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We report the fabrication of a phase photon sieve (PS) on the tip of a standard single mode fiber by focused ion beam (FIB) milling. The fiber tip was dip-coated with a conductive polymer (PEDOT:PSS) as an alternative, more advantageous method to the metallization prior to FIB milling. The near field scans of the intensity profile along the optical axis under fiber illumination of a laser at λ = 1.55 μm are presented. We have analyzed the focusing properties and demonstrated the validity of our structure for light coupling into silicon photonics waveguides with improved efficiency and alignment tolerance.
© 2016 Optical Society of America
1. Introduction
Beam tailoring and micro-imaging techniques are of great interest in many engineering fields such as optical sensing, light coupling and biomedical applications. Practical examples in which beam engineering has been valuable are high precision laser medical procedures [1], particle manipulation by optical tweezers [2] and high-resolution lithography [3]. Nevertheless, mechanical constraints due to the overall system volume, vibration and alignment sensitivity impair field deployment of many of the devised systems, with a general increase of cost and complexity of the fully assembled system. On the other hand, direct integration of diffractive functionality on the tip of optical fibers allows for self-aligned operation, light-weight and mechanically robust systems. Typical techniques employed to pattern sub-micrometer features on optical fiber tips are based on direct beam writing, either through focused ion-beam milling [4] or femtosecond laser ablation [5]. Even though these fabrication techniques are currently expensive, it is expected that the full cost of the final fiber-integrated optical beam shaping system is less costly than bulk system since no accurate positioners and lenses are required to maintain the alignment of the diffractive element with the illuminating beam.
Diffractive optical lenses play an important role in micro and nanoimaging projection, especially Fresnel zone plates (FZP) for their versatility and suitability for integration in optical systems due to their planar nature. Traditionally, an amplitude FZP is a set of alternating transparent and opaque, radially symmetric concentric rings (Fresnel zones). Alternatively, the FZP can be implemented as phase zone plates, i.e., the even and odd zones have a different refractive index or dielectric height originating a phase difference between zones. Phase-FZP have a higher diffraction efficiency than an amplitude FZP [6–8]. Binary FZP radii are given by the following equation [6]:
where f is the focal length, λ is the operating wavelength of the incident radiation, n is the ring order and rn is the ring radius for the nth order [7]. The resolution of a FZP is limited by the smallest zone width, which occurs at the outermost zone [6–8]. To overcome the limitations of a FZP, Kipp et al [9] proposed a photon sieve (PS) as a diffractive lens based on a modified FZP, achieving higher resolution than the width of the smallest structure due to a higher numerical aperture and suppression of the higher orders of diffraction and secondary maxima.In a PS a great number of non-overlapping pinholes are properly distributed across the zones of an underlying FZP. Several theoretical [10,11] and experimental studies on PS have been reported since, targeting a more efficient lens by implementing different pinhole distributions (such as random, fractal and Gaussian) for tailoring of focal point, distribution of secondary orders and maxima suppression [12–14]. Menon et al [3] demonstrated the application of a PS as a focusing element in a scanning-optical-beam-lithography system. Similarly to the FZP, it was reported that phase PS have advantages over the amplitude PS due to the higher numerical aperture [13,15]. While their use has diversified, most applications of FZP and PS are on planar substrates that are posteriorly used as lenses [16,17]. The monolithically integration of these elements on fiber optic systems is evidently beneficial since it suppresses the need for expensive lenses and complex setups. FZP integration on a fiber end was achieved by hot embossing [18] or femtosecond laser ablation [5]. Nevertheless, these prior works had limitations in pattern resolution, alignment accuracy and depth accuracy leading to experimental results with large focal lengths in the range of 300λ to 50000λ and spot sizes in the range of 10λ to 25λ.
This paper presents a study of the near-field beam shaping by an ultra-compact phase PS constituted by sub-wavelength pillars and its evolution in a multi-parametric problem, namely its dependence on the illumination, overall PS design and 3D pillar shape and material re-deposition. A novel approach of fabrication and integration of a phase PS on a single mode fiber is also described. Finally, an example of an application of such compact fiber photon sieve is presented, supported by experimental results on the comparative advantage of using a photon sieve for silicon nanophotonics light coupling.
2. Design and simulation
2.1 Design
Concerning the design of the PS, the radii of the underlying FZP were calculated based on Eq. (1) for wavelength of 1.55 µm and a focal distance of 0.5 µm, purposely chosen to be below the free space wavelength of the light used in the experiments. In a phase FZP or PS, the phase difference between even and odd zones should be π to achieve maximum focusing efficiency, which leads to a etch depth given by
with nmedium being the refractive index of the material outside the optical fiber facet and neff the effective index of the fundamental mode of SMF28e optical fiber at the wavelength of interest. We obtained neff = 1.44536 at 1550 nm from a mode solver, resulting in detch = 1.74 μm as the optimal etch depth for operation in air (nmedium = 1). Under such conditions (π phase difference and an underlying FZP with f = 0.5 µm), the focal distance of the phase PS should be the same as the binary FZP, with similar resolution but with relaxed fabrication tolerance.The range of focal lengths that can be designed on the fiber PS is limited by the mode field diameter of the optical fiber. Since the underlying FZP radii increase with the focal length according to Eq. (1), longer focal lengths will have a lower number of orders overlapping with the core-guided optical mode, causing a weaker modulation of the field and a lower effectiveness of the PS as a diffractive lens. Fabricating the PS on the tip of a multimode fiber relaxes this constraint but increases the sensitivity to fiber bending, therefore decreasing the mechanical robustness of the approach presented in this paper.
On the other hand, the focal length cannot be arbitrarily decreased. By decreasing the focal length, more orders of amplitude pinholes or phase pillars can fit on the same area and a higher diffractive efficiency can be obtained. But this also means the dimensions of the PS elements will decrease and elements with high aspect ratio, defined as the height-to-width ratio of patterned features, will not be feasible from a fabrication point of view [19], thus preventing the patterning of the small features associated with the higher order radius.
Keeping in mind the design etch depth is set, as described earlier, by the operating wavelength and the refractive index of the external medium, and accounting for the fabrication limitations in terms of aspect ratio, as well as the constraints due to the fiber mode field diameter, the PS design freedom is limited in terms of possible focal distances and PS resolution.
The number of zones was chosen taking into consideration the fiber’s single mode distribution, so that most of the light would be diffracted by the pattern, including the fraction of light in the fundamental mode travelling in the fiber cladding. For this reason, we have designed our PS with 10 orders. The phase-jump inducing pillars were evenly distributed inside each zone, as in a conventional photon sieve, with a center-to-center separation of 1.5 times the diameter of the pillar for that zone, complying with the fabrication process limitations. The diameter of the smallest pillars, belonging obviously to the elements of the outermost ring, was 777 nm with an edge-to-edge separation of 389 nm between two consecutive pillars. Table 1 summarizes the dimensions of the designed photon sieve for each order n, in terms of the radius (Rn), diameter (Dn), and zone width (Wn) of the underlying FZP as well as the number of pillars of the designed PS, which are represented in Fig. 1.
Table 1. Dimensions of the Underlying FZP of Fiber Phase Photon Sieve
Fig. 1 (a) Underlying FZP dimensions and zone plate order numbering used for photon sieve generation. (b) 3D rendering of the photon sieve for etch depth detch = 1.74 μm.
2.2 FDTD simulations
In order to understand and characterize the photon sieve with sub-wavelength diffractive features, full-vectorial finite-difference time-domain (FDTD) simulations were performed for a range of different parameters. The 3D FDTD simulation for the idealized structure, i.e. with cylindrical pillars, is shown in Fig. 2, under circular polarized (CP) illumination of a Gaussian launch field with a beam diameter of 10.4 µm, equal to the mode field diameter of the SMF28e fiber. It is clearly observable the presence of multiple focal points and a strong peak near the fiber facet (located at z = 0 μm), similarly to what has been reported for photonic nanojets in microspheres [20,21]. The dependence of the axial intensity of the diffraction pattern on the etch depth (detch) is also presented in Fig. 2, and it is possible to verify that the positions of the various focal points are not very sensitive to small changes in etch depth, but their relative intensity is.
Fig. 2 (a) Intensity distribution on the XZ plane for a photon sieve matching the ideal design of Table 1. (b) Axial field intensity dependence on the etch depth.
The expected diffraction pattern for circular and linear illumination polarizations was investigated. Not surprisingly the diffraction pattern of both polarizations shows to be very similar since the design presents a high level of order and rotational symmetry. Nonetheless the pattern corresponding to the circular polarization exhibits a slightly sharper alternation between areas of destructive and constructive interference while the linear polarization exhibits an elongated pattern. As the diffraction pattern dependence is only fractional, all the simulations presented hereafter were done under circular polarized illumination.
The influence of the launch beam waist on the near field optical intensity evolution after the photon sieve was also studied, by modeling the propagation of different Gaussian source waists (defined as the distance between the points where the source Gaussian intensity decays to 1/e2 of its maximum value). Such variations may occur when light confinement is not the same as in the used optical fiber, either intentionally by design (usage of smaller core fibers) or non-intentionally by spurious effects. The simulations in Fig. 3 show an increased near-field modulation contributing to a sharper variation between maxima and minima of light intensity, with 4 axial foci within the first 20 μm of propagation for the larger beam waist illumination.
Fig. 3 Waist variation of the input field on the FDTD simulation of the PS with cylindrical pillars (with detch = 1.74 µm). Waist radii used were: (a) 3.0 μm, (b) 4.1 μm, (c) 5.2 μm, (d) 6.3 μm and (e) 7.4 μm.
Furthermore, the entire diffraction pattern moves towards the fiber tip as the launch beam waist increases, as seen in Fig. 4. This can be understood considering the classical way of defining a Fresnel zone/phase plate: these structures are classically defined for plane waves input, with the transparent zones (or same height zones in the case of phase plate) corresponding to areas of point sources for which the optical path lengths differ by λ/2, or less, from the optical path of the point source located on the axis of the design. The use of a Gaussian illumination has to be taken into account due to its non-constant radial distribution of intensity.
Fig. 4 Plot of the intensity along the optical axis for different simulated launch beam waist radii, as shown in Fig. 3.
As the waist radius of the Gaussian increases (always maintaining the total input power constant) the weight of the contributions of different pillars changes, as it does the sum of the individual fields of each individual source point on the design. As such we conclude that the illumination field distribution is a major factor, with an extended impact in the diffraction pattern, and so must be recognized as one of the factors to account when designing the structure.
During actual fabrication, there is an unavoidable rounding of steep height profiles. As such the ideal cylinders of constant height will have rounded corners and sloped sidewalls. Therefore, the smaller cylindrical pillars will be convolved into nose cone shapes as depicted in Fig. 5.
Fig. 5 (a) Lumerical FDTD photon sieve topography used for simulations presented in Fig. 6, obtained from (b) SEM micrograph of actual fabricated photon sieve. Note that (a) and (b) have different observation perspectives. Scale bar dimension is 5 µm.
Figure 6 shows the simulation of the fabricated device accounting for the varying pillar heights and their parabolic shape, obtained from SEM imaging of the fabricated photon sieves (see following section on Fabrication, Table 2) . As expected as the higher order rings of the PS are etched down their contribution for the diffractive pattern is reduced, leading to weaker field modulation and a loss of resolution with the corresponding blurring of the PS diffraction pattern, and decreasing of the maximum detectable intensities.
Fig. 6 XZ cross section of the intensity field profile by FDTD simulations of the PS accounting for the parabolic shape and decreasing height of the pillars on the fabricated PS (detch = 1.74 µm) with (a) Centered source at 1550 nm operation wavelength, (b) Centered source at 1540nm operation wavelength and (c) 1 μm x-coordinate displaced source at 1550nm operation wavelength.
Table 2. Height of the Pillars of the Fabricated Phase Photon Sieve
A study of the wavelength dependence of our device was conducted through a simulation of the fabricated structure illuminated by a centered 1540 nm source, as represented in Fig. 6(b). The result was very similar to the 1550 nm simulation, revealing very low wavelength dependence, within a reasonable source bandwidth.
To account for possible fabrication deficiencies and understand the acceptable fabrication tolerance, simulations were performed for different positions of the illumination relative to the milled pattern. Comparing the simulated diffraction pattern, for the case of a displaced illumination relative to the patterned area (1 µm off-center), with the diffraction pattern obtained by a perfectly aligned illumination, their similarity is obvious and expected. The slight effect of beam steering affecting the diffraction pattern is also expected, deflecting the first order maximum (central spot) on the opposite direction of the source displacement and intensifying the higher order maxima (rings) in the region closer to the displaced source, as depicted in Fig. 6(c).
3. Fabrication
A hybrid physical-chemical process was used based on hydrofluoric acid (HF) etch and focused ion beam (FIB) milling to carve the optical fiber and produce a difference in refractive indices between alternating zones.
The optical fiber employed was a single mode fiber at 1550 nm (Corning SMF-28e), with core and cladding diameters of 8.2 μm and 125 μm, respectively. The integrated single mode 1550 nm fiber PS has great potential as an input light coupling alternative for silicon photonics chips and nanophotonics circuits. Fiber preparation steps prior to FIB milling include locating the core on the optical fiber tip and deposition of a conductive coating to minimize charging of the silica fiber and thus minimizing patterning drift and distortion.
By etching with a 9.6% HF buffered dental porcelain gel for 5 minutes, it was possible to selectively etch the core of the single mode fiber, allowing us to mark the core location with precision. The verified etch rate was 60 nm/min for an etch depth of 325 nm, as obtained from Fig. 7. This step is essential to guarantee an easy identification of the core and the correct positioning of the pattern on the FIB-SEM dual system.
Fig. 7 SMF28e optical fiber etched in 9.6% HF buffered gel for a) 5 min, b) 10 min, c) 20 min and d) 40 min. It is visible the preferred etching of the fiber core. The etch depth in the core of the optical fiber is a) 325 nm, b) 590 nm, c) 1105 nm and d) 2365 nm. Scale bar dimension is 5 µm.
Examining Fig. 7 it is noticeable that as the etching time increases, a non-uniform etched area appears in the central region. This may be the result of non-idealities during the fabrication of the optical fiber, such as an unintentional non-uniform GeO2 doping of the fiber core or residual stresses induced by the wide thermal cycles a typical fiber endures during fabrication.
A FIB microscope is a powerful and versatile microfabrication instrument, patterning features down to the nanoscale, offering both deposition and milling directly on the substrate. Similarly to a scanning electron microscope (SEM) an image is generated in a FIB microscope by raster scanning the surface under analysis with particle irradiation focused to a spot by electron optics. In the case of a FIB, typically gallium ions are used, which upon interaction with the materials under irradiation lead to the emission of secondary electrons which are collected in an Everhart-Thornley detector. Due to the large mass of the gallium ion as compared to an electron, there is significant sputtering of the irradiated materials, which can be used for milling by controlling the raster scanning patterning and dwell time.
Modern FIB microscopes allow the control of the patterns to be transferred to a given sample by means of a customized bitmap image or a text stream file, handling both binary height steps or grayscale topography fabrication by modulation of the exposure dwell time by the pixel value on the bitmap or stream file [22].
In FIB based processes the sample must be electrically conductive to avoid charging effects on the surface, which would lead to distortion of the designed patterns. Instead of conventional sputtering or evaporation of a metal layer, an alternative method based on dip-coating of an organic conductive polymer such as PEDOT:PSS [poly(3,4-ethylenedioxythiophene) polystyrene sulfonate sourced from Ossila], was used. PEDOT:PSS is a water soluble polymer and it can be removed after the fiber tip milling, without the need for strong acid etch as commonly required when using platinum or gold sputtered coatings for charge mitigation. This method of sample preparation presents itself as a cheaper, easier and more practical solution due to its simplicity.
The fiber tip was dip coated by hand on the polymer and it was slowly drawn back. The dip coated layer was subsequently oven dried under vacuum (40°C, 10 Torr) for 15 minutes. After inspection of the fiber tips on a SEM, we estimated that coating thickness was inferior to 20 nm and that no surface-tension derived droplet formation is observable on the fiber tip.
Regarding the FIB patterning parameters, we had to take into consideration both electrical and thermal conductivity of the optical fiber to optimize the experimental parameters. Several tests were performed to assess aspects such as deformation of the structures, aspect ratio and milling time. Beforehand, the choice of a milling current as small as possible (in the range of 10 to 50 pA) could seem straightforward. However, as the milling time increases for smaller currents the drift effect was increasingly noticeable as a blurring of the fabricated pattern, due to sample charging and mechanical relaxation of the fiber adhesive to the SEM support. As such, the best choice of parameters for reliable patterning was found to be 30 keV of acceleration voltage for an ion current of 500 pA (35 nm ion beam diameter) resulting in a total patterning time of 20 minutes for our photon sieve design.
In the FIB microscope used in this work (FEI Quanta 3D), the patterning takes place on the white pixels of the bitmap file represented in Fig. 8(a), while the ion beam remains blanked on the black ones. So for the positive mask, the PS was a set of pillars and for the negative a set of holes. From test runs, we concluded that the degree of deformation was higher for the negative mask, since the individual features of the photon sieve became merged to each other.
Fig. 8 (a) Bitmap controlling the exposure scanning of the FIB, defining a photon sieve with 10 orders and (b) SEM micrograph top view of the fabricated structure.
After fabrication it was found that the actual PS etch depth was 1.73 µm, which is within the experimental error and in good agreement with the targeted depth of 1.74 µm. Despite the good control over the etch depth, the aspect ratio of each individual pillar diverged from the designed target, with critical incidence on the most outward and smallest elements which were over-etched and exhibited a nose shape on the z direction. This radial height gradient, summarized in Table 2, is due to the higher concentration of patterned elements at the edge of the design. In that region the distance between individual elements is smaller, so the proximity effect becomes more prominent, with greater impact in densely patterned areas.
4. Experimental setup and characterization
4.1 Experimental setup for near field scanning
The characterization of our fiber probe was carried out by using the experimental setup depicted in Fig. 9. An Agilent C-band tunable laser source was employed to inspect the fiber tip near field distribution at a wavelength of 1550 nm, carrying a total output power of 1 mW. Along the direction of propagation, ZZ, multiple XY scans with steps of 500 nm were performed with the patterned fiber tip fixed and a tapered lensed fiber, with a beam spot of 1.7 μm and working distance of 4.0 μm, placed in a closed-loop piezo-controlled XYZ stage.
Fig. 9 Experimental setup for near field diffraction pattern scanning: a - SMF28e optical fiber; b - patterned fiber tip under test; c - tapered fiber probe. Inset: details of the fiber tip and tapered probe fiber.
The measurement of the near field pattern was naturally affected by the acceptance angle of the fiber probe. In order to minimize the influence of the tapered fiber probe on the measured field pattern of the fabricated fiber phase photon sieve, a blind deconvolution was performed in MATLAB on the acquired set assuming a non-biased initial Point Spread Function, i.e., a 5 by 5 zero valued window [23].
4.2 Near field scans and discussion
The resulting field patterns and its dependence on the probe-fiber tip distance are plotted in Fig. 10. The measurement window wasn’t centered with the field pattern in order to measure higher order diffraction rings. It is clearly visible the diffraction pattern constituted by a concentric ring and central maximum of intensity. The ring doesn’t have a radial uniform intensity which could indicate an angle between the normal of the tip surface and the optical axis of the probe. That originates a XY translation of the field pattern in otherwise assumed transversal scanned slices, which can actually be tracked in field pattern slice plots: the central maximum of intensity moves along the YY direction with the distance to the fiber. Approximately 3 micrometers of vertical displacement for about 15.5 micrometers of displacement offset in the supposed optical axis corresponding to an angle of about 11° between the real optical axis and the initially supposed. This could either be due to an angular misalignment of the testing setup or due to a tilted cleaving of the fiber facet.
Fig. 10 Measured phase photon sieve near field distribution at: (a) 3.9 µm, (b) 8.9 µm, (c) 9.9 µm and (d) 16.4 µm from the patterned fiber end.
The diffraction pattern asymmetry also suggests that the input beam (corresponding to the fundamental fiber mode) may be slightly misaligned with the milled patterned, or a background modulation of the refractive index or topography of the fiber core is present. From the measured diffraction pattern, which shows asymmetry in the intensity distribution along the first order ring, and considering the simulation in Fig. 6(c), (simulation with the source displaced by 1 µm to the right) we can conclude that the fabricated structure may be displaced from the core, despite the HF selective core etching. As for the minor ellipticity observed, this is correlated to a small amount of astigmatism of the ion beam used to pattern the photon sieve.
In the measurement range of Fig. 11, the intensity at the center of the diffraction pattern is negligible until the fiber is about 6 micrometers away from the photon sieve optical fiber. At that point, the diffraction pattern starts to show an axial (2nd order) focal spot, which rises in intensity to its peak about 10 micrometers from the fiber surface, and shows a considerably long depth of focus, slowly decaying after the maximum value, as shown in Fig. 11 and Fig. 12. From the simulations in Fig. 2 and Fig. 6 is clear that the measurement only includes the second order maximum and that the field profile is elongated along the ZZ direction. The first order axial maximum was not easily measurable since the tilt of the fiber facet, previously referred, prevented a straight forward procedure of bringing the probe fiber close to the surface of the patterned fiber tip without touching it. The difficulty was also increased by the unexpected first order central maximum low intensity and small field depth. Therefore the first order central intensity maximum is not present in Fig. 11 measurement because it is located too closely to the fiber facet.
Fig. 11 XZ longitudinal-section of the measured power profile of the fabricated phase PS, as collected with a scanning tapered lensed fiber.
Fig. 12 Optical power collected by the tapered scanning fiber at the center of the optical field distribution as a function of the separation between photon-sieve and the tapered probe fiber.
The first order central maximum was measured using a smaller scanning window to avoid hitting the milled structure with the probe. A higher sampling frequency than in the previous measurements was used to comply with the smaller scanning window and to accommodate the details of the fast varying field near the tip facet. In Fig. 13, the first order axial maximum is observed surrounded by the first order diffraction ring. The maximum vanishes rapidly with the distance to the structure. These results are presented as measured due to the unreliability of the deconvolution method when applied to a limited scanning window.
Fig. 13 XY cross-section of the experimentally measured field intensity at 0.25 µm from the fiber end.
The evolution of the diffraction pattern with the propagation can be advantageous depending on the application: in the case of near-field photolithography the fabricated design allows to write two different features (dots or rings) by just adjusting the distance of the fiber to the surface to print; another application where the varying ring-central spot pattern shows advantages is in optical trapping since it allows to choose from one strongly confining central spot to the possibility of multi-particle trapping tolerated by the ring.
Since the field pattern is not absolutely radially symmetric, a cross-sectional analysis through two perpendicular orientation (horizontal and vertical) of the field pattern was performed in order to determine the full width at half maximum (FWHM) and the beam spot or spot size, defined as peak power divided by the square of the Euler number (1/e2 spot size), of the second order maximum. Fitting a Gaussian distribution to the central maximum, the FWHM along the two fitting directions was determined to be 1.11 μm and 0.91 μm, along the horizontal and vertical directions, respectively. The spot size was 1.48 μm and 1.63 μm, respectively.
To explain the relatively low intensity of the first order axial maximum and the position of the second order maximum further in ZZ than in the simulation, additional hypotheses were assumed and simulations performed, namely the possibility of having an obstacle blocking part of the patterned fiber tip. The blocking, or absorbing, obstruction maybe due to implanted gallium ions from the ion beam milling, combined with a thin carbon layer covering the top of the pillars. The origin of this carbon residue could be due to carbon contamination in the SEM/FIB vacuum chamber, a common issue on multi-user, general purpose microscopy facilities or due to the PEDOT:PSS being heat-affected by the ion milling process in neighboring spots. Another potential source for the absorbing or scattering obstacle at the center of the PS may be the residue left after the HF marking of the fiber core, as seen in Fig. 7.
An optical blocking circular layer of 5 µm of diameter, centered in the PS, was included in the FDTD model, corresponding to the inner diameter of the dark region showing in the first few micrometers of the ZZ axis in the measured field intensity in Fig. 11. Considering that the milling was performed in a circular region with approximately 16 µm of diameter, the presence of a gallium accumulation in a central region of about 5 µm diameter is understandable. Recalling Fig. 7, the non-uniform GeO2 doping of the core, which caused the non-uniform etch, may play a role on the emergence of the absorbing material in the central region of the core through the interaction of the higher concentration of GeO2 of such region with the incoming Ga ions.
The good agreement between this FDTD simulation and measurement (represented in Fig. 11 and Fig. 14, respectively) indeed validates the assumption of the presence of an absorptive material in the central region, hence explaining the difference with the simulation in Fig. 2, namely the weaker first order maximum and the shifting of the second maximum to a farthest z coordinate from the fiber facet. Regarding Fig. 13, since it is presented as measured, without the deconvolution post-processing, it is unsurprising that the small inner ring and maximum shown in the simulation are impossible to identify in the measurement due to resolution constraints.
Fig. 14 FDTD simulation for the PS with parabolic and varying height pillars with an absorbing coating on the top of the central pillar, and 1 µm shifted illumination; (a) XZ longitudinal cut of the intensity profile, and (b) XY cross-section of the field intensity at Z = 0.25 µm.
4.3 Application of the PS for light coupling
A performance test was also conducted, for which the light coupling capability into a silicon photonics waveguide (silicon core width = 400 nm, height = 220 nm, 3 micrometer thick buried oxide under cladding and 2 micrometers thick cladding) of our patterned SMF28 optical fiber tip was compared with a commercial conical lensed fiber from LaseOptics with spot size 1 μm ± 0.25 μm.
Figures 15 and 16 show the comparative coupling performance of both fibers for a CW laser with λ0 = 1550 nm. The scans were performed transversally and longitudinally to the waveguide, i.e. in XX and ZZ directions respectively. Due to experimental constraints, the measurement range in ZZ differs from one probe to the other; for that reason, at z = 1.0 μm, no scan for the LaseOptics probe is presented.
Fig. 15 1D scans of the power coupled into a Si single mode waveguide at different distances z, measured between the waveguide and the probe tip. The probes tested were a commercial conical lensed single mode fiber tip with (1 ± 0.25) μm spot size (LaseOptics) and the PS fiber tip. A cleaved SMF28e fiber was used in all experiments to collect light from the Si waveguide towards the fiber-coupled photodetector. The fibers and the Si waveguide are axially aligned when X is equal to 10 μm.
Fig. 16 2D spatial plots of the coupled power into the waveguide with (a) LaseOptics probe and (b) photon sieve probe. X coordinate represents the lateral shift between the silicon photonics waveguide and each fiber under test and the Z coordinate represents the axial separation between the silicon waveguide edge and the fiber tip. The fibers and the Si waveguide are axially aligned when X is equal to 10 μm.
In the opposite side of the silicon waveguide, a normally cleaved SMF28e fiber was used to collect the light from the waveguide and guide it to the fiber-coupled photodetector. This is the main reason for the large coupling losses in Fig. 15, which are not important for the comparative analysis between the tapered fiber and the photon sieve on a fiber tip. On the other hand, the large collection area of the SMF28e makes it almost insensitive to alignment variations, simplifying the experimental procedure and improving measurement stability.
In Fig. 17, the −3 dB width as a function of fiber to chip separation (Z) has been plotted, determined through the experimental coupled power into the silicon photonics waveguide shown in Fig. 16. For the photon sieve, the minimum −3dB width is 2.62 µm and the maximum peak value is −38.17 dB. As for the LaseOptics tapered fiber, we obtained 1.45 µm and −40.46 dB for the −3dB width and peak value, respectively. The previous plots highlight the enhanced performance of the fabricated fiber, when compared to the commercial available one. From Fig. 17(a) and (b) is clear the higher coupled peak power allowed by the PS fiber and its increased tolerance to lateral and longitudinal misalignment, reflected by the higher values of the −3 dB width and smaller sensitivity to z-displacement (−0.2 dB/μm for the PS versus −0.5 dB/μm for the tapered fiber).
Fig. 17 (a) −3dB width and (b) peak value of the coupled power into the waveguide for the two tested fibers as a function of the separation between the fibers’ tip and the Si waveguide.
5. Conclusion
In conclusion, the fabrication of a phase photon sieve on a single mode optical fiber tip has been presented. The diffractive element was patterned on the optical fiber tip by focused ion beam milling and successfully verified the advantages of dip-coating the fiber with the conductive polymer PEDOT:PSS as an alternative method to metallization prior to FIB milling. The influence of several parameters on the performance of the photon sieve fiber tip, such as the source beam waist and position have been evaluated by numerical simulations. Potential causes and sources of mismatch between simulations and experimental results have been identified. An application of the photon sieve fiber tip in light coupling to silicon photonics nanowaveguides has been demonstrated, with higher coupling efficiency (2.29 dB improvement) and higher alignment tolerance in both transversal and longitudinal directions.
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