Figure 1

(Color online) Discrete diffraction in (a) straight waveguide array with period $d=9\mu \mathrm{m}$. (b) Coupling coefficient normalized to the coupling at the central frequency $C_0$. (c)–(e) Evolution of beam intensity and output intensity profiles after $80\mathrm{mm}$ propagation of a $3\mu \mathrm{m}$ wide input beam for (c) ${\lambda }_r=580\mathrm{nm}$, (d) ${\lambda }_0=532\mathrm{nm}$, and (e) ${\lambda }_b=490\mathrm{nm}$, which correspond to the points “c, d, and e” in (b). Waveguide width is $3\mu \mathrm{m}$ and substrate refractive index is $n_0=2.35$.Reuse & Permissions

Figure 2

(Color online) (a)–(e) Broadband self-collimation in an optimized waveguide array: (a) Waveguide bending profile with the period $L=60\mathrm{mm}$ and modulation parameters $A_1=27\mu \mathrm{m}$, $A_2=42\mu \mathrm{m}$, $z_0=18\mathrm{mm}$. (b) Effective coupling normalized to the coupling in the straight array at the central frequency $C_0=C\left({\omega }_0\right)$. (c)–(e) Evolution of the beam intensity and output intensity profiles for different wavelengths marked (c) ${\lambda }_r=560\mathrm{nm}$, (d) ${\lambda }_0=532\mathrm{nm}$, and (e) ${\lambda }_b=400\mathrm{nm}$ corresponding to marked points in (b). (f)–(h) Frequency-sensitive diffraction in array with the sinusoidal bending profile at the wavelengths corresponding to plots (c)–(e).Reuse & Permissions

Figure 3

(Color online) Wavelength-independent diffraction in an optimized periodically curved waveguide array. (a) Waveguide bending profile with the period $L=40\mathrm{mm}$ and (b) corresponding effective coupling normalized to the coupling in the straight array at the central frequency $C_0=C\left({\omega }_0\right)$. (c)–(e) Evolution of beam intensity and output intensity profiles after propagation of two full periods for the wavelengths (c) ${\lambda }_r=580\mathrm{nm}$, (d) ${\lambda }_0=532\mathrm{nm}$, and (e) ${\lambda }_b=490\mathrm{nm}$, which correspond to the points c, d, and e in plot (b).Reuse & Permissions

Figure 4

(Color online) (a) Monochromatic Talbot effect in the straight waveguide array shown in Fig. 1a: periodic intensity revivals every $L_T^{\left(1\right)}=16.5\mathrm{mm}$ of propagation for the input pattern {1, 0, 0, 1, 0, 0,…} and the wavelength ${\lambda }_0=532\mathrm{nm}$. (b) Disappearance of the Talbot carpet in the straight array when input consists of three components with equal intensities and different wavelengths ${\lambda }_r=580\mathrm{nm}$ [redshifted], ${\lambda }_0=532\mathrm{nm}$ [green], and ${\lambda }_b=490\mathrm{nm}$ [blueshifted]. (c) Multicolor Talbot effect in the optimized structure with wavelength-independent diffraction [see Fig. 3.] Half of the bending period $L∕2=L_T^{\left(2\right)}=53.2\mathrm{mm}$ is equal to the Talbot distance for the corresponding effective coupling length.Reuse & Permissions