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Table 1. Geometrical parameters of the QR-metadiffuser.

Table 1 Geometrical parameters of the QR-metadiffuser.

Related Figures (9)

Figure 1. (a) Scheme of a QRD Schroeder diffuser composed by N=7 wells or quarter wavelength resonators. (b) Metadiffuser composed of N=7 sub-wavelength slits, each of them loaded by M=3 Helmholtz resonators, with slightly different geometry. (c) Detail of a slit of the metadiffuser showing the geometrical parameters of the cavity of a HR (w, and /,) and its neck (w, and 1,).
Figure 1. (a) Scheme of a QRD Schroeder diffuser composed by N=7 wells or quarter wavelength resonators. (b) Metadiffuser composed of N=7 sub-wavelength slits, each of them loaded by M=3 Helmholtz resonators, with slightly different geometry. (c) Detail of a slit of the metadiffuser showing the geometrical parameters of the cavity of a HR (w, and /,) and its neck (w, and 1,).
Figure 2. (a) Dispersion relation inside the (blue) first and (red) second slits of a metadiffuser for the lossless case (continuous lines) and accounting for the thermo-viscous losses (dashed lines), and wavenumber in air (dashed-dotted). The resonance frequencies of the HR are shown as f, and f,. (b) Corresponding phase speed. (c) Phase of the reflection coefficient for each individual slit.
Figure 2. (a) Dispersion relation inside the (blue) first and (red) second slits of a metadiffuser for the lossless case (continuous lines) and accounting for the thermo-viscous losses (dashed lines), and wavenumber in air (dashed-dotted). The resonance frequencies of the HR are shown as f, and f,. (b) Corresponding phase speed. (c) Phase of the reflection coefficient for each individual slit.
Figure 3. (a) Phase and (b) magnitude of the spatially-dependent reflection coefficient of a QRD (black line) and the QR-metadiffuser (red doted). (c) Scaled scheme of the QR-metadiffuser with N=5 and M=2. (d) Near field pressure distribution at 2 kHz of QR-metadiffuser with thickness L=2cm (e) phase grating QRD of thickness L = 27.4 cm and (f) flat plane reflector. (g) Far-field polar distribution of the QR-metadiffuser obtained by TMM (continuous blue) and FEM (dotted black), the reference QRD (dashed-grey), and a plane reflector with same width of the diffusers (continuous red).
Figure 3. (a) Phase and (b) magnitude of the spatially-dependent reflection coefficient of a QRD (black line) and the QR-metadiffuser (red doted). (c) Scaled scheme of the QR-metadiffuser with N=5 and M=2. (d) Near field pressure distribution at 2 kHz of QR-metadiffuser with thickness L=2cm (e) phase grating QRD of thickness L = 27.4 cm and (f) flat plane reflector. (g) Far-field polar distribution of the QR-metadiffuser obtained by TMM (continuous blue) and FEM (dotted black), the reference QRD (dashed-grey), and a plane reflector with same width of the diffusers (continuous red).
Table 2. Geometrical parameters of the PR-metadiffuser.
Table 2. Geometrical parameters of the PR-metadiffuser.
Figure 4. (a) Phase and (b) magnitude of the spatially-dependent reflection coefficient of a PRD (black line) and the PR-metadiffuser (red doted). (c) Scaled scheme of the metadiffuser using N= 6 and M=1. (d) Near field pressure distribution at 1 kHz of a PR-metadiffuser with prime number P=7 and thickness L = 3.5 cm (e) phase grating QRD of thickness L = 17.1 cm and (f) reference flat plane reflector. (g) Far-field polar distribution of the PR-metadiffuser obtained by TMM (continuous blue) and FEM (dotted black), the reference PRD (dashed-grey), and a plane reflector with same width of the diffusers (continuous red).
Figure 4. (a) Phase and (b) magnitude of the spatially-dependent reflection coefficient of a PRD (black line) and the PR-metadiffuser (red doted). (c) Scaled scheme of the metadiffuser using N= 6 and M=1. (d) Near field pressure distribution at 1 kHz of a PR-metadiffuser with prime number P=7 and thickness L = 3.5 cm (e) phase grating QRD of thickness L = 17.1 cm and (f) reference flat plane reflector. (g) Far-field polar distribution of the PR-metadiffuser obtained by TMM (continuous blue) and FEM (dotted black), the reference PRD (dashed-grey), and a plane reflector with same width of the diffusers (continuous red).
Figure 5. (a) Diffusion coefficient of the QR-metadiffuser (blue) optimized at 2000 Hz (marker) and a reference QRD (red). (b) Diffusion coefficient of the PR-metadiffuser (blue) optimized at 2000 Hz (marker) anda reference PRD (red). (c) Corresponding absorption for the QRD case, where the grey lines shows the absorption of individual slits n = 1 and n=5. For these slits, the insets show the complex frequency representation”® of the reflection coefficient (log|R(f,, f;)|?), where f, = Re(f) and f= Im(f). (e) Corresponding absorption for the PRD where the complex frequency representation of the reflection coefficient is shown for the individual slit n= 1 in the inset.
Figure 5. (a) Diffusion coefficient of the QR-metadiffuser (blue) optimized at 2000 Hz (marker) and a reference QRD (red). (b) Diffusion coefficient of the PR-metadiffuser (blue) optimized at 2000 Hz (marker) anda reference PRD (red). (c) Corresponding absorption for the QRD case, where the grey lines shows the absorption of individual slits n = 1 and n=5. For these slits, the insets show the complex frequency representation”® of the reflection coefficient (log|R(f,, f;)|?), where f, = Re(f) and f= Im(f). (e) Corresponding absorption for the PRD where the complex frequency representation of the reflection coefficient is shown for the individual slit n= 1 in the inset.
Table 4. Geometrical parameters used for the broadband metadiffuser using N different slits.
Table 4. Geometrical parameters used for the broadband metadiffuser using N different slits.
Figure 6. (a) Phase and (b) magnitude of the spatially dependent reflection coefficient for an ideal ternary sequence diffuser (black) and a PA-metadiffuser (blue dots). The ternary sequence used, s,, is shown on top. (c) Scaled scheme of the geometry of the hybrid PA-metadiffuser. (d) Frequency dependent absorption for the total structure (blue curve) and individual slits (black curves). The inset shows the complex frequency plane representation of the reflection coefficient for the perfect absorber slits, s, =0. (e) Frequency dependent diffusion for the PA-metadiffuser of L=3cm (blue), a ternary sequence diffuser using phase gratings of L=17cm (dashed red) and ternary sequence diffuser using phase gratings of L=3 cm (black). (f) Far field pol: response at 500 Hz of a ternary sequence with N= 8 wells (dashed-grey), the PA-metadiffuser obtained by TM (continuous black) and FEM (dotted black), and a plane reflector of the same width as the diffusers (red line).
Figure 6. (a) Phase and (b) magnitude of the spatially dependent reflection coefficient for an ideal ternary sequence diffuser (black) and a PA-metadiffuser (blue dots). The ternary sequence used, s,, is shown on top. (c) Scaled scheme of the geometry of the hybrid PA-metadiffuser. (d) Frequency dependent absorption for the total structure (blue curve) and individual slits (black curves). The inset shows the complex frequency plane representation of the reflection coefficient for the perfect absorber slits, s, =0. (e) Frequency dependent diffusion for the PA-metadiffuser of L=3cm (blue), a ternary sequence diffuser using phase gratings of L=17cm (dashed red) and ternary sequence diffuser using phase gratings of L=3 cm (black). (f) Far field pol: response at 500 Hz of a ternary sequence with N= 8 wells (dashed-grey), the PA-metadiffuser obtained by TM (continuous black) and FEM (dotted black), and a plane reflector of the same width as the diffusers (red line).
Figure 7. Far field polar response as a function of the frequency for (a) reference flat plane, (b) N=11QRD panel with a total thickness of 3 cm, (c) QRD panel with total thickness of 56cm and (d) optimized metadiffuser thickness of 3 cm. (e) Normalized diffusion coefficient or the 3cm QRD (dashed black), 32 cm QRD (dashed- dotted red) and optimized metadiffuser using TMM (blue) integrated in third of octaves. The third octave integration is shown in thick lines according to ISO 17497-2:2012®. (f) Corresponding absorption.
Figure 7. Far field polar response as a function of the frequency for (a) reference flat plane, (b) N=11QRD panel with a total thickness of 3 cm, (c) QRD panel with total thickness of 56cm and (d) optimized metadiffuser thickness of 3 cm. (e) Normalized diffusion coefficient or the 3cm QRD (dashed black), 32 cm QRD (dashed- dotted red) and optimized metadiffuser using TMM (blue) integrated in third of octaves. The third octave integration is shown in thick lines according to ISO 17497-2:2012®. (f) Corresponding absorption.
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