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1 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).
2 Nonlinear microscopic images of (a) 3D NPCs fabricated in a ${{\rm LiNbO}_3}$                    L        i        N        b        O            3       crystal by femtosecond laser erasing of the second-order nonlinearity ${\chi ^{(2)}}$            χ              (        2        )             [30] and (b)–(d) 2D and 3D NPCs fabricated by domain inversion in ${{\rm LiNbO}_3}$                    L        i        N        b        O            3       [43], ${{\rm Ba}_{0.77}}{{\rm Ca}_{0.23}}{{\rm TiO}_3}$                    B        a                    0.77                                C        a                    0.23                                T        i        O            3       [31], and ${{\rm Ca}_{0.28}}{{\rm Ba}_{0.72}}{{\rm Nb}_2}{{\rm O}_6}$                    C        a                    0.28                                B        a                    0.72                                N        b            2                          O            6       crystals [46], respectively. These images are obtained using the Čerenkov SH microscopy. Reproduced from [30,31,43,46] with permission.
3 Sheared wavefronts of the wavefront from the micro-objective in							the (a) 		  $ x $		      x		    		 direction and (b) 		  $ y $		      y		    		 direction.
4 Complex Jones matrix calculated for a birefringent digital phantom with an illumination angle of $\theta = 25^ \circ$  θ  =      25    ∘   and $\phi = 0^ \circ$  ϕ  =      0    ∘  . The synthetic measurements were generated using the V-BPM. In order to visualize the complex values, brightness shows the amplitude, and the color-code shows the phase of each Jones matrix component.
5 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			    .
6 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.
7 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.
8 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.
9 2D classification. Representative examples of reconstructed 2D models shown on a logarithmic scale, with each row representing a different sample. The numbers indicate how many patterns had that model as the most likely one. The first two columns show models selected for further processing. The third column shows diffraction from rounded/spherical particles, except in the cub17 case where there were no spherical particles and the model shows diffraction from a dimer instead. The fourth column shows some of the low-contrast models generated by averaging patterns from a diverse set of particles. The resolution at the edge of the circle is 3.3 nm.
10 Wavefront nephogram of the system under 4°C uniform temperature rise load.
11 RI distributions of the (a) background medium, (b) ODT result,							and (c) iODT result. RI distributions of the Opti-ODT results							initialized by the background medium, ODT, and iODT are shown							in (d)–(f), respectively. The horizontal cross sections of							(d)–(f), along with the ground truth, are shown in (g)–(i),							respectively.
12 Multifunctional longitudinal magnetization patterns induced by the high-order AP-LG vortex modes with the radial modes index p and the truncation parameter β. (a1)-(a4) and (b1)-(b4) are β = 2.732, 2.051, and 1.753, and 1.576 when p = 1in the x-y plane and r-z plane, respectively; (c1)-(c4) are β = 3.545, 2.854, 2.506, and 2.411 when p = 3 in the x-y plane; (c1)-(c4) are β = 4.252, 3.489, 3.234, and 3.078 when p = 5 in the x-y plane.