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We present a helix photonic metamaterial that exhibits nondispersive optical rotation in a broad passband at optical frequencies. Several features, including zero dispersion, zero ellipticity, and high transmission, can be simultaneously achieved in the presented structure. Pure optical rotation with extremely low dispersion is exhibited in a broad band covering the optical telecommunication wavelengths along with high transmission above 95%. We show that the chiral responses as well as the wavelength-dependent properties of the passband are governed by the behaviors of adjacent resonances. A systematic study of the optical properties with various geometrical parameters is performed, where the dependence of passband properties on resonance behaviors is examined and discussed. Such broadband dispersion-free optical rotation at optical frequencies may be of great interest for high-performance polarization manipulation and relevant applications.
© 2015 Optical Society of America
1. Introduction
Chiral media have been studied extensively for both scientists and engineers due to many interesting optical properties. For instance, chiral molecules are able to exhibit optical activity and circular dichroism, which are now widely used in spectroscopy, analytical chemistry, and molecular biology [1–3]. An object is chiral if it lacks of any plane of symmetry and center of symmetry [1]. Such feature makes the interaction of light and chiral object enantiomeric, yielding two circular polarizations as the eigenstates. Left- and right-handed circularly polarized light propagating in such media experiences different refractive indices (i.e., circular birefringence) [4]. As a result, transmitted linear polarized light may undergo a rotation of the polarization plane. However, optical activity is quite weak in natural materials such as in sugar solution or quartz, which is inadequate for polarization manipulation in optical devices. Artificial chiral media in this context are of great interest in order to enhance the chiral optical responses. Several reports have shown that artificial chiral media can boost the response of optical activity several orders of magnitude larger than that in natural chiral substances, allowing a range of applications such as ultrathin waveplates [5–7], repulsive Casimir force [8], and nonlinear optical activity [9–11].
Much research attention has been paid to demonstrate chiral structures that can exhibit strong optical activity and circular dichroism. In many schemes, chiral meta-atoms are created by stacking multiple twisted nonchiral layers, where chirality is induced by coupling between layers and large optical activity is exhibited [12–18]. However, the operation band is normally close to resonance, which is inevitably associated with large power losses. Furthermore, the response of these structures is highly dispersive, in which the optical properties are very sensitive to wavelength. This results in limited operation bandwidth, hindering the use in practical applications. Recently, there are some configurations reported to show nondispersive property [19, 20]. Although the dispersive characteristic is improved compared to the resonant-type configurations, transmission of the structure is still highly frequency-dependent and the structures are mainly operated in the microwave regime.
In this work, we present a design based on a helix photonic metamaterial that exhibits nondispersive optical rotation in a broad bandwidth at optical frequencies. Several features that are highly desirable for broadband polarization manipulation, including zero dispersion, zero ellipticity, and high transmission, can be simultaneously obtained in the presented structure. Extremely low dispersion can be achieved in a broad range covering the optical telecommunication wavelengths, along with transmission above 95%. For the single helix structure, a low level of ellipticity below 1% can be maintained over 450 nm, while the structure still exhibits optical activity with a rotatory power of 34°/λ at zero ellipticity. For the structure consisting of intertwined helices, the rotatory power can be increased to above 100°/λ, while the bandwidth exceeds 150 nm. Such excellent broad band features have not been reported in the previous schemes. Such 3D chiral nanosystems can be possibly fabricated by the advanced nanofabrication technologies, such as direct laser writing (DLW) [5], stimulated-emission-depletion (STED) DLW [21], and focused ion/electron beam induced deposition [22, 23]. Here we first examine the optical properties of the helix photonic metamaterials and analyze the corresponding dispersion characteristics of each property with respect to wavelength. We show that the optical activity can be further enhanced by increasing the number of intertwined helices. The wavelength-dependent responses are studied and the dispersion characteristics are shown to be associated with adjacent resonances. In order to study the dependence of dispersion responses on resonance behaviors, a systematic study on the optical properties with various geometrical parameters is performed. Finally, the mechanisms and the resonance features of the broadband dispersion-free chiral response are discussed.
2. Structure and simulation method
The chiral design in this study is a free-standing 2D helix array metamaterial as shown in Fig. 1. Within the array, each helix has one half pitch to decrease the number of resonance modes [24, 25]. Figure 1(a) illustrates the right-handed enantiomers of helix, where the geometry is defined by helix diameter D, wire diameter d, axial pitch height p, helix spacing a, and the number of intertwined helices N. The helices are arranged in C4 symmetric 2D array with a lattice constant 2a in order to reduce the anisotropic effect that leads to polarization conversion. For comparison, the calculations include the cases of N = 1, 2, and 4. The case of N = 3 is not considered in this study owing to a different symmetry group. Figure 1(b) shows a square lattice composed of helices with N = 1. The geometrical parameters of helices are helix diameter D = 360 nm, wire diameter d = 120 nm, axial pitch height p = 1200 nm, and helix spacing a = 550 nm. We carry out the full-field numerical calculations using the 3D software package, Lumerical FDTD Solutions [26] based on finite-difference time-domain (FDTD) method. Periodic boundary conditions are adopted in x- and y-direction with the C4 symmetric lattice as a unit cell. We use the Lorentz-Drude model to describe the dispersion property of gold as [27]
where ωp is the plasma frequency, f0 is the strength, and Γ0 is the damping constant in the Drude term. The Lorentz terms are expressed by the resonances with frequency ωj, strength fj and lifetime 1/Γj. The number of resonances k = 5 [27]. The Lorentz-Drude model in [27] covers a broad range of wavelength, which can fully cover the spectral range of interest in the present structure.
Fig. 1 (a) Perspective view of half-pitch helix structure for intertwined number N = 1 and N = 4 with geometries defined by helix diameter D, wire diameter d, axial pitch height p. (b) Top view of a unit cell of N = 1 half-pitch helix photonic metamaterial with C4 symmetry. a is the helix spacing. (c) Illustration of optical rotation based on a helix photonic metamaterial. Light incidence along the helix axis (z-axis) undergoes a rotation of the polarization plane.
With linearly polarized normal incidence (x-polarized wave along z-direction is employed in this study), as illustrated in Fig. 1(c), one can acquire the information of optical activity of the structure by analyzing the transmitted wave. From the calculation, the transmitted coefficients txx, tyx, txy, and tyy can be obtained, where the first and the second subscripts indicate the output and input polarization, respectively. The C4 symmetry assures circular polarization conversion is absent, and the circular polarized waves are the eigenstates. Therefore, txx = tyy and tyx = −txy, and only txx and tyx need to be considered [13, 14]. The transmission coefficients of right-handed circular polarization (RCP) as t+ and left-handed circular polarization (LCP) as t− can be written as
From Eq. (2), we can calculate the rotation angle of the polarization plane as which is associated to the magnitude of optical activity. The ellipticity, quantifying the strength of circular dichroism, can be calculated by the polar angle of Poincare sphere and Stokes parameter [19] or by the tangent of ellipticity angle [28] as3. Results and discussions
The total transmission T = |txx|2 + |tyx|2 for the single half-pitch helix structure is shown in Fig. 2(a). It can be seen that there are two prominent resonance modes in the spectrum at 1206 nm and 2366 nm, denoted as ω1 and ω2, respectively, where a fairly broad passband with high transmission is located in between (enclosed by the rectangular box). The corresponding polarization rotation and ellipticity are shown in Fig. 2(b). In the vicinity of resonances, the rotation angle varies rapidly with wavelength, which is accompanied with a large ellipticity. Between the resonances, optical activity is still observed while the ellipticity is close to zero. The flat curves for both the rotation angle and ellipticity indicate that these properties are relatively insensitive to wavelength. We further examine the transmission, rotation angle, ellipticity, and the corresponding differential properties with respect to wavelength (i.e. dT/dλ, dθ/dλ, de/dλ) within the band from 1300 nm to 2100 nm as shown in Figs. 2(c)–2(e). Over the wavelength range from 1370 nm to 1829 nm (the shaded regions), the transmission is above 95% with a variation less than 0.02%/nm. The maximum rotation angle is 18.5° with a variation below 0.04 °/nm. The ellipticity is less than 1% with a variation below 0.01 %/nm. These properties show that optical activity can be achieved with high transparency and nearly zero ellipticity. Furthermore, these features can be maintained over a wide band with a nondispersive behavior. Compared to other schemes, this structure demonstrates a much broader operation bandwidth and wavelength-insensitive optical characteristics. The nearly zero ellipticity also implies that the polarization state of a linearly polarized incident wave is maintained after passing through the structure. In typical chiral media, large optical activity normally occurs around resonance, which is accompanied by high loss, polarization distortion, and strong dispersion. These problems can be partially avoided by operating the devices in the band between resonances (i.e. the off-resonance regime) [12–18]. Due to a finite spectral separation between resonances, however, the optical properties are still affected by adjacent resonances, resulting in low transmission and limited bandwidth. On the other hand, the frequency range of resonances of helix structures can be enhanced to exceed one octave [24, 25, 29, 30]. While operating within the band between the well-separated resonances, the optical properties can be less affected by the resonant absorption losses and dispersive responses. Therefore, pure optical rotation can be realized with low loss and dispersive-free characteristics, demonstrating a promising approach toward high performance polarization manipulation.
Fig. 2 Optical properties of the single half-pitch helix structure: (a) transmission, (b) polarization rotation (in red) and ellipticity (in blue). Transmission, polarization rotation, ellipticity and their differential values with respect to wavelength are shown in (c)–(e). The shaded regions indicate the operation band for pure optical rotation (with e < 1%).
In this configuration, several optical properties of the passband are highly associated with the behaviors of adjacent resonances. It has been reported that the number of intertwined helices N plays an important role in the resonance responses [25, 31]. It is thus informative to examine the optical properties in the passband while varying the number of intertwined helices N. Figures 3(a)–3(c) shows the transmission, polarization rotation angle, and ellipticity for N = 2 and 4. As shown in Fig. 3(a), the spectral separation between the two resonances increases to 1241 nm for N = 2 and 1403 nm for N = 4, while the transmission decreases for a larger N due to more metallic losses and a higher reflection. The additional interactions between intertwined helices enhance the strength of resonances, boosting the circular birefringence. This can be observed in the increase of polarization rotation angle with a larger N as shown in Fig. 3(b). The pure rotation angle in the operation band increases from 35.22° for N = 2 to 55.38° for N = 4. The ellipticity remains close to zero in the passband for both cases as shown in Fig. 3(c). To examine in more detail, the optical properties in the passband are zoomed in from 1250 nm to 1750 nm and the corresponding differential properties are analyzed in Figs. 3(d)–3(f). Figure 3(d) shows that the transmission decreases with increasing number of intertwined helices but still exhibits a relatively flat curve over a broad wavelength range. A larger number of intertwined helices results in more dispersive responses in transmission, and similar observations can be made for rotation angle and ellipticity as shown in Figs. 3(e) and 3(f), respectively. For example, the e < 1% bandwidth of N = 2 is in the wavelength range of 1281–1520 nm, while that of N = 4 is in the range of 1295–1450 nm. Therefore, one can see that the increase of intertwined helices enhances the optical rotatory power by virtue of stronger strength of resonances. The spectral separation between resonances is also separated further apart. However, intense interactions result in larger damping, which causes higher losses and larger dispersion. As a result, the available operation bandwidth will be narrower accordingly.
Fig. 3 (a) Transmission, (b) polarization rotation, and (c) ellipticity for various intertwined number N =2, and 4. In passband region the optical properties and their differential to wavelength are shown in (d)–(f) for transmission, polarization rotation, and ellipticity respectively.
The optical properties of the helix metamaterials are closely related to the geometry of the helix structures. The resonance response of individual helix and coupling effects between helices determine the resonance characteristics, such as resonance wavelength, linewidth, and resonance strength. In order to examine the dependence of passband properties on resonance behaviors, we perform a systematic study on the optical properties with various geometrical parameters. The analysis is presented for N = 1. In Fig. 4, we illustrate the differential values of the optical properties with respect to wavelength (i.e. dT/dλ, dθ/dλ, de/dλ) while varying the helix diameter D, wire diameter d, and helix spacing a. The differential values are represented by different colors and the equi-value contour lines of T, θ, and e are also plotted. Figures 4(a)–4(c) show the results for varying the helix diameter D. In Fig. 4(a), one can see that there is a broad area in green, which represents a dispersion-free operation region. The region is roughly bounded by the 95% equi-transmission contour lines, implying that the wavelength-insensitive property is accompanied with high transparency. Two resonances can be clearly identified by the abrupt color change at both sides of the plot, where the resonance wavelength, strength, and bandwidth can be evaluated by the color gradient and the corresponding wavelength. As the helix diameter D increases, a smoother color gradient covering a wider range of wavelengths at the resonance can be observed. It means that the damping of the resonance is stronger with a larger D. Thus, the response near resonance is more dispersive, which narrows the operation bandwidth. In Fig. 4(b), the dispersion-free characteristic is exhibited between the two resonances. The rotation angle is larger with the increase of helix diameter, but the dispersion is also more severe. The differential property and the equi-value contours of e as shown in (c) exhibit a similar behavior with transmission. The dispersion-free region is roughly bounded by the e = 1% contour, and the bandwidth decreases as the helix diameter increases. Figures 4(d)–4(f) show the analysis while varying the wire diameter d. When increasing the wire thickness d, the resonance properties, including resonance wavelength and bandwidth, exhibit a different dependence on d compared to the case of varying D. Meanwhile, enhanced optical activity, as indicated by a larger rotation angle in Fig. 4(e), can be obtained. Figures 4(g)–4(i) show the analysis while varying the helix spacing a. Comparing the patterns with those in Figs. 4(a)–4(c), one can see that the effect of increasing the helix spacing a is similar to the effect of decreasing the helix diameter D.
Fig. 4 Optical properties of single half-pitch helix metamaterials while varying different geometrical parameters. The differential of transmission, polarization rotation, and ellipticity with respect to wavelength (in colors) and their values (in equi-value contour lines) are illustrated respectively in (a)–(c) for varying the helix diameter D, in (d)–(f) for varying the wire diameter d, and in (g)–(i) for varying the helix spacing a.
To explicitly examine the optical activity and the bandwidth, we analyze the relation between the rotation angle and the e < 1% bandwidth based on the variations of helix diameter D, wire diameter d, and helix spacing a for N = 1, as shown in Figs. 5(a)–5(c), respectively. In the analysis, optical activity is evaluated at zero ellipticity by the rotatory power, that is, rotation angle per thickness in one wavelength (°/λ). One can see that the variations of helix diameter D and helix spacing a result in a similar trade-off behavior between the optical rotatory power and the bandwidth. This is consistent with the analysis presented in Fig. 4. In general, when the helices are closely-spaced by increasing D or decreasing a, stronger interactions enhance the optical activity, in which a larger rotation angle can be obtained. Meanwhile, the interactions also cause a broader resonance with stronger damping, which narrows the operation bandwidth. It is interesting to see that such trade-off behavior is not exhibited by increasing the wire diameter d, as shown in Fig. 5(b). This can also be observed in Figs. 4(d)–4(f), where the patterns do not follow a similar dependence as those in varying D and a. Structures with a larger wire diameter exhibit a stronger optical activity as observed by the increase of the rotatory power. However, the e < 1% bandwidth also increases accordingly. Since the properties of the passband are governed by adjacent resonances with opposite Cotton effect, we believe that the increase of wire diameter d may result in some symmetric effects on adjacent resonances, such that a low level of ellipticity in a broad bandwidth is still maintained even with stronger resonances. Such effect may be used to further enhance the optical activity of the structure and is currently under study. Finally, as discussed in the previous section, increasing the number of intertwined helices can effectively enhance the optical activity. Figure 5(d) shows the rotatory power and the bandwidth for N =1, 2, and 4. For N = 1, the rotatory power and the bandwidth are 34.12°/λ and 459 nm, respectively. The rotatory power can be increased to 100.03°/λ for N = 4 while maintaining a broad bandwidth above 150 nm. Here again we see a trade-off between the nondispersive operation bandwidth and the optical rotatory power. Due to a thicker structure, the present design may not yield giant optical activity in terms of rotatory power compared to the previous schemes [16,32,33]. Nevertheless, dispersion-free broadband optical polarization rotation can be achieved accompanied with high transmission and low ellipticity at optical frequencies in the present structures, which hold promises for the implementation of high-performance polarization manipulation and relevant applications.
Fig. 5 The rotatory power and the e < 1% bandwidth while varying the (a) helix diameter D, (b) wire diameter d, and (c) helix spacing a for N = 1, and (d) for N =1, 2, and 4.
4. Conclusion
In conclusion, we numerically present wavelength-independent pure optical rotation with high transmission in a broad bandwidth, achieved by normal incidence along the axis of helix photonic metamaterials. We show that the operation band is located between the resonances exhibiting opposite Cotton effect. Due to the widely separated resonance modes of helix photonic metamaterials, the dispersion-free passband between resonances can be very broad and highly transparent. The optical properties in the passband are shown to be associated with adjacent resonances. A systematic analysis is performed to examine the dependence of the optical properties with respect to various geometrical parameters of the helix structures. The analysis in this study can be used for the design of broadband polarization control devices and applications.
Acknowledgments
The authors would like to acknowledge technical support from Dr. Y. C. Na. This work is supported by the Ministry of Science and Technology of the Republic of China under the following research contracts: NSC102-2221-E-007-116-MY3 and NSC102-2633-M-007-002.
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