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A novel high-speed coherent modulating retro-reflector (MRR) is presented and experimentally demonstrated for free-space optical (FSO) communications by using an in-phase quadrature (IQ) modulator with quadrature phase-shift keying (QPSK) signals to break the conventional speed limitation. The transmission performance is tested in a turbulence-tunable atmospheric cell. The received sensitivity is measured to be 14.7 dB PPB, and the power penalty is 2.0 dB for 20 Gbit/s single-channel QPSK signal at the BER of 0.01 when the temperature difference is 250 °C. Moreover, this MRR scheme is compatible to wavelength-division multiplexing (WDM) technology, and a 60 Gbit/s WDM MRR is demonstrated using three channels with only about 0.6 dB degradation.

Vector light beams (VLBs), manifesting as the non-uniform spatial distribution of polarization states, have shown broad applications in increasing communication capacity. Here, we propose and experimentally demonstrate a spatial phase cross-polarized method for achieving a mode coded modulation of VLBs. By employing the polarization sensitivity of the spatial light modulators (SLMs), the left and the right-handed circularly polarized parts of light beams are modulated with opposite spatial spiral phase to produce VLBs by the coherent combination. Manipulating the spatial phase distribution of the left and the right-handed circularly polarized light beams, the VLBs with 16 modes ([m; l]=[2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8; 0, −1, −2, −3, 1, 0, −1, −2, 2, 1, 0, −1, 3, 2, 1, 0]) are obtained and used to code digital signals. In the experiment, a 60 × 60 pixels flower gray image with 14 400 quaternary numbers are then coded to the 16 modes and decoded successfully after 1 m transmission in free space. And the flower gray image is also recovered accordingly.

The performance of free-space laser communication (FSLC) is greatly decreased by horizontal atmospheric turbulence. Adaptive optics is used to overcome horizontal turbulence. This study investigated the effect of the 3 dB bandwidth of an adaptive optics system (AOS) on FSLC performance by using power-in-bucket (PIB) method, which considers the effect of receiving aperture and then, can accurately evaluate of the effect of system bandwidth on the communication performance. A 9 km horizontal maritime link experiment was performed through adaptive correction to validate the theoretical analysis. Results indicate that the effect of system bandwidth can be accurately evaluated using PIB method. This work provides a basis for designing and evaluating AOSs for FSLC.

In this paper an elliptic vortex beam with fractional topological charge, which is abbreviated as fEVB, is proposed and applied for the free-space optical communications. A method is also proposed to identify the orbital angular momentum (OAM) states of the fEVBs from the shapes and positions of the intensity distributions of the beams in the receiver unit. The fEVBs would have high information capacity and security level in the free-space information transferring as the fEVBs can have much more OAM states than the conventional vortex beams. The simulation results show that the fractional topological charges of the fEVBs can be decoded precisely with the proposed method.

In this work, we demonstrated a Single Input Multiple Output (SIMO)-Visible Light Communication (VLC) system in a free space transmission by utilizing a monolithic integrated PIN array receiver. Here, a 2 × 2 Positive-Intrinsic-Negative (PIN) array is designed as main unit of monolithic integrated PIN array. With the proposed approach, a highest data rate of 1.45 Gbit/s at distance of 1.2 m and maximum distance of 4.2 m with data rate threshold of 1 Gbit/s are successfully achieved with a Bit Error Rate (BER) × 10−3. The experiment demonstrated feasibility of using this PIN array receiver in achieving high efficient free space VLC system, which contributes to the realization of higher integration of the visible light communication system.

This paper investigates an adaptive phase estimator for coherent free-space optical (FSO) communication systems. Closed-form solutions for variance of phase errors are derived when the optical beam is subjected to Gamma-Gamma distributed turbulence. The adaptive phase estimator has improved upon the phase error performance in comparison to conventional phase estimators. We also demonstrate notable improvement in BER performance when applying our adaptive phase estimator to coherent FSO communication systems.

The analytic expressions for the free-space propagation of paraxial and non-paraxial vector Lissajous singularity beams are derived, and used to compare the propagation property of a Lissajous singularity carried by paraxial and non-paraxial vector beams in free space. It is found that the creation of a single Lissajous singularity, the creation and annihilation of pairs Lissajous singularities may take place for the both cases. However, after the annihilation of a pair of singularities, no Lissajous singularities appear in the output field for non-paraxial vector Lissajous singularity beams, which is different from the paraxial vector Lissajous singularity beams.

Generalized frequency division multiplexing (GFDM) with the free space optical channel can be a desirable option for free space optical communication systems as it has numerous benefits such as high spectral efficiency, flexibility, low out of band radiation and low peak-to-average power ratio. In this paper, the closed form expressions of symbol error and outage probabilities with and without pointing errors are derived for GFDM over gamma–gamma channel model. The theoretical results are verified with the Monte-Carlo simulations. Moreover, the impact of turbulence levels and comparison with orthogonal frequency division multiplexing are also explored.

Characteristics of an anomalous vortex beam (AVB) through the paraxial optical systems are studied. The analytical formulas for the AVBs through the aligned and misaligned optical systems are derived by using the Collins integral equation. As the numerical examples, the intensity distributions for the AVBs in the free space and the convergent optical system are given. It is shown that the far fields for AVBs will be determined by the main parameters, such as width of beam waist w0, n, m (n is the order of the AVB, m is the topological charge). Furthermore, the analytical formula of M2 factor of AVB is derived by using the second-order moments associated with the intensity distributions. The study results can provide references for the application of AVBs.

As we know that deformable-mirror (DM) is used in the adaptive optics (AO) systems to compensate atmospheric turbulence in free space optical (FSO) communication system. In order to get rid of the limitations generated by the characters of DM itself, the combinational-deformable-mirror (CDM) adaptive optics (CDM-AO) system is established to correct wave-front aberrations and improve coupling efficiency at the receiver. The analysis of the principle of CDM and the decoupling-working principle based on confinement correction algorithm (CCA) is provided, and the comparison of the correcting results between CDM-AO system and conventional AO system are given. Simulation results indicate that CDM-AO system can correct different aberrations with different characteristics and provide better correction performance than single deformable-mirror (DM) AO system. And the coupling efficiency improvement provided by the correction of AO system is numerically evaluated.

A novel method to reduce the diffraction crosstalk for micro-lens based free space optical interconnects is presented. Instead of using microlenses with uniform transmittance apertures, the use of microlenses with non-uniform transmittance apertures is proposed. It is shown that the diffraction crosstalk which exists in the free space interconnects systems that use microlenses with uniform transmittance apertures can be substantially reduced by using microlenses with Gaussian transmittance. The optical field at the detectors array using both the uniform and Gaussian apertures have been derived and used to calculate the crosstalk. Numerical results have been introduced to show the improvement of the signal-to-crosstalk ratio when using the Gaussian transmittance for the microlens.

In this paper, a hybrid free space optical (FSO)–millimeter wave (mmWave) cooperative system is proposed. Specifically, a cooperative dual-hop decode-and-forward (DF) relaying system coexists with a direct communication link and two scenarios are considered. In the first scenario, the direct link is used for FSO transmission while the DF dual-hop relaying system is used for mmWave transmission. On the contrary, in the second scenario, the direct link is used for mmWave communication whereas the relaying link is used for FSO communication. In both scenarios, the mmWave link experiences Nakagami- m fading while the FSO link suffers gamma–gamma turbulence fading. At the destination, the two signals, i.e., the mmWave and the FSO signals, are jointly detected using an optimum maximum likelihood receiver. To investigate the performance of the proposed systems, novel analytical expressions for the overall average bit error rate (BER) and outage probability are derived. The impact of different system and channel parameters on the overall average BER is investigated. Additionally, the performance of the proposed systems is compared with other setups where only direct mmWave or FSO link exists. Monte Carlo simulation results are provided to corroborate the accuracy of the analysis.

This work expands the study of the impact of the atmospheric scintillation phenomenon in a free-space optical (FSO) communication system. Its behavior is evaluated by means of the bit error rate (BER). The contribution of our work is the BER calculation of the FSO system for different system parameters through simulations of the link combined to the already established scintillation model as the gamma–gamma model. The results show how a FSO link can be impacted by any turbulence regime.

Starting from the vectorial Rayleigh–Sommerfeld formulas, the closed-form expressions of nonparaxial Airy beams are obtained, the paraxial and the nonparaxial energy flow distributions and the angular momentum density distributions of the Airy beams are demonstrated in free space. The effect of the dimensionless perturbation parameter on the nonparaxiality of the Airy beams is discussed.

Cylindrical vector beam is one of the polarized beams whose states of polarization are spatially various and cylindrical symmetric. Owing to their peculiar focusing property, cylindrical vector beam has attracted more and more attentions. In this paper, we propose a method to generate cylindrical vector beam with rotatable polarization in free space. Two spatially homogeneous polarized beams are modified properly into spatially varied polarized beam by the vortex phase plate respectively. Then two phase-coded beams are combined together to generate a cylindrical vector beam. In addition, the polarization directions of cylindrical beams can be rotated continuously to a desired direction. The polarization states of the cylindrical vector beam are calculated by Johns matrix. The focusing properties are simulated by MATLAB.

The dynamic evolution of Riemann–Silberstein (RS) vortices for Gaussian vortex beams with topological charges m = ± 1 in free space is studied. It is shown that for Gaussian on-axis vortex beams there exist both RS vortex with m = + 2 and circular edge dislocation. For Gaussian off-axis vortex beams the circular edge dislocation splits into two RS vortices with opposite topological charges m = ± 1 and the RS vortex with m = + 2 decays into two vortices with same topological charges m = + 1. The motion of RS vortices takes place by varying the propagation distance, waist width, off-axis parameter, or topological charge. RS vortices for Gaussian vortex-free beams can be treated as a special case. The results are illustrated analytically and numerically.

In this paper we consider geometry optimization of a quad-cell alignment detector for short range free space optical interconnects. The alignment technique uses alignment beams and quad detectors to detect different misalignment errors. We show that the size of the quad detector cells can be used as a design parameter to optimize the sensitivity of the alignment system. The sensitivity analysis and error signal generation are presented assuming standard Gaussian beam models. Results on optimum sensitivity for the case of transverse and angular misalignments are presented and discussed.

The intensity distribution and the equal-time complex degree of coherence for the broadband Gaussian Schell-model array beams with different bandwidth propagating in free space are analyzed by the numerical calculation. Results show that the intensity distribution for the broadband Gaussian Schell-model array beams by uncorrelated superposition is rarely affected by the bandwidth; the intensity distribution in the far field for the broadband Gaussian Schell-model array beams by correlated superposition is affected by the bandwidth more obviously than that in the near field. With the increasing of the propagation distance, differences in the equal-time complex degree of coherence for the broadband Gaussian Schell-model array beams with different bandwidth become prominent.

The radially polarized partially coherent Laguerre–Gaussian (LG) ( 0 , 1 ) ∗ beam is introduced and its paraxial propagation properties are studied. The effect of propagation parameters on the intensity distribution, the beam quality, the polarization property and the coherent property of the beam is illustrated analytically and numerically. It is shown that in free space the correlation length has a significant influence on the intensity profile and the degree of polarization.

The closed-form expression for the angular spread of partially coherent annular flat-topped beams propagating through atmospheric turbulence is derived by using the integral transform technique. In comparison with previous work, the results obtained in this paper are more general. It is shown that, except for equivalent Gaussian Schell-model (GSM) beams as pointed out in Ref. [T. Shirai, A. Dogariu, E. Wolf, Opt. Lett. 28 (2003) 610], there also exist equivalent annular and non-annular beams which may generate the same directionality as the corresponding fully coherent Gaussian beam both in free space and in turbulence. The theoretical results are illustrated by numerical examples and interpreted physically.

Spectral characteristics of partially coherent flat-topped (PCFT) beams propagated in a turbulent atmosphere are investigated and an analytical formula for the spectrum S ( ω ) is derived. It is shown that, if the scaling law is valid, the normalized spectrum S ( ω ) of PCFT beams propagating through turbulent atmosphere is the same as the normalized source spectrum S (0) ( ω ), this similarity is valid for any arbitrary order of the circular flat-topped “ N ”. It is proved that if the scaling law is not valid, S ( ω ) of PCFT is different from S (0) ( ω ). Also spectral behavior of PCFT beams in free space and turbulence media is investigated in detail.

A new concept of a free-space, high-speed (Gbps) optical communication system based on spectral encoding of radiation from a broadband pulsed laser is developed. It is shown that, in combination with the use of partially coherent laser beams and a relatively slow photosensor, scintillations can be suppressed by orders of magnitude for distances of more than 10 km. We also consider the spectral encoding of radiation from a LED as a gigabit rate solution of the "last mile" problem and rapid-deployment systems for disaster recovery., Comment: 16 pages, 2 figures

In this paper, it is investigated that how the atmosphere effects on the synchronization accuracy in free-space quantum key distribution (QKD). We measured the synchronization error of a free-space QKD in our near-ground platform. According to experimental results and theoretical calculations, we deduce that the intensity fluctuation of synchronization light due to atmosphere disturbance contributes far more to the synchronization accuracy than others. By using the constant fraction discrimination method, the synchronization error of the free-space QKD, passing through the aerosphere, can be limited within 300 ps which meets the synchronization requirement of a satellite-to-ground QKD system.

We report, the experimental result of a study, conducted to investigate the spectral anomalies in the region of superposition in the Young's double-slit interference experiment. These results are in close agreement with the theoretical study by Pu et al. (J. Pu, C. Cai S. Nemoto, Opt. Express 12 (2004) 5131). The application of this study might be useful in realizing the information transmission in free space, in optical signal processing and optical computing.

A new kind of laser beam, named a decentered controllable elliptical dark-hollow beam (DCEDHB), is defined by a tensor method. The propagation formula for a DCEDHB through an axially nonsymmetrical optical system is derived by vector integration. The derived propagation formula could be reduced to the formula for a controllable elliptical dark-hollow beam (CEDHB) and a controllable dark-hollow beam (CDHB) under certain conditions. As an application example of the derived formula, the propagation characteristics of a DCEDHB in free space are calculated and discussed. As another example we study the propagation properties of coherent and incoherent beam combinations with radial array for DCEDHB.

A new kind of partially coherent beam named partially coherent off-axis flat-topped beam is proposed. The cross-spectral density of this beam can be expressed as a finite series of off-axis Gaussian–Schell-model beams with different parameters. Analytical propagation formulae for the partially coherent off-axis flat-topped beam through aligned and misaligned optical systems are derived. As a numerical example, the propagation properties of the partially coherent off-axis flat-topped beam in free space are discussed.

We show that after propagating through a turbulent medium the normalized spectrum of a beam generated by a class of quasi-homogenous sources is, to a good approximation, equal to the normalized source spectrum. This result is a generalization of a previously derived result for propagation in free space.

A decentered flattened Gaussian beam (DEFGB), is defined by a tensor method. The propagation formula for a DEFGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a generalized decentered elliptical flattened Gaussian beam under certain condition. As an example application of the derived formula, the propagation characteristics of a DEFGB in free space are calculated and discussed. As another example we have studied the properties of superposition with radial array consisted by DEFGB.

A rigorous analysis is presented to deal with the use of spectra generators for free space localized waves in an optical fiber, respecting the boundary conditions and assuring the predominance of the monomodal regime.

A simple scheme is introduced to simplify coupling of the fundamental mode of a single-mode fiber to free-space and/or into another fiber or waveguide. The analysis shows that the lowest-order cladding modes of standard single-mode fiber, which may be readily excited using various fiber-grating technologies, possess superior coupling performance compared to that of the core mode, which in many cases could either circumvent or enhance traditional lens-based coupling schemes for fiber-optic component applications. Experimental measurements verify the predictions of a theoretical model based on the Fresnel diffraction approximation.

We present a rigorous approach to the problem of fully vectorial nonparaxial propagation in free space. This treatment allows us to generalize in a simple way current approximated schemes of solution.

Differential phase shift quantum key distribution scheme has been improved by introducing a passive path selection structure at the transmitter including two polarization controllers used to mark the photon pulses and a polarizing beam splitter to distinguish these pulses so that can make different time delay at the receiver. Theoretical analysis indicates that a free-space-based differential phase shift quantum key distribution system with this proposed improvement will have high efficiency with the utilization ratio of photons reaching 100% under ideal condition.

We examine the Rayleigh hypothesis in the context of scattering of light off photonic crystal interfaces. First, the hypothesis – which was initially suggested for scattering of waves off rough surfaces between homogeneous media – is rephrased to apply to photonic crystal interfaces. Next, an exact and explicit functional form is presented that maps plane photonic crystal surfaces to periodic rough surfaces in free space, so that known criteria for the validity of the Rayleigh hypothesis for scattering at rough surfaces can be applied directly to scattering at the photonic crystal surfaces. The same map also allows the scattering problem to be solved exactly.

We propose a simplified linear formulation of diffraction to make the synthesis of diffractive optical elements more accessible. The main emphasis consists of observing the diffracted field in certain planes in free space as a discrete sum of shifted and weighted replicas of the initial field at least for a wide set of diffracting objects. To illustrate the usefulness of the new formulation, we present several examples of application.

Starting from flattened Gaussian beams, we deduce analytical expressions for the propagation of paraxial circular symmetric beams through a general first-order optical system. It is shown that the propagation of any scalar beam in a paraxial domain takes the same form as that in free space. Three parameters were introduced to characterize the evolution of the propagating beam. Numerical examples are also presented to illustrate the effectiveness of this method.

This paper describes the design of a polarisation controller using a nematic liquid crystal in the infrared. Theoretical comparison of parallel and twisted structures is made. Our samples reach 30 dB contrast and 1.4 dB insertion loss. Twisted nematic cells were used to perform a 4 × 4 strictly non-blocking optical switch at 1.5 μm with 15.2 dB fibre to fibre loss and less than −28 dB cross-talk.

We discuss wave-guide Free Electron Laser gain formulae including inhomogeneous broadening and saturation effects. The analysis is not limited to the low gain regime. It is also proven that, after a proper redefinition, most of the “empirical” formulae exploited for the free space case can be utilised to model the wave-guide evolution.

By applying a self-consistent projection-operator method, developed recently by the author, a complete treatment of the sixty- year-old problem of spontaneously decaying atomic state is achieved. In a new physical interaction picture (in which, without using the mass-renormalization concept, the unobservable interaction of the free electron with the vacuum radiation field is eliminated), by removing the shortcomings of the Weisskopf-Wigner method and taking into account virtual transition effects, explicit finite analytic results for the non-markovian time evolution in the case of Lyman-α spontaneous emission are obtained.

A mathematical method presented in a previous letter to calculate the diffraction pattern of circularly symmetric laser beams propagating in free space is generalized to deal with beams of any shape propagating through optical systems that can be described by an ABCD ray transfer matrix. The method is based on the application of sampling concepts to the generalized Huygens-Fresnel propagation integral. Explicit expressions are given allowing computation of the diffraction pattern by means of simple personal computers. The accuracy of the method is shown in an example by comparison with analytical results.

By treating the boundary conditions correctly, we compute the linewidth of a laser with arbitrary output coupling below and above threshold. In the limit of unit output-mirror transmission, for which any semblance of the cavity to a lasing cavity is completely untenable, we show that the laser linewidth reduces to the natural linewidth of spontaneous emission by atoms in free space. Dependences of the linewidth on the cavity transmission are predicted to be at variance with previously obtained results. We also find a power-independent contribution to the intrinsic linewidth well above threshold.

We show that atoms moving inside cavities experience a velocity-dependent spontaneous emission rate caused by the Doppler shifting of the atomic transition frequency on or off the cavity resonance. This is in contrast to the free space situation, where galilean invariance guarantees that this rate is independent of velocity for atoms in uniform motion.

The spectrum of light, in general, changes when the light interacts with a dispersive medium or when it is diffracted. It may also change on propagation, even in free space, because of the coherence properties of the source. The difference and some similarities between these processes of spectral modification are analyzed.

The evolution of correlation-induced spectral shifts with propagation in free space is investigated in the paraxial regime with particular emphasis on the transition from near to far zone. The dependence of spectral shifts on the state of coherence, the angle of observation, and the source linewidth is studied for partially coherent light generated by planar secondary gaussian Schell-model sources.

Formulas are derived, which make it possible to study the changes produced in the spectrum of a non-stationary ensemble of pulses on propagation in free space or in a linear medium, whether deterministic or random.

In a recent paper [A.B. Katrich, Opt. Commun. 255 (2005) 169], Katrich has claimed that in a 2D free space evanescent waves do not exist because they are not exact solutions of the free space wave equation. We show that his conclusions are not valid, and that evanescent can indeed exist in free space.

We report results of experiments dealing with the effects of partial spatial coherence on the propagation and focusing of gaussian Schell-model beams. The measured coherence-dependences of the beam profile in free space, and of the focal shift and image spot size in optical systems, are in good agreement with recent theoretical predictions.