High-brightness scalable continuous-wave single-mode photonic-crystal laser

Realizing large-scale single-mode, high-power, high-beam-quality semiconductor lasers, which rival (or even replace) bulky gas and solid-state lasers, is one of the ultimate goals of photonics and laser physics. Conventional high-power semiconductor lasers, however, inevitably suffer from poor beam quality owing to the onset of many-mode oscillation1,2, and, moreover, the oscillation is destabilized by disruptive thermal effects under continuous-wave (CW) operation3,4. Here, we surmount these challenges by developing large-scale photonic-crystal surface-emitting lasers with controlled Hermitian and non-Hermitian couplings inside the photonic crystal and a pre-installed spatial distribution of the lattice constant, which maintains these couplings even under CW conditions. A CW output power exceeding 50 W with purely single-mode oscillation and an exceptionally narrow beam divergence of 0.05° has been achieved for photonic-crystal surface-emitting 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 single-mode 1-kW-class semiconductor lasers, which are expected to replace conventional, bulkier lasers in the near future.


Typical CW performance of conventional semiconductor lasers
As mentioned in the main text, conventional semiconductor lasers have limitations regarding their single-mode output power under CW operation. For example, in a conventional edge-emitting-type semiconductor laser, the maximum stripe width that supports oscillation in a single lateral mode is limited to approximately 10 m, and the CW output power is limited to around one watt [S1]. In addition, we should note that these lasers also oscillate in many longitudinal modes.
Toward expanding the stripe width, the adoption of tapered stripes has been investigated. However, such stripes significantly worsen the asymmetry and astigmatism of the beam, resulting in a beam profile that is much different from an ideal Gaussian one [S2]. Similarly, a conventional vertical-cavity surface-emitting laser (VCSEL) also suffers from oscillation in many modes when its emission diameter is widened beyond approximately 5 m, and its single-mode CW output power is limited to a few milliwatts [S3].

Comparison between PCSELs based on Hermitian/non-Hermitian control and those based on an open-Dirac singularity
In the present work, we report on large-scale CW single-mode PCSELs based on Hermitian/non-Hermitian control. As a different approach toward realizing scalable single-mode surface-emitting lasers, utilization of an open-Dirac singularity in a photonic crystal has been recently proposed [S4]. In the following, these two approaches are briefly compared.
The lasers based on an open-Dirac singularity, which can be also categorized as PCSELs, feature triangular-lattice photonic-crystal structures with symmetric circular lattice points which are carefully tuned to realize the open-Dirac singularity. Since this structure possesses C6v symmetry, the vertical radiation constant αv of the lasing mode converges to zero when the resonator size is widened to larger scales. In addition to αv, in actual semiconductor lasers, a fixed amount of fundamental material absorption loss α0 (typically 1 cm -1 ) exists due to free-carrier absorption in the cladding layers, etc.
Considering these facts, the slope efficiency (i.e., surface emission efficiency) of the laser, which is proportional to αv/(αv+α//+α0) where α// denotes the in-plane loss, inevitably converges to zero at larger scales. The random scattering of light induced by fabrication disorders may recover the slope efficiency to some extent [S5] while sacrificing the beam quality. In addition, owing to the C6v symmetry, αv of modes on different band edges converge toward zero as the device size increases, so competition between the modes of different band edges might hinder single-mode operation. It should be also noted that, in [S4], rigorous simulations of I-L characteristics considering carrier-photon interactions were not performed, and experimental demonstrations were limited to resonator (emission) sizes of 64 m under pulsed optical pumping (not under CW current injection).
On the other hand, in our approach based on Hermitian/non-Hermitian control in a double-lattice PCSEL, which has no rotational symmetry, the radiation constant of the lasing band-edge mode (mode A) can be controlled to an appropriate value while keeping those of the other band-edge modes (modes B, C, and D) much higher [S6], even at large scales. In this way, lasing in a single mode can be obtained while also ensuring a high slope efficiency and a high-beam quality single-lobed beam pattern. A detailed comparison between the approach based on an open-Dirac singularity and the approach based on Hermitian/non-Hermitian control is summarized in Table S1 below.

On the Hermitian coupling coefficients R and I
In this section, we explain the Hermitian coupling coefficients R and I, which are defined as ≡ Re 1D 2D pc and ≡ Im 1D 2D pc . Figure S1 shows the schematic illustration of modes A and C, which are expressed with a pair of electric-field vectors Rx+Ry and Sx+Sy. These two combined electric-field vectors are coupled with each other by and its complex conjugate (see also Eq. (5) in the Methods section). Here, we should note that there is a degree of freedom in determining the phase of , which depends on the position of the air holes relative to the boundary of the unit cell. To determine the phase of , we use the position at which non-Hermitian coupling occurs as the reference position [S6]. We thus define the Hermitian coupling coefficient as , by multiplying to . R and I are then defined as ≡ Re 1D 2D pc and ≡
The real part R expresses the overall strength of in-plane feedback of combined 180° and 90° diffractions, which determines the size of the frequency gap between modes A and C. Meanwhile, the imaginary part I determines the phase of the in-plane electric fields, namely, the position of the electric-field node with respect to the position of the air holes, and consequently determines the degree of cancellation of the vertical radiation in mode A at the  point: When I is zero, the vertical radiation is completely cancelled out, and when I becomes non-zero, the light begins to leak out in the vertical direction at a strength proportional to the non-Hermitian coupling coefficient . It should be noted that the imaginary part I is always zero in the case of a single-circular-hole photonic crystal that has C2 rotational symmetry, and that the magnitude of I can be arbitrarily controlled via adjustment of the asymmetry of the two holes in a double-lattice photonic crystal as described in the next section.

Control of R, I and μ in a double-lattice PCSEL with a backside DBR
We explain here how the Hermitian coupling coefficients (R and I) and the non-Hermitian coupling coefficient () can be controlled in a PCSEL (see Fig. S2a) with a double-lattice photonic crystal and a backside DBR mirror. As shown in the inset of On the other hand, the magnitude of the non-Hermitian coupling coefficient, , can be controlled as follows: Because  depends on the phase θDBR of optical interference between upward-radiated light and light reflected by the DBR (see Fig. S2c),  can be controlled by changing θDBR, where θDBR is determined by the thickness of the p-clad layer.

Self-consistent analysis of PCSELs under CW operation
The lasing characteristics of the PCSEL under CW conditions can be simulated based on a self-consistent analysis that considers the interaction among photons, carriers, and thermal effects. Figure S3 shows the calculation flow of this analysis [S7].
First, we set the current density distribution to J(r) and the initial temperature distribution in the photonic-crystal layer to a uniform distribution T(r), where r=(x,y) represents the position in the xy plane. Next, using time-dependent 3D-CWT considering carrier-photon interactions [S8], we calculate the carrier density N(r) and the photon density U(r) in the active layer by taking into account the temperature-and carrier-density dependences of the optical gain and the refractive index. Then, we calculate the heat density distribution Pheat(r) using the following equation: where V is the electrostatic potential considering the threshold voltage and the differential resistance of the PCSEL; dact is the thickness of the active layer; τc is the carrier lifetime; αin is the internal material loss; act is the confinement factor in the active layer; and ng is the group index of the guided mode. The first, second, and third terms on the right-hand side of Eq. (S1) represent the heat generated by the difference between the electrostatic potential and the photon energy, by carrier recombination in the active layer, and by material absorption of the laser light, respectively.
We then change the current temperature distribution T(r) according to the following equation: where τT is the time constant, which is sufficiently longer than the relaxation oscillation period, and Ts(r) is the steady-state temperature distribution expressed as: where f(r) is the temperature distribution of a point heat source, which is determined based on the chip-to-heatsink packaging conditions.
Then, we update the refractive index and gain distributions in accordance with the updated temperature distribution T(r). Using these updated distributions, we repeat the calculation of the carrier density N(r) and optical energy density U(r) until a selfconsistent solution is obtained.