2014 IEEE XXXIV International Scientific Conference Electronics and Nanotechnology (ELNANO)

465

Formation of Complex Structure of Laser Fields for the Radiation Effect on Impurities in Nano-

OptoElectronics Anatoly Negriyko, Svitlana Bugaychuk

Department of Laser Specroscopy Institute of Physics NASU

Kiev, Ukraine negriyko@iop.kiev.ua bugaich@iop.kiev.ua

Vladimir Gnatovskyy Physical Department

Taras Shevchenko National University Kiev, Ukraine

vgatovskyy@ukr.net

Nataliya Medvid’ National University of Food Technology

Kiev, Ukraine alexandr.gnatovsky@gmail.com

Abstract — New method of formation of complicated laser fields for the purposes of precise controllable action of energy on working components in nano-optoelectronics is proposed and considered both theoretically and experimentally. The method consists in using the field with preliminary modulated wavefront to illuminate a phase diffraction element. The cross-modulated response of this scheme gives the resulting beams, which possesses the diffraction limit of the radiation and are stable relative to phase distortions in a technological track.

Keywords — nano-optoelectronics; photon effect; laser beams; correlation transformation

I. INTRODUCTION Contemporary state of the nanotechnology requires state-

of-the-art methods and corresponding instrumentary intended to manipulate an electromagnetic energy over an individual particle either of their small groups. Nowadays different kind of elements, such as diffraction elements, artificial holograms, photonic crystals, are used for purposeful formation of desired distribution of laser energy, for example, for heating of micro-samples, for manipulation of particles with the help of optical tweezers, or for photon influence on micro-, nano-inpurities in nano-photo-electonics [1, 2, 3]. The laser radiation is changing both the amplitude and the phase over the cross-section of the beam after passing through those elements. As a result a new distribution of the energy is created, which should be as much as possible close to the needs. But the calculations show [1], the number of conversion elements unreasonably increases, when is required to form the configuration of energy which are either complicated or time-varying. Therefore such methods, in exception of relatively simple cases, can not be realized.

At the same time the modern technologies, in particular, nanotechnologies, require a wide range of time-varying and geometrically complicated configurations of the energy distribution along tiny area of a technological target. To ensure these requirements, the special methods of formation of beams should be developed that give the diffraction limit of the radiation with subsequent adaptation of them to known techniques aimed at exceeding the diffraction limit. Also it is desirable to use computer methods to control the beam structures, which are created.

All these properties are inherent for the correlation approach to formation of the laser beams. According to this approach, the beam lends itself to action of not only one but two consecutive (in perspective more than two) of diffraction converters. Saying by other words, a diffraction converter is illuminated by the diffraction field, which is formed after a previous converter [4].

Already the first experiments with periodic structures show that the correlation technique based on the diffraction gratings allows one to increase the number of possible configurations, which can be made by the schmes of multiplexing of laser beams [5]. On the other hand, it is known that the correlator based on the diffraction gratings permits to control the angular distribution of the transformed beams in a wide range [6]. Including the schemes, which provide exceeding the diffraction limit [7].

In the present paper it is considered a more complicated case, when the first field among all correlating ones corresponds functionally to elementary structure, i.e. the “point-like”. The structure of the secondary field represents the convolution of the “point-like” structure with a necessary composite figure. Joint use of these two fields (is meant the corresponding diffraction elements) provides the decoding that gives a desired distribution of the energy by dint of relatively simple elements, which can be easy fabricated or can be created as the controllable banners.

II. THEORETICAL PREREQUISITES FOR THE PROPOSED CORRELATION SCHEME

The optical scheme, which performs the proposed method, actually represents the scheme of the correlator for the fields formed by two diffraction elements (see Fig. 1). The laser beam is expanded by the telescope T and directed to the diffraction element (a phase modulator) M1, which presents a complex two-dimensional core generating from the resulting field A ),( yx . This modulator is located on the front focal plane ),( yx of the objective O1. The field of the angular spectrum of the second modulator m2 {F̂= M2} is decoded by the previously created diffraction element { }F̂= *

1 1m M at the coinciding focal planes

978-1-4799-4580-1/14/$31.00 ©2014 IEEE

2014 IEEE XXXIV International Scientific Conference Electronics and Nanotechnology (ELNANO)

466

),( ηξ of these two objective lenses, where 1m~ is determined as the angular spectrum of the complex-conjugate transmission function of the first modulator M1.

Anticipated image A )~,~( yx is formed and observed at the back focal lens )~,~( yx of the second objective O2. The distribution of the energy |A )~,~( yx |2 may be reading by CCD camera for further processing in a computer. Also as the diffraction element M1 may be used a computer-controllable phase transparent, which provides a control of the spatial distribution of its phase relief in the dynamical regime.

In this scheme, the formation of the anticipated spatial distribution of the field A )~,~( yx takes place owing to the Fourier transformation of the diffraction field d2 ),( ηξ by the objective O2. The field d2 ),( ηξ is determined as the product of two distributions:

( ) ( ) ( ), , ,ξ η ξ η ξ η= ⋅2 1 2d m m (1)

The structure of the modulator M1 should be chosen by such a way that its spatial auto-correlation function M1*M1 should correspond to the physical distribution of the intensity in the form of a sharp delta-like maximum (a bright spot on a weak uniform background).

Therefore, if to provide the conditions m2 =),( ηξ m1 ⋅),( ηξ a ),( ηξ , when a {ˆ),( F=ηξ A )},( yx , we obtain:

{F̂ d2 ()},( =ηξ M1*M ⊗)1 A ≈

⊗−− )~,~( yyxxδ A =),( yx A )~,~( yx (2)

In the expression (2) the symbols ⊗ , *, * indicate, respectively, the operations of convolution, correlation and complex conjugation.

In this correlator the possibility to use various pairs of the diffraction elements M1,2 appears to create the resulting diffraction field.

Really, when the diffraction field m2 ),( ηξ is the angular spectrum of the modulator in a form M2=T ⊗ A (namely, is the convolution of the point-structure T with the energy distribution A), and the element, which decodes this diffraction field has the transmittance ( ) ( ){ }ˆ, ,F x yξ η ∗=1m T ,

then, according to the expression (2), the resulting distribution of the energy will depend on the structure of the modulator T ),( yx . This fact gives the advantage to fully utilize the functionality of modern controllable phase transparants. Besides, it is enough to reproduce simple distributions of the phase in this correlation method.

Note, that the proposed scheme is stable to possible changes of the phase of the field in the optical path. Such changes are equivalent to the replacement of the spatial auto-correlation function T∗ T for an arbitrary point-structure with the distribution T ),( yx by the new, but cross-correlation function TT ~* of the distributions T ),( yx and ( ),x yT , where

( ),x yT takes into account the distortion of the phase. This cross-correlation function retains the delta-like maximum, but with a lower intensity, for small phase distortions. This leads to that the signal-to-noise ratio is, but the necessary distribution of the energy |A|2 is saved.

Fig. 1. Optical scheme of the correlator. L is the laser, TV is a register system, PC is a personal computer.

III. EXPERIMENTAL IMPLEMENTATION OF THE METHOD According to the expression (1), the factor ( ),ξ η1m is

determined by the complex conjugation of the field distribution of the modulator M1. It is formed with the help of the objective O1 at the Fourier transformation of the field formed by the modulator M1. So the question arises is the fabrication of the transparent with the transmittance ( ),ξ η1m . In this paper we have used the fact that the Fourier hologram of the field of the modulator M1 has the transmittance exactly ( ),ξ η1m in the direction of the reference beam, according to the equation of the hologram [8]. That is why easy to perform the transformation (1) in this direction if is hologram is illuminated by the field of the angular spectrum of the modulator M2. But for further practical applications of the method appropriate to use either an artificial hologram of the field

( ),ξ η1m , in which the high diffraction efficiency is ensured, or to create an artificial diffraction element with the phase relief, which corresponds to this distribution. In so doing, multiple choices of the modulators M1 and M2 (connected with the structure of T ),( yx ), that was noted above, allows one to select them according to the criterion of the simplicity of the distribution.

Next, we present photos, which explain the correlation process of the formation of the necessary distribution of the energy. In the Fig. 2 (on the left) the photo-masks of the modulators M1 and M2 are shown, which ensure the formation of two closely spaced lines. In the center of the figure, there are shown the angular spectrums of the energy distributions for these modulators in the plane of the hologram (i.e. at the back focal plane of the objective O1). The resulting distribution of the energy in the image plane is shown in the right part of the Fig. 2. It is worth paying attention to that the width of the created linier segments corresponds to the diffraction limit, i.e. is the minimal possible.

Similar photographs for the formation of the distribution in a form of a cross, which is superimposed on a circle, are shown in the Fig. 3. They illustrate applicability of the method for the case of crossing the lines.

2014 IEEE XXXIV International Scientific Conference Electronics and Nanotechnology (ELNANO)

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Fig. 2. Correlation method for the formation of two straight lines with the diffraction limit being satisfied.

Fig. 3. Correlation method for the formation of overlapping cross and circle.

Fig. 4. Formation of a complicated structure of the digits.

In the experiments, which are illustrated in the Fig. 2 and in the Fig. 3, we have used the identical modulator M1, and, correspondingly, the holographic diffraction element ( ),ξ η1m . The difference of the resulting distributions of the energy of the laser radiation is due to different spatial phase structures of the photo-mask M2.

The example of the formation of more composite configuration of the field in the form of figures is demonstrated in the Fig. 4. In this case the modulator with more complicated structure is used.

IV. CONCLUSION In the paper we experimentally demonstrate the possibility

of creating the given energy distributions on the micro-objects with the help of the correlation method. The diffraction elements, which are used, have relatively simple (even binary) phase structures. It is proved that one can obtain practically identical distribution of the energy by using the modulators, which have different structures.

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