Raktim Sarma

Compact spectrometer based on a disordered photonic chip

Summary form only given. Spectrometers are widely used tools in chemical and biological sensing, material analysis, and light source characterization. The development of a high-resolution on-chip spectrometer could enable compact, low-cost spectroscopy for portable sensing as well as increasing lab-on-a-chip functionality. However, the spectral resolution of traditional grating-based spectrometers scales with the optical pathlength, which translates to the linear dimension or footprint of the system, which is limited on-chip. In this work, we utilize multiple scattering in a random photonic structure to fold the optical path, making the effective pathlength much longer than the linear dimension of the system and enabling high spectral resolution with a small footprint. We achieve sub-nm resolution using a scattering medium with the largest dimension of merely 50 μm.

Position-dependent diffusion of light in disordered waveguides

Summary form only given. Diffusion is a statistical description of random walk of a classical particle, and the diffusion constant D0 is the only parameter in the diffusion equation. For light as well as for other kinds of waves, this is an approximation, because the interference of partial waves is ignored [1]. Such interference is essential to Anderson localization. Proper account of the interference effects in random samples of finite size [2] and/or with absorption [3] results in spatial variation of the diffusion coefficient D(r) in the self consistent theory (SCT) of localization.To observe position-dependent diffusion, disordered waveguide structures were fabricated with the silicon on insulator wafer (see Fig. 1a). The patterns were written by electron beam lithography and etched in an inductive coupled reactive ion etcher. The waveguides contained 2D random arrays of air holes that scattered light, and the scattering length was varied by the hole size and filling fraction. The waveguide walls were made of photonic crystals that had complete bandgap in 2D, so that light could not escape laterally. However, light will leak out of the plane while being scattered by the air holes. This vertical leakage can be described by an effective absorption or dissipation. The relevant parameters are the diffusive absorption length ȟa0 and the transport mean free path . The localization length ȟ is determined by and the waveguide width W. Light from a CW laser source was injected into the waveguide from one end, and transported through the random medium. Spatial distribution of light intensity on the sample surface was imaged onto a camera by an objective lens. After entering the random medium, light is attenuated due to competing effects of backscattering and dissipation. I(y, z) was integrated along the transverse y-direction to determine the variation of intensity along the axial z-direction (parallel to the waveguide axis).Fig. lb shows the measured light intensity I(z) inside the ensembles of random waveguides of different width W (blue). The values of ξ and ξασ are obtained by fitting the most diffusive sample (W = 60 μm, longest ξ) with SCT (red dashed line) [2,3]. Using these values, SCT successfully predicts I(z) for all other samples. D(z) corresponding to red curves in Fig. lb are plotted in Fig. lc, showing a suppression of diffusion in the middle of the sample with increase ξασ/ξ (decrease of W) as predicted by SCT.

Rotation-induced evolution of far-field emission patterns of deformed microdisk cavities

A critical issue that hinders the development of chip-scale optical gyroscopes is the size dependence of the Sagnac effect, which manifests as a rotation-induced phase shift or frequency splitting between two counterpropagating waves or resonances, and is proportional to the size of the optical system. We show numerically and theoretically that the far-field emission patterns (FFPs) of optical microdisk cavities depend strongly on rotation and can therefore provide an alternative approach. At low rotation speed where resonant frequencies barely shift with rotation (i.e., a negligible Sagnac effect), the FFPs already exhibit a significant rotation-induced asymmetry, which increases linearly with the rotation speed. We further identify the basic requirements to maximize this effect, including distinct output directions for the clockwise and counterclockwise waves in a cavity mode, as well as a vanishing frequency splitting between one such mode and its symmetry related partner mode. Based on these requirements, we propose several microcavity shapes that display orders of magnitude enhancement of the emission sensitivity to rotation and could stimulate a new generation of optical gyroscopes with small footprints and on-chip integrability.We study rotation-induced asymmetry of far-field emission from optical microcavities, based on which a new scheme of rotation detection may be developed. It is free from the “dead zone” caused by the frequency splitting of standing-wave resonances at rest, in contrast to the Sagnac effect. A coupled-mode theory is employed to provide a quantitative explanation and guidance on the optimization of the far-field sensitivity to rotation. We estimate that a 10 enhancement of the minimal detectable rotation speed can be achieved by measuring the far-field asymmetry, instead of the Sagnac effect, in microcavities 5 microns in radius and with distinct emission directions for clockwise and counterclockwise waves.

Rotating optical microcavities with broken chiral symmetry.

We demonstrate in open microcavities with broken chiral symmetry that quasidegenerate pairs of copropagating-wave resonances are transformed by rotation to counterpropagating ones, leading to a striking change of emission directions. The rotation-induced relative change in output intensity increases exponentially with cavity size, in contrast to the linear scaling of the Sagnac effect. By tuning the degree of spatial chirality with cavity shape, we are able to maximize the emission sensitivity to rotation without spoiling the quality factor.

Control of Mesoscopic Transport by Modifying Transmission Channels in Opaque Media

While controlling particle diffusion in a confined geometry is a popular approach taken by both natural and artificial systems, it has not been widely adopted for controlling light transport in random media, where wave interference effects play a critical role. The transmission eigenchannels determine not only light propagation through the disordered system but also the energy concentrated inside. Here we propose and demonstrate an effective approach to modify these channels, whose structures are considered to be universal in conventional diffusive waveguides. By adjusting the waveguide geometry, we are able to alter the spatial profiles of the transmission eigenchannels significantly and deterministically from the universal ones. In addition, propagating channels may be converted to evanescent channels or vice versa by tapering the waveguide cross-section. Our approach allows to control not only the transmitted and reflected light, but also the depth profile of energy density inside the scattering system. In particular geometries perfect reflection channels are created, and their large penetration depth into the turbid medium as well as the complete return of probe light to the input end would greatly benefit sensing and imaging applications. Absorption along with geometry can be further employed for tuning the decay length of energy flux inside the random system, which cannot be achieved in a common waveguide with uniform cross-section. Our approach relies solely on confined geometry and does not require any modification of intrinsic disorder, thus it is applicable to a variety of systems and also to other types of waves.

Wavelength-scale microdisks as optical gyroscopes: a finite-difference time-domain simulation study

We have developed a finite-difference time-domain algorithm to simulate a wavelength-scale optical gyroscope based on a circular microdisk. In addition to the frequency shift, the rotation-induced changes in the quality factor and far-field emission pattern of the whispering gallery modes are studied. Compared to the closed cavity of same size and shape, an open cavity displays a larger frequency splitting by rotation, due to an increase of the mode size. When the disk dimension is on the order of the optical wavelength, the relative change in quality factor by rotation is over an order of magnitude larger than that in resonant frequency, due to enhanced evanescent tunneling of light. These results point to multiple methods for rotation sensing, monitoring the lasing threshold and the output power or the far-field emission pattern of a rotating microdisk laser, which can be much more sensitive than the Sagnac effect in ultrasmall optical gyroscopes.

Evanescently coupled multimode spiral spectrometer

We designed a high-resolution compact spectrometer based on an evanescently-coupled multimode spiral waveguide. Interference between the modes in the waveguide forms a wavelength-dependent speckle pattern which is used as a fingerprint to identify the input wavelength after calibration. Evanescent coupling between neighboring arms of the spiral results in a non-resonant broad-band enhancement of the spectral resolution. Experimentally, we demonstrated a resolution of 0.01 nm at a wavelength of 1520 nm using a 250 {\mu}m radius spiral structure. Spectra containing 40 independent spectral channels are recovered simultaneously and the operation bandwidth is significantly increased by applying compressive sensing to sparse spectra reconstruction.

Rotation-induced mode coupling in open wavelength-scale microcavities

We study the interplay between rotation and openness for mode coupling in wavelength-scale microcavities. In cavities deformed from a circular disk, the decay rates of a quasidegenerate pair of resonances may cross or anticross with increasing rotation speed. The standing-wave resonances evolve to traveling-wave resonances at high rotation speed, however both the clockwise (CW) and counterclockwise (CCW) traveling-wave resonances can have a lower cavity decay rate, contrary to the intuitive expectation from the rotation-dependent effective index. With increasing rotation speed, a phase locking between the CW and CCW wave components in a resonance takes place. These phenomena result from the rotation-induced mode coupling, which is strongly influenced by the openness of the microcavity. The possibility of a nonmonotonic Sagnac effect is also discussed.

Shape Dependence of Transmission, Reflection, and Absorption Eigenvalue Densities in Disordered Waveguides with Dissipation

The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced transmission in optics and acoustics. Here, we show that in the presence of absorption, density of the transmission eigenvalues depends on the confinement geometry of scattering media. Furthermore, in an asymmetric waveguide, densities of the reflection and absorption eigenvalues also depend of the side from which the waves are incident. With increas- ing absorpotion, the density of absorption eigenvalues transforms from single-peak to double-peak function. Our findings open a new avenue for coherent control of wave transmission, reflection and absorption in random media.

Optical resonances in rotating dielectric microcavities of deformed shape

We investigate numerically rotation-induced changes of optical resonances in wavelength-scale dielectric cavities that are deformed from a circle. The relative change in the quality factor due to rotation is usually larger than that of the resonant frequency, even though both exhibit a threshold behavior, i.e., they barely change at low rotation speed. This threshold is increased at large deformation, which lowers the sensitivity to rotation. Presence of wave chaos can further increase the threshold for rotation-induced changes in resonant frequencies. Unlike the resonant frequency and quality factor, the change in far-field emission pattern by rotation does not display a threshold behavior, thus having a higher sensitivity at low rotation speed. The threshold behavior can be eliminated by designing the cavity shape with special symmetry, and the response of the far-field emission to rotation is also enhanced.