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1. 𝐿₁-distortion of Wasserstein metrics: A tale of two dimensions

   https://doi.org/10.1090/btran/143  

   Baudier, F. ; Gartland, C. ; Schlumprecht, Th. ( August 2023 , Transactions of the American Mathematical Society, Series B)

   By discretizing an argument of Kislyakov, Naor and Schechtman proved that the 1-Wasserstein metric over the planar grid$\{0,1,\dots , n\}^2$has$L_1$-distortion bounded below by a constant multiple of$\sqrt {\log n}$. We provide a new “dimensionality” interpretation of Kislyakov’s argument, showing that if$\{G_n\}_{n=1}^\infty$is a sequence of graphs whose isoperimetric dimension and Lipschitz-spectral dimension equal a common number$\delta \in [2,\infty )$, then the 1-Wasserstein metric over$G_n$has$L_1$-distortion bounded below by a constant multiple of$(\log |G_n|)^{\frac {1}{\delta }}$. We proceed to compute these dimensions for$\oslash$-powers of certain graphs. In particular, we get that the sequence of diamond graphs$\{\mathsf {D}_n\}_{n=1}^\infty$has isoperimetric dimension and Lipschitz-spectral dimension equal to 2, obtaining as a corollary that the 1-Wasserstein metric over$\mathsf {D}_n$has$L_1$-distortion bounded below by a constant multiple of$\sqrt {\log | \mathsf {D}_n|}$. This answers a question of Dilworth, Kutzarova, and Ostrovskii and exhibits only the third sequence of$L_1$-embeddable graphs whose sequence of 1-Wasserstein metrics is not$L_1$-embeddable.

    

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2. Higher-order QAM data transmission using a high-coherence hybrid Si/III–V semiconductor laser

   https://doi.org/10.1364/OL.383137  

   Zou, Kaiheng ; Zhang, Zhewei ; Liao, Peicheng ; Wang, Huolei ; Cao, Yinwen ; Almaiman, Ahmed ; Fallahpour, Ahmad ; Alishahi, Fatemeh ; Satyan, Naresh ; Rakuljic, George ; et al ( March 2020 , Optics Letters)

   We experimentally demonstrate the use of a high-coherence hybrid silicon (Si)/III–V semiconductor laser as the light source for a transmitter generating 20 Gbaud 16- and 64- quadrature amplitude modulated (QAM) data signals over an 80 km single-mode fiber (SMF) link. The hybrid Si/III–V laser has a measured Schawlow–Townes linewidth of$\sim <\#comment/>10\mathrm{k}\mathrm{H}\mathrm{z}$, which is achieved by storing modal optical energy in low-loss Si, rather than the relatively lossy III–V materials. We measure a received bit error rate (BER) of$4.1\times <\#comment/>{10}^{-<\#comment/>3}$when transmitting the 64-QAM data over an 80 km SMF using the hybrid Si/III–V laser. Furthermore, we measure a BER of$<<\#comment/>1\times <\#comment/>{10}^{-<\#comment/>4}$with the Viterbi–Viterbi digital carrier phase recovery method when transmitting the 16-QAM data over an 80 km SMF using the hybrid Si/III–V laser. This performance is achieved at power penalties lower than those obtained with an exemplary distributed feedback laser and slightly higher than those with an exemplary narrow-linewidth external cavity laser.

    

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3. Resonance tuning for dynamic Huygens metasurfaces

   https://doi.org/10.1364/JOSAB.427848  

   Ollanik, Adam J. ; Oguntoye, Isaac ; Ji, Yaping ; Escarra, Matthew D. ( July 2021 , Journal of the Optical Society of America B)

   Metasurfaces with dynamic optical performance have the potential to enable a broad range of applications. We computationally investigate the potential of dielectric Huygens metasurfaces, supporting both electric and magnetic dipole resonances, as a candidate platform for dynamic tuning. The asymmetric response of the two dipole resonances to changes in geometric and material parameters, and the potential for separate control of amplitude and phase, is analyzed. A review of dynamic materials, and their promise and limitations for use in dynamic Huygens metasurfaces, is discussed. Vanadium dioxide (${\mathrm{V}\mathrm{O}}_2$) is recognized as a singularly interesting material, due to its variable refractive index and optical absorption in response to several stimuli. Transmitted phase modulation of$\pm <\#comment/>\mathrm{\pi <\#comment/>}$is computationally demonstrated as a function of decaying resonance utilizing only the first 5% of the insulator-metal transition, corresponding to a temperature change of$<<\#comment/>{10}^{\circ <\#comment/>}\mathrm{C}$. As another case study utilizing asymmetric resonance tuning in response to changing incidence angle, phase modulation ($2\mathrm{\pi <\#comment/>}$range for reflected light and$><\#comment/>1.5\mathrm{\pi <\#comment/>}$for transmitted light) and amplitude modulation (from$\mathrm{R}=1$to$\mathrm{T}=1$) are demonstrated using a simple silicon metasurface with varying incident angle within a range of$\sim <\#comment/>{15}^{\circ <\#comment/>}$on two axes. A promising implementation within a micro-electromechanical system (MEMS)-based spatial light modulator, similar to conventional digital micromirror devices, is discussed.

    

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4. Demonstration of the DC-Kerr effect in silicon-rich nitride

   https://doi.org/10.1364/OL.432359  

   Friedman, Alex ; Nejadriahi, Hani ; Sharma, Rajat ; Fainman, Yeshaiahu ( August 2021 , Optics Letters)

   We demonstrate the DC-Kerr effect in plasma enhanced chemical vapor deposition (PECVD) silicon-rich nitride (SRN) and use it to demonstrate a third order nonlinear susceptibility,${\mathrm{\chi <\#comment/>}}^{(3)}$, as high as$(6\pm <\#comment/>0.58)\times <\#comment/>{10}^{-<\#comment/>19}{\mathrm{m}}^2/{\mathrm{V}}^2$. We employ spectral shift versus applied voltage measurements in a racetrack resonator as a tool to characterize the nonlinear susceptibilities of these films. In doing so, we demonstrate a${\mathrm{\chi <\#comment/>}}^{(3)}$larger than that of silicon and argue that PECVD SRN can provide a versatile platform for employing optical phase shifters while maintaining a low thermal budget using a deposition technique readily available in CMOS process flows.

    

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5. Phase-factor spectra of turbulent phase screens

   https://doi.org/10.1364/JOSAA.429928  

   Muschinski, Andreas ( August 2021 , Journal of the Optical Society of America A)

   The optical phase$\mathrm{\varphi <\#comment/>}$is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phasefactor,$\mathrm{\psi <\#comment/>}=\exp <\#comment/>(i\mathrm{\varphi <\#comment/>})$, are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrum$F_{\mathrm{\psi <\#comment/>}}(\mathit{\kappa <\#comment/>})$of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function,$D_{\mathrm{\varphi <\#comment/>}}(r)=(r/r_c{)}^{\mathrm{\gamma <\#comment/>}}$(where$r_c$is the phase coherence length defined by$D_{\mathrm{\varphi <\#comment/>}}(r_c)=1{\mathrm{r}\mathrm{a}\mathrm{d}}^2$), and a probability density function$p_{\mathrm{\alpha <\#comment/>}}(\mathrm{\alpha <\#comment/>})$of the phase increments for a given spatial lag. We analyze phase screens with turbulent ($\mathrm{\gamma <\#comment/>}=5/3$) and quadratic ($\mathrm{\gamma <\#comment/>}=2$) 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$F_{\mathrm{\psi <\#comment/>}}(\mathrm{\kappa <\#comment/>})$. The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs at$\mathrm{\kappa <\#comment/>}\sim <\#comment/>1/r_c$. 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$\mathrm{\psi <\#comment/>}$statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-order$\mathrm{\varphi <\#comment/>}$counterparts.

    

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