Photonic Crystal Based Subwavelength Imaging and Cloaking Optical Devices

PIERS ONLINE, VOL. 5, NO. 3, 2009 216

O. Vanbesien1, N. Fabre1, X. Mélique1, L. Lalouat2, B. Cluzel2, F. de Fornel2, and D. Lippens1 1Institut d’Electronique, de Microélectroniqueet de Nanotechnologie (IEMN — UMR CNRS 8520) Universitédes Sciences et Technologies de Lille Avenue Poincaré,BP 60069, 59655 Villeneuve d’Ascq Cedex, France 2Institut Carnot de Bourgogne (ICB — UMR CNRS 5209) 9, Avenue A. Savary, BP 47870, 21078 Dijon, France

Abstract— Potentialities of 2.5D dielectric photonic crystals for subwavelength imaging or invisibility cloaking operation at optical wavelengths are studied numerically and experimentally. First, a negative refraction based flat lens is designed, fabricated and characterized. Using scanning near-field optical microscopy, subwavelength imaging (0.8λ) for a deduced refractive index of −1 is obtained at 1.55 µm. Second, an original design aimed to operate as a cloaking device is proposed by combining photonic lattices operating under different regimes, exploiting both pass- and stop-band properties.

1. INTRODUCTION Photonic crystals have been widely studied since two decades for their outstanding potentialities to control the motion of light [1]. Formerly exploited for their band gap properties associated with point or linear defects for wave guiding or multiplexing, they found a second breathe when metamaterials became of prime concern in the electromagnetic research community [2]. The concept of negative refraction, based in the lower part of the spectrum on permittivity and permeability engineering [3, 4], can also be evoked in the case of photonic crystal as pass-bands are considered. Indeed, a band slope reversal with respect to the wave vector, if isotropic, can be interpreted as a negative refractive index. Compared to metal-dielectric metamaterials, full dielectric crystals appear more mature for the optical wavelength range owing to standard technological processes of nanoelectronics for their fabrication [5–8]. Conversely, less versatility will be possible in terms of subwavelength patterning since dispersion properties in such crystals are fixed by the geometrical parameters, namely the periodicity and the filling factor. To quantify the potentialities of 2.5D photonic crystals, we will investigate first the subwavelength imaging by a n = −1 flat lens [9], with special attention to the wave matching [10], and second we will propose an original design for a cloaking device by combining photonic lattices operating under pass- and stop-band conditions [11].

2. SUBWAVELENGTH IMAGING BY A n = −1 PHOTONIC CRYSTAL BASED FLAT LENS To design a photonic crystal (PC) based n = −1 flat lens, we start from a two dimensional triangular air hole lattice patterned in a semiconductor matrix. The refractive index of this matrix corresponds to the first guided optical mode confined in a vertical InP/GaInAsP/InP heterostructure for a wavelength close to 1.55 µm. The PC geometrical parameters are fixed using an optimization procedure we develop base on the exploitation of the cavity modes defined by the finite lens surrounded with air. As we want to demonstrate the focusing properties of such a lens illuminated by a quasi-point source, this procedure allow us to enhance the lens transmission for various incidence angles. A typical band structure is given in Figure 1(a) which corresponds to a filling factor of 38%. The second TE band shows a negative slope and crosses the light line for a/λ = 0.31 (a is the period of the crystal and λ the wavelength in air). As shown in Figure 1(b), the corresponding iso-frequency curve is circular leading to a refractive index value of −1. Moving to a real prototype, the third dimension of space has to be considered. As illustrated by the schematic side view of Figure 2(c), the PC has a finite depth of about 2 µm and a quasi point source is defined using a ridge waveguide (0.6 µm width) to illuminate the lens. The source/lens distance is half the lens thickness. A three- dimensional FDTD calculation at λ = 1.55 µm has been conducted and Figures 2(a) and 2(b) gives PIERS ONLINE, VOL. 5, NO. 3, 2009 217 the E-field density for two specific planes corresponding to a top view at heterostructure level and a side view at source location. These two plots show that the focusing of light is present even if a large reflection dominates at the first interface. Moreover, the spot location behind tends to show a shift of the refractive index value from −1 when the third dimension is included.

(a) (a)

(b)

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Figure 1: (a) Band structure of the triangular Figure 2: 3D FDTD simulation of the photonic crystal photonic crystal lattice described in text; (b) based n = −1 ﬂat lens operating at 1.55 µm; (a) top view, Iso-frequency surface for the second band. (b) side view, (c) schematic side view.

Figure 3 illustrates the experimental results obtained with such an approach. On the left side, a SEM top view of the prototype is given and on can observe the high quality obtained for the lens in terms of periodicity and regularity for the PC. The light is injected on the left and arrows indicate the theoretical positions of focus spots within and behind the lens for n = −1 using ray tracing issued from Snell-Descartes law generalized to negative values of n. On the right side, a SNOM picture of the lens for a wavelength of 1.525 µm is given [12]. This value is chosen to give the brightest spot behind the lens. This image is recorded in air at an altitude corresponding to the confining plane of the vertical heterostructure, approximately 1.7 µm above the InP substrate. First of all, one can note a very high intensity of the optical field at the first lens interface; this reveals a high level of reflection and thus a strong impedance mismatch between air and the lens that remains to be optimized. Second, one can observe interference fringes close to the second interface. This can have various origins related to out of plane dispersion losses or to interaction between the lens interfaces and the collecting probe. Despite all these limitations, a clear spot is visible behind the lens closed to the expected position. Quantitatively, the transmission level is around −30 dB. This spot remains between 1.53 µm and 1.54 µm and the optimal resolution obtained here, obtained after correction induced by the finite size of the probe is 0.8λ. If this value is subwavelength, it doesn’t break the Rayleigh criterion (0.5λ) which was expected with our experimental set-up of collection of propagating optical waves in air. This result is nevertheless very close to the optimal value of 0.66λ calculated by theoreticians with similar configurations. It has to be mentioned that, despite our 2D design procedure, high transmission (brightest spot) and n = −1 (spot position) do not coincide. This can be due to small variations of the real geometrical parameters achieved around the nominal theoretical values or by the influence of the finite depth of the PC in its 3D configuration. Indeed, the results appear quantitatively very sensitive to this set of parameters. However, the wavelength shift between theory and experiment remains very small (less than 2%) and validates our design procedure. PIERS ONLINE, VOL. 5, NO. 3, 2009 218

Figure 3: Experimental results for the photonic lens at λ = 1.525 µm. Left side: SEM top view of the prototype, arrows indicates the light propagation according to Snell’s law. Right side: Scanning near-ﬁeld optical microscope picture of the lens.

This demonstration of focusing by a ﬂat PC lens at optical wavelengths is very encouraging even if light transmission through the lens has to be optimized. The main diﬃculty is here to take into account the multiple incidence angles of the light in front of the lens. Indeed, if n can be found isotropic, it is not the case for the surface impedance which strongly varies with incidence. PC surface engineering is commonly proposed to realize this matching over a limited range of incidence but many questions related to the exploitation of additional surface modes to improve transmission and resolution properties of the lens remain open.

3. A PHOTONIC CRYSTAL BASED OPTICAL CLOAKING DEVICE Negative refraction in PC’s is a general concept which can also be used for cloaking purposes. This search for invisibility is very active with metal-dielectric metamaterials in which permittivity and permeability tensors can be “tailored” as will, including negative or smaller than one values of these constitutive parameters. Using conformal mapping techniques, a precise local engineering of ε or µ enables the design of cloaks which bend light in such a way that anything located inside is hidden to the outside, whatever the type of incoming wave [12, 13]. Using PC’s such a precise engineering is not easily imaginable and other strategies have to be developed to mimic a similar behavior under restricted operating conditions. Figure 4(a) illustrates schematically such a PC based cloaking device. The basic idea is to rebuild behind the device an incident Gaussian plane wave in amplitude and phase as if the device was absent. To this aim, we make use of two different PC’s: PC1 is similar to the one used above and operates with n = −1 at 1.55 µm whereas PC2 is opaque to light at the same wavelength. This can be obtained using a higher filling factor and a bigger period to shift the band gap at 1.55 µm. The light motion passing four times a n = −1/n = 1 interface is shown in grey. The space region to hide is at the center of PC2. The specific form of PC2 (with the two tips) is used to alleviate straight-through transmission at the singular point where the two PC1 are in contact at input and output. With respect to the discussion of paragraph 2, let us mention that PC1 is always illuminated under single incidence which makes possible the simultaneous optimization of transmission and index matching.

(a) (b) (c)

Figure 4: Photonic crystal based cloaking device. (a) Schematic view, PC1 operates in negative refraction regime (n = −1), PC2 is opaque and the grey region at the center is hidden for the incident light whose motion is represented by the arrows. (b) Field intensity under cloaking operation at 1.55 µm. (c) Phase plot of the optical ﬁeld. PIERS ONLINE, VOL. 5, NO. 3, 2009 219

Figures 4(b) and 4(c) illustrate the cloaking operating mode whereas Figure 5 shows the ﬁgure of merit of the device. It can be seen that the incident wave, ﬁrst shared in two parts at input is properly reconstructed at output, at the same frequency, showing a regular phase front typical of a plane wave. The central region of the device is completely isolated. The total insertion loss is around −5/6 dB, which reveals a good transmission at each n = −1/n = 1 interface with losses lower than 1.5 dB. As mentioned before, the device works only for a incident unidirectional plane wave which is a real limitation compared to the metamaterial approach. Conversely, one can note that the hidden area dimension can be chosen as will by enlarging the PC1 extension as long as propagation and insertion losses in PC1 and air remain at reasonable levels. No intrinsic limitation related to the operating wavelength exists with this kind of design. This reasoning can be extended, with the same limitations in mind, to the spatial extension of the incident plane wave.

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Figure 5: Figures of merit of the cloaking device. (a) Transmission properties at 1.55 µm (193 THz). (b) Fourier spectra of the output signal.

4. CONCLUSIONS In this paper, we have shown the potentialities of 2.5D dielectric photonic crystals for subwavelength imaging or invisibility cloaking operation at optical wavelengths. Subwavelength focusing (0.8λ) at 1.525 µm has been obtained with a PC based flat lens. Also, an original design base on the combination of PC’s working under different regimes has shown ability to mimic a cloaking operation for an incident plane wave with a high versatility in terms of hidden zone dimension or incident wave spatial extension. It is believed that the exploitation of abnormal propagation regimes in photonic crystals represents a significant step for nanophotonics and that the proposed devices will become building blocks for the future generation of integrated devices.

ACKNOWLEDGMENT This work is carried out under the framework of an ANR-PNANO project (FANI). One of the authors would thank DGA (Direction Généralede l’Armement) for its financial support.

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