Number Of Spatial Modes Research Articles

Coupling to multi-mode waveguides with space-time shaped free-space pulses

Guided wave optics, including most prominently fiber optics and integrated photonics, very often considers only one or very few spatial modes of the waveguides. Despite being known and utilized for decades, multi-mode guided wave optics is currently rapidly increasing in sophistication in parallel with technological improvements and advancing simulation tools. The physics of multi-mode interactions are usually driven by some initial energy distribution in a number of spatial modes. In this work we introduce how, with free-space input beams having space-time couplings, the different modes can be excited with different complex frequency or time profiles. We cover fundamentals, the coupling with a few simple space-time aberrations, different waveguides, and a number of technical nuances. This concept of space-time initial conditions in multi-mode waveguides will provide yet another tool to study the rich nonlinear interactions in such systems.

Nonlinear impairment scaling in coupled-core multi-core fibers for space-division multiplexing

We study the nonlinear impairment scaling in coupled-core multi-core fibers (CC-MCFs) with core count by evaluating four typical CC-MCFs with different numbers of cores, which have been demonstrated promising for long-haul optical fiber transmissions, using the Gaussian-noise model. The results show that nonlinear signal degradation in CC-MCFs with more cores becomes significantly weaker, which would be of great interest to ultralong-haul transmission in CC-MCFs. We further analyze how the fiber loss, differential group delay and effective mode field area impact on the trend. Moreover, we compare CC-MCFs and few-mode fibers with the same number of spatial modes in terms of nonlinear impairment and find that CC-MCFs tend to achieve better nonlinear performance. It is also shown that few-mode fibers operated in strong coupling regime are quite promising for long-haul transmission.

Spatiotemporal supermodes: Rapid reduction of spatial coherence in highly multimode lasers

Spatial coherence quantifies spatial field correlations over time, and is one of the fundamental properties of light. Here we investigate the spatial coherence of highly multimode lasers in the regime of short time scales. Counter intuitively, we show that in this regime, the temporal (longitudinal) modes play a crucial role in spatial coherence reduction. To evaluate the spatial coherence we measured the temporal dynamics of speckle fields generated by a highly multimode laser with over $10^5$ lasing spatial (transverse) modes, and examined the dependence of speckle contrast on the exposure time of the detecting device. We show that in the regime of short time scale, the spatial and temporal modes interact to form spatio-temporal supermodes, such that the spatial degrees of freedom are encoded onto the temporal modes. As a result, the speckle contrast depends on the number of temporal modes, and the degree of spatial coherence is reduced and the speckle contrast is suppressed. In the regime of long times scale, the supermodes are no longer a valid representation of the laser modal structure. Consequently, the spatial coherence is independent of the temporal modes, and the classical result, where the speckle contrast is suppressed as the number of spatial modes, is obtained. Due to this new spatio-temporal mechanism, highly multimode lasers can be used for speckle suppression in high-speed full-field imaging applications, as we demonstrate here for imaging of a fast moving object.

A novel semiconductor-based, fully incoherent amplified spontaneous emission light source for ghost imaging

Initially, ghost imaging (GI) was demonstrated with entangled light from parametric down conversion. Later, classical light sources were introduced with the development of thermal light GI concepts. State-of-the-art classical GI light sources rely either on complex combinations of coherent light with spatially randomizing optical elements or on incoherent lamps with monochromating optics, however suffering strong losses of efficiency and directionality. Here, a broad-area superluminescent diode is proposed as a new light source for classical ghost imaging. The coherence behavior of this spectrally broadband emitting opto-electronic light source is investigated in detail. An interferometric two-photon detection technique is exploited in order to resolve the ultra-short correlation timescales. We thereby quantify the coherence time, the photon statistics as well as the number of spatial modes unveiling a complete incoherent light behavior. With a one-dimensional proof-of-principle GI experiment, we introduce these compact emitters to the field which could be beneficial for high-speed GI systems as well as for long range GI sensing in future applications.

Control of the size of the coherence area in entangled twin beams

We study the effect of a change in size and spatial profile of the pump beam in an atomic-based four-wave mixing process on the size of the coherence area of the generated entangled twin beams. We perform experiments and develop a theoretical model to obtain a measure of the linear extent or ``radius'' of the coherence area from noise measurements of the twin beams as a function of transmission through a variable size slit. Our results show that an increase in the size of the pump reduces the size of the coherence area. More interestingly, we find that the use of a flat-top pump beam of the same size as a Gaussian pump beam leads to a reduction by a factor of more than 2 in the linear extent of the coherence area. This in turn leads to an increase by a factor of more than 4 in the number of spatial modes that make up the twin beams and a resolution enhancement of the entangled images that can be generated with the four-wave mixing process.

Backscatter analysis based algorithms for increasing transmission through highly scattering random media using phase-only-modulated wavefronts.

Recent theoretical and experimental advances have shed light on the existence of so-called "perfectly transmitting" wavefronts with transmission coefficients close to 1 in strongly backscattering random media. These perfectly transmitting eigen-wavefronts can be synthesized by spatial amplitude and phase modulation. Here, we consider the problem of transmission enhancement using phase-only-modulated wavefronts. Motivated by biomedical applications, in which it is not possible to measure the transmitted fields, we develop physically realizable iterative and non-iterative algorithms for increasing the transmission through such random media using backscatter analysis. We theoretically show that, despite the phase-only modulation constraint, the non-iterative algorithms will achieve at least about 25π%≈78.5% transmission with very high probability, assuming that there is at least one perfectly transmitting eigen-wavefront and that the singular vectors of the transmission matrix obey the maximum entropy principle such that they are isotropically random. We numerically analyze the limits of phase-only-modulated transmission in 2D with fully spectrally accurate simulators and provide rigorous numerical evidence confirming our theoretical prediction in random media, with periodic boundary conditions, that is composed of hundreds of thousands of non-absorbing scatterers. We show via numerical simulations that the iterative algorithms we have developed converge rapidly, yielding highly transmitting wavefronts while using relatively few measurements of the backscatter field. Specifically, the best performing iterative algorithm yields ≈70% transmission using just 15-20 measurements in the regime, where the non-iterative algorithms yield ≈78.5% transmission, but require measuring the entire modal reflection matrix. Our theoretical analysis and rigorous numerical results validate our prediction that phase-only modulation with a given number of spatial modes will yield higher transmission than amplitude and phase modulation with half as many modes.

Error performance analysis for FSO systems with diversity reception and optical preamplification over gamma–gamma atmospheric turbulence channels

The error performance was investigated of free-space optical (FSO) systems that use optical preamplifiers and diversity reception in turbulent atmosphere with gamma–gamma distribution. More specifically, assuming that the dominant sources of the receiver noises are the background light and amplifier spontaneous emission noises, we develop an exact bit-error-rate (BER) expression for binary pulse position modulation (BPPM) by a moment-generating function (MGF) derivative-based method. To gain more insight, we also derive a closed-form asymptotic BER expression for BPPM at high received optical power, by which we obtain the diversity and coding gains of the considered systems. Our analytical results lead to the observations that the attained diversity gain only changes with the gamma-gamma distribution parameters and the number of spatial modes collected by the receiver, while independent on the number of temporal modes passed by the optical preamplifiers. We verify the analytical results by Monte Carlo simulations.

Nonbinary LDPC-Coded Mode-Multiplexed Coherent Optical OFDM 1.28-Tbit/s 16-QAM Signal Transmission Over 2000 km of Few-Mode Fibers With Mode-Dependent Loss

We demonstrate the possibility of nonbinary LDPC-coded mode-multiplexed coherent optical OFDM 1.28-Tbit/s 16-QAM signal transmission over 2000 km of few-mode fiber (FMF) with mode-dependent loss (MDL) by using an advanced mode-coupling compensation scheme. The performance of proposed coded-modulation scheme is evaluated for different number of spatial modes. The simulation results indicate that the MDL is the predominant effect in the long-haul optical transmission based on FMFs. Different pilot-aided OFDM based compensation methods are studied, and it has been found that minimum mean-square estimation with linear interpolation method is the most robust against mode coupling and MDL. We also show that the nonbinary LDPC-coded modulation provides about 1 dB improvement over binary LDPC-coded modulation (16 QAM OFDM and MDL of 25 dB). Finally, we study the degradation of increasing the number of modes and investigate the proposed scheme for different MDL values in both fourand eight-mode fibers.

Characterization of deformable mirrors for spherical aberration correction in optical sectioning microscopy

In this paper we describe the wavefront aberrations that arise when imaging biological specimens using an optical sectioning microscope and generate simulated wavefronts for a planar refractive index mismatch. We then investigate the capability of two deformable mirrors for correcting spherical aberration at different focusing depths for three different microscope objective lenses. Along with measurement and analysis of the mirror influence functions we determine the optimum mirror pupil size and number of spatial modes included in the wavefront expansion and we present measurements of actuator linearity and hysteresis. We find that both mirrors are capable of correcting the wavefront aberration to improve imaging and greatly extend the depth at which diffraction limited imaging is possible.

Scaling of space–time modes with Reynolds number in two-dimensional turbulence

It has been estimated that the number of spatial modes (or nodal values) required to uniquely determine a two-dimensional turbulent flow at a specific time is finite, and is bounded by Re4/3 for forced turbulence and Re for decaying turbulence. The usual computational estimate of the number of space–time modes required to calculated decaying two-dimensional turbulence is ${\cal N}\sim{Re}^{3/2}$. These bounds neglect intermittency, and it is not known how sharp they are. In this paper we use an adaptive multi-scale wavelet collocation method to estimate for the first time the number of space–time computational modes ${\cal N}$ necessary to represent two-dimensional decaying turbulence as a function of Reynolds number. We find that ${\cal N}\sim{Re}^{0.9}$ for 1260 ≤ Re ≤ 40400 over many eddy turn-over times, and that temporal intermittency is stronger than spatial intermittency. The spatial modes alone scale like Re0.7. The β-model then implies that the spatial fractal dimension of the active regions is 1.2, and the temporal fractal dimension is 0.3. These results suggest that the usual estimates are not sharp for adaptive numerical simulations. The relatively high compression confirms the importance of intermittency and encourages the search for reduced mathematical models of two-dimensional turbulence (e.g. in terms of coherent vortices).

Squeezed-light source for superresolving microscopy.

We propose a source of multimode squeezed light that can be used for superresolving microscopy. This source is an optical parametric amplifier with a properly chosen diaphragm on its output and a Fourier lens. We demonstrate that such an arrangement produces squeezed prolate spheroidal waves that are the eigenmodes of the optical imaging scheme used in microscopy and discuss the conditions of the degree of squeezing and of the number of spatial modes in illuminating light.

Nonlinear Analysis of a Cantilever Pipe Containing Pulsatile Flow

In this paper we investigate the nonlinear dynamics of a cantilever elastic pipe that contains pulsatile flow. The equation of motion was derived by using Hamiltonian action function. We use Galerkin's technique to include only finite number of spatial modes in the solution. The stability chart of the time-varying system was computed in the space of the relative perturbation amplitude of the flow velocity and dimensionless forcing frequency using an efficient numerical method based on Chebyshev polynomials. In the near of some critical regions bifurcation diagrams were also computed which show secondary Hopf bifurcations and phase locking followed by chaotic motion.

Incomplete phase conjugation through a random-phase screen I Theory

We investigate phase conjugation of a laser beam aberrated by a thin random-phase screen when the wave front is incompletely sampled by the phase conjugate mirror (PCM). We derive expressions for the average intensity after a double pass of the phase screen both when the PCM is aperture limited and when it is limited by its number of spatial modes.