Jungang Huang

University of South Wales, Wireless and Optoelectronics Research and Innovation Centre, Faculty Member

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James Elkins

School of the Art Institute of Chicago

Zeyad Alahmed

King Saud University

Nicole Herbots

Arizona State University

Estela Blaisten-Barojas

George Mason University

Adam M Croom

Case Western Reserve University

Fikri KULAKOGLU

Ankara University

Elias Chatzitheodoridis

National Technical University of Athens

Vahid Ahmadi

Tarbiat Modares University

Peter Hobson

Queen Mary, University of London

Zabih Ghassemlooy

Northumbria University

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Papers by Jungang Huang

$Research paper thumbnail of Optical fractals: Characterization, cavities, coherence and connections$

Optical fractals: Characterization, cavities, coherence and connections

$Research paper thumbnail of Fresnel diffraction and fractal patterns from polygonal apertures$

Fresnel diffraction and fractal patterns from polygonal apertures

Journal of The Optical Society of America A-optics Image Science and Vision, 2006

Two compact analytical descriptions of Fresnel diffraction patterns from polygonal apertures unde... more Two compact analytical descriptions of Fresnel diffraction patterns from polygonal apertures under uniform illumination are detailed. In particular, a simple expression for the diffracted field from constituent edges is derived. These results have fundamental importance as well as specific applications, and they promise new physical insights into diffraction-related phenomena. The usefulness of the formulations is illuminated in the context of a virtual source theory that accounts for two transverse dimensions. This application permits calculation of fractal unstable-resonator modes of arbitrary order and unprecedented accuracy.

$Fig. 1. Schematic diagram illustrating the coordinate system used to describe diffraction patterns from an aperture 2) illumi- nated by a plane wave of amplitude Up.$

$Fig. 2. Schematic diagram of an aperture of arbitrary shape in the relative coordinates (u,v). where v,(u) and vo(w) are parametric expressions describ- ing the shape of the aperture in the relative coordinate system (see Fig. 2). The edge-wave field E(x,y) is then given by Eq. (2). In many cases it proves to be more effi- cient to consider a specific aperture shape as broken down into an assembly of subapertures. Babinet’s principle can then be employed to generate diffraction patterns. Here we focus our attention on apertures that are regular poly- gons. For a polygon with WN sides, the most obvious decom-$

$For a polygonal aperture (see Fig. 4), the position of a vertex A; is given by the position vector q;. It is also con- venient to define vectors L;=qj,1—q;, t;=L,/L;, and n;, (de- noting the unit outward normal of side L). The position vector of a general point on the side of = L,; can then be represented as q=q;+t;l, where / is the distance from the vertex A;. Using these constructs, it is possible to re- write Eq. (14) in a form more suitable for describing the diffraction pattern from an N-sided regular polygon:$

$For an isosceles triangle [e.g., triangle 1 in Fig. 3(a)] of half-angle 6=7/N, whose vertex is at the origin and whose perpendicular length a is aligned along the é-axis, the edge-wave contributions are given by and A=a\2/nL. An intuitive way of generating the edge- wave pattern of each of the other component triangles le.g., triangles 2, 3,..., and 8 in Fig. 3(a)] is through rota- tional transformation. A rotational transform of an angle ¢ in the aperture plane is equivalent to considering the system with new observation-plane coordinates x’ =x cos d+y sin ¢ and y'=y sin ¢-x cos ¢.$

$Fig. 5. (Color online) Fresnel patterns (normalized intensity distribution, defined by |U(«,y)|?/U?) from (a) triangle, (b) penta- gon, (c) hexagon, and (d) decahedron apertures. quence of equally-spaced positions, separated by a con- stant step h (xj=x)+ih and i=1,...,N), the integration of a function f(x) in the interval [x,xvy], f ral (x)da, is ap- proximated as h [fo/2+f,+-::+fw_1+fw/2], where f;=/f(x;) is the value of the function at position x;. For brevity, we present only a selection of patterns: those for the isosceles triangle (V=3), the pentagon (N=5),the hexagon (N=6), and the decahedron (N=10). These are shown in Fig. 5. The optical wavelength was chosen to be \=0.5 wm, cor- responding to illumination with green light that is readily obtainable from a green laser pointer. It is thus straight- forward to reproduce these patterns experimentally. The radial distance R from the center of the polygon to a circle enclosing the aperture (upon whose circumference all api- ces lie) is taken as R=1 mm, and the distance between ap- erture and image planes is set to L=100 mm (satisfying the paraxiality condition). Figure 5 shows that the pat- tern acquires an increasing degree of fine structure as N increases. As predicted by Eq. (20), patterns from N-sided regular polygonal apertures have N-fold rotation symme- try. Also, corners with smaller angles tend to contribute more widely diffracted light.$

$Fig. 6. (Color online) Fresnel patterns from a triangular aper- ture with different Fresnel number F eff (8) Foy=3.06, L =200 mm; (b) F,7=3.89, L=150 mm; (c) F.g=7.238, L=75 mm; (d) F = 10.56, L=50 mm. (In each case, R=1 mm and \=0.5 wm). Implementation of the FFT approach in such contexts can also lead to reduced accuracy in the data acquired. Deployment of rational approximations in the S-function method introduces some truncation errors, but high- accuracy approximations”*”° can be used without entail- ing great computational overhead. Finally, the numerical$

$Fig. 8. (Color online) Lowest-order modes of unstable resonators (M=1.5, R=1mm) with (a) triangular (N,,=12.5), (b) pentagonal (N.q=82.725), (c) hexagonal (N,,=37.5), and (d) decahedral (N,,=45.225) apertures. Note that a redefinition of a to be the radius of the circumcircle of each polygon yields a value of 50 for N,, in each of these four configurations. The two analytical forms for the edge waves concerned provide a potential physical framework for interpreting diffraction-related phenomena in the Fresnel regime. They also make possible an accurate generalization of Southwell’s virtual source method to include two trans- verse dimensions.”°” This can allow calculation of 2D eigenmode patterns with arbitrary order and to unprec- edented accuracy. Further applications may, for example, be possible in the area of understanding excess quantum noise,’ where the transverse symmetry of a resonator is known to have a significant effect.1*"1$

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Faraday effect in a short pulse propagating in a resonant medium under an ultra-strong magnetic field

Physical Review B, 2008

We propose a dynamical model for description of the nonlinear Faraday rotation experienced by a s... more We propose a dynamical model for description of the nonlinear Faraday rotation experienced by a short pulse propagating in a resonant medium subject to an ultra-strong static magnetic field. Under the assumptions of a sufficiently strong external magnetic field, such that the Zeeman splitting of the quantum system energy levels is large compared to the linewidth of the optical transitions involved and the bandwidth of the incident light, the light effectively interacts with a two-level system. Our numerical simulations show that the Faraday effect under these conditions is significantly distinctive from the one caused by weak to moderately strong magnetic field. Nonlinear coherent effects such as inhomogeneous polarization rotation along the pulse duration and an onset of a circularly polarized stimulated emission and coherent ringing have been demonstrated. Some views on the experimental observation of the predicted phenomena are given.

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$Research paper thumbnail of Fresnel diffraction and fractal patterns from polygonal apertures$

Fresnel diffraction and fractal patterns from polygonal apertures

Journal of The Optical Society of America, 2006

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$Research paper thumbnail of Wide class of new fractal light sources$

Wide class of new fractal light sources

Page 1. CAOL 2008, September 29 - October 4, Alushta, Crimea, Ukraine WIDE CLASS OF NEW FRACTAL L... more

$Research paper thumbnail of Spontaneous spatial fractals: Universal contexts and applications$

Spontaneous spatial fractals: Universal contexts and applications

Reaction-diffusion systems can exhibit a Turing instability in which homogeneous states develop l... more

Spontaneous Optical Fractal Pattern Formation

Physical Review Letters, 2005

We report, for the first time, spontaneous nonlinear optical spatial fractals. The proposed gener... more We report, for the first time, spontaneous nonlinear optical spatial fractals. The proposed generic mechanism employs intrinsic nonlinear dynamics both to generate an initial pattern seed and to fill out structure across decades of spatial scale. We demonstrate this in one of the simplest of nonlinear optical systems, composed of a Kerr slice and a single-feedback mirror. In this case, the smallest pattern scales are limited by either the optical wavelength or the diffusion length of the medium photoexcitation. The dimension characteristics of these particular fractals are also derived.

$Research paper thumbnail of Fresnel diffraction from polygonal apertures$

Fresnel diffraction from polygonal apertures

This study presents for the first time, two complementary analytical techniques for calculating t... more This study presents for the first time, two complementary analytical techniques for calculating the Fresnel diffraction patterns from a polygonal aperture illuminated by a plane wave. These frameworks are exact, in that they do not involve any further approximation beyond the (paraxial) Fresnel integral. Here, regular polygonal apertures are considered. Results are readily extended to describe near-field diffraction from closed apertures of arbitrary shape. These results are of fundamental importance and have specific applications where standard methods, such as fast Fourier transform (FFT) techniques, fail.

$The S-Function and Line-Integral approaches have been used to calculate the diffraction patterns for N-sided polygonal apertures. Extensive computational investigations have verified that our two approaches are completely equivalent, and produce identical results. C(y) and S(z) denote the Fresnel cosine and sine integrals, respectively. These integrals can be evaluated efficiently, and to a prescribed accuracy, using well-known rational approximations.$

$FIG. 3. Diffraction patterns for: (a) triangular, (b) pentagonal, (c) hexagonal, and (d) decahedronal apertures. Parameters are 2. = 0.5 ym, a =1 mm, L = 100a. In these cases, the number of sides is: n = 3,5, 6 and 10 , respectively. Two new general analytical descriptions of Fresnel diffraction patterns from polygon apertures are reported, for the first time. Ou results have fundamental importance as well as specific applications, promising new physical insights into diffraction-relate phenomena. Fractal laser mode patterns, calculated to prescribed accuracy, illustrate the unique power of our new results. The amount of fine detail present in each Fresnel diffraction pattern can be quantified by the effective Fresnel Number Fyy= a°/AL + f(n) [7], where a is the radius of a circle inscribing an n-sided polygon, L is the distance from the aperture to the observation plane (L? » a? is a paraxial approximation inherent to this near-field description), 2 is the wavelength of the illuminating light, and f(n) = 0.30618n?- 0.19533n - 0.68095 is an expression accounting for the geometrical structure of the aperture. Our results verify that the detail of the diffraction patterns increases with an increase of this Fresnel number. FIG. 3 and FIG. 4 illustrate the change in diffraction pattern with the increase of n and decrease of L , respectively.$

$FIG. 4. Diffraction patterns of a triangular aperture at different Fresnel numbers Fy. (a) F.g= 3.06, L = 200 mm, (b) Fyy= 3.89, L = 150 mm, (c) F.g= 7.23, L=75 mm, (d) F.g= 10.56, L =50 mm. Other parameters are } =0.5 ym and a= 1mm.$

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Space phase matching and self-frequency-doubling red laser in Nd:GdCOB crystal

Optics and Laser Technology, 2003

By using the calculation theory of the phase-matching direction and e ective nonlinear coe cient ... more By using the calculation theory of the phase-matching direction and e ective nonlinear coe cient of frequency doubling in biaxial crystal, we calculate the e ective nonlinear coe cients at di erent frequency-doubling phase-matching directions of the three main uorescent lines (936, 1060, 1331 nm) of Nd:GdCOB crystal. The space distribution curves of e ective nonlinear coe cient are drawn. Two crystal specimens are cut at the optimal type I phase matching angles: for specimen 1, Â = 65 • , = 34:6 • (the ÿrst octant); for specimen 2, Â = 66:5 • , = 145:5 • (the second octant). When pumped by Datachroom-5000 pulsed dye laser, the output self-frequency-doubling red laser in specimen 2 is 0:62 mJ, and the corresponding conversion e ciency is 2.5%. Under the same pumping condition, the output red laser of specimen 1 is much smaller than that of specimen 2, which is well in agreement with the theoretical calculation. ?

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$Research paper thumbnail of Optical fractals: Characterization, cavities, coherence and connections$

Optical fractals: Characterization, cavities, coherence and connections

$Research paper thumbnail of Fresnel diffraction and fractal patterns from polygonal apertures$

Fresnel diffraction and fractal patterns from polygonal apertures

Journal of The Optical Society of America A-optics Image Science and Vision, 2006

$Fig. 1. Schematic diagram illustrating the coordinate system used to describe diffraction patterns from an aperture 2) illumi- nated by a plane wave of amplitude Up.$