non-Kolmogorov Power Law Research Articles

Impacts of low-order aberrations on capacity of orbital-angular-momentum quantum states

We use Hypergeometric Gaussian-II (HyGG-II) modes to investigate the impacts of non-Kolmogorov atmospheric turbulence on the Holevo channel capacity of a quantum communication scheme. The capacity of HyGG-II modes can be higher than that of Laguerre–Gaussian modes via modulating the hollowness parameter. The influences of low-order turbulence aberrations including tilt, defocus, astigmatism, and coma on the capacity are also explored. Generally, tilt aberration dominates among all low-order aberrations and defocus and astigmatism aberrations are always negligible. By contrast, the effect of coma aberration can be enhanced to be non-negligible when the turbulence strength or the channel zenith angle is enhanced. We also show that only the total and tilt aberrations are sensitive to the non-Kolmogorov power-law exponent. Our results may contribute to the quantum optical communication as well as aberration compensation in turbulent channels utilizing the novel family of vortex beams.

Performance of a free-space optical communication system employing receive diversity techniques in anisotropic atmospheric non-Kolmogorov turbulence

In this paper, bit error rate (BER) performance of a free-space optical communication (FSOC) system operating in anisotropic non-Kolmogorov weak turbulence is investigated together with the spatial diversity techniques. The spatial diversity techniques are implemented as maximum ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) and applied to the receiver. The propagating beam is the Gaussian beam wave, and the modulation scheme is binary phase-shift keying (BPSK). Results are obtained for various parameters such as the anisotropy factor, non-Kolmogorov power law exponent, photodetector responsivity, equivalent load resistor, electronic bandwidth, Gaussian beam radius, wavelength, propagation distance, and turbulence structure constant. It is found that the spatial diversity technique used at the receiver causes significant improvement in the performance of an FSOC system under the conditions of anisotropic non-Kolmogorov atmospheric turbulence. It is also observed that BER performance improves as the atmospheric turbulence becomes more anisotropic. Among the spatial diversity techniques, SC is inferior to EGC and EGC is inferior to MRC in terms of BER performance.

Oceanic non-Kolmogorov optical turbulence and spherical wave propagation.

Light propagation in turbulent media is conventionally studied with the help of the spatio-temporal power spectra of the refractive index fluctuations. In particular, for natural water turbulence several models for the spatial power spectra have been developed based on the classic, Kolmogorov postulates. However, as currently widely accepted, non-Kolmogorov turbulent regime is also common in the stratified flow fields, as suggested by recent developments in atmospheric optics. Until now all the models developed for the non-Kolmogorov optical turbulence were pertinent to atmospheric research and, hence, involved only one advected scalar, e.g., temperature. We generalize the oceanic spatial power spectrum, based on two advected scalars, temperature and salinity concentration, to the non-Kolmogorov turbulence regime, with the help of the so-called "Upper-Bound Limitation" and by adopting the concept of spectral correlation of two advected scalars. The proposed power spectrum can handle general non-Kolmogorov, anisotropic turbulence but reduces to Kolmogorov, isotropic case if the power law exponents of temperature and salinity are set to 11/3 and anisotropy coefficient is set to unity. To show the application of the new spectrum, we derive the expression for the second-order mutual coherence function of a spherical wave and examine its coherence radius (in both scalar and vector forms) to characterize the turbulent disturbance. Our numerical calculations show that the statistics of the spherical wave vary substantially with temperature and salinity non-Kolmogorov power law exponents and temperature-salinity spectral correlation coefficient. The introduced spectrum is envisioned to become of significance for theoretical analysis and experimental measurements of non-classic natural water double-diffusion turbulent regimes.

On channel capacity of FSO communication systems in anisotropic non-Kolmogorov strong turbulent atmosphere.

Average channel capacity of free space optical (FSO) communication systems using a Gaussian beam with the intensity modulation and direct detection technique is investigated in anisotropic non-Kolmogorov strong turbulent atmosphere. The channel model is selected as gamma-gamma distribution, which is valid for strong turbulence. Obtained results show that anisotropy in both the horizontal and vertical affects the average channel capacity of an FSO communication system positively. Average channel capacity increases with the increase of photodetector quantum efficiency, wavelength, Gaussian beam source size, inner scale length, and non-Kolmogorov power law exponent. An increase of link length, turbulence structure constant, and noise variance causes a decrease in average channel capacity. The average channel capacity falls very little with the increase of outer scale length.

Average channel capacity in anisotropic atmospheric non-Kolmogorov turbulent medium

The average channel capacity of a free space optical (FSO) communication system running an intensity modulated Gaussian beam is examined in anisotropic non-Kolmogorov atmospheric weak turbulence based on Rytov variance. Results are obtained by employing the log-normal distribution of irradiance fluctuations corresponding to weak turbulence regime. Our results show that average channel capacity increases together with the increase in anisotropy factor in x and y direction, non-Kolmogorov power law exponent, quantum efficiency of photo detector, Gaussian beam source size and the inner scale length. However, the average channel capacity is found to decrease when turbulence strength, link length and noise variance increase.

Error performance of optical wireless communication systems exercising BPSK subcarrier intensity modulation in non-Kolmogorov turbulent atmosphere

Abstract Subcarrier intensity modulation (SIM) scheme is preferred due to efficient bandwidth usage superiority over other modulation techniques such as on–off keying (OOK), pulse position modulation (PPM). In this paper, we investigate the bit error rate (BER) performance of optical wireless communication (OWC) system using binary phase shift keying (BPSK) SIM in non-Kolmogorov turbulent atmosphere. We pay attention to the weak turbulence conditions by using Rytov approximation and considering that the receiver is a PIN photodetector. Propagating beam type is Gaussian. It is seen that BER performance of the BPSK SIM OWC is significantly affected from non-Kolmogorov power law exponent, load resistor, responsivity of the PIN photodetector, bandwidth, beam source size, turbulence strength and noise factor.

M-ary pulse position modulation performance in non-Kolmogorov turbulent atmosphere.

The performance of atmospheric optical wireless communication systems in terms of the bit error rate (BER) is investigated when a Gaussian laser beam propagating in non-Kolmogorov turbulence is M-ary pulse-position-modulated (PPM). BER variations against the changes in different parameters such as the non-Kolmogorov power law exponent, symbol number, data bit rate, avalanche photodetector gain, equivalent load resistor, detector quantum efficiency, wavelength, turbulence structure constant, and the Gaussian beam source size are analyzed. Making the design of the PPM optical wireless communication system able to operate in a non-Kolmogorov atmosphere will give better BER performance if the parameters are taken into account in line with the trends presented in our results.

Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence.

Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications.

Fiber coupling efficiency in non-Kolmogorov satellite links

Behavior of the fiber coupling efficiency in non-Kolmogorov satellite links is investigated. Examining the fiber coupling efficiency of downlink versus the non-Kolmogorov power law exponent for different rms wind speeds, zenith angles, receiver lens diameters, structure constants and the wavelengths, the fiber coupling efficiency is found to decrease when the non-Kolmogorov power law exponent increases. At a fixed non-Kolmogorov power law exponent, the fiber coupling efficiency of downlink is found to decrease as the rms wind speed, the zenith angle, the receiver lens diameter or the structure constant increases and the wavelength decreases. For any non-Kolmogorov satellite downlink, the reduction of coherence length will make the optimum design parameter larger. And when the fiber coupling efficiency is considered in the satellite uplinks, the effect of non-Kolmogorov turbulence can be neglected.

Introducing the concept of anisotropy at different scales for modeling optical turbulence.

In this paper, the concept of anisotropy at different atmospheric turbulence scales is introduced. A power spectrum and its associated structure function with inner and outer scale effects and anisotropy are also shown. The power spectrum includes an effective anisotropic parameter ζ(eff) to describe anisotropy, which is useful for modeling optical turbulence when a non-Kolmogorov power law and anisotropy along the direction of propagation are present.

Application of equivalent structure constant in scintillations and BER found for non-Kolmogorov spectrum

The evaluation of system parameters in the non-Kolmogorov turbulent atmosphere involves the structure constant valid at the relevant non-Kolmogorov power law exponent. In some of the existing results, the comparisons of system parameters found under the Kolmogorov and non-Kolmogorov turbulences were made by using the same structure constant for all the power law exponents of the non-Kolmogorov spectrum. In this paper, we evaluate the scintillations and the average Bit Error Rate (〈BER〉) for the flat-topped and the annular beams in non-Kolmogorov turbulence, this time using the equivalent structure constant which is now different for all the power law exponents. It is observed that the scintillations and the 〈BER〉 show completely different behaviour when evaluated with the equivalent structure constant as compared to evaluations with constant structure constant.

Coherence length in non-Kolmogorov satellite links

Behavior of the coherence length in non-Kolmogorov satellite links is investigated. Equivalent structure constants for non-Kolmogorov spectra are employed in order to make relevant comparisons for different non-Kolmogorov power law exponents. Examining the coherence length versus the non-Kolmogorov power law exponent for different rms wind speeds, zenith angles, link lengths, structure constants and the wavelengths, the coherence length is found to decrease when the non-Kolmogorov power law exponent increases. At a fixed non-Kolmogorov power law exponent, the coherence length is found to decrease as the rms wind speed, the zenith angle or the structure constant increases and the wavelength decreases. As the link length increases, the coherence length decreases for power law exponent values smaller than that for the Kolmogorov case. However, an increase in the link length seems not to cause the coherence length to vary appreciably at power law exponent values larger than the Kolmogorov case power law exponent.

Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence: reply

In our recent publication, we have examined the intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence [J. Opt. Soc. Am. A29, 169 (2012)10.1364/JOSAA.29.000169JOAOD60740-3232] in which our comparison of the scintillation indices in the Kolmogorov and in various non-Kolmogorov turbulences was based on the same structure constant, no matter what power law the non-Kolmogorov spectrum takes. In such choice of the fixed structure constant, which is also being used by many researchers in the field [Opt. Express18, 451 (2010)10.1364/OE.18.000451OPEXFF1094-4087; Proc. SPIE6747, 67470B (2007)10.1117/12.737118PSISDG0277-786X; Opt. Commun.285, 880 (2012)], we have found that the variation of the scintillation index against non-Kolmogorov power law exhibits a peak at the worst power law, which happens to be smaller than the Kolmogorov power law of 11/3. Charnotskii commented [J. Opt. Soc. Am. A.29, 1838 (2012)JOAOD60740-3232] on our paper. In this paper, in our to reply to Charnotskii’s comment, we have re-evaluated the scintillation index of flat-topped beam in non-Kolmogorov weak turbulence by employing our recently reported equivalent structure constant [Opt. Lett.36, 4554 (2011)10.1364/OL.36.004554OPLEDP0146-9592] and re-compared the intensity fluctuations in Kolmogorov and in non-Kolmogorov turbulences. As the result of such re-comparison, the worst power law is observed to disappear.

Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence

Results obtained on the intensity fluctuations of flat-topped Gaussian beams in weakly turbulent non-Kolmogorov horizontal atmospheric optics links are represented. Effects on the scintillation index of the power law α that describes the non-Kolmogorov spectrum are examined. Our results correctly reduce to the existing intensity fluctuations of flat-topped beams in Kolmogorov turbulence. Variation of the scintillation index against non-Kolmogorov power law α exhibits a peak at the worst power law α(w), which happens to be smaller than the Kolmogorov power law of 11/3. If the power law is smaller (larger) than α(w), increase in α will increase (decrease) the intensity fluctuations. Evaluation of the scintillation index at the worst power law results in smaller fluctuations for a Gaussian beam at short propagation distances; however, at long propagation distances flatter beams happen to possess smaller fluctuations. The scintillation change versus the source size follows a similar trend regardless whether the flat-topped beam propagates in a Kolmogorov or non-Kolmogorov medium.