective filling factor for the orthogonally-crossed grating can be defined as *f _{eff}* =

*f*+

_{x}*f*-

_{y}*f*•

_{x}*f*. According to the results from 1D grating as shown in Fig. 2, we scanned the filling factor from

_{y}*f*=

_{x}*f*= 0.1 to 0.6 to obtain the highest emissivity. As illustrated in Fig. 5(d), the emissivity can reach 1 both for

_{y}*x*and

*y*directions when

*f*=

_{x}*f*is in the range of 0.3-0.5. With an increase of the filling ratio, the width of the emissivity is increased, which leads to a decrease of the spectral coherence of the emission [27]. Therefore, a smaller filling ratio is preferable when the emissivity is similar.

_{y}Comparing the results for 1D and 2D gratings, we can find that the influence trend of the filling factor on the emission is consistent. For example, when *f _{x}* =

*f*is in the range of 0.3-0.5,

_{y}*f*is in the range of 0.51-0.75, which corresponds to an ascending stage for the emittance in Fig. 2(d).

_{eff}Then we set *Λ _{x}* = 3.2 μm and

*Λ*= 4μm in order to control the resonant wavelength independently for

_{y}*x*and

*y*directions. Based on the results in Figs. 5(b)-5(d), we firstly set

*f*=

_{x}*f*and scan them simultaneously. A broad wavelength range (0.5-4.5 μm) has been scanned at first to understand the spectral position of the higher order modes. As expected, (1,1) mode appears both in

_{y}*x*and

*y*directions which corresponds to

*ϕ*= 0° and 90° respectively, as shown in Fig. 6(a).There is a broad peak in the

*y*-direction locating at ~3.48 μm (marked by a red solid circle) we cannot identify at the moment. As it is quite low and not so close to 4 μm, we can eliminate it by adding a long pass filter in the optical path in the applications. We then investigate the influence of the filling factor on the emittance around the resonant peak corresponding to (

*j*,

_{x}*i*) = (1,0) and (0,1). The results are shown in Fig. 6(b)-6(d). As can be seen, the emissivity from both

_{y}*x*and

*y*directions is relatively high when

*f*=

_{x}*f*= 0.3. We thus fix

_{y}*f*= 0.3 and scan

_{x}*f*. The results in Fig. 6(c) show that, the emissivity from the

_{y}*x*direction increases with a decrease of

*f*while that from the

_{y}*y*direction decreases. As the purpose here is to obtain independent dual-wavelength thermal emission,

*f*= 0.3 seems the best choice. At the same time, we fix

_{y}*f*= 0.3 and scan

_{y}*f*. Similar results are obtained as demonstrated in Fig. 6(d), in which the best emittance (with highest intensity and relative narrow width of the resonant peak for both wavelengths) is achieved for

_{x}*f*=

_{x}*f*= 0.3. This result is similar to that when

_{y}*Λ*=

_{x}*Λ*= 3.2 μm. It may be because that the period 4 and 3.2 μm is close to each other.

_{y}Provided only one emitting wavelength is required, the emissivity is also possible to approach to 1 in this orthogonally-crossed 2D grating by optimizing one of the filling ratios, as shown in the right panel of Fig. 6(d). In our present design, the emissivity can reach 78% and 91% for two independent radiating wavelengths, which are obviously higher than 50% obtained by the checkboard structure [15].

At last, we calculate the E-field distribution at resonant wavelength for both *x* and *y* directions. As shown in the insets of Fig. 6(a), the field is localized in vicinity of the grating, revealing that SPP is excited respectively for both directions again.

## 4. Discussions

The purpose of this paper is to demonstrate a method to design dual-wavelength emitters based on
a single surface, in which the wavelength is mainly determined by the period of the grating. In
the application of detecting gases or liquids, we only need to insert two polarizers with
perpendicular polarizations (*ϕ* = 0° and 90°) to obtain two
independent wavelengths. The higher order modes at short wavelengths and the peak at ~3.48
μm can be eliminated by long pass filters. The ability of the orthogonally-crossed 2D
grating is not limited to produce two single wavelengths. If we rotate the polarizer to the
direction between *ϕ* = 0° and 90°, two wavelengths can be
produced simultaneously. This is because that the surface plasmon can still be excited when
0° <*ϕ* <90° according to Eq. (3). Of course the coupling efficiency for
different resonant wavelengths is related with *ϕ*. As shown in Fig. 7(a), the emittance is dependent on the angle between the
incident polarization and the grating. With an increase of *ϕ*, the
resonant emittance controlled by the *y*-direction grating decreases due to the
reduced coupling efficiency while that controlled by the *x*-direction grating
increases. The E-field distribution is plotted in Fig.
7(b) (for *ϕ* = 45°) and in the movie. Obviously, the
concentrated field near to the grating is shifted from along the *x* direction
(at 3.21 μm) to the *y* direction (at 4.005 μm) as the E-field
direction of the incident wave varies. When *ϕ* = 0° and
*ϕ* = 90°, only one wavelength is at resonant and the emittance is
relatively high for the corresponding wavelength in these two cases.

In addition, it is possible to obtain an emission containing more than two wavelengths if we arrange the structure properly. For example, a three-wavelength emitter can be obtained by arranging three 1D grating by 60° azimuthally. Of course, the interaction between them will be more complicated and the geometric parameters of the grating will be more difficult to be optimized. A useful method to optimize these parameters is the genetic algorithm (GA) [28]. One thing we have to emphasize is that it is impossible to obtain the best geometric parameters by the simulation methods we introduce in our paper. We only propose how to optimize them. The important point here is that the emissivity can be much higher than 50% for both polarizations in our present design. There is still space to improve the emissivity if we use other methods such as GA to optimize the geometric parameters.

As the target of our paper is to obtain high emissivity for both *x*- and *y*-direction, higher emissivity is the most important point to be considered during the process of analyzing variation tendency and searching appropriate geometric parameters. The spectral coherence is considered secondly. If the purpose is to obtain better spectral coherence, the geometric parameters will be different. For example, as can be observed in Fig. 2, a shallower depth and smaller filling factor of the grating would lead to a narrower resonant peak, i.e. better spectral coherence. Provided that the depth of the grating is increased to ~λ/2, the space between neighbor ridges will evolve into microcavities and microcavity resonant modes will be induced [27]. In that case, the polarization characteristic for both wavelengths will disappear. This is out of the range of this paper and we will not discuss here.

Finally, we consider the influence of the temperature since the application of the surface grating is for thermal source. All the above simulations have utilized the dielectric function of tungsten at 298K [18]. Based on the results in reference [27], we fitted out the change of the dielectric constant with temperature and then applied it into our 1D grating. It was found that the peak wavelength red shifts with temperature slowly. The variation of the emissivity is not obvious although the FWHM of the peak increases, which leads to a decrease of quality factor Q (results not shown). These results are consistent with those demonstrated in reference [27]. Furthermore, the geometric parameters were found to influence the emittance of the grating similarly under different temperature. As the main target in our paper is to obtain high emissivity which has been addressed in the above context, we expect that similar dual-wavelength orthogonally polarized radiation can also be generated in the wavelength range of ~3-4 μm at elevated temperature.

## 5. Conclusion

On the basis of the thermal emission from a 1D shallow tungsten grating, we proposed a 2D orthogonally-crossed shallow grating to produce dual-wavelength emission with orthogonally polarizations from a single surface. In the 1D grating, we found that there is optimum filling ratio and grating depth, with which the E-field is more intensively concentrated in vicinity of the air-tungsten interface when SPPs are excited and the thermal emission is higher. In the 2D orthogonally-crossed shallow grating, two wavelengths with an emissivity as high as 78% and 91% can be picked independently by optimizing its geometric parameters. Furthermore, the two wavelengths can be produced simultaneously if the polarization of the picking-polarizer is between 0° – 90°. Our investigations in this paper cannot only deliver understandings of the mechanism of enhancing thermal emission from complicatedly arranged shallow gratings, but also help us developing controllable multi-wavelength thermal radiation with high emissivity from a single surface.

## Acknowledgment

The work was supported by the Project of High-level Professionals in the Universities of Guangdong Province and the National Natural Science Foundation (Grant No. 61378082).

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