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Journal of Lightwave Technology

Modeling of Loss-Induced Superluminal and Negative Group Velocity in Two-Port Ring-Resonator Circuits

Henri P. Uranus, H.J.W.M. Hoekstra

Published Sep 1, 2007• 34 citations
Publisher

Abstract

The group velocity vgof light in two-port ring- resonator (TPRR) circuits with loss is theoretically studied. We point out four possible operation regimes, i.e., "slow" light with positive vg, "slow" light with negative vg, "fast" light with negative vg, and "fast" light with positive vg, where "slow" means |vg|g| > c, with c denoting the velocity of light in vacuum. The temporal behavior of pulses passing through the TPRR for the four operation regimes and the potential of "slow" light TPRR either with positive or negative vgfor sensing applications are also discussed.

DOI
10.1109/jlt.2007.901524

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Numerical observations of negative group velocity in a two-port ring-resonator circuit and its potential for sensing applications

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A two-port ring-resonator circuit is studied theoretically. It is shown that superluminal and negative group velocity (vg) phenomena can occur in both a passive two-port ring-resonator circuit with loss and an active one with gain. We present numerical observations of temporal behavior of a Gaussian pulse passing through circuits having such properties. We also show that when the negative vg is ‘slow’ (|vg|<<c), there is enhanced sensitivity of the phase shift to the ring effective index changes, which suggests its potential for highly sensitive optical sensing applications.

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Recently,there has been interest in modifying the group velocity of optical pulses,resulting in stopped,slow,and fast(superluminal)light.According to the physical theory,fast appears in the anomalous medium,and then it so called light medium.There are many experimeuts to produce fast light,this situation opens up new perspectives for the so called dispersion engineering.For example,signal propagating with a group velocity that exceeds the speed of light in vacuum(c) is intriguing for scientists.And then,the traveling of short wave pulses,microwave pulses and light pulses with group velocity vg,whose values exceed infinity,so called negative group velocity(NGV) propagation.Such circumstance occurs when the peak of a pulse traveling through DUT,exits before the peak of the input pulse has reached the beginning of DUT.This effect is counterintuitive,but it is a discover under the experimental basis.When the group velocity of light in a material is negative,it is the NGV medium. Although NGV are possible particularly in gain systems,there have been some experimental demonstrations of that phenomenon in passive systems,such as the coaxial cables,waveguides,micro-strip lines,and optical fibers,etc.If the experimental configuration used with a higher impedance mismatch,then it permits larger group delays,and a corresponding NGV.If n is the effective refraction index of the medium,we wantfn |f/ndn/df|1 to obtain the NGV. Many experiments showed the group velocity can surpass the light speed c,but scientists still lack the further understanding of the results.In 2001,Scientists obtained the formula v-e=|T|2vg,where v-e is average energy velocity,T is transmission coeficient of the system.If we want v-ec,the condition is vgc|T|-2.Hence it can be concluded that only vg/c is very large,the energy velocity can surpass c.This demonstration opens the door to interesting possibilities. The definition of signal velocity by Brillouin,mathemalical meaning exceeds physical meaning.We argue that undistorted wave group(wave packet) propagation are the first consideration.According to this viewpoint,the theoretical analysis show that superluminal propagation(i.e.superluminal communication) was observed by authors of many NGV researchers.……The superluminal group velocity wave propagation,the negative group velocity wave propagation——each of the two cases has its own use.Now,scientists do research works in these fields: such as optical communication,squeezed light and quantum entanglement.The condusion tell us that,a hight efficiency and low-loss fast light scheme may explore potential applications.

现代传播：中国传媒大学学报•Jan 1, 2013•0 citations
The group velocity vgof light in two-port ring- resonator (TPRR) circuits with loss is theoretically studied. We point out four possible operation regimes, i.e., "slow" light with positive vg, "slow" light with negative vg, "fast" light with negative vg, and "fast" light with positive vg, where "slow" means |vg|g| > c, with c denoting the velocity of light in vacuum. The temporal behavior of pulses passing through the TPRR for the four operation regimes and the potential of "slow" light TPRR either with positive or negative vgfor sensing applications are also discussed.
A two-port ring-resonator circuit is studied theoretically. It is shown that superluminal and negative group velocity (vg) phenomena can occur in both a passive two-port ring-resonator circuit with loss and an active one with gain. We present numerical observations of temporal behavior of a Gaussian pulse passing through circuits having such properties. We also show that when the negative vg is ‘slow’ (|vg|<<c), there is enhanced sensitivity of the phase shift to the ring effective index changes, which suggests its potential for highly sensitive optical sensing applications.
Transfer matrix method (TMM) was used to study the phenomena of ‘slow’- and ‘fast’-light in a single two-port ring-resonator (TPRR) circuit theoretically. Their classifications into ‘slow’- and ‘fast’-light with negative and positive group velocity (v_g), where ‘slow’ means |v_g|<c and ‘fast’ means |v_g|>c, will be introduced. The role of such phenomena in controlling light-matter interaction and pulse delay/’advancement’ will be discussed. Direct experimental observations on pulse temporal behaviors in the regimes of ‘slow’- and ‘fast’-light with negative and positive v_g will be demonstrated, showing large and small pulse ‘advancement’ and delay, respectively. Pulse splitting phenomenon as a transition from a highly delayed to a highly ‘advanced’ pulse and vice versa, will also be experimentally demonstrated. Theoretical simulations on the pulse delay and ‘advancement’ based on the TMM and Fourier transform, which show a good qualitative agreement to the experimental results, will also be presented. The exploitation of ‘slow’-light, either with positive or negative v_g for enhancing light-matter interaction will be discussed through evaluating their effects to the performance of integrated-optical refractometric sensor. It will be shown that when the light is ‘slow’, either with negative or positive v_g, there is enhancement of the sensor sensitivity. An integrated-optical sensor which exploits such properties and exhibits sensitivity of one order better than the present day state-of-the-art commercial Mach-Zehnder interferometer refractometric sensor, will be presented.
Abstract: We report a direct experimental observation of pulse temporal behavior in an integrated optical two-port ring-resonator circuit as a function of coupling strength, including the transition across the critical coupling point. We demonstrate the observation of pulse ‘advancement’ in the negative vg regime and pulse delay in the positive vg regime. We also observed a smooth transition of the pulse shape from highly negative to highly positive vg (or vice versa) through a pulse splitting phenomenon. The observed phenomena agree well to theoretical simulations.
We examined the propagation of nonanalytical points encoded on temporally Gaussian-shaped optical pulses in fast and slow light in an optical ring resonator at $\ensuremath{\lambda}$ = 1.5 \ensuremath{\mu}m. The temporal peak of the Gaussian pulse was either advanced or delayed, reflecting anomalous or normal dispersions in the ring resonator, relevant to under- or overcoupling conditions, respectively. The nonanalytical points were neither advanced nor delayed but appeared as they entered the ring resonator. The nonanalytical points could be interpreted as information; therefore, the experimental results suggested that information velocity is equal to the light velocity in vacuum or the background medium, independent of the group velocity. The transient behaviors at the leading and trailing edges of the nonanalytical points are discussed in terms of optical precursors.
We propose and demonstrate a method for manipulation of group velocity from slow-to-fast light (SFL) in a two-beam Mach–Zehnder interferometer in radio frequency (RF) regime. The subluminal, superluminal, and tunneling propagation regimes occur in a narrow frequency band around the resonance frequency of the interferometer where destructive interference occurs. Importantly, the group velocity at the resonance frequency can be controlled by simply adjusting the transmission magnitude of the signals from the two beams, without changing the length of the interferometer. Models that fully describe the SFL effects in the microwave interferometer system are developed and closed-form expressions for the prediction of group delays at the resonance frequency are obtained. The simple and effective method is verified through numerical calculations and experimental measurements. We also demonstrate that the proposed method applies to a microwave cavity interferometer. A proof-of-concept experiment is performed using a custom open-ended coaxial cable resonator (OE-CCR). Positive and negative group delays are experimentally measured when the resonator is set at different coupling states.
Recently,there has been interest in modifying the group velocity of optical pulses,resulting in stopped,slow,and fast(superluminal)light.According to the physical theory,fast appears in the anomalous medium,and then it so called light medium.There are many experimeuts to produce fast light,this situation opens up new perspectives for the so called dispersion engineering.For example,signal propagating with a group velocity that exceeds the speed of light in vacuum(c) is intriguing for scientists.And then,the traveling of short wave pulses,microwave pulses and light pulses with group velocity vg,whose values exceed infinity,so called negative group velocity(NGV) propagation.Such circumstance occurs when the peak of a pulse traveling through DUT,exits before the peak of the input pulse has reached the beginning of DUT.This effect is counterintuitive,but it is a discover under the experimental basis.When the group velocity of light in a material is negative,it is the NGV medium. Although NGV are possible particularly in gain systems,there have been some experimental demonstrations of that phenomenon in passive systems,such as the coaxial cables,waveguides,micro-strip lines,and optical fibers,etc.If the experimental configuration used with a higher impedance mismatch,then it permits larger group delays,and a corresponding NGV.If n is the effective refraction index of the medium,we wantfn |f/ndn/df|1 to obtain the NGV. Many experiments showed the group velocity can surpass the light speed c,but scientists still lack the further understanding of the results.In 2001,Scientists obtained the formula v-e=|T|2vg,where v-e is average energy velocity,T is transmission coeficient of the system.If we want v-ec,the condition is vgc|T|-2.Hence it can be concluded that only vg/c is very large,the energy velocity can surpass c.This demonstration opens the door to interesting possibilities. The definition of signal velocity by Brillouin,mathemalical meaning exceeds physical meaning.We argue that undistorted wave group(wave packet) propagation are the first consideration.According to this viewpoint,the theoretical analysis show that superluminal propagation(i.e.superluminal communication) was observed by authors of many NGV researchers.……The superluminal group velocity wave propagation,the negative group velocity wave propagation——each of the two cases has its own use.Now,scientists do research works in these fields: such as optical communication,squeezed light and quantum entanglement.The condusion tell us that,a hight efficiency and low-loss fast light scheme may explore potential applications.