Diffraction Gratings and Applications

Loewen, Erwin G.; Popov, Evgeny

doi:10.1201/9781315214849

Cited by 226 publications

(122 citation statements)

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“…To illustrate the reconfi gurable capability of such tunable metasurfaces, we demonstrate a voltage controlled mid- [ 63 ] The wavelength and angle dependent diffraction for an array of resonators ( w = 3 μm, h = 1 μm and d = 4 μm), with n = 5 (inter-resonar phase shift of 72°) is shown in Figure 5 B. The incident plane wave couples only to the +1 diffraction grating mode at 34.5° at an operation wavelength of 11.35 μm.…”

Section: Full Paper Full Paper Full Papermentioning

confidence: 99%

Electrically Reconfigurable Metasurfaces Using Heterojunction Resonators

Iyer

Pendharkar

Schuller

2016

Advanced Optical Materials

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paradigm in reconfi gurable metasurfacebased optics. Here, we use electromagnetics and device simulations to design electrically pumped semiconductor heterostructure resonators capable of arbitrarily tuning the refl ection phase of infrared light with little change in amplitude.Previous approaches for tuning metasurfaces-using metallic resonators coupled to an index tunable background [ 8,[23][24][25][26][27][28] or mechanically changing the shape of metallic resonators [ 5,29,30 ] have been unable to achieve reconfi gurable 2π phase shifts. This inability to achieve 2π phase control stems fundamentally from the nature of the underlying optical antennas. Because the light-matter interaction lengths are subwavelength and the quality factors modest ( Q ≈ 1−10), very large refractive index modulation is needed (Δ n ≥ 1). InSb [31][32][33] or InAs [ 27,34,35 ] support free-carrier index shifts of this magnitude due to their high mobility and low electron effective mass. In our previous theory work, [ 36 ] we demonstrated full 2π tuning of the transmission phase of semiconductor metasurface by modulating the carrier concentration in InSb resonators between 10 17 -10 18 cm −3 . However, we did not consider how to achieve such modulation. Here, we use combined electromagnetic [ 37 ] and device simulations to demonstrate subwavelength 1D heterojunction device resonators with electrically reconfi gurable refl ection phase. We fi rst demonstrate a new resonator geometry that allows for integration of metal electrodes with dielectric-type Mie resonances. Subsequently, we incorporate an InSb based heterojunction device layer into the resonator architecture. This novel device design employs electron and hole blocking layers to achieve large modulations of carrier concentration over electrically large dimensions, enabling near-2π tuning of refl ection phase with minimal changes in refl ection amplitude. Finally, we demonstrate fully continuous and tunable steering of high-quality narrow, diffraction lobes in resonator arrays. Results and DiscussionGiven the need for integrating top and bottom electrical contacts, our basic metasurface element is a modifi ed version of a 1D "strip" resonator sitting atop a refl ecting back electrode shown in

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Section: Full Paper Full Paper Full Papermentioning

confidence: 99%

Electrically Reconfigurable Metasurfaces Using Heterojunction Resonators

Iyer

Pendharkar

Schuller

2016

Advanced Optical Materials

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“…In some applications such as optical imaging [9], [21], the design of the measurement matrix cannot be arbitrary. In optical imaging, the object of interest, signal x, can be passed through an optical diffraction pattern or a mask and an optical Fourier lens.…”

Section: Fourier-friendly Phasecodementioning

confidence: 99%

“…Concretely, A is constrained to be the cascade of (up to a couple of) stages of a diagonal matrix (corresponding to a socalled optical mask or coded diffraction pattern) and a Fourier transform (corresponding to an optical lens). This constraint is motivated by practical optical systems [21], array imaging [22], etc., as also addressed recently by [23].…”

Section: Introduction a Phase Retrieval Problemmentioning

confidence: 99%

PhaseCode: Fast and Efficient Compressive Phase Retrieval Based on Sparse-Graph Codes

Pedarsani

Yin

Lee

et al. 2017

IEEE Trans. Inform. Theory

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Abstract-We consider the problem of recovering a complex signal x ∈ C n from m intensity measurements of the form |a H i x|, 1 ≤ i ≤ m, where a H i is the i-th row of measurement matrix A ∈ C m×n . Our main focus is on the case where the measurement vectors are unconstrained, and where x is exactly K-sparse, or the so-called general compressive phase retrieval problem. We introduce PhaseCode, a novel family of fast and efficient algorithms that are based on a sparsegraph coding framework. We show that in the noiseless case, the PhaseCode algorithm can recover an arbitrarily-close-toone fraction of the K non-zero signal components using only slightly more than 4K measurements when the support of the signal is uniformly random, with order-optimal time and memory complexity of Θ(K)1 . It is known that the fundamental limit for the number of measurements in compressive phase retrieval problem is 4K − o(K) for the more difficult problem of recovering the signal exactly and with no assumptions on its support distribution [1], [2]. This shows that under mild relaxation of the conditions, our algorithm is the first constructive capacity-approaching compressive phase retrieval algorithm: in fact, our algorithm is also order-optimal in complexity and memory. Further, we show that for any signal x, PhaseCode can recover a random (1 − p)-fraction of the non-zero components of x with high probability, where p can be made arbitrarily close to zero, with sample complexity m = c(p)K, where c(p) is a small constant depending on p that can be precisely calculated, with optimal time and memory complexity. As a result, assuming that the non-zero components of x are lower bounded by Θ(1) and upper bounded by Θ(K γ ) for some positive constant γ < 1, we are able to provide a strong 1 guarantee for the estimated signalx as follows: x − x 1 ≤ p x 1(1 + o(1)), where p can be made arbitrarily close to zero. As one instance, the PhaseCode algorithm can provably recover, with high probability, a random 1 − 10 −7 fraction of the significant signal components, using at most m = 14K measurements.Next, motivated by some important practical classes of optical systems, we consider a "Fourier-friendly" constrained measurement setting, and show that its performance matches that of the unconstrained setting, when the signal is sparse in the Fourier domain with uniform support. In the Fourier-friendly setting that we consider, the measurement matrix is constrained to be a cascade of Fourier matrices (corresponding to optical lenses) and diagonal matrices (corresponding to diffraction mask patterns).Finally, we tackle the compressive phase retrieval problem in the presence of noise, where measurements are in the form Ramtin Pedarsani is with the ECE Department at UC Santa Barbara. email: ramtin@ece.ucsb.edu. Dong Yin and Kannan Ramchandran are with the EECS Department at UC Berkeley. email:{dongyin,kannanr}@eecs.berkeley.edu.Kangwook Lee is with the EE Department at KASIT. email: kw1jjang@kaist.ac.kr. This paper was presented in part in Allerton 2015...

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“…This can be visualized in Fig the wavelength of light (λ), the diffracted light will be in phase. The relationship between the wave-vectors of the incident and diffracted waves is so described by means of the well-known Bragg condition [87] 1 :…”

Section: Diffraction Gratingsmentioning

confidence: 99%

“…As there is no feedback of radiated diffraction orders to the guided wave in the grating waveguide, the part of the guided wave energy radiated by a single groove is carried away from the waveguide and the mode enters the next groove with diminished amplitude. Assuming slow change of the mode amplitude within one groove period, the amplitud of the electromagnetic fields of the upwards diffracted wave (E, H) (i. e. a(z)) can be described by the following single differential equation [87]:…”

Section: )mentioning

confidence: 99%

Addressing Fiber-to-Chip Coupling Issues in Silicon Photonics

Conejos¹,

Vicente²

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PrefacioEste trabajo trata sobre fotónica de silicio. Trata, pues, de la manipulación de la luz, o fotones. La luz que transporta la información por todo el planeta.La luz de los sistemas de comunicaciones basados en fibraóptica. La fotónica de silicio es la aplicación a estos sistemas fotónicos que usan silicio como medió optico. La fotónica de silicio estudia la manipulación de la luz en dispositivos a una escala sub-micrométrica (hasta nanométrica) para muchas aplicaciones y, por tanto, también para comunicaciones en particular.Cuando empecé mi trabajo en el NTC como estudiante de ingeniería en 2005, este Centro estaba casi empezando a investigar en el campo, especialmente en el tema del acoplo fibra-chip. Tuve así pues el placer de continuar investigando en el tema como estudiante de doctorado, bajo la supervisión de Pablo, a quien estoy muy agradecido por ello. En los pasados cinco años, la fotónica de silicio se ha convertido en un campo muy activo en el grupo, con al menos diez personas investigando en diferentes aplicaciones. Con los años, hemos intentado desarrollar una exhaustiva comprensión de la complejidad de la fotónica de silicio. Este es uno de los propósitos de este libro: compartir nuestra visión.Muchas de las ideas aquí expuestas son resultado de fructíferas discusiones entre compañeros tanto del interior del grupo como de otros grupos de investigación.Con el riesgo de olvidar a alguien, me gustaría mencionar algunas personas por su nombre.Gracias, Javier, por darme la oportunidad de formar parte del NTC, donde durante estos casi cinco años he conocido gente maravillosa y que nunca olvidaré.Gracias, Alex, por tus ltimas correcciones de la Tesis.Gracias especiales a Pablo, por supervisar excelentemente mi trabajo durante este tiempo, y por su siempre humilde apoyo y ayuda.Gracias, Mariam. Guiarte en tu tesis de master y en tu proyecto final de carrera ha sido un placer. Parte de tu trabajo y muchas de tus valiosas aportaciones están, de algún modo, también incluidas en este libro.Gracias, Antoine, por haber sido mi compañero durante este tiempo. Soy consciente de la increíble persona con la que he estado trabajando. Te deseo todo lo mejor con tu tesis, y mucha suerte tanto en lo personal como en lo profesional.Gracias a todos los estudiantes de doctorado del NTC: Carlos, Rubén, Guillermo, Pak, Jesús, Sara, Ana, Javi, Jose, entre otros.Enhorabuena a los recintes Doctores Ruth y Rakesh, a quienes también deseo lo mejor profesionalmente.Gracias al prometedor equipo de encapsulado que está surgiendo en el NTC:Giani y, recientemente, Mercè. Espero sigamos colaborando juntos por muchos años, especialmente en lo que respecta al laboratorio del banco de alineamiento, donde continuaremos pasando buenos ratos.Este trabajo no habría sido posible sin las manos del equipo de fabricación del NTC, quienes, con el objetivo de poder hacer nuestros experimentos, han procesado tantas obleas como ha sido necesario, y empleado siempre el tiempo que se les ha requierido. Gracias Amadeu, Jose, Juan, Laurent, Paco por...

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Diffraction Gratings and Applications

Cited by 226 publications

References 0 publications

Electrically Reconfigurable Metasurfaces Using Heterojunction Resonators

Electrically Reconfigurable Metasurfaces Using Heterojunction Resonators

PhaseCode: Fast and Efficient Compressive Phase Retrieval Based on Sparse-Graph Codes

Addressing Fiber-to-Chip Coupling Issues in Silicon Photonics

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