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1 TG-SSSI measurements of fundamental and SHG STOVs. (a) Top: Intensity profile 	      ${I_S}({x,\tau})$            I      S        (      x    ,    τ    )	     of fundamental 	      $l = + 1$  l  =  +  1	     STOV; bottom: spatiotemporal phase 	      ${\Delta}{{\Phi}}({x,\tau})$      Δ              Φ        (      x    ,    τ    )	     showing one 	      ${{2}}\pi$            2        π	     winding. (b) Top: SHG output pulse 	      $I_S^{2\omega}({x,\tau})$      I    S          2      ω        (      x    ,    τ    )	     showing two donut holes embedded in pulse; bottom: spatiotemporal phase profile 	      ${\Delta}{{{\Phi}}^{2\omega}}({x,\tau})$      Δ                                Φ                            2        ω              (      x    ,    τ    )	     showing two 	      ${{2}}\pi$            2        π	     windings. Phase traces are blanked in regions of negligible intensity, where phase extraction fails. These images represent 500 shot averages: the extracted phase shift from each spectral interferogram is extracted, then the fringes of each frame (shot) are aligned and averaged, and then the phase map is extracted [23].
2 Simulated wide-field FDCD images and chiral SIM images of chiral                            filaments with different dissymmetry factors controlled by the                            multiplication factor m. (a-c) Deconvolved wide-field                            FDCD images with                                 $m$                                        m                                                                 = 1, 10, and 100, respectively. (d-f) Reconstructed                            chiral SIM images with                                 $m$                                        m                                                                 = 1, 10, and 100, respectively. In this demonstration,                                 $\Delta                                        t$                                        Δ                                        t                                                                 = 1 s and                                 ${I_0}$                                                                                                                                    I                                                0                                                                                                                                                     = 50 W/cm2. The color bar indicates the                            value of the normalized differential fluorescence. Scale bar: 2 μm. The                            yellow arrows mark an area, which shows resolution improvement in chiral                            SIM images.
3 Preprocessed DLHM holograms after normalizing (a) with $I_0^2({\vec r})$      I    0    2    (                    r        →              ) and (b) with $I_0^3({\vec r})$      I    0    3    (                    r        →              ). Intensity reconstructions for (c) the $I_0^2({\vec r})$      I    0    2    (                    r        →              ) normalization and (d) the $I_0^3({\vec r})$      I    0    3    (                    r        →              ) normalization. A loss in the diffraction efficiency of the resulting DLHM holograms is found.
4 Effect of coherence on the intensity distribution of a propagating laser beam from a digital degenerate cavity laser. (a) Intensity distribution with an incoherent laser light beam at ${z} = {0}\;{\rm mm}$      z    =      0          m    m   and ${z} = {12.5}\;{\rm mm}$      z    =      12.5          m    m   (with no intracavity aperture). (b) Intensity distribution of a more coherent laser light beam at ${z} = {0}\;{\rm mm}$      z    =      0          m    m   and ${z} = {12.5}\;{\rm mm}$      z    =      12.5          m    m   (with a 4 mm diameter far-field aperture).
5 Schematic model of adatoms bonding selection on a new step; the red spheres are adatoms, the gray spheres are underneath terrace, and the blue spheres are initial step and initial island.
6 Ballistic expansion, coupling, and interference of two polariton condensates. Recorded (a) and (d) real-space and (b) and (e) far-field PL of two condensates with separation distances 		  ${d_{12}} = 12.7\;{\unicode{x00B5}\text{m}}$		      						  d			  			    12			  					      		      =		      12.7		      		      			µ			m		      		    		 and 		  ${d_{12}} = 89.3\;{\unicode{x00B5}\text{m}}$		      						  d			  			    12			  					      		      =		      89.3		      		      			µ			m		      		    		. Corresponding far-field interference patterns after masking of the emission in real space to block all emission outside the 		  $2\;{\unicode{x00B5}\text{m}}$		      2		      		      			µ			m		      		    		 FWHM of each condensate node are shown in (c) and (f). (g) Distance dependence of the integrated complex coherence factor 		  $|{\tilde\mu_{12}}|$		      			|		      		      						  			    			      μ			      ~			    			  			  			    12			  					      		      			|		      		    		, while keeping the excitation pump power constant at 		  $P = 1.2{P_{\text{thr}}}$		      P		      =		      1.2		      						  P			  			    thr			  					      		    		, where 		  ${P_{\text{thr}}}$		      						  P			  			    thr			  					      		    		 is the measured threshold pump power at a distance of 		  ${d_{12}} = 12.7\;{\unicode{x00B5}\text{m}}$		      						  d			  			    12			  					      		      =		      12.7		      		      			µ			m		      		    		. Blue circles correspond to experimental data and orange squares to GPE simulations. Red curve is a Gaussian fit [Eq. (2)] to the experimental data points. Inset shows the pump power dependence of the coherence between two condensates separated at 		  ${d_{12}} = 12.7\;{\unicode{x00B5}\text{m}}$		      						  d			  			    12			  					      		      =		      12.7		      		      			µ			m		      		    		. False color scale in (f) applies to (b)–(c) and (e)–(f) in linear scale and to (a) and (d) in logarithmic scale saturated below 		  ${10^{- 4}}$		      						  10			  			    −			    4			  					      		    		 of the maximum count rate. Scale bars in (a) and (d) and (b)–(c) and (e)–(f) correspond to 		  $10\;{\unicode{x00B5}\text{m}}$		      10		      		      			µ			m		      		    		 and 		  $1\;{{\unicode{x00B5}\text{m}}^{- 1}}$		      1		      		      						  			    µ			    m			  			  			    −			    1			  					      		    		, respectively.
7 Three-dimensional data set recorded in one monochromator scan and corrected for spaceenergy coupling. The microstructured sample, a group of three thin-film ${{\rm{VO}}_2}$                              V          O                    2       squares with an edge length of 30 µm, is imaged along one dimension (here, $y$  y). Spatially resolved x-ray emission is recorded in-parallel ($x,y$  x  ,  y plane), while the incident energy ($z$  z axis) is scanned. Shown are projections of the 3D data onto each plane, representing traditional RIXS maps (incident versus emitted energies) on the $x,z$  x  ,  z plane, spatial maps of absorption spectra in the $y,z$  y  ,  z plane, and spatial maps of emission spectra in the $x,y$  x  ,  y plane. Isolines and surfaces for a relative intensity of 70% are shown, respectively, as a black line on the projection planes and in a pseudo-3D representation.
9 A system of nanospheres each with the radius 	      $a^{(t)}$		  		    a		    		      (		      t		      )		    		  			    , which are distributed arbitrarily in the space and illuminated by a plane wave with the wave number 	      $k$		  k			    .
10 Residual maps from polishing the lattice backed mirror. The								locations of each map: (a) 12 o’clock, (b) 3 o’clock,								(c) 6 o’clock, and (d) center. The								peripheral samples (a)–(c) are at the same radial								distance, which is equal to the mounting radial								distance.
11 (a), (b) Measured surface profiles (10 mm full scale in $x$  x and $y$  y) for two characteristic TIF spots from series B (using ${r_t} = {{50}}\;{\rm{mm}}$            r      t        =            50                    m      m      , ${r_i} = {{50}}\;{\rm{mm}}$            r      i        =            50                    m      m      ; ${d_t} = {{150}}\;{\rm{\unicode{x00B5}{\rm m}}}$            d      t        =            150                    µ              m            ; ${R_t} = {{250}}\;{\rm{rpm}}$            R      t        =            250                    r      p      m      ; ${\alpha _{\textit{ts}}} = {0.5}^\circ$            α                        ts                      =            0.5        ∘  ; $t = {{30}}\;{\rm{s}}$  t  =            30                    s      ) with (a) ${\alpha _{t0}} = {1.1}^\circ$            α              t        0              =            1.1        ∘  , which has a peak-to-valley (PV) height of 0.63 µm, and (b) ${\alpha _{t0}} = {3.9}^\circ$            α              t        0              =            3.9        ∘  , which has a ${\rm{PV}} = {0.92}\;{\rm{\unicode{x00B5}{\rm m}}}$            P      V        =      0.92                µ              m            . (c), (d) Corresponding calculated time averaged velocities, ${V_r}$            V      r       (over a 10 mm square aperture); $z$  z axes are in units of m/s. (e), (f) Corresponding effective hydrodynamic pressure distribution (${\sigma _h}$            σ      h      ) calculated using Eq. (20); $z$  z axes are in units of MPa.
12 Spatiotemporal HBT effect under different values of (a)-(h) 	      $\sigma _{\textrm {I}}$		  		    σ		    		      			I		      		    		  			    , (i)-(p) 	      $\sigma _{\textrm {cs}}$		  		    σ		    		      			cs		      		    		  			     with (a)-(d), (i)-(l) 	      $q_{12}$		  		    q		    		      12		    		  			     = 0 and (e)-(h), (m)-(p) 	      $q_{12}$		  		    q		    		      12		    		  			     = 0.0001 cm	      $^{-1}$		  		    		    		      −		      1		    		  			    . Other parameters are 	      $\sigma _{\textrm {I}}$		  		    σ		    		      			I		      		    		  			     = 2 cm, 	      $\sigma _{\textrm {cs}}$		  		    σ		    		      			cs		      		    		  			     = 0.1 cm, 	      $\sigma _{\textrm {t}}$		  		    σ		    		      			t		      		    		  			     = 10 ps, 	      $\sigma _{\textrm {ct}}$		  		    σ		    		      			ct		      		    		  			     = 10 ps, 	      $z$		  z			     = 1000 m and 	      $q_{14}$		  		    q		    		      14		    		  			     = 	      $q_{12}/10$		  		    q		    		      12		    		  		  		    /		  		  10			    .