Phase-modulating lasers toward on-chip integration

Controlling laser-beam patterns is indispensable in modern technology, where lasers are typically combined with phase-modulating elements such as diffractive optical elements or spatial light modulators. However, the combination of separate elements is not only a challenge for on-chip miniaturisation but also hinders their integration permitting the switchable control of individual modules. Here, we demonstrate the operation of phase-modulating lasers that emit arbitrarily configurable beam patterns without requiring any optical elements or scanning devices. We introduce a phase-modulating resonator in a semiconductor laser, which allows the concurrent realisation of lasing and phase modulation. The fabricated devices are on-chip-sized, making them suitable for integration. We believe this work will provide a breakthrough in various laser applications such as switchable illumination patterns for bio-medical applications, structured illuminations, and even real three-dimensional or highly realistic displays, which cannot be realised with simple combinations of conventional devices or elements.


1-1. Without perturbation (square-lattice PCSEL)
In the absence of an applied perturbation, the phase-modulating resonator of an iPM laser (d = 0) corresponds to a square-lattice PCSEL. This subsection discusses the resonance mechanism in square-lattice PCSELs. Supplementary Fig. S2a

1-2. With perturbation (iPM lasers)
In the case of iPM lasers, the air-hole positions do not coincide with the square lattice (d ≠ 0), as indicated in Fig. 2b. Since the air holes are centred (points C) on the perimeter 3 of a circle centred on point O in Fig. 2b, and these positions vary according to the phase distribution, the distance between neighbouring air holes also varies. However, as shown in Fig. 4e, the observed angular and wavelength dependences correspond to that of the square-lattice structure (Fig. 4f), and lasing occurs at the band edge of the square-lattice structure (Figs. 4d and e). We can therefore conclude that the perturbation is sufficiently small that lasing in the square-lattice structure is not prevented. In other words, light at the lasing wavelength forms a two-dimensional standing wave in the in-plane directions (-X and -Y directions). The light wave is then diffracted in the vertical direction (Z direction). The diffraction process can be understood in the following two steps. Firstly, scattering occurs at a boundary between media with different refractive indices, in our case at the air-hole boundaries. Next, the scattered light waves interfere with each other. For the square-lattice structure, the air holes are arranged periodically and the scattered light waves form a plane wave in the vertical direction. In contrast, the air holes in iPM lasers are not periodic, and therefore the scattered light waves deviate from a plane wave, so that the phase is modulated according to the rotation angle  for each air hole. 4

Suppression of zero-order light
As mentioned in the main text, the central spot (referred to as zero-order light) is thought to arise from a modulation residue. It is therefore expected to decrease by increasing the degree of modulation. This can be achieved by increasing d in Fig. 2b. In practice, both the zero-order light and the twin image can easily be removed by placing a shutter above the device. In addition, the suppression of zero-order light and twin images in a computer-generated hologram is discussed in reference S1. However, our goal is to demonstrate the generation of arbitrary beam patterns, and therefore the suppression of zero-order light is outside the scope of the present article. This issue will be discussed in a further publication.

Band edge of the photonic band structure
In photonic crystals, including square-lattice PCSELs, the angular and wavelength dependences relate to the photonic band structure. 17 In this structure, the zero-gradient point is known as the band edge. The light-wave group velocity at the band edge is zero.
Lasing oscillation is considered to occur at the band edges of the  point where the feedback effect reaches maximum intensity. 12 In iPM lasers, lasing takes place at the band edge of the  point, as shown in Figs. 4d and e. This indicates that the formation 5 of a two-dimensional standing wave for lasing occurs by means of the two-dimensional distributed feedback effect in iPM lasers, as also occurs in square-lattice PCSELs.