1. Introduction

The control of light with artificial structures is one of the key issues in modern photonics. Recent advances in nanotechnology have made such a control possible using periodic sub-wavelength dielectric structures, i.e. photonic crystals. In particular, various photonic devices with planar photonic crystals have been employed to control propagation and/or emission of light and have attracted a widespread attention within the last decade. Among them are ultrahigh quality factor optical micro-cavities and control of spontaneous emission [1,2], ultraslow light propagation wave guiding [3,4] and control of the beam pattern emitted by a semiconductor laser [5].

Conventionally, photonic crystals are composed of simple elements such as square- or cylindrical-shaped holes. Introduction of low-symmetry elements allow one to employ the concept of chirality in the photonic crystal design and to control the polarization state of light. In particular, three-dimensional (3D) chiral photonic crystals that possess a well defined sense of twist allow one to create a polarization-sensitive stop-band, i.e., materials that reflect a particular circularly-polarized component of the incident light wave. Despite a considerable complexity, such 3D chiral photonic crystals can be fabricated by using a layer-by-layer approach [6] or by a two-photon direct-laser-writing technique [7].

The control of light polarization using planar structures has been achieved with metal nanogratings [8–10] in which strong coupling of photons with surface plasmons enhance the three dimensional polarization effect [11,12] in quasi-two-dimensional structures. Surface plasmon resonances give rise to such strong optical effects as enhanced light transmission through sub-wavelength holes [13], suppression of light extinction [14] and other linear and nonlinear optical phenomena [15–17]. Unfortunately, despite a high optical rotation power, excessive losses do not allow chiral metal nanogratings to compete with 3D all-dielectric structures in the polarization control.

For applications of quasi-two-dimensional structures for polarization control the beam that corresponds to the zeroth transmission order in the diffraction pattern is most important because it preserves direction of propagation of the incident light wave. However in recent experiments on the polarization-sensitive diffraction in dielectric chiral planar structures [18,19], no polarization effect has been observed in the zeroth diffraction order, neither in the reflected nor in the transmitted light. This experimental finding strongly contradicts to the rigorous diffraction theory, which predicts a strong polarization rotation for a zeroth diffraction order in transmission [12].

In this letter, we report on the observation of optical activity with extraordinary rotational power in planar chiral photonic crystals formed by a dielectric chiral sub-wavelength-period grating on a planar dielectric waveguide. From the dependence of the polarization effect on the angle of incidence, we found that Fabry-Pérot resonance and the coupling between dielectric waveguide and photonic crystals forms high-Q resonant modes i.e. photonic crystal waveguide modes, which lead drastic resonant enhancement of optical activity.

 

Fig. 1. (a). Structure of the on-waveguide planar chiral photonic crystal. The polarization ellipse of the zeroth transmitted light is schematically shown. φ is the angle between the polarization azimuth of the incident wave and Y-axis of the square lattice. ψ is the incident angle for p-polarized light. Δ represents the polarization azimuth rotation angle. The thickness of the chiral pattern is t=410 nm, the waveguide layer thickness is h=820 nm, widths of the gammadion line and opening are w=120 nm, l=70 nm, and the period is 600 nm. The arrows besides φ and ψ indicate the direction of rotations. The layout of this figure describes the case of φ=0 and ψ=0. (b). SEM image of the on-waveguide planar chiral structure. The scale bar corresponds to 600 nm. (c). Polarization azimuth rotation Δ for normal incidence measured at 634nm. The measured polarization azimuth rotation Δ is fitted by an oscillating function of the incident polarization azimuth φ; Δ=θ+δθcos(φ+φ ₀), where θ is chirality-induced rotation, δθ≪θ describes birefringence due to imperfectness of the square pattern, φ ₀ is a constant. (d). The dispersion curves of the TE guided modes obtained from Eq. (2).

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2. Samples and experimental setup

The planar chiral photonic crystal consists of a 410 nm thick TiO₂ chiral nanograting with a period of d=600×600 nm, a TiO₂ waveguide layer with a thickness of 820 nm, and a silica substrate. The on-waveguide photonic crystal structure was designed to possess a four-fold rotational symmetry about the substrate normal (see Figs. 1(a) and (b)). The design and fabrication of the samples are reported in detail elsewhere.

Measurements were performed in a wavelength range from 520 nm to 1550 nm (0.80–2.4 eV) by using tungsten and xenon lamps (Δλ~2 nm) as a light source and applying a polarization modulation technique described in [20].

3. Measurement at normal incidence

The transmission spectra of two chiral photonic crystals with opposite senses of twist at normal incidence are presented in Fig. 2(a). One can observe that the transmission is nearly independent on the sense of twist in the whole spectral range, while pronounced sharp resonant features and broad modulation features are associated with excitation of waveguide modes and Fabry-Pérot resonance, respectively (see below).

In contrast to the result of chiral metal nanograting that showed large birefringence [8, 9], the observed chirality-induced (i.e. independent on the polarization azimuth of the incident light wave) polarization effect is about 10 times stronger than that caused by in-plane linear birefringence, which originates from the deviation of the structure symmetry from C₄ (Fig. 1(c), also see [11]).

The spectra of the chirality-induced polarization azimuth rotation θ and ellipticity η of the transmitted wave at normal incidence are shown in Figs. 2(b) and 2(c), respectively. One can readily see that both θ̣ and η have opposite signs for structures with left and right senses of twist in the whole spectral range though the transmission is nearly independent on the sense of twist. The achieved polarization azimuth rotation is as high as 26.5 degrees at a wavelength of 638 nm. By comparing Figs. 2(b) and 2(c) one can observe that ellipticity is nearly equal to zero when the polarization azimuth rotation reaches a maximum and vice versa. This is consistent with the Kramers-Kronig relations and implies that a planar alldielectric polarization-only or ellipticity-only conversion device can be manufactured with an appropriate design of the structure. Comparison of Figs. 2(a)–2(c) allows us to conclude that the spectral positions of the resonance features in the transmission spectra (Fig. 2(a)) coincide with those in the polarization spectra (Figs. 2(b) and 2(c)). This indicates that the chirality-induced polarization effect is associated with waveguide resonances and Fabry-Pérot resonances.

4. Measurement at oblique incidence

In order to explore the observed spectral properties, we tilted the chiral photonic crystal with respect to the grating normal (see Fig. 1(a)) and acquired the data for p-polarized incident light. The angle of incidence was changed from ψ=0° to +6° with 1° increment.

In the presence of a periodic structure on the top of the waveguide, the excitation of the waveguide mode with an in-plane wave vector β is possible by coupling through the momentum of the periodic structure. The resonance condition of such photonic crystal waveguide mode in the case of the square grating with period d is given by the following equation [21]:

where k _‖ is in-plane component of the incident light wavevector, x and y are unit vectors along relevant Cartesian axes of the grating, and m_x and m_y are integers. The dispersion relation for the TE mode is given by the following equation [21,22]:

where k is the amplitude of k _‖, l is the thickness of the waveguide layer and n_f, n_c, and n_s are the refractive index of waveguide layer, clad layer and substrate, respectively. M=0,1,2,3⋯ is the mode number. A similar equation can be written for the TM mode [22], however we will not present it here for clarity.

 

Fig. 2. Transmission (a), chirality-induced polarization azimuth rotation (b) and ellipticity (c) spectra for all-dielectric chiral photonic crystal. Red and blue lines refer to the results obtained with left- and right- twisted gammadions, respectively. The waveguide resonances with m ² _x+m ² _y=1,2,4 are indicated.

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One can observe from Eqs. (1) and (2) that each mode in our structure can be described by a set (M,m_x,m_y), which defines the mode frequency and direction of propagation. The analysis of the dispersion relations given by Eq. (2) indicates that the band structure strongly depends on the period d, while a variation of the refractive indices and thickness of the waveguide affects only cut-off frequencies. This allows us to employ this simplified picture to allocate the observed resonances in the transmission spectra to particular waveguide modes.

Figure 1(d) shows the dispersion of TE modes with M=0,1,2,3 obtained from Eqs. (1) and (2), calculated by considering the waveguide thickness l=1230 nm and the chiral layer with an effective refractive index n_f=2.0 sandwiched between dielectrics with refractive indices n_c=1.0 and n_s=1.5. In this phenomenological analysis, as the first approximation, we ignore the complicated design of the chiral grating on the waveguide. The obtained frequencies of TM modes are slightly higher than those TE modes.

Figures 3(a) and 3(b) show the transmission spectra of the chiral photonic crystal with a left sense of twist measured for p-polarized incident light. We plotted the spectra in the (E,ψ) plane, where E is the incident photon energy. In the transmission spectra, in addition to the photonic crystal waveguide-mode resonances, intensity modulation caused by Fabry-Pérot interference is also observed. One can observe that splitting of the transmission dip takes place at a non-zero ψ only in the case of a waveguide mode because of the degeneracy with a non-zero in-plane component of the photon wave vector. Each of the three waveguide resonances observed lower than 1.5 eV in Fig. 3(a) has a branch, which is independent of incident-angle; while four resonances observed at photon energies above 1.5 eV do not have such branches. We can conclude that the former ones belong to the waveguide modes with m ² _x+m ² _y=1 and the later ones to m ² _x+m ² _y=2 by examining the dispersion relation which is shown in Fig. 1(d). We show some of the allocated waveguide modes numbers in the brackets in Fig. 3(a). We would like to notice that broad and clear resonance around 1.95 eV is not waveguide but Fabry-Pérot resonance modes (see below).

 

Fig. 3. The incident angle dependences of transmittance (a) and chirality-induced azimuth polarization rotation (b) for p-polarized incident light. The waveguide resonances are allocated by showing (M,m ² _x+m ² _y) in (a).

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The incident-angle dependence of the polarization rotation is the same as that of the waveguide and (especially in high frequency region) Fabry-Pérot resonance modes of the transmission spectra. This implies that these resonances play a crucial role in the optical activity of dielectric chiral photonic crystal.

5. Calculation and discussion

To examine the validity of such an interpretation, we performed numerical calculation by using the reformulated Fourier modal method for crossed gratings with four-fold-rotational symmetry [23]. The geometrical parameters were taken from the Scanning Electron Microscope (SEM) pictures of the fabricated samples (see Fig. 1(b)). The wavelength dependence of the refractive index of TiO₂ and silica were obtained by our measurement and provided by the substrate manufacturer, respectively. Since we found that the deposited TiO₂ film exhibit a slight loss that influences the resonance peak magnitude significantly, we assumed a small imaginary part (0.001) for the index of TiO₂ in numerical calculation. The spectral positions of TE waveguide resonances at normal incidence are indicated by blue arrows in Fig. 4(a). In Fig. 4(b) showing the dependence of the transmission on the angle of incidence, the waveguide resonances are indicated by black circles because they are hardly seen due to strong intensity variation caused by the Fabry-Pérot interference. The waveguide resonances are readily distinguishable because they are associated with very sharp dips in the transmission spectra. By comparing Figs. 3 and 4 one can see that the calculation well reproduces the features of measured spectra. In particular, the numerical simulation also shows that there is a correspondence between waveguide or Fabry-Pérot resonance modes resonances and polarization effect.

 

Fig. 4. (a). Calculated transmission and chirality-induced polarization azimuth rotation spectra at normal incidence. Experimental data are also shown for comparison. The spectral positions of TE waveguide resonances at normal incidence are indicated by blue arrows. (b) Incident angle dependences of transmittance for p-polarized incident light. The black circles and black lines indicate the dip positions of waveguide-resonance because they are hardly seen due to large intensity variation caused by Fabry-Pérot interference. The waveguide resonances are allocated by showing (M,m ² _x+m ² _y) (c) The incident angle dependence of chirality-induced azimuth polarization rotation for p-polarized incident light.

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We can see that waveguide modes with different values of m ² _x+m ² _y manifest themselves very differently in the polarization rotation. Waveguide modes with larger m ² _x+m ² _y appear at shorter wave length region and tend to show larger polarization rotation. This makes polarization effects more sensitive to the details of the structures.

It is instructive to compare the optical activity in metal and dielectric chiral structure. We have already reported that, in metal nanogratings, the polarization rotation arises due to a mutual twist of the electric field vector in the air-metal and metal-substrate interferences. The magnitude of the polarization effect in metal grating is enhanced by the surface plasmon resonance because of the magnitude of the local field increase [11]. In dielectric chiral structure, it is difficult to achieve enhancement of the local electric filed comparable with that caused by a surface plasmon mode. However, the magnitude polarization effect can be enhanced due to anomalously long lifetime of the high-Q resonant waveguide modes, which account for difference in the coupling of left- and right- circular polarized light with dielectric structure of particular sense of twist. In addition, in the case of the dielectric chiral structures, Fabry-Pérot resonances also enhance a optical activity in the higher frequency region.

6. Conclusion

In conclusion, we demonstrate that on-waveguide chiral photonic crystals can rotate transmitted light polarization by more than 25 degrees with a very small in-plane linear birefringence. Measurements of the angle of incidence and polarization dependence reveal that the resonant excitation of high-Q waveguide and Fabry-Pérot resonance modes leads to a drastic enhancement of polarization effects. These results open new opportunities for all-optical polarization control and allow one to realize efficient polarization modulation of light using all-dielectric planar structures in ultrafast optical communication [24] and quantum information technology [25].