The optical phase
We demonstrate a Bell state analyzer that operates directly on frequency mismatch. Based on electro-optic modulators and Fourier-transform pulse shapers, our quantum frequency processor design implements interleaved Hadamard gates in discrete frequency modes. Experimental tests on entangled-photon inputs reveal fidelities of
- Award ID(s):
- NSF-PAR ID:
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Page Range / eLocation ID:
- Article No. 280
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The optical phase
is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phase factor, , are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrum of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function, (where is the phase coherence length defined by ), and a probability density function of the phase increments for a given spatial lag. We analyze phase screens with turbulent ( ) and quadratic ( ) phase structure functions and with normally distributed (i.e., Gaussian) versus Laplacian phase increments. We find that there is a pronounced bump in each of the four phase-factor spectra . The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs at . The bump is unrelated to the well-known “Hill bump” and is not caused by diffraction effects. It is solely a characteristic of the refractive-index statistics represented by the respective phase screen. We show that the second-order statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-order counterparts.
We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the
th input carrying a phase delay of . The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay ; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., , or ); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% for ), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for to 122 nm for ), and (c) increased crosstalk within the C-band (from to when the tunable range increases from 2 to 4).
We report on spectroscopic measurements on the
transition in neutral europium-151 and europium-153 at 459.4 nm. The center of gravity frequencies for the 151 and 153 isotopes, reported for the first time in this paper, to our knowledge, were found to be 652,389,757.16(34) MHz and 652,386,593.2(5) MHz, respectively. The hyperfine coefficients for the state were found to be , and , , which all agree with previously published results except for A(153), which shows a small discrepancy. The isotope shift is found to be 3163.8(6) MHz, which also has a discrepancy with previously published results.
By discretizing an argument of Kislyakov, Naor and Schechtman proved that the 1-Wasserstein metric over the planar grid
has -distortion bounded below by a constant multiple of . We provide a new “dimensionality” interpretation of Kislyakov’s argument, showing that if is a sequence of graphs whose isoperimetric dimension and Lipschitz-spectral dimension equal a common number , then the 1-Wasserstein metric over has -distortion bounded below by a constant multiple of . We proceed to compute these dimensions for -powers of certain graphs. In particular, we get that the sequence of diamond graphs has isoperimetric dimension and Lipschitz-spectral dimension equal to 2, obtaining as a corollary that the 1-Wasserstein metric over has -distortion bounded below by a constant multiple of . This answers a question of Dilworth, Kutzarova, and Ostrovskii and exhibits only the third sequence of -embeddable graphs whose sequence of 1-Wasserstein metrics is not -embeddable.
The use of multispectral geostationary satellites to study aquatic ecosystems improves the temporal frequency of observations and mitigates cloud obstruction, but no operational capability presently exists for the coastal and inland waters of the United States. The Advanced Baseline Imager (ABI) on the current iteration of the Geostationary Operational Environmental Satellites, termed the
Series (GOES-R), however, provides sub-hourly imagery and the opportunity to overcome this deficit and to leverage a large repository of existing GOES-R aquatic observations. The fulfillment of this opportunity is assessed herein using a spectrally simplified, two-channel aquatic algorithm consistent with ABI wave bands to estimate the diffuse attenuation coefficient for photosynthetically available radiation, . First, an in situABI dataset was synthesized using a globally representative dataset of above- and in-water radiometric data products. Values of were estimated by fitting the ratio of the shortest and longest visible wave bands from the in situABI dataset to coincident, in situ data products. The algorithm was evaluated based on an iterative cross-validation analysis in which 80% of the dataset was randomly partitioned for fitting and the remaining 20% was used for validation. The iteration producing the median coefficient of determination ( ) value (0.88) resulted in a root mean square difference of , or 8.5% of the range in the validation dataset. Second, coincident mid-day images of central and southern California from ABI and from the Moderate Resolution Imaging Spectroradiometer (MODIS) were compared using Google Earth Engine (GEE). GEE default ABI reflectance values were adjusted based on a near infrared signal. Matchups between the ABI and MODIS imagery indicated similar spatial variability ( ) between ABI adjusted blue-to-red reflectance ratio values and MODIS default diffuse attenuation coefficient for spectral downward irradiance at 490 nm, , values. This work demonstrates that if an operational capability to provide ABI aquatic data products was realized, the spectral configuration of ABI would potentially support a sub-hourly, visible aquatic data product that is applicable to water-mass tracing and physical oceanography research.