Manipulating hyperbolic transient plasmons in a layered semiconductor

Anisotropic materials with oppositely signed dielectric tensors support hyperbolic polaritons, displaying enhanced electromagnetic localization and directional energy flow. However, the most reported hyperbolic phonon polaritons are difficult to apply for active electro-optical modulations and optoelectronic devices. Here, we report a dynamic topological plasmonic dispersion transition in black phosphorus via photo-induced carrier injection, i.e., transforming the iso-frequency contour from a pristine ellipsoid to a non-equilibrium hyperboloid. Our work also demonstrates the peculiar transient plasmonic properties of the studied layered semiconductor, such as the ultrafast transition, low propagation losses, efficient optical emission from the black phosphorus’s edges, and the characterization of different transient plasmon modes. Our results may be relevant for the development of future optoelectronic applications.


REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): Quesfions the authors need to address: -it is not clear ho3w the authors get the dielectric funcfion results shown in Fig. 1D.If the real of of the dielectric funcfion is negafive, there is no need for pump-probe, BP's plasmons could be imaged with CW lasers.The authors need to clarify how these results were achieved, and whter they are supported by theirs or others work performed in determining the dielectric funcfion, for example using ellipsometry or other methods.
-the work does not make it clear what the role of thickness is in the measured fringes, the authors need to clarify why the thicknesses used were selected and how thickness is related to fringe spacing?-it is also not clear why the pump frequency were selected?The authors need to say clearly why the reasoning for the choice of the pump wavelength/ For example would a pump frequency of 532 nm give the same result?-a related issue is will the authors see plasmonic modes they observe if they were to use CW laser rather than pump-probe?A few sentences jusfifying pump-probe requirement would be helpful to less experts along with the choice a specific pump laser frequency determinafion -how was the anisotropy axis determined in BP? authors need to describe the process -the authors need to address the effect of degradafion on their measurements.BP degrades soon after exposure to ambient condifion, even though it is exfoliated in ambient.Light (IR beam) also accelerates the degradafion.How does degradafion affect measurements?-if the BP was encapsulated (for example by hBN), would the result be any different?

Suggesfions:
-In the Abstract and elsewhere in the ms the authors use statements like: "In this lefter, we succeeded an acfive topological plasmonic dispersion transifion in the black phosphorus 2D semiconductor with an opfical carrier incubafion, i…" since the BP studied is severl layers thick, perhaps best to say "layered BP" instead of "2D BP" -last paragraph of Introducfion; The photo-pumping process in work injects ample hot charge carriers into the BP, thereby triggering hyperbolic add… in our work

-Results and Discussion
In Fig. 1a, an experimental setup of the nanoscopy with… add this (see Methods)

Reviewer #2 (Remarks to the Author):
This manuscript explores the acfive topological plasmonic dispersion transifion in black phosphorus (BP) induced by ultrafast laser pulses.This phenomenon can be understood through photo-induced electronic transifions, which result in changes in the dielectric tensors of BP.Ufilizing ultrafast nanoscopy, the manuscript demonstrates the remarkable characterisfics of these transient hyperbolic plasmons.While the transient polariton mode of the SiO2/BP/SiO2 heterostructure was previously demonstrated in Nature Nanotech 12, 207-211 (2017), that work did not achieve the acfive topological transifion which is vitally important for optoelectronic applicafions.Furthermore, when compared to the study in Science 371, 617-620 (2021) where the photo-induced topological transifion of WSe2 was presented, the transient hyperbolic plasmons in BP discussed in this manuscript exhibit superior plasmonic properfies, including a longer propagafion length, efficient edge-excited plasmons, and coexistence of the short lifefime propagafing mode and the long lifefime localized mode.Overall, this work indeed represents a significant fundamental improvement over prior research.Therefore, I would like to recommend this publicafion in Nature Communicafions after thoroughly addressing the following quesfions and comments.
1.In the first paragraph on page 4, the authors should provide a clearer explanafion of how dielectric screening impacts the dielectric elements or provide a relevant citafion.2.In order to enhance the depicfion of the photo-induced hyperbolic plasmonic response, it is suggested that the authors consider incorporafing the near-field image s3 of a prisfine BP/gold stacked structure in Fig. 1h.3.In the first paragraph on page 6, it would be beneficial if the authors could provide further elucidafion on why the influence of light penetrafion depth is not typically taken into account in most polaritonic materials.Alternafively, they could support their statement by referencing a relevant citafion that supports this asserfion.4.In the inset of Fig. 2d, the depicfion of BP atop Si is misleading, potenfially causing readers to interpret it as a cross-secfion of the sample.To address this concern, I suggest the authors to align the arrangement of the BP and Si slab in the inset with the configurafion depicted in Fig. 2a.5.The authors presented an interesfing finding regarding the independence of BP thickness on the wavelength of transient plasmons.They aftribute this phenomenon to the unchanging thickness (120 nm) of the space charge layer.Fig. S4 shows a clear trend where the polariton wavelength increases with the increasing thickness of doped BP.It is worth nofing that this paper solely presents experimental results from BP samples with thicknesses exceeding 120 nm.To further strengthen the validity of the theorefical calculafions depicted in Fig. S4, it is advisable to include measurements of the polariton wavelength for BP samples with thicknesses below 120 nm.This addifional data would provide further support for the theorefical framework.6.Fig.4d shows the dynamics of the near-field amplitude intensity s3 of the first bright fringe.Could the authors explain the significant decrease in intensity s3, which falls below the prisfine level after 17 ps?Addifionally, I am curious to know if this mechanism would have any effect on the fiftings presented in Fig. 4c.
Reviewer #3 (Remarks to the Author): In the manuscript, the authors reported pump-induced hyperbolic plasmons in black phosphorus (BP) visualized with near-field opfical imaging and spectroscopy.The transient hyperbolic regime was first demonstrated by imaging the conical propagafion of polaritons of BP placed on top of a Au disk launcher.Then the authors carried out systemafic angle-dependent and thickness dependent measurements to further study the observed hyperbolic plasmon polaritons.I only have a few quesfions and comments before recommending for publicafion.
1.In Fig. 1 the authors demonstrated that transient hyperbolicity using nano-imaging.However, the probe frequency used for the imaging in Fig. 1h (850 -1200 cm-1) seems to cover both hyperbolic and non-hyperbolic frequency range, according to Fig. 1d.It would be ideal if the same imaging experiment can be done using narrow-band probe, centering around e.g.950 cm-1 (hyperbolic) and 1150 cm-1 (nonhyperbolic) to further demonstrate the crossover.The authors should also consider providing the topography image corresponding to Fig. 1h as well as the near-field imaging at negafive fime delay, similar to the ones in Fig. 4a.
2. What is the carrier density corresponding to 0.5 mJ/cm^2 pump fluence?
3. The nearly constant plasmon wavelength with varying BP thickness shown in Fig. 3 is interesfing but also raises some quesfion.I understand the argument about the finite penetrafion depth causing BP thicker than 100 nm to have the same transient plasmon wavelength.However, one can study BP films thinner than 100 nm, which should have homogeneous doping and will have more pronounced thickness dependence at e.g.20 nm and 60 nm.Is the reason for lack of thinner BP samples in the current manuscript related to the surface degradafion?
Minor issue, at page 7, second to last paragraph, the authors wrote "The low inifial carrier density is aftribute to the absence of polaritons fringes at \tau=-2 ps."I think the authors meant the other way around, i.e. absence of fringe is aftributed to low carrier density.