Chiral nanostructures producing near circular polarization

Optical properties of chiral nanostructured films made of Al1−xInxN using a new growth mechanism — curved-lattice epitaxial growth — are reported. Using this technique, chiral films with rightand left-handed nanospirals were produced. The chiral properties of the films, originating mainly from an internal anisotropy and to a lesser extent from the external helical shape of the nanospirals, give rise to selective reflection of circular polarization which makes them useful as narrow-band near-circular polarization reflectors. The chiral nanostructured films reflect light with high degree of circular polarization in the ultraviolet part of the spectrum with leftand right-handedness depending on the handedness of the nanostructures in the films. © 2014 Optical Society of America OCIS codes: (160.1585) Chiral media; (160.4236) Nanomaterials; (160.4760) Optical properties; (310.6860) Thin films, optical properties. References 1. Q. Wu, A. Lakhtakia, and I.J. 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Introduction
The optical properties of chiral sculptured thin films (STF's) make them well suited for applications such as polarizations filters [1], handedness inverters [2] and bandpass filters used in optical fiber communication [3], to mention a few.The realization of such chiral films is commonly done by glancing angle deposition (GLAD), a self-shadowing technique for fabricating thin films with tailored nanostructural properties [4][5][6][7].By using various materials and tailoring the pitch of the nanostructures, chiral STF's can be engineered to obtain desired optical and physical properties [6].
However, a known problem with GLAD is the broadening of the columns when the films grow thicker [8] making films with large pitches a challenge to manufacture.In this study we have used controlled curved-lattice epitaxial growth (CLEG) [9] to produce nanorods with a curved, single-crystalline morphology with not only an external chirality (the spiral shape of each nanocolumn) but also with an internal chirality due to an in-plane compositional gradient.The compositional gradient results in an in-plane birefringence which rotates throughout the film with the same nominal period as the external chirality.This method has been employed to produce chiral thin films with a high thickness to pitch ratio.Our material of choice is the semiconductor Al 1−x In x N, where x can be chosen to tailor the band-gap [11].With the Al 1−x In x N material system we have the possibility to fabricate unique structures with tailored polarization properties in both reflection and transmission mode.The aim of this work is to explore the optical properties in general and specifically the ability to reflect polarized light with high degree of circular polarization.Mueller-matrix spectroscopic ellipsometry (MMSE) has been used to determine the optical properties of right-and left-handed chiral nanostructured films as well as non-chiral nanostructured films.MMSE is a very suitable, non-destructive technique for investigations of advanced optical materials including the present chiral semiconductor [12,13].

Theory
In the Stokes formalism, the polarization state of light is described by a four-element column matrix often called a Stokes vector, where, in a Cartesian coordinate system, I = I x + I y , Q = I x − I y , U = I +45 • − I −45 • and V = I r − I l , where I x and I y denote irradiance of linear polarization in the x and y directions, respectively, I +45 • and I −45 • denote irradiance of linear polarization in the +45 • , and −45 • directions, respectively and I r and I l denote irradiance of right-and lefthanded circular polarizations, respectively.I is thus the total irradiance, and Q and U describe the linear part of the polarization state.The fourth parameter, V , describes the circular part of the polarization state [14].
The change in polarization as well as the change in degree of polarization of light when it interacts with a sample is described in the Stokes-Mueller formalism by where S i is the Stokes vector of the light incident on the sample, S o is the Stokes vector of the reflected light and M is a 4x4 matrix known as the Mueller matrix [15] which depends on the properties of the sample [17].It is common to normalize a Stokes vector to I and a Mueller matrix to M 11 , and in this work we will use this practice for S i and M so that I i = 1 and Any polarization state can be described by Q, U and V [18].All linear polarization states, as well as their azimuth will only affect Q and U whereas circular polarization states affect only V .When the incident light is unpolarized, i.e. S i = [1, 0, 0, 0] T (T denotes transpose), the reflected light S o will have a Stokes vector equal to the first, normalized, column of the Mueller matrix, [1, m 21 , m 31 , m 41 ] T = [1, P] T where P T is the polarizance vector [14].
From the Stokes parameters the degree of polarization, P, can be derived and with I = 1 we define We can also define the degree of linear polarization as and the degree of circular polarization as where the sign of P C determines the handedness of the polarized light.A positive value corresponds to right-handed polarization, and a negative value corresponds to left-handed polarization.The degree of polarization varies between 0 for completely unpolarized light and 1 for completely polarized light.For any other value of P the light is partially polarized and it can then be described as a sum according to where superscripts u and p indicate unpolarized and polarized parts, respectively.

Sample preparation
Al 1−x In x N nanorod films were fabricated with the CLEG technique using dual magnetron sputter deposition on sapphire substrates with vanadium nitride buffer layers as described in detail elsewhere [9].Due to shadowing effects during deposition, the individual nanorods will have a higher concentration of Al on one side and of In on the other side.Assuming a morphology similar to that of previous studies [9], x in Al 1−x In x N is estimated to have a mean value of 0.3 and a variation from one side of one nanorod to the other of approximately 18% (∆x ≈ 0.18).The difference in lattice constants will result in a curving of the nanorods towards the Al rich side.The difference in refractive index between AlN and InN will also cause a refractive index gradient across each nanorod.By introducing a rotation of the substrate during deposition this gradient will rotate with increasing height of the nanorods.The result will be twofold: An internal chirality due to rotation of the refractive index gradient and an external chirality due to the curved nanorod, which in turn depends on the height gradient of the crystal lattice.All nanorods will be aligned to each other with respect to both the internal and the external chirality.This work focuses on films deposited in three ways.Chiral films were grown on substrates which were rotated 19 times in 90 • steps during deposition, either clockwise or anti-clockwise (as seen from the ambient) to produce right-or left-handed films of nanospirals, respectively.In addition straight nanorod films were grown on substrates rotated continuously with several turns per deposited monolayer.In the latter case the curving of the nanorods can be neglected, producing a non-chiral film with straight nanorods.
Thus the chiral films each consist of 20 sublayers with curved nanorods, with each consecutive layer grown at a 90 • (-90 • ) angle to the previous layer for left-(right-) handed samples.The result in each case will be a fourfold stepwise helical staircase structure of five complete turns.Notice that the samples are similar to the ones presented in [16] which, however are continuously helical and not stepwise helical.Straight nanorods are also analyzed in the current report.

Instrumentation
All optical measurements were done using a dual rotating compensator ellipsometer (J.A. Woollam Co., Inc).The instrument provides all 16 elements of the Mueller matrix in the spectral range of 245≤ λ ≤1700 nm.The ellipsometer is equipped with a sample holder allowing for measurements with 360 • azimuthal sample rotation ϕ, as well as variable incidence angle θ .In this study ϕ was varied between 0 • and 360 • in steps of 5 • and θ between 20 • and 65 • in steps of 5 • .Only data for λ in the range of 245 nm to 1000 nm are reported.The software CompleteEASE (J.A. Woollam Co., Inc.) was used to calculate P and P C .
The scanning electron microscopy (SEM) images were taken by a LEO-1550 FE-SEM.

Structural characterization
Figure 1 shows SEM images of films grown using the three growth schemes.The height of  The curvature of the nanorods is due to the gradient in lattice parameters in Al 1−x In x N described above.This difference in lattice parameter causes the thickness to vary from side to side in each nanorod so that each monolayer forms a wedge.When the wedges are stacked the structure will curve towards the Al rich side, as schematically shown in Fig. 2 between two atomic layers 17 nm apart will be 1.5 • ± 0.5 • [9].The first and last atomic layer of each 20 nm nanorod would then be at an angle (α in Fig. 2(a)) of ∼ 1.8 • with respect to each other.This is just enough for the curve of the rods to be noticeable in an SEM image (Fig. 1).
Thus it is not so much the external chirality that gives rise to the optical properties, but rather the internal chirality of each nanorod that forms a repetitive pattern throughout the height of the sample [16].at θ =25 • whereas P C for other incident polarization states can be seen in the appendix.There is no correlation between the starting orientation of the substrate during deposition and the starting angle (ϕ =0) of the measurements.Therefore, when presenting the data in Fig. 3, ϕ was chosen individually for the right-handed and left-handed samples to display data where they show similar features but with opposite handedness.

Optical characterization
For the sample with straight nanorods, ϕ was chosen to show the highest value of m 41 recorded in the measurements.The chosen growth parameters result in films with high P C in the near-UV with largest values at 350 nm for the left-handed film and at 370 nm for the right-handed film.At the selected sample orientation the degree of circular polarization of the right-handed film exceeds 0.89.Ellipses representing the polarization state with highest P C can be seen as insets in Fig. 3. Some interference oscillations due to the thickness of the transparent film are also seen.
In the case with the straight-nanorod film non-zero values in m 41 can be seen which could be an effect of the nanorods being slightly tilted away from the sample surface normal.As can be seen in Fig. 4 there are two values of ϕ where m 41 are zero for all wavelengths, namely at 65 the tilted nanorods are parallel to the plane of incidence, and the upper-right four and lower-left four elements of the Mueller matrix will all be zero, including m 41 [21].However, simulations and optical modeling suggest that the values in m 41 are too large to be explained solely by a tilt of the nanorods and that it is likely that also the nominally straight nanorods have a compositional gradient and therefore an internal chirality, not unlike the one in the nanospirals.The true origin of the non-zero values in m 41 is under investigation and will be dealt with in future publications.The full Mueller matrix of each sample can be found in the appendix as ϕ-λ and θ -λ contour plots.In order to sort out the most important data only the polarizance vector will be displayed here.As discussed in chapter two, the polarizance vector equals the Stokes vector of the reflected light when the incident light is unpolarized and according to Eq. ( 6) the third element of the polarizance vector shows the degree of circular polarization.Figure 4 show results from MMSE measurements at different sample orientations at a fixed incident angle of 25 • .The data are shown as ϕ-λ contour plots of the polarizance vector with the element values in color code.In Fig. 4(a) the polarizance vector of the sample with a left-handed chiral film is shown.In a narrow band at approximately 350 nm the absolute value of m 41 is large which, according to Eq. ( 6), corresponds to a high degree of circular polarization.The sign is negative which means that the unpolarized light incident on the left-handed chiral film is, to a large extent, reflected as left-handed polarized light for all orientations of the sample.For the film with a right-handed structure (Fig. 4(c)) the same behavior is found on 370 nm but in this case with a positive value of m 41 , that is, the unpolarized incident light is reflected as right-handed and wavelength is shown in Fig. 5 as a θ -λ contour plot and the effect of filtering unpolarized light into circularly polarized light is found in a narrow band centered on 370 nm for the righthanded nanorods and on 350 nm for the left-handed nanorods.The polarization phenomenon can be seen to shift slightly towards shorter wavelengths (blue shift) with increasing θ .This is consistent with the behavior of optical properties of chiral sculptured thin films as found by simulations [6,23] and experimental investigations [13].

Left handed
The transformation of the polarization state upon reflection seems to be almost independent of the azimuth angle ϕ for the two chiral films investigated.The small angular variations are probably caused by imperfections in the layered structure of the films.The difference in spectral response between the two chiral films is attributed to the difference in thickness and pitch between the films.This effect may be utilized as a means to shift the wavelength dependence of the filtering properties or to broaden the wavelength range by making a distribution of pitches throughout the length of the nanospirals as has been done by Park et al. using GLAD [24].filters for other wavelengths and with different bandwidth.

Appendix
Here is presented the degree of circular polarization, Pc, of the light reflected from the samples studied, assuming incident light of various polarization states.The incident polarization states used are represented by the following Stokes vectors defined in a Cartesian xyz-system with the xz-plane equal to the plane of incidence: Pc is calculated according to Eq. ( 6) and presented in Figs.6-14 with Pc calculated for unpolarized incident light as a reference.
Figures 4 and 5 in section 4.2 show the polarizance vectors of the samples as ϕ-λ and θλ contour plots.For a more complete description of the optical properties, the full Mueller matrices, again as ϕ-λ and θ -λ contour plots, of the samples are presented in Figs.15-20 with auto-scaling for each matrix element to emphasize details.The incidence angle, ϕ, and rotation angle, θ are the same as in Figs. 3 and 5.  Wavelength, λ (nm) Rotation Angle, φ (°)  Wavelength, λ (nm) Angle of Incidence, θ (°)  Wavelength, λ (nm) Angle of Incidence, θ (°)

Figure 1 .
Figure 1.Scanning electron microscopy images of a) right-handed nanospirals, b) straight nanorods and c) left-handed nanospirals.d) Top view of straight nanorods.

Figure 2 .
Figure 2. Schematic view of a nanorod, curved due to the difference in lattice constant between the Al-rich (green color) side and the In-rich side (red color).a) A side view of a nanorod as deposited without substrate rotation.The curvature is strongly exaggerated and in the real structure the angle α is approximately 1.8 • .b) One period of a right-handed four-fold stepwise helical staircase nanospiral where the substrate has been rotated three times in 90 • steps.

Figure 3
Figure 3 shows P C of light reflected off the three samples if illuminated with unpolarized light

Figure 3 .
Figure 3. Degree of circular polarization, P C , at 25 • incidence angle for a) a sample with a right-handed chiral film, b) a sample with a straight nanorod film and c) for a sample with a left-handed chiral film.The insets show the shape of the near-circular polarization state at their respective peak values (solid curves) inscribed in perfect circles (dashed curves).

Figure 4 .
Figure 4. Polarizance vectors, [m 21 , m 31 , m 41 ] T , at a fixed θ (25 • ) of films with a) a lefthanded chiral film, b) a straight nanorod film and c) a right-handed chiral film.Notice that the sharp borders between colored areas in the figure are due to the color scale used and that all transitions are gradual.

#Figure 5 .
Figure 5. Polarizance vectors, [m 21 , m 31 , m 41 ] T , at the same ϕ as in Fig. 3 of samples with a) a left-handed chiral film, b) a straight nanorod film and c) a right-handed chiral film.

Figure 15 .
Figure 15.Normalized Mueller matrix, at a fixed θ (25 • ) of a sample with a left-handed chiral film.

Figure 16 .
Figure 16.Normalized Mueller matrix, at a fixed θ (25 • ) of a sample with a right-handed chiral film.

Figure 17 .
Figure 17.Normalized Mueller matrix, at a fixed θ (25 • ) of a sample with a straight nanorod film.

Figure 18 .
Figure 18.Normalized Mueller matrix, at a fixed ϕ of a sample with a left-handed chiral film.

Figure 19 .
Figure 19.Normalized Mueller matrix, at a fixed ϕ of a sample with a right-handed chiral film.

Figure 20 .
Figure 20.Normalized Mueller matrix, at a fixed ϕ of a sample with a straight nanorod film.