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  • Open Access

Modified light emission from a dipole in lossy and graded-index spherical structures

Farzaneh Adibzadeh1,*, Martijn Wubs2,3, and Nicklas Anttu1

  • *Contact author: farzaneh.adibzadeh@abo.fi
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APS Open Sci. 1, 000119 – Published 1 September, 2026

DOI: https://doi.org/10.1103/1xgq-h68w

Abstract

Energy transfer and light emission behavior at subwavelength scales are governed by near-field interactions between an emitter and its surrounding refractive-index environment, which can modify emission at the nanoscale and influence the far-field response in devices such as solar cells and light-emitting diodes (LEDs). Here, we analyze light emission in a spherical structure using a classical point dipole model with emphasis on how near-field interactions affect the spontaneous emission rate, as quantified by the Purcell factor. The system is studied under two refractive-index configurations: (1) an abrupt transition from an inner sphere to the surrounding medium and (2) a gradual transition with a graded refractive index, considered for both nonabsorbing and absorbing surrounding media. Our findings show that, within the fixed-amplitude dipole considered here, even a strong increase in near-field absorption does not lead to a comparable reduction in the far-field emission. In this model, the source supplies the additional power required to compensate for such near-field losses. This distinction between near-field enhancement and radiated power to the far field is important, for example, in studies of photon recycling in semiconductors and other optoelectronic devices, where both near-field absorption and radiative emission are present. An abrupt transition in the refractive index produces repeated peaks in the Purcell factor as a function of the inner sphere radius, whereas a graded refractive index smooths these peaks. In a graded system, with increasing grading thickness, the Purcell factor converges to the refractive index of the inner sphere when the grading thickness reaches the order of the wavelength. This behavior indicates that, even when the inner sphere has a higher refractive index than the surrounding medium, the emission is not limited by the surrounding refractive index. Thus, a graded refractive-index profile provides a viable strategy for mitigating reflection losses in emission. These insights are valuable for designing photon out-coupling and photon-recycling schemes and offer a pathway for improving the performance of optoelectronic devices, including solar cells and LEDs.

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APS Open Sci. 1, 000119– Published 1 September, 2026
Vol. 1
  • Received 9 April 2026
  • Revised 8 July 2026
  • Accepted 10 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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