Abstract
Realizing largescale singlemode, highpower, highbeamquality semiconductor lasers, which rival (or even replace) bulky gas and solidstate lasers, is one of the ultimate goals of photonics and laser physics. Conventional highpower semiconductor lasers, however, inevitably suffer from poor beam quality owing to the onset of manymode oscillation^{1,2}, and, moreover, the oscillation is destabilized by disruptive thermal effects under continuouswave (CW) operation^{3,4}. Here, we surmount these challenges by developing largescale photoniccrystal surfaceemitting lasers with controlled Hermitian and nonHermitian couplings inside the photonic crystal and a preinstalled spatial distribution of the lattice constant, which maintains these couplings even under CW conditions. A CW output power exceeding 50 W with purely singlemode oscillation and an exceptionally narrow beam divergence of 0.05° has been achieved for photoniccrystal surfaceemitting lasers with a large resonant diameter of 3 mm, corresponding to over 10,000 wavelengths in the material. The brightness, a figure of merit encapsulating both output power and beam quality, reaches 1 GW cm^{−2} sr^{−1}, which rivals those of existing bulky lasers. Our work is an important milestone toward the advent of singlemode 1kWclass semiconductor lasers, which are expected to replace conventional, bulkier lasers in the near future.
Main
Semiconductor lasers boast various beneficial features that cannot be found in other lasers (for example, gas, solidstate and fibre lasers), such as compactness, high efficiency and high controllability, and they are key devices for various applications in modern society, including telecommunications and optical recording. Realizing semiconductor lasers that also operate in a single mode with high output power and high beam quality remains an ultimate yet elusive goal in photonics and laser physics. Such semiconductor lasers are in demand for many emerging applications, including nextgeneration laser processing, remote sensing, longrange freespace communications and even light propulsion for spaceflight^{5,6,7,8}. Conventional semiconductor lasers are limited by the maximum emission area that can support singlemode operation; namely, widening the emission area to increase the output power leads to the onset of manymode oscillation, which degrades the beam quality^{1,2}. Even worse, under continuouswave (CW) operation, the beam quality is prone to degrade further due to a thermally induced refractive index distribution inside the resonator, which is one of the critical factors responsible for unstable oscillation^{3,4} (Supplementary Text Section 1 has more details).
The photoniccrystal surfaceemitting laser (PCSEL)^{9,10,11,12,13,14,15} shows potential to overcome the above limitations of conventional semiconductor lasers. The PCSEL achieves lasing oscillation of a twodimensional standing wave at a singularity (Γ, M and so on) point in its photonic band structure. By tailoring the design of the unit cell of its photonic crystal, the mutual optical couplings inside the photonic crystal can be tuned to enable singlemode oscillation over a large area. One unitcell design proposed for this purpose is the double lattice^{15}, in which one lattice point group is shifted from a second in the x and y directions by approximately one quarter of the wavelength in the material. In this double lattice, the strength of inplane optical coupling, which can be referred to as Hermitian coupling since it is not accompanied by radiation loss, is weakened by destructive interference of waves diffracted by 180° and 90° at each of the two lattice points. Consequently, optical losses of higherorder modes from the periphery of the resonator increase compared with that of the fundamental mode, resulting in a wider threshold gain margin between these modes and thus, more stable oscillation in the fundamental mode. Based on this concept, CW lasing oscillation with an output power of 7 W and a brightness of 180 MW cm^{−2} sr^{−1} was experimentally demonstrated using PCSELs with circular resonant diameters of 800 μm (ref. ^{15}).
Following the above developments, a design guideline to realize singlemode oscillation over areas of even larger (≥3 mm) diameters was recently reported^{16} based on the control of not only the Hermitian coupling described above, but also nonHermitian coupling, which accompanies radiation loss. In addition, another related approach toward realizing scalable singlemode photoniccrystal lasers was also reported^{17}, although the resonant (emission) size achieved in experiments therein was less than approximately 64 μm. (Supplementary Text Section 2 has a brief comparison between these two approaches).
The most important outstanding challenges are, therefore, twofold. One is to investigate whether singlemode operation of PCSELs can be truly scaled to extremely large (≥3 mm) diameters; the other is to investigate whether singlemode operation can be maintained even under CW conditions, where disruptive thermal effects appear. Here, we first show that it is indeed possible to realize singlemode oscillation even in a PCSEL with a 3mm diameter, corresponding to over 10,000 wavelengths in the material, by simultaneously controlling the Hermitian and nonHermitian couplings. Then, we introduce a latticeconstant distribution to compensate for the thermal effects and thereby maintain the controlled Hermitian and nonHermitian couplings even under CW conditions. By doing so, we finally experimentally achieve 50W CW operation in a single mode (with a single wavelength) with a very narrow beam divergence angle of 0.05° (corresponding to a beam quality M^{2} ≈ 2.36). The brightness of the developed laser reaches 1 GW cm^{−2} sr^{−1}, which is more than one order of magnitude greater than that of conventional semiconductor lasers and even rivals those of existing bulky gas and solidstate lasers. The strategies demonstrated here are expected to be applicable to scaling up the diameter of the device to 10 mm, leading to the 1kW class, highbeamquality operation of PCSELs.
Hermitian and nonHermitiancontrolled PCSEL
First, we describe the strategy to realize singlemode oscillation in a largescale PCSEL. The left panels of Fig. 1a,b show typical electricfield distributions of the fundamental and higherorder modes in a PCSEL with a diameter of L. As L increases, the inplane losses (that is, light escaping from the periphery of the resonator) of both the fundamental and higherorder modes converge toward zero, and thus, the ability to discriminate between these modes via inplane loss greatly diminishes. Accordingly, we instead consider mode discrimination via vertical radiation loss (that is, the radiation constant), which remains high even when L becomes large. As illustrated in the right panels of Fig. 1a,b, the (first) higherorder mode is double lobed, and consequently, it has a slightly larger inplane wave number than the singlelobed fundamental mode. Our strategy is to make the radiation constant at the wave number corresponding to the (first) higherorder mode sufficiently larger than that of the fundamental mode by controlling the Hermitian and nonHermitian couplings in a doublelattice photonic crystal.
Figure 1c,d illustrates the Hermitian and nonHermitian couplings of four fundamental waves, labelled R_{x}, S_{x}, R_{y} and S_{y}, in a doublelattice structure, where the former and latter couplings do not and do accompany radiation loss, respectively. In Fig. 1c, the coefficients κ_{1D} and κ_{2D±} express the strengths of Hermitian coupling at angles of 180° and ±90°, respectively. The selfcoupling of the four fundamental waves without radiation loss is expressed by κ_{11} (not shown in the figure). In Fig. 1d, the coefficients iμ and iμe^{±iθpc} express the strengths of nonHermitian couplings at angles of 0° (that is, selfcoupling) and 180°, respectively, via the radiative waves, where μ is the magnitude of the nonHermitian coupling coefficient, θ_{pc} is a phase change associated with ±180° nonHermitian coupling and i is the imaginary unit.
Owing to such optical couplings among the four fundamental waves, four resonant cavity modes are constructed. In a doublelattice photonic crystal with mirror symmetry about the axis of y = x, two of these modes (labelled A and C) are antisymmetric modes whose electricfield vectors are antisymmetric about this axis, and the remaining two modes (labelled B and D) are symmetric modes whose electricfield vectors are symmetric about this axis. The radiation constant, as well as the frequency, of each mode is analytically derived as a function of the inplane wave number k using threedimensional coupledwave theory^{16,18}. The frequency and radiation constant (δ_{A}, α_{A}) of mode A, which has the lowest radiation constant among all four modes, and those (δ_{C}, α_{C}) of its counterpart mode C are expressed as (Methods has the details of the derivation)
Here, δ_{A} +iα_{A}/2 and δ_{C} + iα_{C}/2 correspond to the negative and positive squareroot terms, respectively, and the inplane wave number k is taken along the Γ–M direction (that is, \({k}_{x}={k}_{y}=k/\sqrt{2}\)), so that the symmetry of the electric fields coincides with the symmetry of the photonic crystal along the line of y = x. In equation (1), R and I correspond to the real and imaginary parts of the Hermitian coupling coefficient, respectively; namely, \(R\equiv {\rm{Re}}\left[\left({\kappa }_{1{\rm{D}}}+{\kappa }_{2{\rm{D}}}\right){{\rm{e}}}^{{\rm{i}}{\theta }_{{\rm{pc}}}}\right]\) and \(I\equiv {\rm{Im}}\left[\left({\kappa }_{1{\rm{D}}}+{\kappa }_{2{\rm{D}}}\right){{\rm{e}}}^{{\rm{i}}{\theta }_{{\rm{pc}}}}\right]\). R expresses the overall strength of inplane feedback of combined 180° and 90° diffractions at the Γ point, which determines the size of the frequency gap between modes A and C. I determines the phase of the inplane electric fields, specifically the position of the electricfield node with respect to the position of the air holes, and consequently, it determines the degree of cancellation of the vertical radiation in mode A at the Γ point. (Details on R and I are explained in Supplementary Text Section 3).
Figure 1e shows α_{A} as a function of k calculated using equation (1) for several selections of R and μ, while I was adjusted so that α_{A} at k = 0 was identical in all cases. Evidently, decreasing R and μ simultaneously while maintaining their balance increases the curvature of dispersion around the Γ point, resulting in an abrupt change of α_{A} with respect to k. Consequently, the threshold margin Δα_{v} between the fundamental and higherorder modes near the Γ point can be increased, whereupon singlemode oscillation is expected even for large 3mmdiameter PCSELs (Methods has a note on Δα_{v}).
Based on the above strategy, we developed a 3mmdiameter PCSEL, whose R and I values were controlled by changing the lattice separation (d) and the balance of airhole sizes (x) of a doublelattice structure (Fig. 1c and Supplementary Text Section 4) and whose μ value was controlled by changing the thickness of the pAlGaAs clad layer, which affects the degree of optical interference between front sideemitted and back sidereflected radiative waves^{16} (Fig. 1d and Supplementary Text Section 4). Figure 2a shows finished 3mmdiameter PCSELs fabricated based on an air holeretained metal–organic vapourphase epitaxy regrowth technique^{19}. A meshwindow nelectrode was deposited onto an nGaAs substrate (emission side) for uniform current injection across the entire 3mmdiameter area.
We first measured the frequencies and radiation constants of modes A and C around the Γ point of the fabricated device as plotted in Fig. 2b,c and then, estimated the coupling coefficients R, I and μ by fitting the analytical values given by equation (1) to their experimental values (Methods has details). The bestfit results were R ≈ 15 cm^{−1}, I ≈ 25 cm^{−1} and μ ≈ 38 cm^{−1}; these values correspond to the case of the red line in Fig. 1e, in which a large threshold margin Δα_{v} is expected. Then, we measured lasing characteristics of the PCSEL under pulsed conditions. Here, the PCSEL was not mounted to a heat sink, which limited the maximum tolerable injection current and hence output power even under pulsed conditions. The current–light output (I–L) characteristics measured at room temperature in Fig. 2d show that lasing oscillation occurred at a threshold injection current of I_{th} ≈ 20 A. Figure 2e shows a farfield pattern (FFP) of the emitted beam above the threshold (1.3 I_{th}). As indicated by the crosssectional profile of the FFP (Fig. 2f), a very narrow beam divergence angle of 0.045° was achieved, which we attribute to the small yet appropriately balanced values of R and μ as described above.
Highbrightness CW singlemode PCSEL
CW current injection induces a spatially nonuniform temperature distribution inside the PCSEL due to the accumulation of heat. We simulated the effects of heat accumulation on the lasing characteristics of a 3mmdiameter PCSEL under CW conditions based on a selfconsistent analysis^{20} of the interaction among photons, carriers and thermal effects (Supplementary Text Section 5 for details). Figure 3a,b shows the calculated inplane temperature distribution near the active layer at a sufficiently large CW injection current of 110 A (chosen upon consideration of the experimental conditions described later). As shown, the temperature at the centre of the current injection area becomes higher than at the periphery, which results in the downward convexshaped bandedge frequency distribution shown in Fig. 3c via a change in refractive index. This frequency distribution perturbs the electric field of the fundamental mode, and consequently, it induces multimodal behaviour and broadens the emitted beam, as shown in Fig. 3d. To suppress such unwanted effects, we introduce a spatial variation Δa(x,y) to the lattice constant of the photonic crystal, which compensates for a temperature distribution ΔT_{comp}(x,y), as shown in Fig. 3e,f (Methods has details). Figure 3g shows the bandedge frequency distribution calculated at an injection current of 110 A following the introduction of this latticeconstant distribution. This figure clearly shows that a uniform frequency distribution is obtained, owing to the mutual cancellation of the temperatureinduced and lattice constantinduced changes of the bandedge frequency. As a result, the emission of a singlemode beam with a very narrow divergence angle is expected to be obtained, as shown in Fig. 3h.
Applying the above strategy, we developed the 3mmdiameter PCSEL with the preinstalled latticeconstant distribution. Figure 4a shows a finished 3mmdiameter PCSEL mounted on a package. The coupling coefficients of the device were estimated as R ≈ 24 cm^{−1}, I ≈ 14 cm^{−1} and μ ≈ 44 cm^{−1} (Methods has details). Figure 4b shows I–L characteristics of the 3mmdiameter PCSEL under CW conditions. The threshold current was 25 A, and the slope efficiency was approximately 0.72 W A^{−1}. A CW output power exceeding 50 W was obtained from the singlechip PCSEL at injection currents of 100–110 A. Figure 4c shows the FFPs at several injection currents, and Fig. 4d shows the 1/e^{2} beamwidths of FFPs as functions of the injection current. Remarkably, the divergence angles in the x and y directions became minimal (0.05°) at 100–110 A, where the frequency distributions due to the temperatureinduced refractive index change and the preinstalled latticeconstant distribution were designed to cancel each other out. We note that the divergence angle was slightly larger in the y direction than in the x direction due to a small residual side lobe with an intensity of approximately 1/e^{2} of that of the main peak; this side lobe can be eliminated in the future by further optimizing the preinstalled latticeconstant distribution. From the divergence angles, including the small residual side lobe, the beam quality M^{2} was estimated to be 2.36. The CW laser brightness, evaluated using the measured output power and FFP widths at 110 A, was 1 GW cm^{−2} sr^{−1}. Furthermore, the laser spectra at several injection currents are shown in Fig. 4e. Although several modes were seen to oscillate at lower injection currents, singlemode oscillation was achieved at injection currents of 100–110 A (corresponding to a CW output power of around 50 W). The measured spectral width at this injection current was 3 pm, which was limited by the spectral resolution of our spectrometer. As this resolution was finer than the predicted spectral spacing between the fundamental and next higherorder modes, we may say that purely singlemode oscillation was achieved. We note that M^{2} ≥ 2 in spite of singlemode oscillation is due to the superGaussian electromagneticfield intensity profile caused predominantly by the uniform current injection. The dependence of the laser spectrum on the injection current agrees with that of the beam divergence angle plotted in Fig. 4d. These results show that the preinstalled latticeconstant distribution together with the control of Hermitian and nonHermitian couplings inside the doublelattice structure has contributed to the realization of purely singlemode, high beam quality, highpower CW operation of an ultralargearea PCSEL.
Conclusions
We have developed largescale PCSELs by control of Hermitian and nonHermitian couplings to suppress the oscillation of higherorder modes, and we have introduced a latticeconstant distribution to maintain these controlled couplings even under CW operation. By doing so, we have realized 50W singlemode (or singlewavelength) oscillation of a PCSEL with an ultralarge diameter of 3 mm, corresponding to over 10,000 wavelengths in the material. The 50W CW output power and a very narrow beam divergence of 0.05° (M^{2} ≈ 2.36) correspond to a brightness of 1 GW cm^{−2} sr^{−1}, which rivals those of existing bulky lasers. Controlling the Hermitian and nonHermitian coupling coefficients (R, I and μ) and introducing a latticeconstant distribution suitable for devices of even larger scales (for example, 10mm diameters) are expected to contribute to the realization of 1kW class, highbeamquality operation of PCSELs. Our work is an important milestone toward the replacement of conventional, bulkier solutions and toward innovation in a wide variety of industrial applications, from smart material processing to aerospace applications.
Methods
Derivation of frequencies and radiation constants of modes A and C
The frequency and radiation constant (δ_{A}, α_{A}) of mode A, which has the lowest radiation constant among all four modes, and those (δ_{C}, α_{C}) of its counterpart mode C can be obtained by solving the following equation based on threedimensional coupledwave theory^{16,18}:
The first and second terms on the righthand side of equation (2) represent the Hermitian and nonHermitian coupling processes described in Fig. 1c,d, respectively. The third term on the righthand side of equation (2) represents the deviation of the wave number from the Γ point in an arbitrary direction represented by wave numbers \({k}_{x}\) and \({k}_{y}\), which induces a change in the eigenfrequency of each mode.
Here, we consider the eigenfrequencies of the modes in the Γ–M direction (\({k}_{x}={k}_{y}=k/\sqrt{2}\)), which is parallel to the axis of symmetry of the doublelattice photonic crystal (y = x). Based on the symmetry along y = x, the coupledwave matrices on the righthand side of equation (2) can be block diagonalized using the basistransformation matrix P:
as
Then, the coupledwave equation (2) can be divided into the following two forms:
and
where equation (5) gives the coupling between a pair of electricfield vectors R_{x} + R_{y} and S_{x} + S_{y}, which leads to the formation of modes A and C (Supplementary Fig. 1).
The frequencies and radiation constants of modes A and C can be then derived from equation (5) as follows:
where δ_{A} + iα_{A}/2 of mode A and δ_{C} + iα_{C}/2 of mode C correspond to the negative and positive squareroot terms, respectively, and R and I are defined as \(R\equiv {\rm{Re}}\left[\left({\kappa }_{1{\rm{D}}}+{\kappa }_{2{\rm{D}}}\right){{\rm{e}}}^{{\rm{i}}{\theta }_{{\rm{pc}}}}\right]\) and \(I\equiv {\rm{Im}}\left[\left({\kappa }_{1{\rm{D}}}+{\kappa }_{2{\rm{D}}}\right){{\rm{e}}}^{{\rm{i}}{\theta }_{{\rm{pc}}}}\right]\), respectively.
Note on the threshold gain margin Δα _{v}
It is difficult to specify a general value of Δα_{v} sufficient for singlemode oscillation in PCSELs. However, we have found that increasing Δα_{v} by simultaneously reducing R and μ contributes to the preservation of singlemode oscillation even in the presence of a nonuniform inplane refractive index distribution borne by various physical phenomena. These findings will be reported separately.
Estimation of the coupling coefficients R, I and μ of the fabricated devices
To estimate the coupling coefficients R, I and μ of the fabricated device shown in Fig. 2a, we derived the photonic band structure around the Γ point by measuring the subthreshold spontaneous emission spectra at various radiation angles (corresponding to inplane wave numbers), whose peak emission wavelengths and line widths corresponded to the band frequencies and radiation constants, respectively. The frequencies and radiation constants of modes A and C are plotted in Fig. 2b,c. R, I and μ were then estimated by fitting the analytical frequencies and radiation constants given by equation (1) to their measured values.
On the other hand, it was difficult to estimate the coupling coefficients of the fabricated device shown in Fig. 4a by directly measuring the photonic band structure around the Γ point due to the preinstalled latticeconstant distribution. Thus, the coupling coefficients were instead estimated by evaluating the shape of the embedded air holes.
Design of the preinstalled latticeconstant distribution
The distribution of the latticeconstant variation Δa(x,y), which compensates for a temperature distribution ΔT_{comp}(x,y), is determined as follows:
Here, a is the original lattice constant, n_{eff} is the effective refractive index of the photonic crystal at room temperature, and dn/dT is the rate of change of refractive index with respect to temperature. Based on equation (8) and the selfconsistent analysis of photon–carrier–thermal interactions (Supplementary Text Section 5), we introduced the latticeconstant distribution shown in Fig. 3e,f.
Data availability
The data that support the plots within this paper and other findings of this study are available within this article and Supplementary Information, and they are also available from the corresponding author upon request.
Code availability
The details of threedimensional coupledwave theory simulations are available in Supplementary Information, and their associated codes are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was partially supported by the project of the Council for Science, Technology and Innovation; the Cross Ministerial Strategic Innovation Promotion Program; Photonics and Quantum Technology for Society 5.0 (finding agency: QST); and the Japan Society for the Promotion of Science (GrantinAid for Scientific Research 22H04915).
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S.N. supervised the entire project. M.Y. and S.K. performed the device fabrications and the measurements with K.Izumi, M.D.Z. and K.Ishizaki. T.I. performed the theoretical analysis with M.Y. and J.G. S.K., T.I. and M.Y. performed the numerical simulation. S.N. and M.Y. discussed the results and wrote the paper with T.I. and J.G.
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Yoshida, M., Katsuno, S., Inoue, T. et al. Highbrightness scalable continuouswave singlemode photoniccrystal laser. Nature 618, 727–732 (2023). https://doi.org/10.1038/s41586023060598
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DOI: https://doi.org/10.1038/s41586023060598
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