Liquid Crystal Focusing Device
Modal control principle of liquid crystal (LC) spatial modulators was suggested more than quarter of a century ago, and it was described for the first time in the papers [1, 2]. Fundamentally new approach to the generation of continuous profile of phase transmission of nematic LC layer with large aperture is considered in these papers. The additional homogeneous high-resistance transparent layer – controlling electrode is introduced into the construction of modulator on low-resistance coating with the hole, which plays the role of aperture. It allows implementing the adaptive lenses with different configurations, which focusing properties can be controlled by means of variation of voltage amplitude and frequency. Capability to use the frequency of control voltage and not only amplitude for the control of LC lens parameters gives principle difference to the considered approach in comparison with the approach described in the papers [3, 4] where the profile of phase delay is formed by means of boundary field. Besides, the aperture of implemented lenses, which are described in the papers [3, 4], is restricted by several hundreds of micrometers, and due to use of control electrode these restrictions were removed. On the basis of considered approach a number of modal LC devices was developed: spherical and cylindrical adaptive lenses with the size of aperture of more than 1 mm and control voltages of not more than 10 V, wavefront correctors with adjustable response function, adaptive lenses with optically-controlled focal distance [2, 5–8].
OF LC FOCUSING DEVICE
Liquid-crystal focusing device is represented by the device made on the basis of crossed substrates of cylindrical modal LC lenses, which are integrated into one construction (see Fig. 1). Transparent high-resistance coatings (surface resistance from 100 kOhm/square and to units of MOhm/square) and low-resistance non-transparent stripe contacts are applied on glass substrates. Substrates are located in such a way that their contact electrodes are perpendicular to each other. The layer of nematic LC is located between the substrates; the thickness of this layer is set by spacers, and initial planar orientation is determined by orienting coatings applied on substrates. LC of BL037 brand produced by Merck with the thickness of 10µm was used in our experiments; aperture of the device was 1x1 mm. The type of used LC determines the spectral range, in which the light modulation can take place. In our case – it is visible and near infrared spectral ranges. When alternating electric potentials with a given amplitude and phase are applied to the contacts, the voltage spatial distribution is formed in the aperture zone inducing the reorientation of molecules in the LC layer (S-effect). It results in the change of spatial distribution of phase delay introduced by LC layer into the propagating light wave.
The operation principle of device, its mathematical model and basic operation modes are described in the papers [14–16]. In particular, it was shown that practically significant distributions of phase delay can be obtained under the operation mode with low modal parameter, for the realization of which it is required to decrease the frequency and/or resistance of high-resistance coatings in certain manner. In this mode the influence of frequency on voltage distribution becomes negligibly low, and its type (and respectively shape of profile of phase delay) is determined by the amplitudes and relative phases of potentials.
Equipotential lines of potentials in the operating space of device can be one of two types: elliptical (in the form of ellipses and circles) and parabolic (in particular case, in the form of parallel straight lines). These distributions of potentials are transformed into the relevant phase profiles in the form of elliptical and circular truncated cones or cylindrical surface (examples of the relevant phase profiles are given in Fig. 2).
LIGHT FIELDS GENERATED
BY LC FOCUSING DEVICE
4-channel LC modulator allows focusing the light field into the point and generate fields with transverse distribution of intensity in the form of segment and so-called contour light fields (with transverse distribution of intensity in form of rings, ellipses) (Fig. 3).
In order to obtain the contour light fields or in order to focus field into the point, it is necessary to form the phase profile with the shape of truncated circular cone. When the plane homogeneous light wave propagates through the optical transparency with such phase transmission in the area of Fresnel diffraction, at small distance from LC focusing device, in transverse plane the points with maximum intensity will be located at the contour of the curve repeating the form of equipotential lines of voltage profile. Thus, against the general background quite bright light ring will be formed, for which the ratio between intensity of light contour and intensity of surrounding dark area is 5 ч 15 depending on the device aperture and thickness of LC layer. Ring size decreases with the increase of the distance from focusing device, and in some plane the intensity distribution is focused into the point-type spot (Fig. 4). It should be noted that due to the fact that rings and then spots are formed in some range of distances along the axis of radiation propagation we can speak about the formation of hollow light tube and longitudinal light segment in far area by LC focusing device .
Similarly to the fields with transverse distribution of intensity in the form of ring, it is possible to obtain the light fields with transverse distribution in the form of ellipse, for this purpose it is required to generate the phase profile of LC focusing device in the form of elliptical cone. At the same time, it is possible to implement the voltage distributions with elliptical equipotential lines and random orientation of main axes relative to aperture boundaries. In this case the voltages supplied to contacts will depend in certain way on the amplitude at one of the contacts, coordinates of elliptical cone center, ratio between its axes and rotation angle of main axes of ellipse relative to the aperture boundaries of LC focusing device. Understandably, these dependences are more complex than in case with orientation of ellipse main axes in parallel with amplitude boundaries. By forming the elliptical profile of phase delay with random orientation of ellipse main axes we can obtain the relevant distributions of light intensity.
If you generate the voltage distributions in the form of ellipse, size of which will be slightly larger than the size of aperture, the lines with constant phase of phase delay profile will be not closed within the limits of aperture, in other words, they will have appearance of arcs of circles or ellipses. It will allow obtaining the distribution of light field, in which the points with maximum intensity are located along the contour of analogous curve or in the form of arc of circle or ellipse, in the near area from focusing device.
In order to focus the light into transverse segment, it is necessary to generate the profile of phase delay in the form of surface of cylindrical lens. For this purpose it is necessary to set the voltage distributions with equipotential lines in the form of parallel straight lines. The optical transparency with such phase transmission will focus the plane homogeneous light wave into the light segment, position and orientation of which can be controlled by means of variation of amplitude and/or phase of potentials applied to contacts (Fig. 5).
CONTROL OF LIGHT FIELDS GENERATED BY LC FOCUSING DEVICE
Control of size of transverse intensity distributions
In order to generate the light ring, the profile of phase delay in the form of truncated cone is used. The size of ring will depend on the width and depth of phase deflection of phase profile. The depth of phase deflection and therefore the size of light ring in the set plane can be controlled by changing the potentials at the contacts of LC focusing device. The higher the amplitude of potentials supplied to the contacts of LC focusing device is, the lower the ring radius will be (Fig. 6). Similarly, the size of light fields with transverse distribution of intensity in the form of ellipse can be altered.
Control of Light Field Shape
The shape of transverse distribution of intensity can be controlled from ring to ellipse and vice versa by changing the parameters of control voltage. For example, if it is required to transform the voltage distribution in such a way so that equipotential lines in the form of circles would turn into the elliptical lines without center displacement, then the potential amplitudes on one of the substrates should be altered by the same value (Fig. 7).
Control of Position of Light Rings
and Focused Spots
It is possible to control the position of circular cone base center by changing the amplitude and/or phase of potentials applied to contacts. Respectively, it is possible to control the position of generated point-like light spot or ring and move these distributions in the set plane within the boundaries of the area of focusing device aperture display.
Capability of movement of light rings or ellipses allows fulfilling one more methods of generation of C-shaped distributions. Nonclosure of the lines of constant phase of phase delay profile will be provided by the displacement of the centers of elliptical or circular cone to the aperture boundaries.
Control of Orientation and Position
of Light Segments and Ellipses
Distributions in the form of segments or ellipses can be turned (their orientation can be changed relative to aperture boundaries) and moved as well. The task of movement of the fields generated by LC focusing device in the form of ellipses with random orientation or distributions in the form of light segments is significantly complicated in comparison with the task of movement of intensity distribution in the form of concentric rings or focused spots. However, the ratios between focusing device parameters for the movement of ellipses and segments with random orientation (also with their simultaneous turn) were obtained even for these cases , and the relevant movements of light fields were performed experimentally. Thus, two last columns in Figure 3 illustrate the movement and turn of light field in the form of ellipse.
It is important to note that control of light fields (their shape and size) can be performed very gradually (theoretically, continuously). Such capability is provided by the use of solid control electrode in LC focusing device for the formation of voltage distribution in the aperture area. It allows obtaining the smooth continuous profile of phase delay and gradually changing the voltage distribution on focusing device aperture by means of variation of potentials in contact electrodes. Practically, the capability of smooth control is restricted by the discreteness of control voltages supplied from control unit and it can be enhanced at the expense of reduction of discreteness degree.
EXPERIMENTS IN MANIPULATION
One of the possible applications of LC focusing device consists in its use in the structure of optical tweezers. For the first time, the experiments in optical micro-manipulation with the use of LC devices with modal control principle were carried out by the authors . LC lens performed the additional radiation focusing into the point at required distance. Movement of micro-object was performed using two-dimensional LC deflector (prism), which allowed changing the inclination angle of light, which was incident on lens. Four-channel LC modulator allowed combining these both functions, and at the same time together with controlled point traps the contour traps (in the form of rings and ellipses) , С-shaped traps , traps in the form of light segments [21, 22] were implemented.
The distinctive feature of LC focusing device consists in the fact that it operates at transmission regime (although, if necessary, the reflection mode can be executed), which allows simplifying constructively the scheme of its incorporation into optical manipulator (Fig. 8). Different experiments in capture and manipulation of single micro-particles and their groups were carried out. Latex spheres with various diameters weighed in water, particles of aluminum, silver and their conglomerations, micro-objects with biological origin were used in the capacity of micro-objects. Frames from video with the relevant experiments are given in Figures 9-14.
Considered 4-channel LC modulator allows executing the phase delays in the form of truncated cones – cylindrical and elliptical with random orientation and in the form of quazi-cylindrical lens. Thus, using only four control contacts it is possible to generate the various intensity distributions in the form of rings, ellipses and segments with random orientation; also it is possible to control gradually their size, position, shape using the solid electrode at the expense of potential variation. Use of LC focusing device in the structure of optical tweezers allows implementing dynamically controlled point and contour optical traps and traps in the form of light segments. At the same time, due to the fact that considered focusing device operates at transmission regime, the scheme of optical tweezers is simplified and their dimensions become smaller. It should be noted that LC focusing device can be constructively implemented in the variant for reflection operation. Due to refraction character of operation, 4-channel LC modulator has greater efficiency in comparison with multi-pixel modulators, which are characterized by diffraction losses. The device operates within visible and near IR ranges and has quite high radiation strength: experiments were carried out at the densities of radiation power supplied to the focusing device up to 30 W/cm 2.
Thus, taking into account the technological peculiarities and relative low cost, the functional capabilities of 4-channel LC modulator make it possible to speak of its application perspectiveness in various applied tasks.