Broadband opto-electro-mechanical effective refractive index tuning on a chip

The energy-based methods as the Dispersion Relation (DR) and Response Theory of Optical Forces (RTOF) have been largely applied to obtain the optical forces in the nano-optomechanical devices, in contrast to the Maxwell Stress Tensor (MST). In this work, we apply first principles to show explicitly why these methods must agree with the MST formalism in linear lossless systems. We apply the RTOF multi-port, to show that the optical force expression on these devices can be extended to analyze multiple light sources, broadband sources, and multimode devices, with multiple degrees of freedom. We also show that the DR method, when expressed as a function of the derivative of the effective index performed at a fixed wave vector, may be misinterpreted and lead to overestimated results. Optical (transverse gradient) forces between two adjacent dielectric structures, due to the overlap of the evanescent field of the guided modes, were proposed by Povinelli et al. [1]. The optical forces can be rigorously calculated using the Maxwell Stress Tensor (MST) formalism [2] or, alternatively, in linear lossless dielectric materials, it may be obtained directly from the device's dispersion relation as a function of one of the structure's degrees of freedom (gap) [1,3,4]. Due to its computational simplicity and physical insights, the latter method has been more used than the former [3,4]. Furthermore, the Dispersion Relation (DR) method can be further simplified to express the optical force as a function of the mode effective (refractive) index derivative, with respect to the gap, leading to two expressions: one where the derivative must be performed at a fixed wave vector [5], and another where it must be performed at a fixed angular frequency [6][7][8]. The latter expression version can also be obtained in an alternative formal manner, by using the recently developed Response Theory of Optical Force (RTOF) method, proposed by Rakich et al. [9,10]. Besides that, all these expressions must agree with the MST formalism [1,9].In this letter, we apply first principles to explicitly show why these energy-based methods must agree with the MST formalism. We analyze a typical nano-optomechanical device to show that the DR method, expressed in terms of the effective index with derivative performed at a fixed wave vector, may overestimate the optical force if the correct transformations are not used, thus disagreeing with the MST. We also use the RTOF theory to extend the correct expression to more general cases.For a nano-optomechanical system composed of pure dielectric materials, the conservation of linear momentum states that [2,11]:where EM is the electromagnetic momentum density, ME is the mechanical momentum (or the force) density, and ⃡ is the Maxwell Stress Tensor (MST), which represents the momentum flux, given by [2,11]: where ( , ) and ( , ) are the electric and magnetic field, respectively, 0 and 0 are the vacuum electric permittivity and magnetic permeability, respectively, and the symbol * denotes their complex conjugate, an...

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“…(9) was used in [5,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and Eq. (13) in [6-9, 16, 33-46].…”

mentioning

confidence: 99%

Optical forces through the effective refractive index

Rodrigues

Almeida

2017

Opt. Lett.

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“…Additionally, it is necessary to statically tune the rings of the FWM-resonator as well as the drop filters. Opto-electro-mechanical tuning of the refractive index in waveguides is suitable for cryogenic operation and demonstrations of large index shifts with low loss have been presented [32]. The number of available spectral multiplexing modes depends on the bandwidth over which…”

Section: Discussionmentioning

confidence: 99%

“…24,26,27,32] and switching only the classical fields significantly improves the loss-budget over other types of multiplexing.AcknowledgmentsThis work was supported by the Danish National Research Foundation through the Center of Excellence SPOC (Silicon Photonics for Optical Communication), DNRF 123. M H acknowledges funding from VILLUM FONDEN.…”

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confidence: 99%

Unidirectional frequency conversion in microring resonators for on-chip frequency-multiplexed single-photon sources

et al. 2019

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Microring resonators are attractive for low-power frequency conversion via Bragg-scattering fourwave-mixing due to their comb-like resonance spectrum, which allows resonant enhancement of all four waves while maintaining energy and momentum conservation. However, the symmetry of such mode structures limits the conversion efficiency to 50% due to the equal probability of up-and downconversion. Here, we demonstrate how two coupled microrings enable highly directional conversion between the spectral modes of one of the rings. An extinction between up-and down-conversion of more than 40 dB is experimentally observed. Based on this method, we propose a design for on-chip multiplexed single-photon sources that probabilistically generate photon pairs across many frequency modes of a ring resonator and subsequently convert them to a single frequency-thereby enabling quasi-deterministic photon emission. Our numerical analysis shows that once a photon is generated, it can be converted and emitted into a wave packet having a 90% overlap with a Gaussian with 99% efficiency for a ratio between intrinsic and coupling quality factors of 400.

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“…A similar platform was adapted for out-of-plane displacement of a slab above the waveguide, as in Fig. 2a 3, and used both parallel plate and gradient electrical field force actuation [44], including an in-depth analysis of optical loss [45]. In silicon, the concept in Fig.…”

Section: A Phase Shiftersmentioning

confidence: 99%

“…Devices that rely on out-of-plane displacement of a slab on top of a waveguide, on the other hand, benefit from the near-atomically-flat top and bottom surfaces, and usually feature lower roughness-induced losses. However, reported devices using such an architecture have so far relied on beams that are not entirely phase mismatched to the guided mode, effectively becoming a lossy asymmetric directional coupler [44], [45], [64].…”

Section: A Phase Shiftersmentioning

confidence: 99%