Pump-controlled modal interactions in microdisk lasers

We demonstrate an effective control of nonlinear interactions of lasing modes in a semiconductor microdisk cavity by shaping the pump profile. A target mode is selected at the expense of its competing modes either by increasing their lasing thresholds or suppressing their power slopes above the lasing threshold. Despite the strong spatial overlap of the lasing modes at the disk boundary, adaptive pumping enables an efficient selection of any lasing mode to be the dominant one, leading to a switch of lasing frequency. The theoretical analysis illustrates both linear and nonlinear effects of selective pumping and quantifies their contributions to lasing-mode selection. This work shows that adaptive pumping not only provides a powerful tool to control the nonlinear process in multimode lasers, but also enables the tuning of lasing characteristic after the lasers have been fabricated.

Figure 1

Fabricated GaAs microdisk. (a) Top-view and (b) tilt-view scanning electron microscope images of a GaAs microdisk. (c) Magnified view of the part highlighted in (b) reveals the sidewall roughness of the disk. (d) A schematic showing the spatial intensity profile of the pump beam is modulated to control the lasing modes in the microdisk.

Figure 2

Lasing spectra with different pump patterns. (a) Under uniform ring pumping, many modes lase simultaneously. (b)–(f) Lasing spectra when modes (i)–(v) are the target as the dominant lasing mode with adaptive pumping. Insets: The final optimized pump profiles in gray scales with darker color corresponding to higher intensity.

Figure 3

Emission intensity as a function of pump power for (a) mode (i) and (b) mode (iv) under uniform ring pumping (black crosses) and nonuniform pumping (red squares) to optimize mode (i). Insets: The intensity distribution of (a) uniform and (b) optimized pump profiles. Dashed lines represent the linear regression of the data points below and above the lasing threshold. The intersection of the two lines determines the lasing threshold pump power, and the slope of the line above the threshold gives the power slope of the lasing mode. (c),(d) Lasing thresholds and power slopes for modes (i)–(v) under uniform pumping (patterned bars) and adaptive pumping (filled bars). Mode (i) becomes the dominant lasing mode because the inhomogeneous pumping suppress all other competing modes by greatly increasing their lasing thresholds.

Figure 4

Emission intensity as a function of pump power for (a) mode (iv) and (b) mode (iii) under uniform ring pumping (black crosses) and nonuniform pumping to select mode (iv) (red squares). Insets: The intensity distribution of (a) uniform and (b) optimized pump profiles. (c),(d) Lasing thresholds and power slopes under uniform pumping (patterned bars) or selective pumping (filled bars). The target mode (iv) becomes the dominant lasing mode even though its lasing threshold is not the lowest because adaptive pumping greatly suppresses the power slopes of the competing modes.

Figure 5

(a),(c),(e) Lasing thresholds and (b),(d),(f) power slopes for modes (i)–(v) after optimizing for modes (ii), (iii), and (v). Patterned bars represent the case for uniform pumping and filled bars are for selective pumping. While the target mode does not necessarily have the lowest lasing threshold, its power slope becomes the highest among all lasing modes.

Figure 6

Numerical simulation of switching of lasing order by adaptive pumping of a microdisk with rough boundary. The disk radius is 3 $\mu \mathrm{m}$ and the refractive index is 3.13. (a),(b) Calculated spatial distribution of magnetic field ($|H_z|$) for two TE-polarized high-$Q$ modes, labeled mode 1 and 2, respectively. Mode 1, at $\lambda =917.7$ nm, has $Q$ factor of $1.20\times {10}^5$. Mode 2, at $\lambda =902.9$ nm, has $Q$ factor of $1.09\times {10}^5$. Mode 1 in (a) consists predominantly of CCW propagating WG wave with radial number 1 and azimuthal number 57. Mode 2 in (b) is primarily a WG modes of radial number 1 and azimuthal number 58, but contains additional WG waves of higher radial order number 7 due to disorder-induced mode mixing. (c) Lasing intensity for modes 1 and 2 as a function of pump strength $D_0$ with uniform ring pumping (dashed lines) or nonuniform pumping to select mode 2 (solid lines). Mode 1 lases first before mode 2 with uniform pumping, but the lasing order switches, i.e., mode 2 lases first, with the nonuniform pump profile (inset) shown in the gray scale with darker color corresponding to stronger pumping. $D_0$ is normalized to the lasing threshold of mode 1 with uniform ring pumping.

Figure 7

Numerical simulation of changing the power slopes of lasing modes by adaptive pumping of a microdisk with rough boundary. The disk radius is 3 $\mu \mathrm{m}$ and the refractive index is 3.13. (a),(b) Calculated spatial distribution of magnetic field ($|H_z|$) for two WG modes of second radial order, labeled mode 1 and 2, respectively. (c) Lasing intensity for these two modes with uniform ring pumping (dashed lines) and nonuniform pumping to make mode 2 stronger than mode 1 (solid lines). The optimized pump profile found by the genetic algorithm does not change the lasing order but greatly suppresses the power slope of mode 1 (black lines).