Propagation characteristics of Bessel beams generated by continuous, incoherent light sourcesby Ceren Altıngöz, Berna Yalızay, Selcuk Akturk

Journal of the Optical Society of America A


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Propagation characteristics of Bessel beams generated by continuous, incoherent light sources

CEREN ALTINGÖZ,1 BERNA YALIZAY,1,2 AND SELCUK AKTURK1,* 1Department of Physics, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey 2e-mail: *Corresponding author:

Received 4 May 2015; revised 19 June 2015; accepted 7 July 2015; posted 8 July 2015 (Doc. ID 240210); published 28 July 2015

We investigate the propagation behavior of Bessel beams generated by incoherent, continuous light sources.

We perform experiments with narrowband and broadband light emitting diodes, and, for comparison, with a laser diode. We observe that the formation of Bessel beams is affected minimally by temporal coherence, while spatial coherence determines the longitudinal evolution of the beam profile. With spatially incoherent beams, the fringe contrast is comparable to the coherent case at the beginning of the Bessel zone, while it completely fades away by propagation, turning into a cylindrical light pipe. Our results show that beam shaping methods can be extended to cases of limited spatial coherence, paving the way for potential new uses and applications of such sources. © 2015 Optical Society of America

OCIS codes: (030.1640) Coherence; (050.1960) Diffraction theory; (100.2650) Fringe analysis. 1. INTRODUCTION

The generation and use of nondiffracting light beams is of increasing recent interest for both fundamental and applied aspects [1]. In particular, Bessel beams formed by various approximate methods can exhibit quasi-diffraction-free propagation, as well as self-reconstruction over extended distances [2]. These beams are demonstrated to be enabling in a broad range of applications, such as plasma channel generation [3], optical particle manipulation [4], and material processing [5,6].

Fundamental studies, as well as applications of Bessel beams, are performed predominantly with coherent (e.g., laser) sources. Indeed, the earliest theoretical works on diffractionfree propagation by Durnin and co-workers are also based on monochromatic fields and plane-waves (with k-vectors distributed over the surface of a cone) [7,8]. As a result, high spatial and temporal coherence might seem to be a prerequisite for Bessel beam formation.

On the other hand, questions still remain about the relative importance of spatial and temporal degrees of coherence, as well as the consequences of partial coherence in Bessel beam generation. To this end, Fischer et al. investigated Bessel beams formed by white-light sources passing through an axicon, and concluded that temporal coherence is not of significant importance in the axial interference patterns [9]. They performed experiments with various sources with different spatial and temporal coherences, and observed the typical Bessel beam pattern in all cases, albeit with varying fringe numbers and visibilities. Among these sources, light-emitting diodes (LEDs) require further attention because of their intermediate spatial and temporal coherence, and rapidly growing practical use.

Various types of LEDs are shown to be capable of forming

Bessel beams [10], the depth of the nondiffracting zone being strongly dependent on the emitter profile. In a more extensive work, performances of LEDs and laser-type semiconductor sources (lasers diodes or LDs) are compared [11].

A detailed theoretical analysis of the effects of coherence on diffraction-free propagation is performed by Bouchal and

Peřina [12]. Partial coherence is modeled by using superposition of plane-wave components with controlled angular correlation. As the coherence decreases, the lowest-order Bessel beams (with a central bright spot) exhibit broadening of the central lobe and smoothening of the fringe structure. For higher-order modes (i.e., optical vortices), incoherence fills the central null and destroys the vortex structure.

In this work, we present our comparative experimental work on the formation of quasi-nondiffracting beams by sources of varying temporal and spatial coherence. We particularly focus on propagation dynamics of these beams, i.e., investigate the beam profiles and the corresponding fringe visibilities as a function of propagation distance. We observe that, in addition to spatial coherence, the plane of observation is also critical to the observed beam profiles. In the case of a narrowband LED

Research Article Vol. 32, No. 8 / August 2015 / Journal of the Optical Society of America A 1567 1084-7529/15/081567-09$15/0$15.00 © 2015 Optical Society of America source, for example, a high-quality Bessel-like beam in the near field progressively evolves into a light pipe with no fringe structure at farther propagation distances.

We perform experiments using a LD, a narrowband LED, and a broadband LED, all operating in continuous regime.

The sources represent high, partial, and low spatial and temporal coherences, respectively. We observe that the formation of

Bessel beams is affected minimally by temporal coherence, consistent with observations in previous studies. On the other hand, we demonstrate that spatial coherence determines the evolution of the beam profile during propagation along the Bessel zone.

We first present a brief theoretical background and our experimental approach. We then present detailed experimental results on radial and longitudinal intensity profiles, observed with the three sources. Finally, we show a quantitative analysis of the fringe visibilities for each case. 2. THEORETICAL BACKGROUND AND


A. Bessel Beams

Bessel beams are diffraction-free (propagation-independent) solutions of the Helmholtz equation. In cylindrical coordinates, the electric field envelopes of the Bessel beam follow the form [8]

Er;φ; z  E0 expikzzJnkrr expinφ; (1) where Jn is the nth order Bessel function of the first kind, and kz and kr are longitudinal and radial wave vector components.

In the lowest-order case of n  0, the radial intensity profile appears as a bright spot surrounded by concentric rings of decreasing amplitude. The associated intensity of a Bessel beam is given by