Manipulation of High-Order Scattering Processes in Ultrasmall Optical Resonators to Control Far-Field Emission

Brandon Redding, Li Ge, Qinghai Song, Glenn S. Solomon, and Hui Cao

Phys. Rev. Lett. 112, 163902 – Published 25 April 2014

Abstract

By imposing a set of harmonic perturbations to a microcavity boundary, we induce conversion and mixing of orbital angular momentum of light via surface scattering. Multiple scattering paths are available due to high-order scattering, which can be greatly enhanced by quasidegenerate resonances. By manipulating the relative strengths of these scattering processes, we theoretically synthesize the angular momentum spectra of individual modes so as to control their far-field patterns. We demonstrate experimentally that in wavelength-scale cavities of a fixed shape, the neighboring modes can have dramatically different emission directionality. This phenomenon is robust against slight shape deviation and surface roughness, and provides a general mechanism to control the emission direction of ultrasmall resonators.

Received 26 September 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.163902

Authors & Affiliations

Brandon Redding¹, Li Ge^2,3, Qinghai Song⁴, Glenn S. Solomon⁵, and Hui Cao^1,*

¹Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
²Department of Engineering Science and Physics, College of Staten Island, CUNY, Staten Island, New York 10314, USA
³The Graduate Center, CUNY, New York, New York 10016, USA
⁴Department of Electronic and Information Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China
⁵Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA

^*hui.cao@yale.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 112, Iss. 16 — 25 April 2014

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Comparison of three neighboring modes in a wavelength-scale cavity which exhibit totally different emission patterns. The cavity boundary is defined by $ρ (θ) = R [1 - 0.069 \cos (2 θ) + 0.008 \cos (3 θ) - 0.0014 \cos (4 θ)]$ . (a)–(c) Intracavity intensity distribution calculated by the FDFD method for the three modes at $k R = 4.37$ , 4.71, 5.03. They are similar to whispering-gallery modes with dominant azimuthal number $m_{0} = 10$ , 11, 12. (d)–(f) Far-field emission pattern for the modes in (a)–(c). The red areas represent the numerical results, and the black solid curves represent the second-order perturbation calculation. The emission direction of these three modes changes from forward ( $θ = 0 °$ ) to bidirectional to backward ( $θ = 180 °$ ), which is not captured by the second-order perturbation treatment, illustrating the importance of higher-order scattering processes.
Reuse & Permissions
Figure 2
Analysis of orbital angular momentum components in the three modes shown in Fig. 1. (a)–(c) Amplitude $| B_{m} |$ for each angular momentum component, represented by the azimuthal number $m$ , in the far field. The red crosses connected by the solid line represent the numerical results, and the open squares are calculated by the second-order perturbation theory. The arrow marks the $m_{0} - 6$ angular momentum component in each mode. (d)–(f) The phase difference of $B_{m}$ between the numerical simulation and the second-order perturbation theory. The phase change of $B_{m_{0} - 6}$ and its stronger presence in the $m_{0} = 12$ mode appear to be responsible for the switch of emission direction.
Reuse & Permissions
Figure 3
Experimental comparison of the emission directionality of lasing modes in three microdisks of the same shape and slightly different size. (a)–(c) SEMs of three microdisks fabricated with the same shape (indicated by the red dotted line). The lasing wavelength, $λ$ , and $k R$ are indicated for each microdisk. (d)–(f) The far-field emission pattern measured for each mode. The emission direction changes from forward to bidirectional to backward for three neighboring modes, in good agreement to the numerical results in Fig. 1.
Reuse & Permissions
Figure 4
Robustness of emission directionality against fabrication error. (a) and (b) SEMs of two microdisks with the same shape as in Fig. 1 (red dotted line) and designed to support lasing in the $m_{0} = 12$ mode. The lasing modes are at $k R = 5.02$ and 5.07. Both modes have far-field emission patterns similar to Fig. 3. (c) The emission directionality $U$ for five microdisks showing a clear switching of directionality with $k R$ . Furthermore, all three cavities supporting the $m_{0} = 12$ mode ( $k R \sim 5.1$ ) show similar emission directionality indicating that the far-field pattern is robust to slight variations in the cavity shape and surface roughness.
Reuse & Permissions

Physical Review Letters