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arXiv:1806.05608 · Applied Optics

Propagation and asymmetric behavior of optical pulses through time-dynamic loss–gain-assisted media

Piyali Biswas, Harsh K. Gandhi, Vaibhab Mishra, Somnath Ghosh

Published Aug 23, 2018• 3 citations
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Abstract

We report an asymmetric behavior of optical pulses during their propagation through a time-varying linear optical medium. The refractive index of the medium is considered to be varying with time and complex, such that a sufficient amount of gain and loss is present to realize their effect on pulse propagation. We have exploited the universal formula for optical fields in time-varying media. Numerically simulated results reveal that pulses undergo opposite temporal shifts around their initial center position during their bi-directional propagation through the medium along with corresponding spectral shifts. Moreover, the peak power and accumulated chirp (time derivative of accumulated phase) of the output pulse in both propagation directions are also opposite in nature, irrespective of their initial state. Numerically simulated behavior of the pulses agrees well with the analytical solutions.

DOI
10.1364/ao.57.007167

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We report an asymmetric behavior of optical pulses during their propagation through a time-varying linear optical medium. The refractive index of the medium is considered to be varying with time and complex, such that a sufficient amount of gain and loss is present to realize their effect on pulse propagation. We have exploited the universal formula for optical fields in time-varying media. Numerically simulated results reveal that pulses undergo opposite temporal shifts around their initial center position during their bi-directional propagation through the medium along with corresponding spectral shifts. Moreover, the peak power and accumulated chirp (time derivative of accumulated phase) of the output pulse in both propagation directions are also opposite in nature, irrespective of their initial state. Numerically simulated behavior of the pulses agrees well with the analytical solutions.
Abstract We demonstrate the nonreciprocal propagation of optical pulses in a linear dispersive medium with a time-varying refractive index. The change of refractive index with time breaks the time-translation symmetry of the spatially homogeneous medium compelling it to be inherently nonreciprocal. A time-reversal asymmetric field ratio of the counter-propagating optical pulses along with a frequency shift leading to spectral nonreciprocity in such dynamic media have been observed. The findings have emerged a new avenue to realize nonreciprocal light flow in dynamically tuned integration-feasible photonic systems.
Pulse propagation in maser-type traveling-wave amplifiers with a homogeneously broadened transition is treated by a formalism analogous to the Bloch equations. Phenomenological dephasing (T2) and recovery (T1) times are defined, and a linear (nonsaturable) loss mechanism is included. In the numerical calculations, only the case of negligible excitation during the time it takes a pulse to pass is considered. When pulses are allowed to grow until the amplifier is ``saturated,'' steady-state pulses having a unique shape and intensity independent of the initial pulse are found. The parameters of these steady-state pulses depend only on the ratio of the linear loss and gain coefficients. Steady-state pulses have a peak intensity that decreases monotonically from infinity to zero as the linear loss coefficient varies from zero to the gain coefficient, while the pulse width correspondingly varies from zero to infinity, and the pulse energy varies from a finite value to zero. Steady-state pulses propogate at a velocity less than that of the small signal velocity in the medium.
We consider the fundamental noise properties of propagation through slow- and fast-light optical media based on gain or loss processes. For purely quantum mechanical reasons, any gain or loss process will add noise to a transmitted light field. We derive a relation between the noise figure describing the decreased signal-to-noise ratio of the transmitted laser pulse and the fractional delay or advancement of the pulse. We apply these results explicitly to the situation of operation on the line center of a gain or loss line. We find that for an ideal gain medium the noise figure never exceeds a factor of two. For a loss medium, there is no limit as to how large the noise figure can become. The increased noise in this case is the result of the random loss of photons from the optical field.
The propagation properties of the chirped Gaussian pulse through gain-dispersion medium are studied by using the definition of complex wave number and the method of diffraction integral.The analytical expressions for the spectrum distribution and the temporal-spatial distribution of the chirped Gaussian pulse are given for the case of the gain-spectrum of Lorentzian distribution.The propagation properties,such as the spectrum distribution,temporal-spatial distribution,variations of the pulse width and the spectrum width,as well as the spectrum shift,etc,were analyzed in detail.It is shown that the pulse still keeps the Gaussian shape in temporal domain when the chirped Gaussian pulse propagates in the gain-dispersion medium,whereas the pulse will undergo the variation of the pulse width.During the propagation,the decrease of the spectrum width and the spectrum shift can be influenced by the chirped parameter.The larger the chirped parameter is,the more obvious the effects of broadening of pulse width and compression of spectrum width are.Furthermore,the spectrum shift increases with the propagation distance.For the given chirped parameter,the spectrum shift will tend to be a constant along the propagation distance.
I derive a simple model for the propagation of a smooth pulse detuned outside a gain line. The pulse moves superluminally and with little distortion provided the medium is not longer than the saturation length. If the medium is longer than this, two effects occur: amplified spontaneous emission interferes with the pulse (although this interference averages to zero over many experiments) and the magnitude of the group delay increases only logarithmically with the length. I argue that both of these effects are inherent to any optical system with gain. Numerical simulations of the superluminal pulse agree with the model presented. \textcopyright{} 1996 The American Physical Society.
We experimentally measure the propagation delays for chirped optical pulses with asymmetric temporal envelope functions, through a resonantly absorbing dye solution. The transmitted pulses suffer a strong deformation and the arrival times are dramatically modified by the interaction between the chirp and the absorption effect of the sample. It is shown that the arrival time, represented by the centroid of energy of the transmitted pulse, can be well described by the reshaping delay and has a greater significance than the peak of the pulse.