An accurate variational analysis of single-mode diffused channel waveguides

Sharma, Anurag; Bindal, Pushpa

doi:10.1007/bf00625812

Cited by 33 publications

(21 citation statements)

References 16 publications

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“…Figure 2(b) shows the corresponding symmetric double-well potential V e (x) ≃ n s − n e (x) obtained by the effective index approximation. To derive n e (x), the measured 2D index profile n(x, y) was fitted [see dashed curves in Fig.2(a)] by the relation [24] n(x, y) ≃ n s + ∆n[g(x − a/2) + g(x + a/2)]f (y), where ∆n ≃ 0.0124 is peak index change,…”

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confidence: 99%

Visualization of Coherent Destruction of Tunneling in an Optical Double Well System

et al. 2007

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We report on a direct visualization of coherent destruction of tunneling (CDT) of light waves in a double well system which provides an optical analog of quantum CDT as originally proposed by Grossmann, Dittrich, Jung, and Hänggi [Phys. Rev. Lett. 67, 516 (1991)]. The driven double well, realized by two periodically-curved waveguides in an Er:Yb-doped glass, is designed so that spatial light propagation exactly mimics the coherent space-time dynamics of matter waves in a driven double-well potential governed by the Schrödinger equation. The fluorescence of Er ions is exploited to image the spatial evolution of light in the two wells, clearly demonstrating suppression of light tunneling for special ratios between frequency and amplitude of the driving field.PACS numbers: 42.50. Hz, 03.65.Xp, 42.82.Et Control of quantum tunneling by external driving fields is a subject of major relevance in different areas of physics [1,2]. The driven double-well potential has provided since more than one decade a paradigmatic model to investigate tunneling control in such diverse physical systems as cold atoms in optical traps, superconducting quantum interference devices, multi-quantum dots and spin systems. Depending on the strength and frequency of the driving field, suppression [3,4] or enhancement [5] of tunneling can be achieved. Tunneling enhancement is usually observed for high field strengths and driving frequencies close to the classical oscillation frequency at the bottom of each well. Since the enhancement generally involves a transition through an intermediate state which is chaotic for strong enough driving amplitudes, it is often referred to as "chaos-assisted tunneling" [1,6]. Observations of chaos-assisted tunneling have been reported in atom optics experiments [7] and in electromagnetic analogs of quantum mechanical tunneling [8,9]. In particular, tunneling enhancement has been observed in two coupled optical waveguides [9]. In the opposite limit, Grossmann, Hänggi and coworkers [3] found that, for certain parameter ratios between amplitude and frequency of the driving, tunneling can be brought to a standstill. They termed this effect "coherent destruction of tunneling" (CDT) and, since then, it has been of continuing interest. Driven tunneling is related to the problem of periodic nonadiabatic level crossing and Landau-Zener (LZ) transitions [1,10]. In particular, in the strong modulation limit CDT may be viewed as a destructive interference effect [10]. In spite of the great amount of theoretical work devoted to CDT, to date most of experimental evidences of CDT are rather indirect. In condensed-matter systems, dephasing and many-particle effects make tunneling control more involved [11]. In Ref.[12] coherent control of Rabi oscillations in Josephson-junction circuits irradiated by microwaves has been reported, however the condition for CDT was not reached. Quantum interference effects and evidences of CDT in qubit systems have been recently reported in [13,14], whereas suppression of quantum diffusion, als...

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confidence: 99%

Visualization of Coherent Destruction of Tunneling in an Optical Double Well System

et al. 2007

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“…The vEIM (Hammer and Ivanova 2009) is equivalent to one iteration without incorporation of any losses. In all earlier applications of the Vopt method (Sharma 1989;Sharma and Bindal 1992), a 2-D transverse profile has been reduced to a 1-D transverse profile. In the present case, a 1-D transverse profile along with a longitudinal index variation is reduced to a 1-D longitudinal distribution n 2 z (z) which allows simple computation of reflection and transmission spectra of the 2-D waveguide grating.…”

Section: Optimal Variational (Vopt) Methodsmentioning

confidence: 99%

“…In both cases, transverse waveguide used does not take into account the presence of index variation along the length of the Bragg structure. Our approach takes this into account by making the variational effective index method iterative on the lines of the optimal variational (Vopt) method that we had developed earlier (Sharma 1989;Sharma and Bindal 1992). In this approach, the method of Hammer and Ivanova (2009) can be considered as the first order iteration, while we have shown significant improvement by the use of more than one iterations (Bindal and Sharma 2010).…”

Section: Introductionmentioning

confidence: 97%

Modelling of photonic crystal waveguides: a simple and accurate approach

Bindal

Sharma

2011

Opt Quant Electron

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We present an improved variational effective index method for reduction of 2-D Bragg grating problems to 1-D and show significant improvements particularly at smaller wavelengths. The method is based on the optimal variational (Vopt) method, which we have earlier used successfully for conventional waveguides. A 1-D transverse profile along with a longitudinal index variation are reduced to a 1-D longitudinal distribution, reflection and transmission spectra of which have been studied for both the TE and TM modes by transfer matrix methods. An accurate modeling for the out of plane scattering losses has been presented which occur when a guided wave propagating in a conventional waveguide impinges on a photonic crystal waveguide. Taking these losses into account brings the results pretty close to those of a rigorous 2-D Helmholtz solver QUEP, improving them remarkably over the variational EIM (vEIM) results.

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“…In this chapter we report a procedure to obtain the refractive index profile and in turn the process parameters for fabrication of waveguide from the desired modal field. It has been shown that the best variational separable field for a channel waveguide corresponds to the solution of two equivalent planar waveguides 1 in the x and y directions. We have used this concept coupled with a variational analysis for the fields of planar waveguides to design channel waveguides with a desired modal field.…”

Section: Introductionmentioning

confidence: 99%