Open Access
Add to BibSonomy
Abstract
Focusing is a fundamental optical technique that has been widely implemented via lenses. Here, we demonstrate direct focusing from a band-edge surface-emitting laser, whose emission area is 200 µm × 200 µm, without any lenses. To achieve this, a phase-modulating layer is incorporated into the laser cavity. This layer acts simultaneously as a lasing cavity similar to that of a photonic crystal laser and as a holographic spatial-phase modulator, which transforms the output beam into a focusing beam by slightly shifting the positions of holes from a periodic square lattice. Beam profiles along the surface normal clearly show that direct focusing occurs with a focal length and focal spot size of 310 µm and 6.1 µm, respectively. The focal length agrees well with the theoretical value, and the focal spot size is 2.0 times the diffraction-limited size, which indicates that the higher transverse modes are sufficiently suppressed. In addition, the power density at the focus is 540 times higher than that at the near-field plane. Interestingly, a focus pattern is also observed in the opposite direction at the near-field plane, which indicates that a converging beam and a diverging beam are simultaneously emitted because of the nature of the in-plane band-edge laser. The conventional beam patterns of semiconductor laser cavities are limited to the regime of two-dimensional projection based on a Fourier hologram. In contrast, we demonstrate the simplest form of a three-dimensional point cloud based on a Fresnel hologram, which is quite useful for micro-sensing applications such as microfluidics, flow cytometry, blood sensors, and endoscopy.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Since the development of semiconductor lasers [1] in the early 1960s, they have spread throughout modern society because of their compactness, high efficiency, and high reliability. However, the output beam patterns of ordinary edge-emitting semiconductor lasers are asymmetric and must be reshaped through coupling of lenses for collimation, correction of astigmatism, and focusing, depending on the application. Inevitably these discrete optical elements, which must be aligned accurately, make production more complex and hinder stability and robustness.
In contrast, surface-emitting lasers (SELs), such as the vertical-cavity surface-emitting laser (VCSEL), offer a circular beam pattern and a planar fabrication process that easily supports coupling with a microlens [2] or metalens [3–5]. The photonic crystal surface-emitting laser (PCSEL) [6–9] which is developed by Noda’s group is especially attractive because it offers a collimated light source with a narrow beam divergence that also enables lens free. Later they developed the Modulated-PCSEL (M-PCSEL) [10–12] in which the positional or areal modulation is introduced into the PC cavity so as to control the beam pattern. On the basis of the PCSEL technologies, we developed and demonstrated two-dimensional (2D) beam patterns by introducing modulation of a 2D photonic crystal (PC). This is achieved by shifting the positions of holes from periodic lattice points according to a detour phase hologram [13,14]. We call the resulting laser an integrable phase-modulating surface-emitting laser (iPMSEL) [15–21]. For all SELs, although the planar process is suitable for lens integration, alignment errors are unavoidable. In this sense, integration of the focusing property into the lasing cavity would be highly desirable because it would lead to a perfectly aligned light source while not requiring any space for lens placement.
However, the output beam pattern is still limited to controlling the far-field pattern (FFP), which is a 2D projection as shown in Fig. 1(a), whereas focusing within a finite distance requires the formation of 3D point clouds as shown in Fig. 1(b). The distinguishing feature between these approaches is the light waves composing the output beam patterns (see supplementary section S1) [13,22]. Specifically, the 2D beam pattern is treated as a linear combination of plane waves, which corresponds to a Fourier hologram, as shown in Fig. 1(c). In contrast, the 3D beam pattern is treated as a linear combination of parabolic waves, which corresponds to a Fresnel hologram, as shown in Fig. 1(d). In other words, the 2D beam pattern is an ordinary pattern projection, whereas the 3D beam pattern enables focusing, thereby ultimately enabling 3D imaging. Complete “holographic” control of the output beam thus requires 3D control. To demonstrate the simplest form of a 3D beam pattern, we have obtained direct focusing from an iPMSEL for the first time by imposing parabolic phase modulation.
Fig. 1. Schematics of (a) a 2D projection and (b) a 3D point cloud. (c) The 2D projection is composed of plane waves, whereas (d) the 3D point cloud is composed of parabolically distorted light waves.
In this work, first, we describe the iPMSEL device structure and the design of its phase-modulating layer for focusing. Second, we describe how we measured the device’s lasing characteristics, including the beam profile along the propagation axis. Third, we report the experimental results of those measurements; in particular, we compare the focal spot size to the diffraction-limited size. Finally, we discuss the physics of the property of direct focusing, in which a converging beam and a diverging beam are simultaneously emitted, in relation to a focus pattern that is simultaneously observed in the opposite direction along the propagation axis because of the nature of the in-plane lasing cavity.
2. Device structure for focusing
2.1. Device structure
We explain the iPMSEL’s structure and fabrication process in this section, while the output beams (converging and diverging) are discussed later. Figure 2 shows a schematic of the iPMSEL and a summary of its layer structure. The basic structure is based on that of an ordinary semiconductor laser, but a phase-modulating layer is embedded near the active layer.
In the fabrication process, first, an N-cladding layer, active layer, and phase-modulating layer are formed on a N-GaAs substrate. Second, an array of holes is formed on the phase-modulating layer by using electron-beam (EB) lithography and dry etching to shift holes from the lattice points of the virtual square-lattice 2D PC. Third, a P-cladding layer and P-contacting layer are regrown on the phase-modulating layer by metal-organic chemical vapor deposition (MOCVD), and P and N electrodes are then formed by ordinary photolithography. The P electrode is a 200 µm × 200 µm square that corresponds to the emission area (see supplementary section S2 for the details).
Figure 3(a) shows the shape of a hole in the phase-modulating layer, which is designed to be octagonal. The lattice constant of the virtual 2D PC is a = 202 nm, and the filling factor, meaning the area ratio of holes with respect to the unit cell, is ff = 28%. Note that the lattice constant is determined so as to satisfy the oscillation in the M-point band edge of the square-lattice 2D PC, where surface-normal diffraction does not occur directly [17]. A hole is shifted onto a circle whose center corresponds to a lattice point and whose radius is set to r = 0.08a. We call this approach the circular-shifting method. Note that this method achieves 2π modulation even though the shift is not large. This is a distinctive feature of phase modulation in the in-plane lasing cavity. Moreover, the strong 0th-order out-of-plane diffraction is prevented at the M-point band edge, which is the nature of the diffraction in M- point band edge [17]. Note also that this shifting method can be attributed to the detour phase method, as pointed out in a previous work [15] (see supplementary section S3). While only the phase term is modulated in this work, it should be notified that the amplitude term can also be modulated by changing the hole size in accordance with the detour phase method.
Fig. 3. Structure of the phase-modulating layer. (a) Schematic of the method to shift a hole from a lattice point O. (b) Phase distribution in the near-field plane. Schematic views of the 2D PC (c) without the shift and (d) with the shift.
2.2. Design of phase-modulating layer
Conventional 2D projection is achieved through the following steps [15–17]. Once the FFP is determined, we calculate the complex electromagnetic (EM) field of the near-field pattern (NFP) via an inverse Fourier transform process based on Fraunhofer diffraction; then, we extract the phase term ϕp (x,y) from the EM field of the NFP. Because the M-point band edge is selected, the phase of the shift vector, ϕs(x,y) = (π/a)(x + y), should be added to obtain the phase distribution [17]. As x and y represent the lattice point’s position, the phase of the shift vector gives a checkerboard-pattern phase distribution alternating between 0 and π. Holes are thus shifted in accordance with the resultant phase distribution ϕ = ϕp + ϕs. The calculation based on Fraunhofer diffraction uniquely determines the projection pattern without depending on the distance. In this case, the basic components of the output light waves are plane waves, as shown in Fig. 1(c). As for 3D projection, the output light waves require another basic component that changes along the direction of propagation. For this purpose, it is natural to consider parabolically distorted light waves based on Fresnel diffraction, as shown in Fig. 1(d). (See supplementary section S1 for the details.)
For focusing, we simply consider the phase distribution condition in the phase-modulating layer so that surface-normal incident light waves in that layer have the same optical length at the focus, which is the ordinary condition of a flat lens. This is achieved by replacing the conventional phase term ϕp for 2D projection with a phase term ϕf for focusing, which is formulated as
The resultant phase distribution ϕ = ϕf + ϕs is shown in Fig. 3(b). Note that the phase difference between neighboring holes must be below 2π, or the phase will not be correctly expressed because of 2π uncertainty. Accordingly, Fig. 3(b) also shows an enlarged view of the phase distribution, which clearly satisfies this condition. As noted above, the checkerboard-like phase distribution is due to the phase of the shift vector, ϕs. To provide an intuitive understanding of the phase-modulating layer, we show a schematic view of holes in the layer without modulation in Fig. 3(c) and with modulation in Fig. 3(d). The total phase distribution ϕ causes holes to shift with a concentric lens pattern, while neighboring twin holes whose phase difference is around π seem to move together because of the phase of the shift vector, ϕs.
3. Measurement setup
3.1. Lasing characteristics
The setup for measuring lasing characteristics, including the light-current characteristics (L-I curve), spectrum, and FFP, is briefly explained here. The NFP setup is explained in the next section.
For operation of the iPMSEL, an LD driver (ILX Lightwave, LDP-3830) was used with temperature control by a Peltier controller (Daitron, DPC-100). The pulse width, duty, and temperature were set at 50 ns, 1%, and 25°C respectively. The light intensity was measured by a photodiode with a neutral density filter (Ophir, PD300-3W-v1) placed in front of the iPMSEL. The spectrum was measured by an optical spectrum analyzer (Yokogawa, AQ6373) through a single-mode fiber (Optron Science, SM98PKSP). The FFP was measured by a CCD camera (Hamamatsu, ORCA) through FFP optics (Hamamatsu, A3267-12) by using a beam profiler (Hamamatsu, Lepas-12). To suppress the camera’s halation, the beam intensity was properly attenuated by a neutral density filter (Hamamatsu, A7659-01) for both the FFP and NFP.
3.2. Focusing-beam profiles
The NFP measurement setup is shown in Fig. 4. The output beam was collected and collimated by an objective lens and measured by a CCD camera (Hamamatsu, ORCA) through relay optics. When the focus of the objective lens was adjusted at the near-field plane, the position of the lens was defined as z = 0. The beam profiles along the optical axis were then observed by shifting the position z of the objective lens. The magnification of the objective lens was set to 20x for wide-range measurement to obtain the entire focusing-beam profile, and it was increased to 100x for narrow-range measurement to evaluate the focal spot.
To verify the validity of this setup, we also used it with an LED before using it with the iPMSEL. The LED showed diverging beam profiles along the optical axis, whereas the iPMSEL showed a clear focusing property. Because the focal spot size near the focus was sustained, it was presumably valid to measure the focal spot size.
4. Characteristics of iPMSEL
4.1. Lasing characteristics
Figure 5(a) shows the light-current characteristics of the iPMSEL for room-temperature pulse operation. The threshold current was 0.41 A, and the slope efficiency was 0.12 W/A. The lasing spectrum, FFP, and NFP for operation at 1.0 A are shown in Figs. 5(b-d), respectively. The lasing spectrum showed a narrow peak with a wavelength of 938.75 nm. The FFP had a square pattern in which the beam divergence in the x and y directions was around 34°. In the NFP, the emission spread over the 200 µm × 200 µm emission area. Interference fringes were clearly seen in the NFP as well as the FFP which might reflect the phase distribution shown in Fig. 3(b).
Fig. 5. Lasing characteristics of the iPMSEL: (a) the light-current output characteristics, (b) lasing spectrum, (c) far-field pattern, and (d) near-field pattern.
4.2. Focusing characteristics
Figure 6 shows beam profiles along the propagation axis in the positive z direction (20x) with an operating current of 1.0 A. The profiles clearly show that focusing occurred as expected. Figure 7(a) shows a detailed beam profile at the focus (100x). The measured focal length of 310 µm agreed well with the theoretical value of 320 µm. To evaluate the focal spot sizes in the x and y directions, cross sections along those directions through the peak of the focal spot were obtained and are shown by the black circles in Figs. 7(b) and (c), respectively. The spot size was estimated from the width between the 1/e2 values with respect to the peak of the Gaussian fitting, as shown by the red lines in the figures. The estimated spot sizes in the x and y directions were 6.08 µm and 6.05 µm, respectively. The diffraction-limited spot size was estimated to be 3.01 µm (see supplementary section S5), whereas the focal spot size was about 2.0 times greater, which indicates that the higher transverse modes were sufficiently suppressed. We also estimate that the power density at the focus was 540 times higher than that at the near-field plane, which was roughly estimated as follows. The ratio of the focal spot area to the emission area was estimated as 1086, but the diverging beam coexisted as discussed later, so the value was halved. Note that backside emission also occurs: it is reflected at the P electrode 2 µm below the phase-modulating layer and bounced back to the frontside. Therefore, we expect that the focusing beam at the frontside interferes with the focusing beam at the backside, which is shifted by 2 µm along the propagation axis. Here, we ignored the interference and simply added the focusing beams because their in-plane phases vary rapidly in contrast to the plane wave.
Fig. 6. Beam profiles along the propagation axis. The beam profiles near the focus are saturated because the brightness was adjusted at the near-field plane (z = 0.00 mm).
Fig. 7. (a) Beam profile at the focus (z = 0.31 mm), obtained by using a high-resolution objective lens, and cross-sectional plots through the peak along (b) the x axis and (c) the y axis.
5. Discussion
It is interesting that the beam profiles shown in Fig. 6 can be distinguished as two types along the propagation direction: a focusing beam and a diverging beam, as shown in Fig. 8. This is due to the nature of the in-plane oscillation, which uses the band edge. In the lasing mechanism of a band-edge laser, including the iPMSEL, a standing wave is formed by in-plane diffraction. This means that in-plane waves simultaneously exist in both the direction of in-plane diffraction—i.e., the Γ-M direction in this case—and the counter direction. For intuitive understanding of this phenomenon, the in-plane light waves in the phase-modulating layer are depicted in Fig. 8. When one of the in-plane light waves is imposed by the phase modulation described by Eq. (1), the counter-propagating light-wave is imposed by negative phase modulation, which is described by replacing the negative sign with a positive sign in Eq. (1). As the positive sign of the phase of the lens immediately indicates the diverging beam, this is the origin of that beam. In other words, the 1st-order beam corresponds to the focusing beam, while the negative 1st-order beam corresponds to the diverging beam. This phenomenon was also observed in beam profiles in the counter direction of the optical axis, as shown in Fig. 9. Note that the images in Fig. 9 are virtual, whereas those in Fig. 6 are real. The beam profiles in both the positive and negative directions coincided with each other as though they formed twin images due to the ±1st-order beams. The slight difference between Fig. 6 and fig. 9 might be caused by interference between converging beam and diverging beam, or slight deviation of the optical axis. This is the distinguishing feature for focusing of band-edge lasers. Note that the same beam profiles were obtained when we imposed a positive sign on the phase modulation in Eq. (1), which corresponded to a concave lens. This is the same reason why the 1st-order beam corresponded to the diverging beam while the negative 1st-order beam corresponded to the focusing beam in this case.
Fig. 8. (a) Schematic of the output focusing beam of the in-plane lasing cavity. The converging beam is emitted along the propagation axis simultaneously with a diverging beam, which is attributed to counter-propagating in-plane light waves. Note that focusing also occurs along the counter-propagation axis. (b) Example of a beam profile at z = 0.10 mm. Besides the converging beam, the diverging beam is also clearly observed.
Fig. 9. Beam profiles in the counter direction of the propagation axis. Note that these profiles are virtual images that correspond to the diverging beam.
In conclusion, we demonstrated direct focusing from a surface-emitting laser with an emission area of 200 µm × 200 µm. The design of the phase-modulating layer for focusing was based on the simplest form of a Fresnel hologram. The direct focusing had a focal length and focal spot size of 310 µm and 6.1 µm, respectively. The focal length agreed well with the theoretical value, and the focal spot size was 2.0 times the diffraction-limited size, which indicates that the higher transverse modes were sufficiently suppressed. We also found that the power density at the focus was 540 times higher than that at the near-field plane. Interestingly, the converging beam and a diverging beam were simultaneously emitted because of the nature of the in-plane band-edge laser. Conventional beam patterns from a semiconductor laser cavity are limited within the regime of 2D beam projection based on a Fourier hologram, whereas we demonstrated the simplest form of a 3D point cloud based on a Fresnel hologram, which is quite useful for microscale applications such as microfluidics, medical treatments, and endoscopy.
Acknowledgments
The authors are grateful to A. Hiruma (President), H. Toyoda (Director), M. Yamanishi (Research Fellow), T. Hara, M. Niigaki, Y. Yamashita, K. Nozaki, T. Hirohata, T. Edamura, A. Watanabe, and Y. Kurosaka of HPK for their encouragement throughout this work, and to A. Higuchi and M. Hitaka for their assistance with epitaxial growth. Part of this work was supported by Japan Science and Technology Agency (JST); Center of Innovation Program (COI) (JPMJCE1311).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. W. W. Chow, S. W. Koch, and M. Sargent III, “Semiconductor-laser physics,” Springer (1994).
2. V. Bardinal, T. Camps, B. Reig, D. Barat, E. Daran, and J. B. Doucet, “Collective micro-optics technologies for VCSEL photonic integration,” Adv. Opt. Technol. 2011, 1–11 (2011). [CrossRef]
3. Y. C. Chang, M. C. Shin, C. T. Phare, S. A. Miller, E. Shim, and M. Lipson, “2D beam steerer based on metalens on silicon photonics,” Opt. Express 29(2), 854–864 (2021). [CrossRef]
4. P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photonics Rev. 11(3), 1600295 (2017). [CrossRef]
5. J. Engelberg and U. Levy, “The advantages of metalenses over diffractive lenses,” Nat. Commun. 11(1), 1991 (2020). [CrossRef]
6. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999). [CrossRef]
7. K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014). [CrossRef]
8. M. Yoshida, M. De Zoysa, K. Ishizaki, Y. Tanaka, M. Kawasaki, R. Hatsuda, B. S. Song, J. Gelleta, and S. Noda, “Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow-divergence beams,” Nat. Mater. 18(2), 121–128 (2019). [CrossRef]
9. R. Morita, T. Inoue, M. De Zoysa, K. Ishizaki, and S. Noda, “Photonic-crystal lasers with two-dimensionally arranged gain and loss sections for high-peak-power short-pulse operation,” Nat. Photonics 15(4), 311–318 (2021). [CrossRef]
10. T. Okino, K. Kitamura, D. Yasuda, Y. Liang, and S. Noda, “Positionmodulated photonic-crystal lasers and control of beam direction and polarization,” in Proc. Conf. Lasers Electro, Opt., 2015, Paper SW1F.1.
11. S. Noda, K. Kitamura, T. Okino, D. Yasuda, and Y. Tanaka, “Photonic-Crystal Surface-Emitting Lasers: Review and Introduction of Modulated-Photonic Crystals,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1–7 (2017). [CrossRef]
12. R. Sakata, K. Ishizaki, M. D. Zoysa, S. Fukuhara, T. Inoue, Y. Tanaka, K. Iwata, R. Hatsuda, M. Yoshida, J. Gelleta, and S. Noda, “Dually modulated photonic crystals enabling high-power high-beam-quality two-dimensional beam scanning lasers,” Nat. Commun. 11(1), 3487 (2020). [CrossRef]
13. J. Goodman, Introduction to Fourier Optics, 3rd ed, (Roberts & Co Publishers, 2005).
14. B. R. Brown and A. W. Lohmann, “Complex Spatial Filtering with Binary Masks,” Appl. Opt. 5(6), 967–969 (1966). [CrossRef]
15. Y. Kurosaka, K. Hirose, T. Sugiyama, Y. Takiguchi, and Y. Nomoto, “Phase-modulating lasers toward on-chip integration,” Sci. Rep. 6(1), 30138 (2016). [CrossRef]
16. Y. Takiguchi, K. Hirose, T. Sugiyama, Y. Nomoto, S. Uenoyama, and Y. Kurosaka, “Principle of beam generation in on-chip 2D beam pattern projecting lasers,” Opt. Express 26(8), 10787–10800 (2018). [CrossRef]
17. K. Hirose, Y. Takiguchi, T. Sugiyama, Y. Nomoto, S. Uenoyama, and Y. Kurosaka, “Removal of surface-normal spot beam from on-chip 2D beam pattern projecting lasers,” Opt. Express 26(23), 29854–29866 (2018). [CrossRef]
18. Y. Kurosaka, K. Hirose, A. Ito, M. Hitaka, A. Higuchi, T. Sugiyama, Y. Takiguchi, Y. Nomoto, S. Uenoyama, and T. Edamura, “Beam pattern projecting on-chip lasers at visible wavelength,” Proc. of Conference on Lasers and Electro-Optics2019, paper SM4N.2.
19. K. Hirose, H. Kamei, T. Sugiyama, and Y. Kurosaka, “200×200 µm2 structured light source,” Opt. Express 28(25), 37307–37321 (2020). [CrossRef]
20. “iPMSEL,” https://www.hamamatsu.com/jp/en/our-company/about-crl/optical-materials/ipmsel.html.
21. Y. Kurosaka, K. Hirose, H. Kamei, and T. Sugiyama, “Replication of band structure in an arbitrary wave vector by holographic modulation,” Phys. Rev. B 103(24), 245310 (2021). [CrossRef]
22. B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13(2), 160–168 (1969). [CrossRef]
