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We investigate the effect of doped E r 3 + ion concentration on an electromagnetically induced grating in an E r 3 + -doped yttrium aluminum garnet (YAG) crystal. Due to the change of electric dipole moment and spontaneous emission decay induced by E r 3 + ion concentration, the Fraunhofer diffraction of the solid-state grating is sensitively dependent upon E r 3 + ion concentration. The three-level E r 3 + ion system with a closed loop leads to probe gain appearing in some concentrations of the E r 3 + ion, which significantly improves the first-order diffraction efficiency of the solid-state grating. Furthermore, it is demonstrated that the relative phase, signal detuning, and grating thickness have different effects on the first-order diffraction efficiency of the solid-state grating under different concentrations of the E r 3 + ion. Therefore, our scheme may provide a basis for selecting a suitable concentration to realize high-efficiency optical switching and routing in future integrated systems.

We introduce here double electromagnetically induced grating (DEIG) using a tripod atomic structure, wherein two probe and signal fields with different frequencies simultaneously experience an atomic grating. Properties of presented DEIG can be substantially modified by the detuning of the applied fields. It has also been found that applying an incoherent pump field has a remarkable influence on the high-order diffraction efficiencies. Amplification of travelling weak lights via the incoherent pump field results in large diffraction efficiencies in the first-order and second-order directions. Such a novel scheme might open up the possibility for designing a two-qubit switch that would be advantageous to quantum information processing and quantum networking.

We present a theoretical study on the generation of an electromagnetically induced grating (EIG), based on Zeeman coherence oscillations, in a duplicated two-level atomic system. We show that the pure amplitude grating is obtained in the resonance case of multi-photon detuning. In this system, transferring of light energy from the zero order to the first order occurs by tuning the intensity and detuning of the coupling field. Physical mechanisms of the results are discussed using cases beyond the multi-photon resonance condition. Additionally, in the duplicated two-level system, we can create a two-dimensional EIG by splitting the coupling field into two orthogonal components. Optical properties of the proposed two-dimensional grating are also controlled by the intensity and detuning of the coupling field.

The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.

For the first time, to the best of our knowledge, we investigate the photonic band gap (PBG) structure through scanning the frequency detunings of the probe field, the dressing field, and the coupling field in the static and moving electromagnetically induced grating (EIG) field. When we scan the frequency detuning of the coupling field, the PBG structure and six-wave-mixing band gap signal (SWM BGS) appear at the right of the electromagnetically induced transparency (EIT) position. But the PBG structure and SWM BGS appear at the left of the EIT position in the case of scanning the probe field frequency detuning. Also, on the condition of scanning the probe field frequency detuning, the SWM BGS appears in two frequency ranges. Moreover, in the moving PBG structure, nonreciprocity of the SWM BGS can be obtained. Furthermore, the intensity, width, and location of the SWM BGS can be modulated through changing the frequency detunings and intensities of the probe field, the dressing field, and the coupling field; the sample length; and the frequency difference of coupling fields in EIG. Such a scheme could have potential applications in optical diodes, amplifiers, and quantum information processing.

An electromagnetically induced phase grating (EIG) controlled by coherent population trapping (CPT) in a four-level Y-type atomic system is studied. The CPT condition promotes significantly the dispersion of light into the first-order diffraction in constructing a phase modulation grating by transferring energy from zero-order to first-order diffraction. The diffraction efficiency of the phase grating is enhanced by up to 30% of the total probe intensity at the first-order diffraction. The present atomic scheme takes full advantage of the microwave-driven field for generating the EIG, which induces the quantum coherence and controls linear and nonlinear behaviors of the present system. Furthermore, it is noticed that the higher-order diffraction intensities are improved via a microwave-driven field and the phase and amplitude of the microwave field can improve the efficiency of the phase grating. These novel results could find potential applications in developing new photonic devices, such as all-optical switching at low light levels.

An electromagnetically induced phase grating controlled by spontaneous generated coherence (SGC) in a four-level N-type atomic system is studied. The results indicate that the diffraction efficiency of the phase grating is dramatically enhanced due to the existence of SGC, and an efficient electromagnetically induced phase grating can be obtained. A novel result is considerable improvement of the intensity of higher-order diffractions via relative phase between applied laser fields. Furthermore, it is found that the frequency detuning of the switching and coupling fields with the corresponding atomic transition, incoherent pumping, and the interaction length can improve the efficiency of the phase grating in the present atomic model.

Reflectivity and spectral properties of a thick reflection grating are discussed for the second-order Bragg diffraction regime. Analytical expressions for the reflection and gain coefficients are obtained with the help of the developed theory. A procedure is proposed for determining the wavelength of laser oscillations generated in an optically active grating. The influence of the second harmonic of dielectric permittivity spatial modulation on reflection and spectral characteristics of a grating was also analyzed. Comparison of the approximate results obtained by the proposed approach and by the numerical solution is carried out, and their excellent agreement is demonstrated.

We report a new, to the best of our knowledge, method for detection of dynamic population gratings in Er-doped fibers with saturable absorption that is based on observation of the transient fluorescence resulting from fast displacement of the recording interference pattern. The signal appears due to essentially different relaxation times of the fluorescence in bright and dark fringes of the light pattern. The experimental results obtained at the recording wavelength λ=1492 nm in a single-mode fiber with 5600 ppm Er demonstrate good agreement with the theoretical model based on a saturable two-level system. Unlike conventional diffraction-based techniques, the proposed method results in the local grating amplitude value and can be used for characterization of the grating amplitude spatial profile. It can also be suitable for characterization of the grating formation processes in other bulk and thin-film media with saturable absorption.

We show that electromagnetically induced transparency suppresses nonlinear absorption of all orders in a multilevel atomic system and leads to selective, multiphoton excitation of resonantly coupled atomic states. Under appropriate conditions, higher-order nonlinear absorption becomes dominant and selective steady-state population inversion is created among the resonantly coupled states.

We report experimental studies of electromagnetically induced transparency in Λ-type and ladder-type atomic systems realized in 87Rb atoms cooled and confined in a magneto-optical trap. Complete transparency is observed in the Λ-type system with a moderate coupling field. Comparison between the two systems reveals that at the line center of a weak probe transition, destructive interference occurs for the Λ-type system, whereas constructive interference occurs for the ladder-type system. We discuss conditions of complete transparency in the Λ-type system that contains hyperfine magnetic sublevels. Our experimental measurements for the two systems agree with theoretical calculations based on simple three-level Λ-type and ladder-type models.

We have observed electromagnetically induced transparency (EIT) in rare-earth Pr3+-doped Y2SiO5 over the spectral hole-burning temperature. The transmission of the probe laser beam is increased by a factor of exp(1.4) at 12 K when a coupling laser of 1.2 kW/cm2 is applied to the system. The observation of EIT over the spectral hole-burning temperature in a rare-earth–doped solid represents important progress toward high-density echo-based optical memories at higher temperatures.

Multiple optical interference patterns generate phase gratings in Bi12SiO20 as a result of the photorefractive effect. Because of the nonlinear response of the space-charge field to the optical interference pattern, these primary gratings interact and cause the formation of additional gratings at frequencies that are combinations of the primary grating frequencies. Only the diffusion regime is considered in the present investigation. In our setup, two primary gratings are induced as the result of interference among one reference and two closely situated object beams. The interference between the two object beams leads to a negligible photorefractive grating, because the photorefractive Bi12SiO20 crystal cannot respond to the corresponding large fringe spacing. We show theoretically that nonlinear combinations of gratings are introduced through this third interference pattern even though the corresponding grating itself is absent. We obtain analytical expressions for the fundamental frequency components of the space-charge field in the special case of a weak reference beam. In the general case, the frequency components of the space-charge field are calculated numerically by the use of Fourier transforms and are incorporated into the coupled-wave equations. The optical beam propagation method is then used for solving these equations numerically. The effect is probed in a three-wave mixing experiment that uses a sinusoidal phase modulation on one of the object beams to control the grating strength. With this technique one of the gratings is specifically canceled out, and the relative change of the diffraction efficiency in the remaining grating is measured. It is shown that nonlinear combinations of gratings may cause relative changes of more than 35% in the diffraction efficiency. The theoretical predictions are in excellent agreement with our experimental results and the cross talk observed in dynamic optical interconnects.

With a coherent pump laser coupling two electron levels in quantum wells, Coulomb and light-induced electronic renormalization is investigated according to the density-functional theory. On the basis of the renormalization, the optical response function for intersubband absorption of a probe light beam is studied. Both the electromagnetically induced transparency and the probe light amplification without inversion are observed. The influences of the pump field strength, frequency detuning, electron density, and δ-doping position are determined.

A systematic experimental and theoretical study of first-order grating coupling to surface plasma waves existing at an air–Ag interface is presented. The experiment extends beyond previous work to grating depths comparable with the grating period. The grating profiles range from sinusoidal to rectangular. For TM-polarized incident radiation this grating depth range includes the entire spectrum of surface-plasma-wave-radiation coupling—from underdamped, to nearly 100% coupling, to overdamped and the disappearance of the resonance from the zero-order reflectance measurements. Strong polarization and absorption effects are observed for the deepest gratings. A simple theoretical model, based on the Rayleigh hypothesis and retaining only resonant diffraction terms without a small-signal approximation being made, provides good agreement with the experimental results.

The concept of a grating in real and frequency space is examined in the context of a three-pulse optical excitation cycle applied to a pseudo two-level model system. The calculations are done analytically using the Liouville-operator formalism in matrix form. It is shown that a continuous transition occurs from a grating in real space to a grating in frequency space when the first two excitation pulses separate in time. During this transition, the role of the population-relaxation time constant (T1) is taken over by the dephasing time constant (T2) bringing out the irreversible nature of the loss of coherence in an excited state. The underlying space-time transformation when moving from a grating in real space to a grating in frequency space further clarifies the loss in symmetry of the scattering pattern induced by a probe pulse by attributing it to the law of causality. It is finally concluded that the generalized grating concept is a powerful means of analyzing or predicting the effects of multiple-pulse multicolor optical-coherence experiments.

The properties of the photorefractive effect were investigated using the holographic grating technique in nominally pure LiNbO3 crystals. Gratings were created with different write-beam crossing angles between 2.5° and 8.0°, and the angular distributions of the scattered probe-beam intensity were measured. Scattering maxima were observed at several different angles, and each spot was found to have a different erasure-decay rate. This is attributed to diffraction from a complex grating having multiple Fourier components. A theoretical method is presented for analyzing these types of data and obtaining information concerning the refractive-index modulation of each component of the grating. Computer fits of small-angle-scattering patterns for each diffraction maximum are shown to provide accurate values for the grating thickness and the grating depth. A comparison is made between results obtained from this technique and those obtained by measurements of the scattering efficiency at the Bragg angle with special attention focused on the importance of beam geometries in laser-induced grating experiments.