Optical fiber meta-tips: Supplementary information



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Supplementary Figure S3 |Morphological characterization.a, b AFM topographic images (2-D top view and 3D perspective view, respectively) pertaining to MT3 sample after the FIB milling of the gold layer. The rectangular shaded area delimits a set of 42 nanoholes (six supercell replicas) considered in the statistical study (see Supplementary Table S1).

Prototype fabrication

The fabricated samples are affected by imperfections and tolerances inherent to the fabrication process. In order to investigate the geometrical deviation of the nanohole shapes with respect to the nominal design, we carried out an extensive morphological characterization of the fabricated samples. For instance, with reference to the MT3 sample, Supplementary Figure S3shows the atomic-force-microscope (AFM) topographic images of the fiber tip after the FIB patterning. Multiple measurements on the nanoholesidelengths () are performed on the image, with results summarized in Supplementary Table S1. More specifically, a set of 42 nanoholes is considered (rectangular shaded area in Supplementary Figure S3a), which basically comprises seven replicas (rows) of the six-elementsupercell (see Table 1 and Figure 2c inset). It can be observed that the measured values are always slightly larger than the nominal-design ones, with relative errors within the range 4-9%. This is attributable to the Gaussian shape of the ion beam, which creates a smoothed profile of the nanoholes along the edges. Another fabrication-related issue is the gallium ion doping of the silica substrate that occurs during the patterning,4 which may induce unmodeled variations in the fiber refractive index.



Supplementary Table S1 |Morphological characterization.Statistics of AFM measurements of the nanoholesidelengths () pertaining to a set of 42 elements (shaded rectangular area in Supplementary Figure S3a) in MT3 sample.





element #1

element #2

element #3

element #4

element #5

element #6

row #

























1

598

438

450

362

410

218

439

609

359

445

202

411

2

592

445

456

362

404

218

433

595

360

431

205

406

3

598

431

444

355

404

211

439

589

365

438

205

411

4

587

424

461

369

410

205

444

595

360

438

194

404

5

592

431

456

369

404

191

439

589

358

424

202

400

6

592

445

456

355

404

205

444

589

353

445

205

402

7

587

431

444

362

416

205

439

589

358

445

210

392

mean (nm)

592

435

452

362

407

208

440

594

359

438

203

404

std.dev. (nm)

4

8

7

6

5

9

4

7

4

8

5

7

nominal (nm)

560

410

420

340

385

190

410

560

340

420

190

385

abs.err. (nm)

32

25

32

22

22

18

30

34

19

18

13

19

rel.err. (%)

6

6

8

6

6

9

7

6

6

4

7

5

Overall, the fairly good agreement observed between measurements and numerical simulations seems to indicate a substantial robustness of the designs with respect to these fabrication-related tolerances and imperfections.

In view of the unconventional nature of the fiber-tip substrate for the electron beam evaporation system, it is important to verify the gold layer thickness. To this aim, after the deposition, a KrF pulsed excimer laser (Optec LB1000, operating at a wavelength of 248nm) is used to mill a rectangular hole into the gold layer. A 4mJ energy is used, with attenuation of 30%, repetition rate of 50Hz, and exposure time of 1s. The thickness measurement is performed by means of an AFM (Agilent Technologies 5420), using a proper fiber holder. The measurement is made in contact mode with a Nanosensors PPP-CONT tip, at a speed of 1ln/s, and yields a thickness value of about 51.3nm, very close to the nominal value of 50nm.

In connection with the SiOx overlay deposited for the surface-sensitivity characterization,it is well known that, in the PECVD process, the reaction can be in the mass-transport-limited regime, where the rate is dependent on the supply of the gas to the surface. Fluid dynamics in the chamber plays a major role in the deposition rate, and the presence of the fiber can cause turbulence around the tip. Therefore, a measurement of the overlay thickness on the fiber tip is crucial.Similar to the previous measurement, a rectangular slot is milled on the fiber tip, after the oxide film deposition, by exposure to an excimer laser. In this case, a 6mJ energy is used, with attenuation of 60%, repetition rate of 150Hz, and exposure time of 1s. Subsequently, the thickness of the oxide layer is inspected via an AFM measurement, which yields a value of about 40nm.



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