1. INTRODUCTION

Optical vortex beams, due to their structured intensity profiles and orbital angular momentum (OAM) as an extra degree of freedom, can be used for next-generation optical and optoelectronic technologies. Such beams have been demonstrated to have improved performances over conventional optical beams in applications such as optical microscopy [1–3], communication [4–6], and optomechanical manipulation [7–9]. Vortex beams constitute a family of orthogonal mode sets of which multiple modes can simultaneously be harnessed in a complex system resulting in composite vortex (CV) beams. These CV beams have been demonstrated to expand the horizon of the application of optical vortex beams. CV beams consisting of multiple modes were used to experimentally demonstrate enhanced free space transmission capacity [10]. CV beams have been explored for simultaneous optical manipulation of multiple targets [11]. Differential rotational-Doppler shift in modes of a CV beam reflected from a rotating body was used to demonstrate remote detection of a spinning object [12]. Over the past few decades, there have been several reports on the generation, manipulation, and detection of different types of vortex beams [13–21]. These methods mostly relied on the use of commercially available off-the-shelf spatial light modulators (SLMs), displays, and optical components as the beam generation element, which made the setup large [22,23]. However, to expand the application domain of CV beams, integrated on-chip solutions are very desirable [24]. Recently, several methods have been reported to address this issue using fabricated on-chip structures such as phase plates [25,26], diffraction gratings [27,28], micro-cavities [29–31], and metasurfaces [20,32]. However, these are high aspect ratio structures and have a stringent constraint on dielectric thickness, determined by the wavelength ($\lambda$) of light and/or other design parameters. Fabrication and design of such structures, due to the thick dielectric layer, varying thickness profile, and high aspect ratio, are challenging tasks. Therefore, there is need for an on-chip integrated ultra-low aspect ratio structure for the generation of optical vortex beams in the visible range, with a simple and planar fabrication process.

In this work, a simple method is proposed for the efficient generation of CV beams in the leaked radiation from plasmon-coupled hybrid ultra-thin dielectric fork gratings (h-UFGs). Conventionally, dielectric gratings show a trade-off between the dielectric thickness and its diffraction efficiency [33]. For dielectric thickness $\ll \lambda$, the diffraction efficiency is reduced drastically and therefore needs to be enhanced. Transmission enhancement due to plasmon excitation in corrugated metal structures has earlier been reported [34]. In Section 2, based on a similar principle, it is computationally shown that the reduction in the efficiency of vortex beam generation can be compensated for by introducing a thin continuous gold layer (Au, 30 nm) between the grating and the substrate. Different UFGs with optimized geometric parameters were fabricated using standard electron beam lithography and characterized using leakage radiation microscopy. In Section 3, the optical properties of the vortex beams generated using the fabricated UFGs are discussed. These beams, depending on the grating vector, showed a specific wavelength and polarization selectivity. This method was further extended to enhance the diffraction efficiency of h-UFGs for the generation of CV beams. These results can help in designing integrated ultra-low aspect ratio optical-phase-singularity structures compatible with the planar fabrication process for enhanced functionality of optical sources, detectors, and sensors.

 

Fig. 1. Effect of dielectric and Au thickness. (a) Schematic cross-sectional illustrations of different UFG structures used in FDTD simulations, viz., Str-1: $\pi$-phase step $\approx \lambda$ thickness, Str-2: ultra-thin dielectric $\approx \lambda /10$ thickness, Str-3: ultra-thin dielectric/Au $\approx \lambda /10$ thickness with 30 nm Au layer. The grating period and fill factor are 550 nm and 0.5, respectively. (b) Simulated transmitted far-field diffraction pattern with a zoomed image of the first-OD to show the doughnut beam profile obtained in ${\pm}1$-OD. The apparent zeroth-OD distortion is due to overexposure of the zeroth-OD in the figure. (c) Comparison of first-OD intensities for three structures shown in (a) at two wavelengths, $\lambda = 632.8\;{\rm nm}$ and 532 nm, respectively shown as red and green bars. It can be observed that the diffraction efficiency decreases with the reduction in dielectric grating thickness for both wavelengths, but increases with the addition of the Au metal layer, although not for both the wavelengths. (d) Effect of Au thickness on the first-OD intensity showing maximum intensity at ${\approx} 30\;{\rm nm}$ thickness for $\lambda = 632.8\;{\rm nm}$. (e) Effect of grating period $\Lambda$ on resonance wavelength. It can be observed that the resonance wavelength shows a redshift with the increase in $\Lambda$. (f) ${E_z}$ profile for a small region of the grating cross section of Str 3 [shown in (a)] for TM incidence polarization, at three different wavelengths marked as points 1–3 in (e).

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2. PLASMON-INDUCED ENHANCEMENT IN UFG

A. Computational Analysis

UFGs of size $10\;\unicode{x00B5}{\rm m} \times 10\;\unicode{x00B5}{\rm m}$ and different dielectric thicknesses were simulated using a commercial finite-difference time-domain analysis software package (Lumerical FDTD Solutions). Figure 1(a) shows a schematic of the three simulated structures, viz., Str-1: $\pi$-phase step grating, Str-2: UFG, Str-3: UFG/Au, which consists of polymethyl methacrylate (PMMA) as a dielectric (grating period $\Lambda = 550\;{\rm nm}$; refractive index ${n_d} = 1.49$), defined on a semi-infinite glass as substrate (${n_{\rm{sub}}} = 1.52$) with semi-infinite air as supersaturate (${n_{\rm{air}}} = 1$). Figure 1(b) shows the transmitted far-field diffraction pattern and magnified first-order diffraction (OD) of a UFG, obtained for a monochromatic plane wave incident normally on these structures. The doughnut-shaped transverse intensity profile, a characteristic of optical vortex beams, was observed in the first-OD. For the unit intensity incident plane wave, the absolute diffraction efficiency of a diffraction order was calculated as the sum of intensities of all the pixels in that order. Further, for ease of comparison, absolute diffraction efficiencies of all the structures were normalized with respect to that of Str-1. Figure 1(c) shows the normalized diffraction efficiency of these structures for 532 nm and 632.8 nm incident wavelengths.

The diffraction efficiency of a binary phase grating is known to be maximum for $\pi$-phase step gratings [33]. Thus, the dielectric thickness for Str-1 was chosen to be $0.5\lambda /({n_d} - 1)$, i.e., 645 nm and 543 nm PMMA for 632.8 nm and 532 nm excitation wavelengths, respectively. As expected, the reduction in dielectric thickness resulted in the reduction of the first-OD efficiency of Str-2. For UFGs of thickness 80 nm (Str-2), the normalized diffraction efficiency was reduced to 18.7% for 632.8 nm and 3.3% for 532 nm, as shown in Fig. 1(c). In Str-3, an Au layer was introduced between the grating and the substrate and was simulated for different Au thicknesses (${t_{\rm{Au}}}$). The first-OD intensity for different ${t_{\rm{Au}}}$ showed a bell-shaped behavior for $\lambda = 632.8\;{\rm nm}$ with the maximum at ${t_{\rm{Au}}} \approx 30\;{\rm nm}$, as shown in Fig. 1(d). For the optimized thickness of 30 nm, the first-OD efficiency was enhanced and was found to be almost equal (88.5%) to that of Str-1 at 632.8 nm excitation wavelength; however, no such enhancement was observed at 532 nm excitation. This can be understood from the simulated first-OD transmission intensity plot shown in Fig. 1(e), which shows the dependence of the resonance wavelength of UFG/Au structures on the grating period. It was observed that the 550 nm period UFG/Au was resonant at red wavelengths and not at the green. For the red and higher wavelengths, the 550 nm grating period is sub-wavelength in nature, such that the first-OD is evanescent on the air side. Surface plasmon polaritons (SPPs) are excited on the grating–Au interface for the wavelength at which the momentum of the evanescent wave satisfies the SPP dispersion relation [35]. This was corroborated by the field enhancement in the electric field plot simulated for three different wavelengths for transverse magnetic (TM) incident polarization, as shown in Fig. 1(f). The $z$ component of the electric field (${E_z}$) was enhanced at the resonant wavelength when compared to the off-resonant wavelengths. This field enhancement was not observed for transverse electric (TE) incident polarization (not shown here), as SPP exists only for TM polarization [35]. Owing to two factors—SPP decay length in Au being much greater than the Au layer thickness, and SPP momentum matching with a substrate radiative mode—the power in the excited SPP mode is coupled to the matched radiative mode in glass substrate as leaked radiation [36]. Thus, the resonance peak in the leaked first-OD intensity plot shown in Fig. 1(e) was observed for TM but not for TE polarization. Further, it is important to note that Str-3 has an additional reflection and absorption due to the Au layer, and hence the total transmitted power in these two structures is different. Therefore, for a better comparison of power in the first-OD, the relative diffraction efficiency, defined as the fraction of the transmitted power in the first-OD, was calculated and found to be 18 times higher for Str-3 when compared to Str-2.

 

Fig. 2. Experimental setup. (a) Schematic of the experimental setup used for characterization. ${\theta _G}$ represents the azimuthal angle of the grating vector, whereas ${\theta _P}$ and ${\theta _A}$ respectively represent the azimuthal angle of the polarizer and analyzer pass axis with reference to ${\theta _G}$. (b) SEM image of $\Lambda = 550\;{\rm nm}$ and $\ell = 4$ UFG/Au sample. (c) Small segment of the real plane image of UFGs/Au of $\Lambda = 400\;{\rm nm}$ and 550 nm in CPA configuration (${\theta _P}= 45^ \circ$, ${\theta _A} = - {45^ \circ}$) under broadband illumination. It can be observed that the color of the UFG/Au image changes with $\Lambda$. (d) Fourier plane image of a $\Lambda = 550\;{\rm nm}$, $\ell = 16$ UFG/Au in CPA configuration under red laser illumination. It can be observed that both first orders show doughnut beam intensity profile, and the zeroth order is suppressed. (e) Interferogram of the first-OD of UFGs/Au with a reference Gaussian beam for three different values of $\ell$.

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B. Experimental Methods

PMMA (950 k, A2) was spin-coated on Au (30 nm) coated BK7 glass cover-slips, and its thickness was measured to be ${\sim}80\;{\rm nm}$ using a spectroscopic ellipsometer. Standard electron beam lithography was used to fabricate $200\;\unicode{x00B5}{\rm m} \times 200\;\unicode{x00B5}{\rm m}$ UFGs with different charges ($\ell$) and $\Lambda = 400\;{\rm nm}$ and 550 nm. Figure 2(b) shows an SEM image of one of the fabricated UFGs/Au ($\Lambda = 550\;{\rm nm}$, $\ell = 4$) around the fork dislocation. These UFGs were characterized for their optical response using an inverted optical microscope (Nikon TiU Eclipse) in transmission mode, schematic shown in Fig. 2(a). A high numerical aperture (${\rm NA} = 1.45$) $100 \times$ oil immersion objective was used to collect the plasmon decoupled leakage radiation from UFG/Au samples. A linear polarizer was used to polarize the incident light from two optical sources, a 632.8 nm He–Ne laser and 532 nm solid-state laser, illuminating the sample at normal incidence. The transmitted light was collected using the microscope objective and passed through another polarizer, labeled as an analyzer, before capturing real plane and Fourier plane (FP) images of the sample using a camera. The pass axes of the polarizer (${\theta _P}$) and analyzer (${\theta _A}$) were specified with reference to the direction of the grating vector (${\theta _G} \equiv {0^ \circ}$). A crossed polarizer–analyzer (CPA, ${\theta _P}= 45^ \circ,\;{\theta _A}= 135^ \circ$) configuration was used to block the direct transmission, i.e., the zeroth-OD, and capture the leaked radiation, i.e., first-OD. To study the polarization properties of the vortex beams, an iris diaphragm before the camera was used to isolate the leaked radiation. Figure 2(c) shows the real plane images of UFGs ($\Lambda = 400\;{\rm nm}$ and 550 nm) captured using a broadband ($\lambda \approx 400\;{\rm nm}-700\;{\rm nm} $) tungsten halogen lamp for illumination in the CPA configuration. The dominant green and red colors, respectively, for $\Lambda = 400\;{\rm nm}$ and 550 nm UFGs were observed due to the excitation of lattice-plasmon resonance at the respective wavelengths, i.e., wavelengths of the leaked radiation. Figure 2(d) shows the FP image of a UFG ($\Lambda = 550\;{\rm nm}$, $\ell = 16$) under red laser illumination. The doughnut beam obtained in the first-OD was interfered with a reference Gaussian beam to confirm the presence of phase singularity. Figure 2(e) shows the interferogram obtained for three different UFGs ($\Lambda = 550\;{\rm nm}$, $\ell = 2$, 4, and 16), where the number of edge dislocations corresponds to the topological charge of the phase singularity.

3. RESULTS AND DISCUSSION

The fabricated UFGs/Au were characterized in FP under monochromatic illumination to understand the polarization properties of UFGs. Figure 3 shows FP images of the leaked radiation for $\Lambda = 550\;{\rm nm}$, $\ell = 4$ UFGs/Au under $\lambda = 632.8\;{\rm nm}$ laser illumination, for different polarizer–analyzer configurations. First, ${\theta _P}$ was varied from 0° to 90° without inserting the analyzer in the optical path to understand the effect of incident polarization on first-order coupling efficiency. It was observed that first-OD efficiency was maximum (5.7% of zeroth-OD) for ${\theta _P}= 0^ \circ$, i.e., TM polarization, and decreased monotonically to a minimum (0.6% of zeroth-OD) at ${\theta _P}= 90^ \circ$, i.e., TE polarization, as shown in the first column of Fig. 3. This was due to the fact that the first-OD of the TM component can couple to SPP on the air–Au interface, the radiative decay of which resulted in enhanced transmission, whereas the same was not true for the TE component. [34].

 

Fig. 3. Intensity profiles of the first-OD of $\Lambda = 550\;{\rm nm}$, $\ell = 4$ UFGs/Au, for different polarizer–analyzer configurations, under identical red laser illumination and camera exposure settings. Dashed-line borders show the CPA configuration. It can be observed that UFGs/Au have polarization selectivity.

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Next, an analyzer was introduced in the setup to determine the polarization of the vortex beam in the leaked radiation. It was observed that for both TE and TM, the polarization of the leaked radiation remained the same as incident polarization, i.e., no polarization rotation from UFGs. For any other ${\theta _P}$, the incident polarization can be represented as the weighted sum of intensities and polarization of TM and TE, and so was observed in the leaked radiation. However, due to the higher coupling efficiency of the first-order TM component, the weights of the components in the leaked radiation were different from that of the incident beam, resulting in polarization rotation. These effects can be observed in Fig. 3 for ${\theta _P}= 45^ \circ$ (equal TM and TE in the incident beam), where due to the dominant TM component in the leaked radiation, the resultant polarization of the leaked radiation was rotated to TM, i.e., maximum intensity for ${\theta _A}= 180^ \circ$. The polarization rotation was found to be maximum in this case, i.e., ${\theta _P}= 45^ \circ$ and decreased to zero for both ${\theta _P}= 0^ \circ$ and 90°, as can be inferred from the CPA configurations highlighted by the white dotted boundary in Fig. 3. For further characterizations, zeroth-OD was eliminated by using a CPA configuration with ${\theta _P}= 45^ \circ$.

The fabricated UFGs/Au of $\Lambda = 400\;{\rm nm}$ and 550 nm, designed to be resonant with green and red incident wavelengths, respectively, were characterized for their wavelength selectivity by co-illuminating them with wavelengths $\lambda = 532\;{\rm nm}$ and 632.8 nm. The intensities of both sources were adjusted to have equal contribution in the zeroth-OD. Figure 4 shows the intensity profile of the leaked radiation of UFGs of $\ell = 2,4,16$ for each $\Lambda$. It was observed that although the incident beam had both red and green wavelengths, the leaked radiation showed the vortex beam with a dominant wavelength corresponding to the respective resonant wavelength. The red to green wavelength contrast ratio for $\Lambda = 400\;{\rm nm}$ (550 nm) was calculated to be ${\approx} 2{:}51$ (17:2), showing the selection of the resonant wavelength and strong quenching of the non-resonant ones. These SPP vortex fields carry OAM, and the generation of these fields can be attributed to the superposition of planar SPPs with specific spatial phase distribution [37]. Interestingly, it was also observed that the outer $1/{e^2}$ intensity radius ${\rho ^\ell}$ at a given wavelength was independent of charge $\ell$, as can be seen in Fig. 4, and was decided by the physical size of the UFG. This can be attributed to the collection optics of the microscope, where the vortex beam generated by the UFG was immediately collimated by the short working distance (0.17 mm) and high NA (1.4) $100 \times$ objective lens. This can be explained with the assumption that ${\rho ^\ell}$ at the point of generation (just after the UFG/Au) is equal for all $\ell$ and is dependent on the physical size of the UFG. The relation between ${\rho ^\ell}$ and the beam waist $w$ of the generated vortex beam is given by Eq. (1) [38]:

Equation (2) can be derived using Eqs. (1), (1a), and (1b) for ${\rho ^\ell}$ in terms of the Rayleigh range ${z_R}$ of the generated vortex beam:

 

Fig. 4. Intensity profiles of vortex beams obtained in the leaked radiation of UFGs/Au for different charges $\ell = 2$, 4, and 16 and grating period $\Lambda = 400\;{\rm nm}$ and 550 nm for CPA configuration and co-illumination with wavelengths $\lambda = 532\;{\rm nm}$ and 632.8 nm. It can be observed that UFGs/Au have wavelength selectivity.

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For the experimentally relevant values of $\lambda = 632.8\;{\rm nm}$, $\rho _0^\ell = 100\;\unicode{x00B5}{\rm m}$, $z = 0.17\;{\rm mm}$, and $|\ell | \le 16$, the value of $z/{z_R}$ calculated using Eq. (2a) was ${\lt}1/23$. Thus, Eq. (2) is simplified to ${\rho ^\ell}(z) \approx \rho _0^\ell = 100\;\unicode{x00B5}{\rm m}$, i.e., equal to the physical size of the UFG and independent of $\ell$. The same was found to be true even at the output Fourier port of the microscope where $\rho _0^\ell$ and $z$ were 3 mm and 15 cm, respectively.

The UFGs/Au were structurally modified by replacing their central regions with other UFGs of different $\ell$ to generate plasmon-coupled CV beams. The resultant hybrid structure consisted of an inner disc region of radius ${r_{\rm{in}}} = 50\;\unicode{x00B5}{\rm m}$ and an outer hollow disc region of radii ${r_{\rm{in}}} = 50\;\unicode{x00B5}{\rm m}$ and ${r_{\rm{out}}} = 100\;\unicode{x00B5}{\rm m}$. The detailed design of these hybrid gratings for the generation of CV beams has been reported earlier [39]. H-UFGs with $\Lambda = 550\;{\rm nm}$ and different combinations of inner (${\ell _{\rm{in}}}$) and outer (${\ell _{\rm{out}}}$) charges were designed and characterized for the generation of plasmon-coupled CV beams. Figure 5(a) shows a schematic of a fabricated h-UFG and the experimentally obtained intensity profile of a plasmon-coupled CV beam in the leaked radiation for ${\ell _{\rm{out}}} = + 2$ (upright fork) and ${\ell _{\rm{in}}} = - 2$ (inverted fork) combination. It can be inferred from the interferogram that the central null in the intensity profile corresponds to a phase singularity of charge ${-}{2}$, whereas the four peripheral nulls correspond to a phase singularity of charge ${+}{1}$. To better understand experimentally observed intensity profiles, the transverse intensity and phase profiles of these CV beams were also generated analytically. The analytical expression of the TE field profile of a CV beam in cylindrical coordinates ($r,\phi$) is given by Eq. (3), as the sum of Laguerre Gaussian (LG) modes corresponding to the inner (${{\rm LG}^{{\ell _{\rm{in}}}}}$) and outer (${{\rm LG}^{{\ell _{\rm{out}}}}}$) regions of the h-UFGs [39]. The intensity and phase profile obtained using this equation for ${\ell _{\rm{in}}} = - 2$ and ${\ell _{\rm{out}}} = + 2$ is shown in Fig. 5(b) in the first column. The differences in the analytical and the experimental results were attributed to two reasons. First, the beam radii of ${{\rm LG}^{{\ell _{\rm{in}}}}}$ and ${{\rm LG}^{{\ell _{\rm{out}}}}}$ should be different, as they are respectively dependent on the size of the inner and the outer regions (as discussed earlier with reference to Fig. 4). Second, the outer region of an h-UFG is a hollow disc and has an extra parameter ${r_{\rm{in}}}$, which affects the resultant beam shape. Similar to the relation between the $1/{e^2}$ beam radius and the UFG radius, the inner and outer $1/{e^2}$ radii of the beam intensity profile of the vortex beam ${{\rm LG}^{{\ell _{\rm{out}}}}}$ generated from the hollow disc region can be shown to be independent of ${\ell _{\rm{out}}}$ and determined by the physical size of the h-UFG (${r_{\rm{in}}} = 50\;\unicode{x00B5}{\rm m}$, ${r_{\rm{out}}} = 100\;\unicode{x00B5}{\rm m}$). Therefore, to account for these observed properties of CV beams, the standard LG mode equation was modified appropriately for the inner and outer regions as given in Eq. (4):

 

Fig. 5. CV beams generation using h-UFGs: (a) schematic of a ${\ell _{\rm{in}}}/{\ell _{\rm{out}}} = - 2/ + 2$ h-UFG along with the experimentally obtained intensity profile and interferogram of leaked radiation. The interferogram shows an inverted fork of charge two at the center surrounded by four upright forks, each of charge one. (b) Analytically generated intensity and phase profiles of CV beam as the sum of $\ell = - 2$ and $\ell = + 2$ LG beams. The first column shows the analytical results for the two LG beams having the same beam waist ($w$). The second column shows the analytical results for the adjusted $w$, to obtain better resemblance to the experimentally obtained intensity profile. In the third column, the radius of curvature ($R$) of the two LG beams was adjusted to obtain a further closer resemblance to the experimental results. The white dotted circles indicate the positions of phase singularity.

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Figure 6 shows the experimental and analytical intensity profiles for different ${\ell _{\rm{in}}}/{\ell _{\rm{out}}}$ combinations. The formation of these composite beams in the leaked radiation from h-UFGs indicated that the different spatial phase profiles imparted to the SPP in the different regions of the hybrid gratings were preserved in the leaked radiation. Further, it can be observed that the radius of the CV beam intensity profile was insensitive to both constituent charges ${\ell _{\rm{in}}}$ and ${\ell _{\rm{out}}}$, similar to the simple vortex beams shown in Fig. 4. From the analytical analysis, it was observed that the generated CV beams showed intensity profiles with a central null of charge ${\ell _{\rm{in}}}$ surrounded by $|{\ell _{\rm{out}}} - {\ell _{\rm{in}}}|$ number of peripheral nulls each of charge unity, which was similar to that obtained using an SLM in our earlier paper [39]. All generated CV beams were found to be TM polarized, identical to those of the individual modes of vortex beams, as discussed above. Compared to the CV beams generated using SLM, the beams generated using UFGs/Au showed beam intensity radii insensitive to ${\ell _{{\rm in}}}$ and ${\ell _{{\rm out}}}$. Also, these beams were wavelength and polarization selective, along with a much smaller footprint, making UFG/Au a potential candidate for on-chip low aspect ratio i.e., the ratio of dielectric thickness to dielectric width (here 80 nm:275 nm or $80 \; {\rm nm}:200 \;{\rm nm} \lt 0.4$) structures for efficient CV beam generation.

 

Fig. 6. Plasmon-coupled CV beams: experimentally obtained (top) and analytically generated (bottom) intensity profiles of CV beams for different ${\ell _{\rm{in}}}/{\ell _{\rm{out}}}$ combinations.

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4. CONCLUSION

Through simulations, UFGs/Au were shown to be efficient for the generation of vortex beams. Through experiments, UFGs/Au were shown to be polarization and wavelength selective. The outer radii of the beams thus generated were found to be independent of $\ell$ and decided by the physical size of the gratings. Finally, h-UFGs/Au were used for the generation of plasmon-coupled CV beams. These CV beams were also polarization and wavelength selective. These results show that UFGs/Au have the potential for applications involving on-chip optoelectronic devices and sensors.