Far field of binary phase gratings with errors in the height of the strips

Diffraction gratings are not always ideal but, due to the fabrication process, several errors can be produced. In this work we show that when the strips of a binary phase diffraction grating present certain randomness in their height, the intensity of the diffraction orders varies with respect to that obtained with a perfect grating. To show this, we perform an analysis of the mutual coherence function and then, the intensity distribution at the far field is obtained. In addition to the far field diffraction orders, a "halo" that surrounds the diffraction order is found, which is due to the randomness of the strips height.

Binary gratings with random heights

We analyze the far-field intensity distribution of binary phase gratings whose strips present certain randomness in their height. A statistical analysis based on the mutual coherence function is done in the plane just after the grating. Then, the mutual coherence function is propagated to the far field and the intensity distribution is obtained. Generally, the intensity of the diffraction orders decreases in comparison to that of the ideal perfect grating. Several important limit cases, such as low- and high-randomness perturbed gratings, are analyzed. In the high-randomness limit, the phase grating is equivalent to an amplitude grating plus a “halo.” Although these structures are not purely periodic, they behave approximately as a diffraction grating.

Diffraction by random Ronchi gratings

In this work, we obtain analytical expressions for the near-and far-field diffraction of random Ronchi diffraction gratings where the slits of the grating are randomly displaced around their periodical positions. We theoretically show that the effect of randomness in the position of the slits of the grating produces a decrease of the contrast and even disappearance of the self-images for high randomness level at the near field. On the other hand, it cancels high-order harmonics in far field, resulting in only a few central diffraction orders. Numerical simulations by means of the Rayleigh–Sommerfeld diffraction formula are performed in order to corroborate the analytical results. These results are of interest for industrial and technological applications where manufacture errors need to be considered.

A bright z=5.2 lensed submillimeter galaxy in the field of Abell 773 HLSJ091828.6+514223

During our Herschel Lensing Survey (HLS) of massive galaxy clusters, we have discovered an exceptionally bright source behind the z = 0.22 cluster Abell 773, which appears to be a strongly lensed submillimeter galaxy (SMG) at z = 5.2429. This source is unusual compared to most other lensed sources discovered by Herschel so far, because of its higher submm flux (∼200 mJy at 500 μm) and its high redshift. The dominant lens is a foreground z = 0.63 galaxy, not the cluster itself. The source has a far-infrared (FIR) luminosity of L_FIR = 1.1 × 10^14/μ L_⨀, where μ is the magnification factor, likely ∼11. We report here the redshift identification through CO lines with the IRAM-30 m, and the analysis of the gas excitation, based on CO(7–6), CO(6–5), CO(5–4) detected at IRAM and the CO(2–1) at the EVLA. All lines decompose into a wide and strong red component, and a narrower and weaker blue component, 540 km s^−1 apart. Assuming the ultraluminous galaxy (ULIRG) CO-to-H_2 conversion ratio, the H_2 mass is 5.8×10^11/μ M_⨀, of which one third is in a cool component. From the CI(^3P_2−^3 P_1) line we derive a C_I/H_2 number abundance of 6 × 10^−5 similar to that in other ULIRGs. The H_2O_p(2, 0, 2−1, 1, 1) line is strong only in the red velocity component, with an intensity ratio I(H_2O)/I(CO) ∼ 0.5, suggesting a strong local FIR radiation field, possibly from an active nucleus (AGN) component. We detect the [NII]205 μm line for the first time at high-z. It shows comparable blue and red components, with a strikingly broad blue one, suggesting strong ionized gas flows.