Cw Propagation Research Articles

Generation of self-induced-transparency gap solitons by modulational instability in uniformly doped fiber Bragg gratings

We consider the continuous-wave (cw) propagation through a fiber Bragg grating that is uniformly doped with two-level resonant atoms. Wave propagation is governed by a system of nonlinear coupled-mode Maxwell-Bloch (NLCM-MB) equations. We identify modulational instability (MI) conditions required for the generation of ultrashort pulses in both anomalous and normal dispersion regimes. From a detailed linear stability analysis, we find that the atomic detuning frequency has a strong influence on the MI. That is, the atomic detuning frequency induces nonconventional MI sidebands at the photonic band gap (PBG) edges and near the PBG edges. Especially in the normal dispersion regime, MI occurs without any threshold condition, which is in contrast with that of conventional fiber Bragg gratings. We also perform a numerical analysis to solve the NLCM-MB equations. The numerical results of the prediction of both the optimum modulation wave number and the optimum gain agree well with that of the linear stability analysis. Another main result of the present work is the prediction of the existence of both bright and dark self-induced transparency gap solitons at the PBG edges.

Turbulence-induced square-root broadening of the Raman fiber laser output spectrum

The output characteristics of the conventional one-stage Raman fiber laser (RFL) are described in an optical wave turbulence formalism. Simple analytical expressions describing RFL output power and its spectral shape are presented, and square-root law for the output spectrum broadening law has been discovered. The indications of the turbulent-like spectral broadening in other types of cw fiber lasers and propagation phenomena in fibers are also discussed.

Generation of Bragg solitons through modulation instability in a Bragg grating structure

In this article, we consider the continuous wave (cw) propagation through the nonlinear periodic structure that consists of alternating layers of both positive and negative Kerr coefficients along the propagation direction. We investigate the modulational instability (MI) conditions required for the generation of ultrashort pulses for the nonlinearity management system. We study the occurrence of MI at the top and bottom edges of the photonic band gap (PBG) where the forward and backward propagating waves are strongly coupled because of the presence of the grating structure. We also study the MI when cw is detuned from the edges of the PBG into the anomalous and normal dispersion regimes. In addition, we discuss the existence of gap solitons for the nonlinearity management system in the upper and lower branches of the dispersion curve through the MI gain spectra. We observe the generation of higher order solitons in the nonlinear periodic structure when the input power is increased beyond a certain critical level. Finally, we discuss the generation of higher order Bragg grating solitons through the intensity evolution of the forward and backward propagating fields.

Backscattering in stratified time-dependent random media—CW and narrow-band pulse propagation

We consider backscattering in a random stratified medium where the wave-speed fluctuations depend on time and on the range coordinate, which is normal to the planes of stratification. For the limit where the correlation time is shorter than the mean scattering time, we first derive radiation-transport equations that govern the range evolution of the spectra of the ensemble-averaged forward-and back-propagating components of the field and their bichromatic coherence functions. The latter are governed by integro-differential equations that account for the broadening of the signal spectra due to the time dependence of the random fluctuations. When the correlation time is longer than both the period of the radiating signal and the travel time of a wavefront across a range correlation length, the spectrum of the radiation due to a monochromatic CW excitation remains confined to a narrow band over extensive ranges. This permits a quasi-monochromatic approximation, whereby the integro-differential equations produce ordinary differential equations that govern the quantities of interest. We use this approximation to track the power flux associated with the propagation of a narrow-band pulse.

Characterizations of the internal waves and their effects on sound propagation in the central area of the Yellow Sea

In the late summer of 1996, a joint China–USA experiment was performed in the central area of the Yellow Sea. The analysis of the data from thermistor string and CTD reveals that (1) there was intense internal wave activity in the experimental area, and the isotherm displacement induced by internal waves could be as large as 8 m; (2) the power spectrum of the vertical displacement had a significant peak near the M2 tide frequency, and was approximately proportional to ω−3/2; and (3) the internal wave field was dominated by first-order modes. Based on the observed properties of the internal waves, a model of the induced sound-speed distribution is developed, and computer simulations are conducted for cw and wideband signal propagation by using the PE method. Numerical results are presented for comparison with the experimental data. [Work supported by NNSF of China and ONR of USA.]

Experimental observation and statistics of multipath from terrain with application to overland height finding

Data is presented from an airborne experiment designed to evaluate electromagnetic pulse scattering from a variety of terrain types for the application of overland height finding. The one-way propagation data was collected at ultrahigh frequency (UHF) and very high frequency (VHF) frequencies using a 3-MHz pulsed CW signal with the radars mounted on two aircraft. A statistical analysis of the data shows that the probability of a detectable ground reflection and the strength of that reflection vary as a function of the terrain roughness. We introduce a broad-band synthesis technique in which Fourier theory is used to generate a time-domain response from a CW propagation model. Results from this technique agree well with the experimental observations, but the lack of detailed terrain information does not allow exact reproduction of the fine details.

Simulation studies of narrow-band and cw acoustic propagation through a shallow-water internal wave

The effects of a shallow-water, solitary internal wave on cw and narrow-band acoustic propagation have been studied using computer simulations. Numerous observations have been made of solitary internal waves in shallow water. These internal waves travel along the near-surface thermocline for some distance without loss of coherence. Due to their prevalence, they have been cited as the likely cause of the anomalous effects observed in some recent shallow-water acoustic measurements. In order to test this hypothesis, computer simulations of acoustic propagation through an internal wave have been made using an ocean-acoustic PE propagation computer model (EFEPE), fast Fourier transformations (FFTs), and beamforming algorithms. A narrow band of frequencies was used with the center frequency at 250 Hz. The resulting frequency-dependent fields were then converted into the time domain via an FFT. Beamforming algorithms were used to analyze the field structure. Examples will be shown that contrast the internal wave effects on cw propagation and on narrow-band propagation. [Work supported by ONR and NRL.]

Nonlinear progressive wave equation model for transient and steady-state sound beams

NPE is a nonlinear progressive wave equation and associated computer code that yields a time domain solution for propagation in an acoustic waveguide. In the present study, the NPE equation is modified to describe axisymmetric sound beams in the paraxial approximation. The modified version of NPE is employed to describe three cases of radiation from a baffled piston: linear transient propagation, linear cw propagation, and nonlinear cw propagation. Alternative schemes to initialize the moving window that is convected by NPE are discussed for each type of problem. The linear transient signal or linear cw signal evaluated by NPE is compared to the direct prediction of the transient or steady-state Rayleigh integral. The nonlinear signal evaluated by NPE is compared to experimental data in the near and far field. The results show that NPE gives good results for all three propagation problems, in some cases at close regions where the paraxial approximation was previously believed to be inaccurate.

Remote sensing of seabed compressional wave attenuation from acoustic cw propagation experiments combined with the bottom shear modulus profiler (BSMP) database

As a result of recent ONR shallow water ARI, an accurate database of the compressional wave velocity, the shear wave velocity, and the density of the sediment for the continental shelves of Northeastern U.S. is available (Yamamoto and Trevorrow, in this conference). It has been shown that the model structures of acoustic waves propagating in these shallow waters are very accurately modeled using the BSMP database as compared with the cw propagation experiments [J. Acoust. Soc. Am. Suppl. 1 88, S106 (1990)]. In this paper, it is shown that the compressional wave attenuation within the seabed can be accurately determined from the wave-number energy spectra of cw propagation data from range-independent environments. The seabed geoacoustic data so obtained are then used in the modeling of acoustic cw propagation in range-dependent cases using Fred Tappert's PE code and compared with Bill Carey's experiments. Excellent agreements between model calculations and experiments are obtained, indicating the accuracy and stability of the combined BSMP-cw experiments for determination of seabed compressional wave attenuation in shallow water. [Work sponsored by ONR.]

A VLF propagation experiment off the coast of Oregon: Measurements and numerical predictions

The Naval Research and Development Activity (NORDA) recently conducted a very low-frequency (VLF) acoustic experiment in a sloping bottom environment off the coast of Oregon. A 16-element vertical hydrophone array was deployed in water depths of 200 and 400 m. An upslope and two cross slope explosive shot lines were completed. In addition, an upslope cw (15 Hz) tow was recorded. This paper uses the results of this experiment to investigate the importance of bottom shear and bathymetric variation on energy partitioning between water and ground paths. The measured data are compared with predictions from SAFARI, a range-independent model that allows conversion to shear energy in the bottom, and PE, an acoustic model that allows variable bathymetry. Two different PE codes are used, viz., IFDPE and a PE pulse code recently developed at NORDA (M. Collins), which allows for subbottom structure that is not necessarily parallel to the ocean bottom. Measured cw propagation loss and explosive shot record sections are compared with predicted results from both SAFARI and PE.

Probability density measurements for cw propagation in the Arctic ocean

An experimental investigation of signal amplitude and phase fluctuations under Arctic conditions has been conducted. The data were sampled from low‐frequency cw transmissions during the FRAM IV experiment in April 1982. The signals were generated at the Tristen ice camp and received at the FRAM IV ice camp located north of Spitzbergen. The average water depth along the propagation paths was 3000 m. The range was approximately 275 km. The 28 receivers were positioned along a vertical array at depths from 30 to 960 m. The single hydrophone data exhibited a high signal‐to‐noise ratio (⩾10 dB) and a high phase stability. The measured phase was modified by means of a frequency shift to compensate for relative platform motion. Histograms of the single hydrophone amplitude and phase were examined for goodness of fit to hypothetical density functions. Amplitude and phase distributions were consistent with a multipath fluctuation model, at the 0.05 level of significance. These densities are associated with a partially saturated process. They were first theoretically derived by P. N. Mikhalevsky [J. Acoust. Soc. Am. 72, 151–158 (1982)].

The uniform WKB normal mode code: Applications to cw and broadband propagation

The increased interest in the modeling of underwater acoustic signals which are time limited or possess significant frequency bandwidth has resulted in a variety of broadband propagation codes. However, these codes are typically limited in utility by extremely long run times or in accuracy by simplifying assumptions. The approach taken here it to use uniform asymptotic approximations to the normal modes of the sound channel to obtain both accuracy and numerical efficiency. These approximations are based on the WKB approach but include corrections for modes that turn near boundaries and near mode turning points. This uniform WKB model approach leads to further efficiencies in multiple frequency broadband or pulsed propagation. The accuracy of this approach and the importance of these corrections is first illustrated for a cw signal. Subsequent examples show accurate results for both broadband and time pulsed signals. Run time comparisons show reductions of two orders of magnitude in comparison to conventional broadband codes.

Depth dependence of the temporal characteristics of cw propagation in the Arctic Ocean

Previous work by P. Mikhalevsky [J. Acoust. Soc. Am. 70, 1717–1722 (1981)] investigated the temporal characteristics of cw signals propagating in the Arctic Ocean. The previous work was limited to receivers at a depth of 91 m. In this paper, the temporal characteristics will be extended to 28 hydrophones in a vertical array with depths from 30 to 960 m. The data were taken during the FRAM IV experiment in April 1982. The signals were generated at the Tristen ice camp and received at the FRAM IV ice camp located north of Spitzbergen. The range of approximately 275 km was over the Mid-Ocean Ridge; the average water depth along the path was 3000 m. Most of the data examined are at a high signal-to-noise ratio (> 10 dB) which makes it possible to study the temporal fluctuation and the statistics of the cw signals at different depths. By employing a mode filtering technique, the temporal dependence of the amplitude and phase of the lowest order mode has been investigated. The drift rates of the ice camps were negligible during the transmission periods and hence the results apply to transmission between essentially fixed stations.

Acoustic fluctuations on the space and time scale of large ocean eddies

As a rule, ocean acoustic propagation over several hundred kilometers, the space scale of a large eddy, will be by multipath. Also, in general, the multipath will be sufficiently complex that interference effects will introduce difficulties in relating cw propagation fluctuations to environmental processes. However, recent analytical and experimental results from a test of several months duration demonstrate that these difficulties can be overcome by a proper selection of source and receiver depths in the water column. The test results are at a frequency of 206 Hz and the range between source and receiver is in excess of 500 km. Quantitative results on acoustic transmission fluctuation will be presented on all time scales from a few minutes to several months.

Estimation of background ambient noise levels from the spectral analysis of time series with application to cw propagation-loss measurements

An application of percentile measurements is presented as a method for estimating background ambient noise levels from spectral density functions. The advantage of a percentile method over an average method is that it allows an accurate measure of background noise containing a sine wave, that is essentially independent of the sine-wave amplitude. This feature makes the percentile method very useful in the measurement of cw propagation loss, where it is frequently necessary to subtract an estimate of the background noise from a signal-plus-noise measurement, including the case when the noise contains sine waves close in frequency to the cw signal. A percentile-level estimate may be easily used to calculate an average level estimate for chi-square data and it is found that a percentile estimator is just as accurate and essentially just as stable as an average estimator. Theory based on chi-square statistics and experimental data from the ambient sound field in the deep ocean are shown to be in good agreement.

Estimation and interpretation of acoustic cw phase fluctuation spectra

A fundamental question exists regarding how well information about ocean processes can be extracted from a time series of cw acoustic phase and amplitude when the propagation channel consists of multiple acoustic paths. In this paper, it is shown that there are at least two multipath propagation conditions under which an acoustic cw propagation experiment can be used to measure properties of the sound-speed field and the ocean processes along the propagation path: narrow-band (frequency-modulation) path-length modulation of all paths, and wide-band (frequency-modulation) path-length modulation of a dominant path. A dominant path is one with power which exceeds the power on all other paths plus noise by at least 6 dB. Signal processing techniques for measuring the fluctuation spectra in both multipath situations are described and performance estimates are derived. The factors which limit how well information can be extracted are discussed.

Acoustic fluctuations using the parabolic profile

Calculations were performed using the normal‐mode solutions for the parabolic profile to determine the behavior of the acoustic field when either the axial or maximum profile sound speed was altered slightly from an unperturbed value. It was found that incrementing either the axial or maximum profile speed by small amounts produced a change in the focal length of the parabolic profile, which in turn caused a range‐dependent compression or expansion of the unperturbed acoustic field with no noticeable distortion for frequencies less than 400 Hz and range less than 550 km. Approximating the effect of the first‐mode semidiurnal internal tide by appropriate variations in axial velocity, this fact was used to show that for cw propagation between fixed source and fixed receiver, the fluctuation in acoustic amplitude produced by the internal tide can be obtained by sampling the amplitude function for the unperturbed profile a distance Δr either side of the range in question, where Δr is the distance the unperturbed acoustic field is shifted due to the change in axial speed produced by the internal tide. For a moving source, a range‐dependent critical source speed was determined such that for source speeds equal to or less than the critical speed, the effect of the internal tide predominates as a source of acoustic fluctuations, while for source speeds greater than this critical speed the effect of source motion is paramount.

Long-range low-frequency CW propagation in the deep ocean: Antigua-Newfoundland

The acoustic fields of shallow sources operating at 13.89 and 111.1 Hz were measured on a deep sound-channel hydrophone located near Antigua, W. I. The sources were towed away from the receiver along a great circle track to a maximum range of 2800 km. Convergence zones were observed at long range, and their positions were found to be frequency dependent. The average rate of increase of transmission loss with increasing range was less than that for cylindrical spreading. The propagation characteristics are explained in terms of the measured oceanographic features.

The Effects of Horizontally Varying Internal Wave Fields on Multi-Path Interference of Refracted-Refracted Propagation about the Deep Sound Channel Axis

Fluctuations of CW signals transmitted through real ocean paths are characterized by smooth slow variations in phase and rapid noise-like variations in amplitude. These variations are the result of internal waves, which perturb the sound-speed field and thereby produce time-varying multi-path interference. This study is concerned with modeling the effects of horizontal and vertical variations in the sound-speed field on multi-path interference of CW propagation for the particular case of refracted-refracted ray paths. The vertical sound-speed profile is approximated by two layers of linear gradient and arbitrary horizontal variations are introduced by numerical methods. The travel times along individual ray paths are influenced by fluctuations of the internal wave fields with horizontal scales which are (1) approximately equal to the cycle distance of the ray paths or (2) greater than several cycle distances of the ray. Both types of disturbances induce multi-path interference but the later also produces phase shifts for all ray paths. The model approximates fixed-system experiments on CW propagation between Eleuthera and Bermuda. We show that horizontally invariant internal tide cannot cause both phase and amplitude statistics which are consistant with experiment.

Multipath Signal Interference in Time-Dependent Propagation Channels

Formulas previously derived for multipath CW propagation in time-dependent channels are shown to be special cases of corresponding formulas for repreated-pulse propagation. General expressions that relate the CW and repeated-pulse average power outputs in time-dependent channels are derived.