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Optics and Spectroscopy

Light slowdown in Bragg waveguide

G. G. Kozlov, Valerii S Zapasskii, V. V. Ovsyankin

Published Sep 1, 2010• 5 citations
Publisher

Abstract

A Bragg waveguide is analyzed from the viewpoint of obtaining slow light. It is shown that, for this system, a complete mathematical analysis of the pulse propagation with allowance for leakage is possible. Calculations are presented that show that, in a TiO 2 /SiO 2 -based Bragg waveguide, one can obtain a group index of ∼1000 with a spatial decay length of ∼3 mm for a nanosecond-scale pulse. Distortion of the pulse due to the group index dispersion proves to be acceptable, in this case, for the pulse propagation length of about 3 mm, which corresponds to the fractional pulse delay ∼10. We also analyze the propagation of the light pulse in the Bragg waveguide with a quantum well inside and show possibility of obtaining a group index of ∼10000.

DOI
10.1134/s0030400x10090146

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A Bragg waveguide is analyzed from the viewpoint of obtaining slow light. It is shown that, for this system, a complete mathematical analysis of the pulse propagation with allowance for leakage is possible. Calculations are presented that show that, in a TiO 2 /SiO 2 -based Bragg waveguide, one can obtain a group index of ∼1000 with a spatial decay length of ∼3 mm for a nanosecond-scale pulse. Distortion of the pulse due to the group index dispersion proves to be acceptable, in this case, for the pulse propagation length of about 3 mm, which corresponds to the fractional pulse delay ∼10. We also analyze the propagation of the light pulse in the Bragg waveguide with a quantum well inside and show possibility of obtaining a group index of ∼10000.
We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite-difference-time-domain Maxwell–Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse.
We have studied the dispersion of ultrafast pulses in a photonic crystal waveguide as a function of optical frequency, in both experiment and theory. With phase-sensitive and time-resolved near-field microscopy, the light was probed inside the waveguide in a non-invasive manner. The effect of dispersion on the shape of the pulses was determined. As the optical frequency decreased, the group velocity decreased. Simultaneously, the measured pulses were broadened during propagation, due to an increase in group velocity dispersion. On top of that, the pulses exhibited a strong asymmetric distortion as the propagation distance increased. The asymmetry increased as the group velocity decreased. The asymmetry of the pulses is caused by a strong increase of higher order dispersion. As the group velocity was reduced to 0.116(9) .c, we found group velocity dispersion of -1.1(3) .10(6) ps(2)/km and third order dispersion of up to 1.1(4) .10(5) ps(3)/km. We have modelled our interferometric measurements and included the full dispersion of the photonic crystal waveguide. Our mathematical model and the experimental findings showed a good correspondence. Our findings show that if the most commonly used slow light regime in photonic crystals is to be exploited, great care has to be taken about higher-order dispersion.
We study slow light pulse propagation in a photonic crystal structure consisting of a dispersive and absorptive dielectric material and compare it with the constant wave case. The group index and the transmission are investigated for the example of an ensemble of semiconductor quantum dots embedded in a photonic crystal waveguide by FDTD Maxwell‐Bloch simulations. The total group index scales linearly with the material based group index while the transmission has a power dependency on the material based absorption coefficient.
This Thesis lies within the field of Slow and Fast Light (SFL) technologies, which are currently receiving much attention because of their interesting applications, ranging from optical information processing to enhanced precision sensing and interferometry. These technologies are based on systems that exhibit steep positive dispersion to propagate a light pulse at group velocity well below the speed of light in vacuum (slow light) or steep negative dispersion to achieve pulse propagation at superluminal or even at negative group velocity (fast light). SFL effects thus arise in a myriad of materials exhibiting spectral resonances. Current efforts in this field are mainly focused on the manipulation of material gain or absorption resonances by nonlinear optical processes (material SFL) or on the optimization of photonic band-gap structures, without substantial material dispersion, but where structural dispersion comes as a result of the coupling between the light wavelength and the characteristic length of the system (structural SFL). This Thesis focuses on the theoretical and experimental analysis of electromagnetic pulse propagation with abnormal group velocities in two kind of linear and passive devices. In the first part of the Thesis a new system exhibiting structural SFL is demonstrated. It deals with multiple-beam interferometers and provides a comprehensive study of the arising of SFL in this system devoid of photonic band gaps. A theoretical model that fully describes the allowed pulse propagation regimes and its performance in terms of both the interferometer's and the pulse characteristics is developed. Considering amplitude modulated pulses, the capabilities and limitations of SFL effects in this kind of system are retrieved by quantifying typical figures of merit like fractional delay, pulse distortion and Delay-Bandwidth Product. The theoretical framework is valid for any frequency region and the model predictions are probed by performing experiments in the radiofrequency range and through exact numerical simulations in the optical range. The simplest interferometer, with only two branches, is first considered since it is widely used in actual communication systems. It is analytically demonstrated that slow light cannot possibly be sustained and that the total attenuation drives the changes in the pulse propagation regimes. By increasing the number of branches, group delay tuning from slow to fast light regimes occurs if the optical length of one of the branches is slightly changed. In the second part of the Thesis, the ability of mono- and multilayer structures to speed up or slow down electromagnetic pulses is investigated, with special emphasis on their reflection properties. Namely, Distributed Bragg Reflectors (DBRs) and Fabry-Perot filters, common in today's communication systems, are examined. These structures were fabricated to operate in the microwave and in the radiofrequency range with the aim of confirming theoretical predictions. Experimental results of their frequency- and time-domain characterization are compared with simulations. An advantage of operating in these frequency ranges is that the transmission and reflection phase function can be measured with a two port vector network analyzer. Such a simple measurement of this key function that determines the pulse propagation regime cannot be directly performed in the optical range. Moreover, microstrip DBRs were designed and their potential application as a negative group-delay circuit to improve the efficiency of feedforward amplifiers, which are commonly used for cancelling inherent distortion in microwave amplifiers, is explored.
We demonstrate that propagation direction and velocity of optical pulses can be controlled independently in the structures with multiscale modulation of the refractive index in transverse and longitudinal directions. We reveal that, in arrays of waveguides with phase-shifted Bragg gratings, the refraction angle does not depend on the speed of light, allowing for efficient spatial steering of slow light. In this system, both spatial diffraction and temporal dispersion can be designed independently, and we identify the possibility for self-collimation of slow light when spatial diffraction is suppressed for certain propagation directions. We also show that broadening of pulses in space and time can be eliminated in nonlinear media, supporting the formation of slow-light optical bullets that remain localized irrespective of propagation direction.