1. Introduction

An optical vortex beam is a beam that possesses a phase distribution along the azimuthal direction. The beam has a doughnut-shaped intensity profile with null intensity at the center of the beam cross-section due to a phase singularity, exhibiting a well-known Laguerre–Gaussian mode, which is a solution of the paraxial wave equation with a cylindrical coordinate system. Due to the spiral phase front, the beam has optical angular momentum. Because of these peculiar characteristics, optical vortex beams have attracted much attention in a variety of applications, such as optical multiplexing transmission [1], quantum information communication [2], and optical tweezers [3]. Furthermore, nano-order material processing using a high-power, short-pulse optical vortex beam has also been reported, and these beams are also very interesting for use in materials processing [4].

This kind of beam, which is also called an optical angular momentum (OAM) beam, is mainly generated by using a hologram that is constructed by superposition of a Gaussian mode and a Laguerre–Gaussian (LG) mode [5], or by using the spiral phase plate that gives the beam an optical path difference along the azimuthal direction [6]. In the former case, the + 1 or −1 order diffracted beams that pass through the hologram are used. Therefore, the configuration is simple, but the beam axis is different from that of the incident plane wave. In the latter case, although the beam axis is the same as that of the incident plane wave, the spiral phase plate needs high accuracy in order to add an optical path difference smaller than the wavelength. Very recently, different approaches have been proposed, such as using a meta-surface to realize a spatial phase modulator [7] and using a silicon ring waveguide to diffract different phases [8]. All of these approaches, however, require elements external to the optical sources. On the other hand, one approach for making an optical vortex mode generator in a single chip by using a VCSEL and a ring-DBR waveguide has been suggested. In this approach, the VCSEL is used not as a vertical light emitter but for propagating light in the horizontal direction and for diffracting the mode by changing the diffraction phase on the ring-shaped waveguide [9]. Although this approach can realize a single-chip optical vortex mode emitter, the beam cannot be generated with a doughnut shape but with a semicircular shape, because of its structure.

From the above circumstances, we considered photonic-crystal surface-emitting lasers (PCSELs) as candidacies for realizing a single-chip optical vortex beam source. PCSELs are semiconductor lasers that use the photonic crystals’ large area, two-dimensional resonant effect, and surface-emitting lasing action whose output light is diffracted in the vertical direction of the photonic crystal [10–12]. In principle, the lasers can maintain single-mode lasing over a large area; as a result, 200 μm² lasers with powers of 1 W under continuous-wave conditions while maintaining an M² value of ~1 have been realized [13]. Because of these characteristics, these lasers have been considered as optical sources for generating ideal Gaussian beams. There is also a possibility of processing the laser output surface. Therefore, if optical elements that give a phase difference along the azimuthal direction to the output beam could be integrated with the laser in a simple way, it would be possible to obtain a vortex beam from a single chip. In future, such devices are expected to be universally used in the fields of communication and microscopy due to their compactness, as well as in laser processing due to their high-power oscillation. In this paper, we show the generation of an optical vortex beam by processing a quasi-spiral phase plate on the substrate surface of a PCSEL.

This manuscript consists of four sections, including this introduction. In Section 2, we describe the process of fabricating a surface-processed PCSEL for generating an optical vortex beam. In Section 3, we describe the characterization of the output beam emitted by the fabricated laser, in terms of the far-field patterns and phase distributions, compared with those from an unprocessed PCSEL. In Section 4, we summarize this manuscript and describe future prospects.

2. Fabrication of surface-processed photonic-crystal lasers

A PCSEL possesses a two-dimensional photonic-crystal layer near the active layer of a conventional semiconductor laser structure. Figure 1(a) shows a schematic image of its structure. The PCSEL that we describe here consisted of GaAs/InGaAs multiple quantum wells in an active layer based on GaAs materials, and its lasing wavelength was designed to be 980 nm. We first prepared a two-dimensional photonic crystal with right-angled isosceles triangle air-holes in order to obtain a beam close to an ideal Gaussian beam [14,15], with a square lattice arrangement having a lattice constant equal to that of the wavelength in the medium, as shown in Fig. 1(b). With this photonic crystal structure, the output beam is diffracted in the vertical direction, because it uses a two-dimensional resonance mode at the Γ-point of the photonic-crystal band structure. This photonic-crystal layer is embedded in a laser structure having a p-n junction formed by a wafer bonding technique [16], and the beam emission surface of the GaAs substrate is processed to fabricate a three-dimensional, eight-segmented spiral structure that gives the beam a phase difference of 0 to 2π along the azimuthal direction. In this case, each step is 40 nm in consideration of the wavelength in the medium. Thus, a 1st order Laguerre–Gaussian beam can be obtained from the top surface of the device. We performed photolithography on the n-type GaAs substrate by aligning the center point of a p-type electrode prepared at the bottom of the device, which corresponds to the center of the electrically driven area, in other words, the beam envelope, using an infrared transmitted image. Photomasks with three different patterns were prepared, as shown in Fig. 1(c). After performing exposure with pattern 1, we placed the structure into a solution of sulfuric acid and hydrogen peroxide to etch to a depth of 160 nm using the pattern mask. Then, we aligned and exposed pattern 2 and etched to a depth of 80 nm. Finally, using pattern 3, we etched to a depth of 40 nm. As a result, a spatial phase plate with eight divisions having steps of 40 nm each was processed on the top surface of the PCSEL. Figure 1(d) shows an image of the top surface obtained by atomic force microscopy (AFM) after the processing. By averaging out the surface roughness of each step, we confirmed that the height of each step is ~40 nm. The maximum surface irregularity (peak to valley) was ~10 nm in height and ~600 nm in diameter. This height was less than 5% of the wavelength in the medium and the diameter was less than 2% of beam diameter. Therefore, we considered that such roughness may cause scattering, but that it should not disturb the beam profile. The misalignment between the center of the p-side electrode and the center of the structure was ~3 μm, judging from the transmitted image obtained by an infrared camera. It is worth mentioning that such surface processing can, of course, be performed by dry-etching as well as by a wet-etching process. However, at least in our evaluation, the roughness of the surface using the wet-etching process was better than that using the dry-etching process, because of the by-products of resist and etching gas deposited during the repeating patterning and etching steps, which are difficult to completely remove. After the above surface processing, we deposited an insulator on the top surface with an adequate thickness to be non-reflective, formed an n-side window electrode, and then mounted the chip to complete the surface-processed PCSEL.

 

Fig. 1 (a) Schematic image of a photonic-crystal surface-emitting laser (PCSEL). (b) Scanning electron microscope (SEM) image of photonic-crystal layer with lattice constant a = 294 nm. (c) Fabrication process of 8-segmented spiral structure on the top surface of the PCSEL. We performed photolithography and wet-etching three times with three different masks. (d) Atomic force microscopy (AFM) image of the processed surface.

Download Full Size | PDF

3. Characterization

3.1 Far-field pattern and polarization

Figure 2(a) shows the far-field pattern from a non-surface-processed PCSEL and Fig. 2(b) shows that from a surface-processed PCSEL prepared with an identical process except for the surface processing. Without surface processing, the far-field pattern showed a perfect single lobe, whereas with surface processing, the beam had a null point. A single lasing peak was observed as shown in the spectrum in Fig. 2(c). (The broad emission at longer wavelengths is due to spontaneous emission.) Figs. 2(d) and 2(e) show beam polarization profiles of the two PCSELs. The beam from the non-surface-processed PCSEL has dominant intensity in the direction of 0 degree polarization rather than in the direction of 90 degree polarization. Its distribution in the 0 degree direction is a single lobe, while that in the 90 degree direction is a double lobe. Likewise, the beam from the surface-processed PCSEL has dominant intensity in the direction of 0 degree polarization rather than in the direction of 90 degree polarization. However, here the intensity distributions in both directions are double lobes. Judging by the change of intensity distribution in the 0 degree direction, we suggest that a null point has appeared due to a phase singularity. The reason that the beams have intensity in the direction of 90 degree polarization is presumably because the photonic-crystal lattice points were not perfectly asymmetric [12,15].

 

Fig. 2 Far-field patterns of (a) non-surface-processed PCSEL and (b) surface-processed PCSEL. (c) Lasing spectrum of (b). (d, e) Polarization profiles of (a, b).

Download Full Size | PDF

Next, it is worth noting that the beam intensity in Fig. 2(b) has an uneven distribution. As shown in Fig. 2(a), the beam was obtained from a single-lobed beam that passed through the spatial phase plate shown in Fig. 1(d). The misalignment of the surface processing was approximately 3 μm, as mentioned in Section 2, and the position difference between the center of the surface processed area and the center of the p-type electrode that mainly dictates the beam intensity envelope (more accurately, errors due to current injection and fabrication errors are included) was evaluated to be 3 μm. Such alignment errors cause the output beam to be a superposition of a Gaussian mode and a Laguerre–Gaussian mode. We confirmed that when we assumed a maximum optical axis difference of 6 μm between the Gaussian mode and the Laguerre–Gaussian mode, an uneven beam intensity distribution was obtained.

3.2 Interference patterns

Motivated by the above characteristics, next we evaluated the beam phase front by using the self-interference method. The experimental set-up is shown in Fig. 3(a). The output beam from the PCSEL was collimated, was transmitted through a double slit, formed of two slits with 5 μm width and 200 μm separation, and was then focused onto a CCD camera using a lens. The beam was collimated to a size much larger than the slit separation of 200 μm. When the beams that passed through the slits interfered on the screen (CCD), the phase difference between positions A and B (both y positions were the same) in Fig. 3(b) can be written as:

 

Fig. 3 (a) Experimental set-up for evaluating self-interference patterns. (b) Schematic image of the beam (l = 1) passing through the double slits and phase difference between the slits. (c) Calculation results of self-interference pattern of vortex beam. Experimental results from (d) non-surface-processed PCSEL and (e) surface-processed PCSEL. Twisted interference fringes are clearly observed in (e).

Download Full Size | PDF

Figures 3(d) and 3(e) show the self-interference patterns of the beams from the non-surfaced-processed PCSEL and the surface-processed PCSEL, respectively. In the case of the surface-processed PCSEL, twisted interference fringes were observed, whereas parallel interference fringes were observed in the case of the non-surface-processed PCSEL. The result for the surface-processed PCSEL clearly shows that a null point at the center of the beam cross-section was generated by the phase singularity.

4. Summary

We have generated an optical-vortex beam by fabricating an eight-segmented phase plate on the top surface of a PCSEL. Even though there has been an uneven beam intensity distribution, the self-interference fringes have clearly shown the beam’s phase singularity. The uneven intensity profile is caused by the unavoidable error which is due to the fact that the beam intensity envelope is not precisely the same as the center of the electrode, because of the current injection errors caused by the mounting process. In future, it is expected that an optical vortex beam will be generated by designing the photonic crystal itself. The optical vortex beams generated by PCSELs, which are semiconductor lasers having the potential to be both compact and high power, are promising for expanding the applications of such beams to a wider range of fields (including laser processing).