Influence of residual disorder on the anticrossing of Bloch modes probed in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math>space

Thomas, Nicolas Le; Zabelin, V.; Houdré, R.; Kotlyar, M. V.; Krauss, Thomas F.

doi:10.1103/physrevb.78.125301

Cited by 28 publications

(34 citation statements)

References 42 publications

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“…15 More recently, some theoretical calculations predicted that group velocities smaller than c / 100 could not be achieved in so-called W1 or W3 waveguides, ͑1 and 3 lines defect, respectively͒, with the current state-of-the-art technology. 10,16 In addition Engelen et al highlighted two regimes of light propagation featuring a "group-velocity range of c / 7 down to c / 200" in chirped W1 waveguides. 17 In view of the recent results in the literature, the light transport in slow light structures has to be clarified, prompting a strong need for a convincing experimental signature of the transition between ͑i͒ the dispersive regime, where the concept of group velocity applies, and ͑ii͒ the diffusive regime.…”

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confidence: 99%

Light transport regimes in slow light photonic crystal waveguides

et al. 2009

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The dispersive properties of waves are strongly affected by inevitable residual disorder in man-made propagating media, in particular in the slow wave regime. By a direct measurement of the dispersion curve in k space, we show that the nature of the guided modes in real photonic crystal waveguides undergoes an abrupt transition in the vicinity of a band edge. Such a transition that is not highlighted by standard optical transmission measurement, defines the limit where k can be considered as a good quantum number. In the framework of a mean-field theory we propose a qualitative description of this effect and attribute it to the transition from the "dispersive" regime to the diffusive regime. In particular we prove that a scaling law exists between the strength of the disorder and the group velocity. As a result, for group velocities v g smaller than c / 25 the diffusive contribution to the light transport is predominant. In this regime the group velocity v g loses its relevance and the energy transport velocity v E is the proper light speed to consider.

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Section: Introductionmentioning

confidence: 99%

Light transport regimes in slow light photonic crystal waveguides

et al. 2009

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“…Above this value, the CCW mode deflects from the ideal cosine-shaped dispersion and gets smoothly coupled into a fast-decaying evanescent mode that emerges from the top and the bottom of the dispersion band. The maximum achievable value of the group index ͑n g = 330͒ is strongly limited by the structural disorder and intrinsic out-of-plane losses, which significantly modify the ideal dispersion diagram as was discussed in [12].…”

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Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides

et al. 2009

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We experimentally investigate the dispersion curve of an integrated silicon-on-insulator coupled-cavity waveguide in a photonic crystal environment using a technique based on far-field imaging. We show that a chain of eight coupled cavities of a moderate Q factor can form a continuous dispersion band characterized by extremely flat dispersion and a group index of 105± 20 within a 2.6 nm wavelength range. The experimental results are well reproduced by theoretical calculations based on the guided-mode expansion method. Evanescently coupled optical resonators concatenated in a chain, so-called coupled-cavity waveguides (CCWs) [1,2], are currently regarded as a possible solution for integrated delay lines in on-chip optical circuits [3,4]. Their ability to slow down the light pulses relies on the storage time associated with each of the cavities that form the CCW. The periodic in-line arrangement of the cavities leads to a dispersion relation that governs the propagation properties of the guided light. A decrease of the coupling between the cavities results in a decrease of the slope of the dispersion curve, i.e., a drop in the group velocity of the guided light. The length of the CCW has a strong impact on the dispersion properties. For a CCW of a finite length, the dispersion curve is sampled with a number of points equal to the number of the cavities N. If the linewidth ␦ of the cavity mode is narrow compared to the entire bandwidth ⌬ of the CCW divided by N, the optical transmission is composed of wellseparated sharp peaks [5,6]. In such a regime, an input pulse of bandwidth ⌬ is transformed into its convolution with a frequency comb formed by the CCW, and a propagating pulse is slowed down at the expense of the distortion of its shape. In the other case, i.e., if ␦ ജ⌬ / N, the dispersion curve of the CCW is expected to be smooth and continuous and a transmission band is formed. Creation of such a band is essential for practical applications, as the optical signal can propagate without distortion only if all its spectral components are equally transmitted. Taking into account that the propagation loss of the CCW mode is scaled with ␦, the optimum case for the management of propagation of light pulses isTo predict the behavior of light pulses in real CCWs as well as the limitations of these structures, a precise experimental knowledge of the entire dispersion curve is crucial. However, when an entire band is transmitted instead of separated sharp peaks, the dispersion curve cannot be inferred from a simple transmission experiment as in [5].In this Letter, we accurately determine the experimental dispersion curve of an integrated silicon on insulator (SOI) CCW in the regime of a continuous transmission. The measurement is based on a Fourier space imaging technique that analyzes the intrinsic out-of-plane losses of the CCW structure. We show that a chain of eight cavities can support a slow-light mode with group index of 105± 20 over a bandwidth as large as 0.33 THz ͑2.6 nm͒.The coupled-cavity structure under cons...

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“…Such fundamental effects can be directly visualized in experiment with near-field measurements, which can be used to recover the amplitude, phase, and polarization of the electric field at all spatial locations in the plane of the waveguide [1]. This information can then be used to extract the dispersion characteristics of the guided modes.A commonly used approach to the dispersion extraction is through the spatial Fourier-transform (SFT) of the field profiles, since peaks in the Fourier spectra correspond to the wavenumbers of guided modes [2,3,4]. However, there exists a fundamental limitation on results obtained with SFT: ∆k ≥ 2π/L, where ∆k is the resolution of the wavenumber, and L is the structure's length.…”

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“…A commonly used approach to the dispersion extraction is through the spatial Fourier-transform (SFT) of the field profiles, since peaks in the Fourier spectra correspond to the wavenumbers of guided modes [2,3,4]. However, there exists a fundamental limitation on results obtained with SFT: ∆k ≥ 2π/L, where ∆k is the resolution of the wavenumber, and L is the structure's length.…”

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Bloch-mode extraction from near-field data in periodic waveguides

Ha¹,

Sukhorukov²,

Dossou³

et al. 2009

Opt. Lett.

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We demonstrate that the spatial profiles of both propagating and evanescent Bloch-modes in a periodic structure can be extracted from a single measurement of electric field at the specified optical wavelength. We develop a systematic extraction procedure by extending the concepts of high-resolution spectral methods previously developed for temporal data series to take into account the symmetry properties of Bloch-modes simultaneously at all spatial locations. We demonstrate the application of our method to a photonic crystal waveguide interface and confirm its robustness in the presence of noise. Periodically modulated optical waveguides offer new possibilities for controlling the propagation of light. Resonant scattering from periodic modulations can be used to tailor the dispersion, enabling in particular a dramatic modification of the group velocity and realization of slow-light propagation. Such fundamental effects can be directly visualized in experiment with near-field measurements, which can be used to recover the amplitude, phase, and polarization of the electric field at all spatial locations in the plane of the waveguide [1]. This information can then be used to extract the dispersion characteristics of the guided modes.A commonly used approach to the dispersion extraction is through the spatial Fourier-transform (SFT) of the field profiles, since peaks in the Fourier spectra correspond to the wavenumbers of guided modes [2,3,4]. However, there exists a fundamental limitation on results obtained with SFT: ∆k ≥ 2π/L, where ∆k is the resolution of the wavenumber, and L is the structure's length. Therefore, accurate dispersion results can only be obtained for long waveguides, extending over many periods of the underlying photonic structure. Another limitation of the SFT method is that it cannot provide information on the dispersion of evanescent waves, which may play an important role close to the structure boundaries or interfaces between different waveguides. For example, evanescent waves enable efficient excitation of slow-light waves without a transition region [5].Alternative methods for dispersion extraction have been developed to overcome the shortcoming of the SFT method. It was shown that an interference of two counter-propagating modes can be used to extract their wavenumbers [6], however this technique is not applicable under the presence of multiple propagating modes or evanescent waves. Recently, it was demonstrated that dispersion extraction in multi-mode waveguides with in principle unbounded resolution is possible even for short waveguide sections [7,8], using approaches based on an adaptation of high-resolution spectral methods previously developed for the analysis of temporal dynamics [9,10]. In this work, we introduce an important generalization of such methods taking into account the spatial symmetry properties of modes in periodic waveguides. We show that beyond the dispersion relations, it is possible to extract the spatial profiles of all guided modes. Our method is applicable to an...

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Influence of residual disorder on the anticrossing of Bloch modes probed inkspace

Cited by 28 publications

References 42 publications

Light transport regimes in slow light photonic crystal waveguides

Light transport regimes in slow light photonic crystal waveguides

Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides

Bloch-mode extraction from near-field data in periodic waveguides

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