WO2011120582A1

WO2011120582A1 - Method and device for generation of accelerating airy beams

Info

Publication number: WO2011120582A1
Application number: PCT/EP2010/054385
Authority: WO
Inventors: Selcuk AKTÜRK
Original assignee: Aktuerk Selcuk
Priority date: 2010-03-31
Filing date: 2010-03-31
Publication date: 2011-10-06

Abstract

According to the present invention, conventional positive and negative cylindrical lenses are used to obtain Airy beams. Airy lens construction relies on making use of one positive and one negative cylindrical lenses of same absolute value of radii of curvatures. The lenses are then cut from the centers and the Airy lens in which one half of the positive lens being connected on top of the half of the negative one yields a very good approximation to a surface with shape of a cubic polynomial. Therefore the Airy lens of the invention replaces the complex cubic polynomial shape lens which is required for applying cubic spatial phase to the incoming light beam. Airy beams are formed by passing a laser beam through the center of the hence obtained Airy lens and consequent Fourier transform.

Description

METHOD AND DEVICE FOR GENERATION OF ACCELERATING

AIRY BEAMS

Technical Field of the Invention

The present invention relates to a device, namely an optical element for generation of accelerating airy beams and a method of generating such beams.

Background of the Invention

Applications of lasers commonly require focusing to increase the intensity of light and hence the efficiency of the process under use. When laser beams are focused with a conventional lens, a focal spot is generated. The longitudinal depth of focal region is inversely proportional to the square of the focal spot size. This means that laser beams focused to smaller sizes stay intense over shorter distances. This effect is due to a phenomenon called diffraction, which results from the wave nature of light. Diffraction usually causes limitations on laser applications. Another property of the laser beams focused with conventional lenses is that the maximum intensity on the beam propagates along a straight line, which again seems to be a fundamental physical property. There have been recent advances which showed that both phenomena mentioned above can be altered. Firstly, the work of Durnin showed that special classes of beams (which he called "diffraction-free beams") propagate without diffraction or almost so [J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58(15), 1499-1501 (1987)]. Durnin showed that when the transverse intensity profile of the beam is in the form of zeroth order Bessel function of the first kind, the light intensity stays unchanged during propagation. Such Bessel beams consists of a central intense core and concentric rings of magnitude described by the Bessel function. The theoretical Bessel beams carry infinite amount of energy. As a result, it is not possible to generate an ideal diffraction-free beam. Approximations are possible, however. Practically, one can generate quasi-Bessel beams, which exhibit long line focal regions. Their depth of focus is much larger compared to beams of similar core sizes focused with a regular lens [J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177(1 - 6), 297-301 (2000)].

More recently, Siviloglou et al. showed that beams with transverse profiles in shape of Airy function also exhibits diffraction-free propagation [G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99(21 ), 213901 -213904 (2007); G. A. Siviloglou and D. N. Christodoulides, "Accelerating finite energy Airy beams," Opt. Lett. 32(8), 979-981 (2007)]. Similar to Bessel beams, Airy beams can also be constructed with finite energy resulting in focal lengths much longer compared to the traditional beams of same focal spot size. More remarkably, however, Siviloglou et al. showed that Airy beams also exhibit "acceleration". This exotic property yields a focal spot which does not propagate along a straight line, but it rather moves on a parabola [G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of Airy beams," Opt. Lett. 33(3), 207-209 (2008)].

Airy beams are perfectly physical because they are formed by redistribution of the energy on the transverse plane. In other words, the average energy still propagates along a straight line, yet the focal spot (which contains the maximum intensity, and hence is useful for most applications) moves on a curved path. In addition to acceleration, Airy beams also exhibit "self-healing" [J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, "Self-healing properties of optical Airy beams," Opt. Express 16(17), 12880-12891 (2008)]; if a small section of the beam is blocked, it is reconstructed after brief propagation.

Airy beams were first demonstrated by Siviloglou et al. in 2007. They showed that laser beams can be turned into Airy beams by introduction of a cubic spatial phase and performing an optical Fourier transform. The cubic phase is applied by a computer controlled liquid-crystal spatial light modulator. It can be applied in one or two transverse dimensions, generating one or two dimensional Airy beams, respectively. The Fourier transform can be done by propagating the laser to the far field or by using a focusing lens. This initial work and others later experimentally proved the diffraction-free and acceleration properties of airy beams. Soon after the experimental development of Airy beams, they started to be used in applications of lasers [K. Dholakia, "Optics: Against the spread of the light," Nature 451 (7177), 413-413 (2008]. Polynkin et al. used Airy beams to generate curved plasma channels in air [P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, "Curved Plasma Channel Generation Using Ultraintense Airy Beams," Science 324(5924), 229-232 (2009)]. The use of Airy beam provided the advantage that emissions from different sections of the plasma were angularly resolved. Airy beams were also used in particle trapping applications [J. Baumgartl, M. Mazilu, and K. Dholakia, "Optically mediated particle clearing using Airy wavepackets," Nat. Photon. 2(1 1 ), 675-678 (2008)]. Since the focal point moves along a parabola, particles can be trapped in the focal region and moved out to the side. This idea was used to drag particle to different locations, without needing to translate the beam or the sample.

The exotic behavior of Airy beams mentioned above also call for more applications. They started to be available only very recently and new applications can be expected to emerge soon. However, in order to be able to increase the use of these beams, it is paramount that the method of their generation be simplified. So far there have been only two methods developed for Airy beam generations. The first method is using spatial light modulators, as mentioned above. Even though this method works well, it requires expensive equipment and advanced computer control. As a result, it limits the widespread use of Airy beams. The second method for Airy beam generation uses nonlinear optical processes. The method uses three-wave mixing in a specially tailored photonic crystal structure [T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, "Nonlinear generation and manipulation of Airy beams," Nat. Photon. 3(7), 395-398 (2009)]. At the output of the crystal and after optical Fourier transform, second harmonic frequency of the input laser is turned into Airy beam. This method is also unlikely to find widespread use as it works only for high peak power lasers and requires specially fabricated materials.

The present invention proposes a new method for generation of Airy beams in a simple manner in which a new optical element, i.e. an "Airy lens" is used The use of Airy lens is very simple: one only needs to pass the laser beam through it and perform the optical Fourier transform either by propagation to far field or using a conventional lens. The method does not require expensive equipment or computer control. More importantly, the Airy lens is made very easily, by using readily available conventional cylindrical lenses.

As mentioned above, to turn a regular laser beam into an Airy beam, one needs to apply cubic spatial phase to the incoming light beam. In principle, this can be done by using a lens which has a surface with shape of a cubic polynomial. However, polishing a glass with such a shape is difficult, costly and time consuming.

According to the present invention, conventional lenses which are inexpensive and readily available, most of the time off-the-shelf are used. Objects of the Invention

Primary object of the present invention is to provide a method and device to simplify generation of Airy beams.

Another object of the present invention is to provide a method and device for generation of Airy beams in which use expensive equipment and advanced computer control is avoided. Further an object of the present invention is to provide a method and device for generation of Airy beams whose use is not limited to high peak power lasers and which does not require specially fabricated materials.

Summary of the Invention

Brief Description of the Figures

Accompanying drawings are given solely for the purpose of exemplifying a device for generation of Airy beams whose advantages over prior art were outlined above and will be explained in detail hereinafter: The figures are solely intended to delineate the technical context in which the present invention lies; they do not represent the boundaries of the scope of protection as claimed.

Fig. 1 and 2 respectively demonstrate the transverse intensity profiles of Bessel and Airy beams.

Fig. 3 demonstrates side and front views of the construction elements making up the Airy lens according to the present invention. Fig. 4 demonstrates the phase generated by the Airy lens according to the present invention in comparison with the cubic polynomial fit. Fig. 5 demonstrates the configuration of the elements according to the method of generating Airy beams of the present invention.

Fig. 6a and 6b respectively demonstrate theoretical and experimental profiles of Airy beam using the Airy lens according to the present invention.

Fig. 7a and 7b demonstrate the position of the peak intensity along the two transverse dimensions, as a function of the propagation distance.

Detailed Description of the Invention

The Airy lens according to the present invention is constructed as described below.

According to the present invention, conventional positive (1 1 ) and negative (12) cylindrical lenses are used to obtain Airy beams. Airy lens (20) construction relies on making use of one positive (1 1 ) and one negative (12) cylindrical lenses of same absolute value of radii of curvatures. The lenses (1 1 , 12) are then cut from the centers and the Airy lens (20) in which one half of the positive lens (1 1 ) being connected on top of the half of the negative one (12) yields a very good approximation to a surface with shape of a cubic polynomial. In order for achieving the desired Airy lens (20), cylindrical lenses (1 1 , 12) with radii of curvatures +500 mm and -500 mm are used. To generate Airy beams in two transverse directions, two Airy lenses rotated 90° with respect to each other were used. Airy beams are formed by passing a laser beam (He-Ne laser) through the center of the Airy lens (20) and consequent Fourier transform. Fourier transform can be performed either by going to the far field or using a lens. In order for performing Fourier transform in a more compact manner, a lens (13) of a certain focal length (for example 125 mm) can be used in which case the desired compact setup will be achieved.

The efficiency of the Airy lenses (20) constructed according to the present invention can be evaluated by comparing transverse intensity profile of the beams with calculated intensity profiles. The transverse beam profile at various propagation distances can be measured using a CCD camera. To trace the positions of the intensity maxima, "reference points" are recorded by removing the Airy lenses and directly measuring the centers of the incoming laser beam. As shown in Fig.6a and 6b, the experimental profile closely resembles what is expected from theory.

Next, since one of the most interesting properties of Airy beams is acceleration, this behavior can be confirmed by measuring the position of the focal spot (peak intensity). Fig. 7a and 7b show the position of the peak intensity along the two transverse dimensions, as a function of the propagation distance. The focal positions closely follow a parabola. As a result, the beams generated through the Airy lens also clearly exhibit acceleration. In summary, the optical element (Airy lens) of the present invention can be used to turn laser outputs into accelerating Airy beams. The Airy lens is made of standard cylindrical lenses and is very inexpensive and easy to construct. It requires no computer control or programming. Because of its simplicity and cost effective nature, the Airy lens has the potential to increase the use and applications of accelerating Airy beams.

Claims

Claims:

1 . A lens comprising a positive (1 1 ) and a negative (12) half of cylindrical lenses such that one half of the positive lens (1 1 ) is connected on top of one half of the negative lens (12) whereby said constructed lens is utilized to generate accelerating Airy beams.

2. A lens comprising a positive (1 1 ) and a negative (12) half of cylindrical lenses as in Claim 1 wherein radius of curvature of one of said cylindrical half lenses (1 1 , 12) is up to maximum 50 % greater than that of the other cylindrical half lens (1 1 , 12).

3. A lens comprising a positive (1 1 ) and a negative (12) half of cylindrical lenses as in Claim 2 wherein said cylindrical lenses are of substantially same value of radii of curvatures.

4. A lens comprising a positive (1 1 ) and a negative (12) half of cylindrical lenses as in Claim 1 , 2 or 3 wherein said cylindrical lenses (1 1 , 12) have radii of curvatures of +500 mm and -500 mm.

5. A method of constructing a lens (20) suitable for generating Airy beams, said method comprises the steps of cutting one positive (1 1 ) and one negative (12) cylindrical lenses from the centers and connecting one half of the positive lens (1 1 ) on top of the half of the negative one (12),

6. A method of constructing a lens (20) suitable for generating Airy beams as in Claim 5 wherein said positive (1 1 ) and negative (12) cylindrical lenses are of substantially same value of radii of curvatures.

7. A method of generating Airy beams, said method comprising the steps of constructing a lens as in Claim 1 and further comprising the steps of passing a laser beam through the center of said lens (20) and performing Fourier transform.

8. A method of generating Airy beams as in Claim 7 wherein Fourier transform is performed either by going to the far field or using a lens.