# Optimal focusing of a beam in a ring vortex

TL;DR: In this article, a simple optical setup that achieves this kind of focusing employing a phase plate as unique optical component is presented, where the annular focal field is modulated by an azimuthal phase of integer order q that converts the field in a ring vortex.

About: This article is published in Optics Communications.The article was published on 2015-12-01. It has received 4 citations till now. The article focuses on the topics: Optical vortex & Vortex.

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TL;DR: A simple method to generate a configurable annular vortex beam (AVB) with the maximum possible peak intensity, employing a phase hologram whose transmittance is the phase of a Bessel beam.

Abstract: We discuss a simple method to generate a configurable annular vortex beam (AVB) with the maximum possible peak intensity, employing a phase hologram whose transmittance is the phase of a Bessel beam. Due to its maximum intensity, the AVB provides the optimal density of the orbital angular moment. Another attribute of the generated AVB is the relatively high invariance of the intensity profile when the topological charge is changed. We demonstrate the advantages and flexibility of these AVBs for optical trapping applications.

78 citations

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07 Jul 2017

TL;DR: In this paper, a design method of an annular vortex array mask plate with controllable vortex number was proposed, which can achieve arbitrary control of the dark nuclear number of the ring, thus having very important application prospects in particle manipulation technology.

Abstract: The invention relates to a design method of an annular vortex array mask plate with controllable vortex number. By means of computer generated hologram principle, light beam complex amplitude computational simulation is carried out to superimpose two perfect vortex beam mask plates with different radii, so that an annular vortex array can be generated in a far field. Cone angles of two axicon lens are adjusted to control the light ring superposition degree of concentric perfect vortexes, thus achieving generation of an annular vortex array. The annular vortex array can achieve arbitrary control of the dark nuclear number of the ring, thus having very important application prospects in particle manipulation technology.

7 citations

01 Jan 2004

TL;DR: In this article, the authors used a DRAM contact-hole layout as an example to demonstrate that the same phase shift mask design technology for vortex mask can be applied to double line-space phase-shift mask method.

Abstract: Vortex phase-shift mask had been shown to have excellent image quality by Marc Levenson et al. [1, 2]. However, its application has been restricted to uniform contact-hole arrays and non-uniform contact holes on uniform grid requiring double exposure technique. In this paper, we show that random contact holes in a real layout can be imaged using vortex phase shift mask, with a single exposure. We use a DRAM contact-hole layout as an example. At minimum half-pitch size of 80nm (k1=0.28) and pitch of 160nm, using 193nm stepper with 0.68 numerical aperture and 0.3 degrees of partial coherence, we are able to achieve 0.4um DOF with 10% exposure latitude. The possibility of using a single exposure and low NA stepper should far outweigh the increased cost of vortex mask for high volume products. In comparison, the corresponding alternating phase-shift mask, however, can only achieve 0.2um DOF at 10% exposure latitude, even with the aid of higher numerical aperture of 0.90 and high degrees of partial coherence of 0.15. For non-uniform contact holes, image asymmetry is an issue. We show OPC-corrected images that are substantially symmetrical. Phase error is always a concern for any phase-shift mask. We show that substantial process windows remain even in the presence of phase errors. Furthermore, we demonstrate that random contact-hole layout can be successfully phase-shifted using vortex phase-shift method. Finally, we shall that the same phase-shift mask design technology for vortex mask can be applied to double line-space phase-shift mask method [3].

5 citations

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TL;DR: In this paper, an optical vortex element (OVE) was used to generate an annular vortex beam (AVB) at a determined distance without the use of external optical elements such as lenses and axicons.

Abstract: In this work, we show the conversion of a Gaussian beam into an annular vortex beam (AVB) by means of an optical vortex element (OVE). This is a simple phase plate which generates the AVB at a determined distance without the use of external optical elements such as lenses and axicons. We discuss the interesting features and the advantages of the OVE respect to other methods to generate AVB such as the conventional vortex (CV) and the helical axicon (HA). The OVE presents the highest intensity peak respect to both the CV and the HA. Another important feature is that the OVE and the HA maintain a fixed annular radius; in contrast the CV changes the annular radius, while the topological charge is modified. The OVE is displayed on a spatial light modulator (SLM) in order to generate experimentally the AVBs. We demonstrate the features of the AVB generated and measure the high angular velocities achieved due to the angular momentum transfer to 3 μm particles.

### Cites background from "Optimal focusing of a beam in a rin..."

...a Gaussian beam, into an AVB of integer topological charge q with the maximum possible peak intensity [13, 16]....

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##### References

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01 Oct 1999

TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.

Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.

19,503 citations

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TL;DR: This work demonstrates entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum, which provides a practical route to entangled states that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography.

Abstract: Entangled quantum states are not separable, regardless of the spatial separation of their components This is a manifestation of an aspect of quantum mechanics known as quantum non-locality An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography

2,811 citations

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TL;DR: In this article, the orbital angular momentum of photons is exploited to achieve multi-dimensional entanglement in higher dimensions, i.e., the state of the electromagnetic field with phase singularities (doughnut modes).

Abstract: So far experimental confirmation of entanglement has been restricted to qubits, i.e. two-state quantum systems including recent realization of three- and four-qubit entanglements. Yet, an ever increasing body of theoretical work calls for entanglement in quantum system of higher dimensions. Here we report the first realization of multi-dimensional entanglement exploiting the orbital angular momentum of photons, which are states of the electromagnetic field with phase singularities (doughnut modes). The properties of such states could be of importance for the efforts in the field of quantum computation and quantum communication. For example, quantum cryptography with higher alphabets could enable one to increase the information flux through the communication channels.

2,021 citations

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TL;DR: Black or reflective particles can be trapped in the dark central minimum of a doughnut laser beam produced using a high efficiency computer generated hologram to carry angular momentum transferred from the central phase singularity beam.

Abstract: Black or reflective particles can be trapped in the dark central minimum of a doughnut laser beam produced using a high efficiency computer generated hologram. Such beams carry angular momentum due to the helical wave-front structure associated with the central phase singularity even when linearly polarized. Trapped absorptive particles spin due to absorption of this angular momentum transferred from the singularity beam. The direction of spin can be reversed by changing the sign of the singularity.

1,431 citations

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TL;DR: It is demonstrated that en route to the molecular scale, the resolving power increases with the square root of the saturation level, which constitutes a new law regarding the resolution of an emerging class of far-field light microscopes that are not limited by diffraction.

Abstract: Utilizing single fluorescent molecules as probes, we prove the ability of a far-field microscope to attain spatial resolution down to 16 nm in the focal plane, corresponding to about 1/50 of the employed wavelength. The optical bandwidth expansion by nearly an order of magnitude is realized by a saturated depletion through stimulated emission of the molecular fluorescent state. We demonstrate that en route to the molecular scale, the resolving power increases with the square root of the saturation level, which constitutes a new law regarding the resolution of an emerging class of far-field light microscopes that are not limited by diffraction.

502 citations