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Subdiffractive confinement of ultrashort mid-IR pulses with photonic funnels

Jacob LaMountain, Amogh Raju, Dan Wasserman, Viktor A. Podolskiy

TL;DR

The paper analyzes how ultrafast mid-infrared pulses propagate through hyperbolic metamaterial photonic funnels, revealing that funnel dispersion generally broadens short pulses but that negative pre-chirping can restore subdiffraction confinement while compressing the pulse at the tip. Using FEM-based monochromatic funnel solutions combined with time-domain synthesis for linearly chirped Gaussian pulses, the authors show that 100 fs bandwidth-limited inputs can be transformed into ~200 fs signals with substantial, albeit geometry- and material-dependent, intensity enhancements (up to tens of times under favorable conditions). The minimum achievable pulse duration is bounded by the type-I hyperbolicity bandwidth and intrinsic material losses, but reducing loss or optimizing funnel geometry and doping can significantly improve peak intensities and confinement durations. The results establish a framework for ultrafast spatio-temporal control in all-semiconductor designer-metal funnels and suggest generalization to other spectral ranges via appropriate hyperbolic metamaterials.

Abstract

The ability to control the spatial distribution of light, particularly in deep sub-wavelength areas, is important for a range of materials science, microscopy, and communications applications. Separately, materials science and communications rely on the ability to temporally shape the evolution of electromagnetic pulses. In this work we investigate theoretically the propagation of ultrafast pulses inside hyperbolic metamaterials-based photonic funnels, which have been recently used to achieve deep subwavelength (wavelength/30) concentration of monochromatic mid-infrared light. By analyzing the complex spatio-temporal dynamics of the pulse-funnel interaction, we show that photonic funnels, in general, broaden bandwidth-limited ultrafast Gaussian pulses. We demonstrate that this broadening can be mitigated by pre-chirping the incoming light, realizing simultaneous intensity enhancement and spatio-temporal compression of mid-wave IR light in the all-semiconductor "designer metal" funnel platform. Our analysis suggests that, in combination with linear chirp, designer-metal-based photonic funnels can be utilized with 100 fs bandwidth- and diffraction-limited pulses to produce wavelength/30-scale signals of ~200 fs duration, with intensity enhancement on the order of 5. Lowering material absorption can further enhance the peak intensity. The results presented can be used to assess the perspectives of ultrafast sub-diffraction light manipulation in other portions of the electromagnetic spectrum by adjusting the (meta)material composition of the funnels.

Subdiffractive confinement of ultrashort mid-IR pulses with photonic funnels

TL;DR

The paper analyzes how ultrafast mid-infrared pulses propagate through hyperbolic metamaterial photonic funnels, revealing that funnel dispersion generally broadens short pulses but that negative pre-chirping can restore subdiffraction confinement while compressing the pulse at the tip. Using FEM-based monochromatic funnel solutions combined with time-domain synthesis for linearly chirped Gaussian pulses, the authors show that 100 fs bandwidth-limited inputs can be transformed into ~200 fs signals with substantial, albeit geometry- and material-dependent, intensity enhancements (up to tens of times under favorable conditions). The minimum achievable pulse duration is bounded by the type-I hyperbolicity bandwidth and intrinsic material losses, but reducing loss or optimizing funnel geometry and doping can significantly improve peak intensities and confinement durations. The results establish a framework for ultrafast spatio-temporal control in all-semiconductor designer-metal funnels and suggest generalization to other spectral ranges via appropriate hyperbolic metamaterials.

Abstract

The ability to control the spatial distribution of light, particularly in deep sub-wavelength areas, is important for a range of materials science, microscopy, and communications applications. Separately, materials science and communications rely on the ability to temporally shape the evolution of electromagnetic pulses. In this work we investigate theoretically the propagation of ultrafast pulses inside hyperbolic metamaterials-based photonic funnels, which have been recently used to achieve deep subwavelength (wavelength/30) concentration of monochromatic mid-infrared light. By analyzing the complex spatio-temporal dynamics of the pulse-funnel interaction, we show that photonic funnels, in general, broaden bandwidth-limited ultrafast Gaussian pulses. We demonstrate that this broadening can be mitigated by pre-chirping the incoming light, realizing simultaneous intensity enhancement and spatio-temporal compression of mid-wave IR light in the all-semiconductor "designer metal" funnel platform. Our analysis suggests that, in combination with linear chirp, designer-metal-based photonic funnels can be utilized with 100 fs bandwidth- and diffraction-limited pulses to produce wavelength/30-scale signals of ~200 fs duration, with intensity enhancement on the order of 5. Lowering material absorption can further enhance the peak intensity. The results presented can be used to assess the perspectives of ultrafast sub-diffraction light manipulation in other portions of the electromagnetic spectrum by adjusting the (meta)material composition of the funnels.
Paper Structure (10 sections, 8 equations, 5 figures)

This paper contains 10 sections, 8 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Photonic Funnels
  3. Shape and Confinement Scale Metrics
  4. Materials Response
  5. Methods
  6. Time and frequency response of chirped Gaussian pulses
  7. Simulation of Chirped pulses propagating through photonic funnels
  8. Results
  9. Discussion
  10. Conclusions

Figures (5)

  • Figure 1: (a) Funnel schematic and (b) Intensity distribution of funnel illuminated from below by monochromatic circularly polarized light; inset shows a normalized trace of intensity across the path indicated by the dotted line, 50 above the funnel tip.
  • Figure 2: Wavelength dependence of (a) the permittivity of the plasmonic layers and (b) the components of the effective permittivity tensor of the HMM; background color represents elliptic ($\epsilon_\perp,\epsilon_{zz}>0$), type-I hyperbolic ($\epsilon_\perp>0,\epsilon_{zz}<0$) and type-II hyperbolic ($\epsilon_\perp<0,\epsilon_{zz}>0$) frequency ranges, respectively.
  • Figure 3: Field intensity as a function of time for the $T_\mathrm{c}=\qty{460}{\fs}$-long pulse with central wavelength $\lambda_0=\qty{14.5}{\um}$ and $\alpha=-4.5$. Anomalous reflection from the oblique HMM-air interface sends highly confined intensity-enhanced critical angle modes towards the funnel tip.
  • Figure 4: Response of linear-sidewall hybrid funnels to linearly chirped pulses showing (a) intensity enhancement and (b) FWHM at tip as a function of chirp parameter and input duration; green dashed curve sweeps parameters with GDD of 1.6e4; (c,e) intensity above substrate-air interface (dashed curves) and 50 above funnel tip (solid curves) and (d,f) confinement radius as functions of time for chirped (orange) and unchirped (blue) source pulses. The results shown in (c,d) and (e,f) are for the pulses marked by $\times$ and $+$ in (a,b), respectively. The vertical lines in (d,f) show times of maximum (dashed) and half-maximum (solid) tip intensity, while the shaded curves show scaled traces of tip intensity.
  • Figure 5: Materials and funnel response with hypothetical low-loss plasmonic core showing (a) plasmonic layer permittivity; (b) components of the effective permittivity tensor of HMM; (c) intensity enhancement; and (d) FWHM at tip as functions of chirp parameter and source pulse duration. Dashed green lines in (c,d) trace parameters with GDD of 2.4e4.