**3.2 Binary diffractive convex lens with 150-**μ**m focal length**

Although the binary diffractive lens was effective in controlling the luminous intensity, diffraction efficiency was reduced when the diffraction angle was decreased (Lalanne et al., 1999; Kleemann et al., 2008). Furthermore, the focal length of the fabricated binary diffractive lens is 2 mm. In order to realize a thin LED light source, the focal length has to be shorter. In this section, to improve the diffraction efficiency and shorten the focal length, we designed the binary diffractive convex lens with 150-μm focal length.

In this study, a binary diffractive lens with a focal length of approximately 150 μm was designed and light propagation of the plane wave was simulated by the finite domain time difference (FDTD) method. Fig. 8 shows the field intensity distributions for TE polarization of the binary diffractive lens. The simulation parameters were λ = 632 nm, n = 1.575 (refractive index of the PET film), and n0 = 1.0 (refractive index of air). The value of the period in part of the fringe was smaller than that in the center. The designed lens was placed along the x-axis (z = 0). The light was incident from z = 0 to the +z direction, resulting in the light being focused at x = 0 μm and z = 140 μm. After focusing, the light was spread with

Fabrication of Binary Diffractive Lens on Optical Films by Electron Beam Lithography 147

*N*=1 *N*=2 *N*=4


(b) d12=2.12 μm

Posistion (mm)

*N*=1 *N*=2 *N*=4


Position (mm)

To determine the reason for these results, the binary diffractive lenses with only first period (d1 = 13.78 μm) and 12th period (d12 = 2.12 μm) were fabricated. Fig. 11 shows the far-field light distribution of both lenses. In the case of d1 = 13.78 μm, the first-order diffraction is observed when *N* = 4. Because d1 is considerably larger than the wavelength of light, the first-order diffraction cannot be observed when *N* is small. On the other hand, in the case of d12 = 2.12 μm, the first-order diffraction is observed when *N* = 1, and it disappears by increasing the number of N. Therefore, in order to improve the diffraction efficiency of the diffractive lens, it is necessary to control the intensities of the zero- and first-order

Intensity (mV)

*N*=1 *N*=2 *N*=4

Fig. 11. Far-field light distribution of the binary diffractive lenses in the case of (a) d1 =

Fig. 10. Far-field transmitted intensity distribution of the fabricated lens

0.01

diffractions by choosing the binary structures.

=13.78 μm


Position (mm)

(a) d1

13.78 μm and (b) d12 = 2.12 μm

Intensity (mV)

0.1

1

Intensity (mV)

10

100

time because of diffraction. Therefore, a binary diffractive lens with a micrometer-order focal wavelength is expected to provide a small and thin light source for controlling the luminous intensity distribution. On the basis of the results of section 3.1, we speculated that the LED light can be focused at 140 μm.

Fig. 8. Field intensity distributions for TE polarization of the binary diffractive lens

The binary diffractive lens with a 150-μm focal length was fabricated; its size was 100 × 100 μm2 and thickness was 570 nm, as measured by ellipsometry. Fig. 9 shows the SEM image of the fabricated binary diffractive lens (*N* = 4) on the PET film. The diffractive lens, whose width was almost the same as the designed lens, was obtained.

Fig. 9. SEM image of the fabricated binary convex diffractive lens with a 150-μm focal length (N = 4) on the PET film

The far-field transmitted intensity distribution of the fabricated lens is characterized by red laser light (λ = 635 nm). The aperture with a diameter of 100 μm was used for eliminating the light escaping from the edge of the lens. Fig. 10 shows the far-field transmitted intensity distribution of the fabricated lens with different *N* values (1, 2, 4). The focal length of this lens, which is estimated from this distribution, is approximately 160 μm, which is almost same as that in the FDTD simulation. For higher *N* values, the intensity of first-order diffraction decreases.

time because of diffraction. Therefore, a binary diffractive lens with a micrometer-order focal wavelength is expected to provide a small and thin light source for controlling the luminous intensity distribution. On the basis of the results of section 3.1, we speculated that

Fig. 8. Field intensity distributions for TE polarization of the binary diffractive lens

③

width was almost the same as the designed lens, was obtained.

10μm

① ②

(N = 4) on the PET film

diffraction decreases.

The binary diffractive lens with a 150-μm focal length was fabricated; its size was 100 × 100 μm2 and thickness was 570 nm, as measured by ellipsometry. Fig. 9 shows the SEM image of the fabricated binary diffractive lens (*N* = 4) on the PET film. The diffractive lens, whose

1 μm

Fig. 9. SEM image of the fabricated binary convex diffractive lens with a 150-μm focal length

The far-field transmitted intensity distribution of the fabricated lens is characterized by red laser light (λ = 635 nm). The aperture with a diameter of 100 μm was used for eliminating the light escaping from the edge of the lens. Fig. 10 shows the far-field transmitted intensity distribution of the fabricated lens with different *N* values (1, 2, 4). The focal length of this lens, which is estimated from this distribution, is approximately 160 μm, which is almost same as that in the FDTD simulation. For higher *N* values, the intensity of first-order

Fabrication ・・・ ・・・

③*1.15 μm*

①*13.78 μm*

Design

②*5.73 μm* lens

①*13.80 μm*

②*5.80 μm*

③*1.20 μm*

Focal length 140μm

Focal point

the LED light can be focused at 140 μm.

Fig. 10. Far-field transmitted intensity distribution of the fabricated lens

To determine the reason for these results, the binary diffractive lenses with only first period (d1 = 13.78 μm) and 12th period (d12 = 2.12 μm) were fabricated. Fig. 11 shows the far-field light distribution of both lenses. In the case of d1 = 13.78 μm, the first-order diffraction is observed when *N* = 4. Because d1 is considerably larger than the wavelength of light, the first-order diffraction cannot be observed when *N* is small. On the other hand, in the case of d12 = 2.12 μm, the first-order diffraction is observed when *N* = 1, and it disappears by increasing the number of N. Therefore, in order to improve the diffraction efficiency of the diffractive lens, it is necessary to control the intensities of the zero- and first-order diffractions by choosing the binary structures.

Fig. 11. Far-field light distribution of the binary diffractive lenses in the case of (a) d1 = 13.78 μm and (b) d12 = 2.12 μm

**8** 

*Italy* 

**Photocontrolled Reversible** 

*Center for Biomolecular Nanotechnologies @UNILE,* 

**Photochromic Polymers** 

*Istituto Italiano di Tecnologia* 

**Dimensional Changes of Microstructured** 

Despina Fragouli, Roberto Cingolani and Athanassia Athanassiou

Stimuli-responsive polymeric materials are able to change their chemistry and their conformation upon an external signal. The external signal may be derived from a change in temperature, chemical composition or applied mechanical force of the specific material, or can be triggered externally with exposure to an electric or magnetic field or to light irradiation. In this respect, a photochromic substance is a stimuli responsive material which is characterized by its ability to alternate between two different chemical forms having different absorption spectra, in response to light irradiation of appropriate wavelengths (Brown 1971). Due to this important property, a significant amount of effort has been devoted to the formation of polymeric materials functionalized with photochromic molecules for the creation of photosensitive "smart material" systems, that change reversibly their physical and chemical properties by the use of light. The corresponding reversible effects of the molecules such as dipole moment, surface energy, refractive index, and volume are preserved in the polymer matrix, and have numerous promising applications in devices for three-dimensional (3D) optical memories, (S. Kawata & Y. Kawata 2000), in actuators (Yu et al 2003, Athanassiou et al 2005), in holographic or diffractive optics, (Fu et al 2005, Tong et al 2005) or in microfluidics, (Caprioli et al 2007, Walsh et al 2010) etc. Concerning microfluidic devices using photochromic plastic films, the transportation of fluids happens without the need for their molecules to be charged, as done in other studies (Mitchel 2001). This is achieved by gradually modifying the surface tension, and thus the wettability, by irradiating with increasing time along the direction of the fluid movement (Ichimura et al 2000). The gradual wettability changes are exclusively based on the photochemical modification of the embedded photochromic molecules caused by the photoisomerization process. In addition, in the case of the diffraction gratings the development was generally done by interference of different polarized laser beams, or by electric-field application, and the modification of their diffraction efficiency is connected with the changes of the refractive index of the photochromic molecules during this

Here we present how the volume changes induced to the photochromic polymers by the photoisomerization of their embedded photochromic molecules, can improve significantly

**1. Introduction** 

procedure (Yamamoto et al 2001, Fu et al 2005).
