Graphene, undoubtedly the largest star due to its extraordinary properties in various fields among the 2-D materials, has been intensively employed to design the optical modulators since the first graphene-based modulator has been successfully demonstrated in 2011 [1], [2], [3], [4], [5]. Although enjoying the ultrafast carrier mobility of graphene, graphene-based modulators still suffer from  the  intrinsic resistor–capacitor (RC) delay, to go beyond the bottleneck, various all-optical methods have been introduced and widely implemented in constructing graphene-based modulators [6], [7], [8], [9], [10], [11]. Surface plasmon polariton (SPP) characteristics of graphene have been also incessantly studied and employed to realize the SPP-based graphene modulators in nanophotonics, which are highly demanded in the integrated photonic systems [12], [13], [14], [15], [16], [17]. Nevertheless, no matter for what kind of modulators, outstanding with the features of high modulation speed and efficiency, graphene-based modulators are mostly working in the near-infrared regime and still limited in expanding to the other spectrums such as visible regime  [1], [8], [13].

Recently, with the rapid development of the van der Waals heterostructures based on 2-D materials, the combination of graphene and other 2-D materials has triggered a lot of interests in exploring the new phenomena and potential optical functions [18], [19], [20], [21], [22]. As for black phosphorus (BP) with extraordinary in-plane anisotropy, since its bandgap can be dynamically tuned with the number of layers and extended to the visible regime and mid infrared regime, it may compensate graphene in several applications and help graphene go beyond the intrinsic limits in some spectrums. As a matter of fact, the application of graphene/black phosphorus heterostructure has become a heated topic to be studied, photodetectors, field effect transistors (FET) and absorbers based on graphene/black phosphorus heterostructure are all theoretically and experimentally investigated [23], [24], [25], [26]. Therefore, it occurs to us that by combining black phosphorus with conventional graphene nanostructures, it could help graphene-based modulators to go beyond the waveband limit and work in the visible regime. More interestingly, the graphene/black phosphorus heterostructure can also be served as a SPP structure, which can efficiently enhance the light–matter interaction and produce a marked effect in constructing the modulators. However, up to now, the underlying mechanism of how the incident light angle affects the modulation of graphene/black phosphorus heterostructure is still unexplored. Besides, it is still of great need to determine the crystal orientation of black phosphorus, which may broaden the understanding of how the in-plane anisotropy of black phosphorus and the incident light angle manipulate the whole modulation properties of the graphene/black phosphorus heterostructure.

In this article, an all-optical plasmonic modulator based on graphene/black phosphorus heterostructure is proposed, which exhibits the angle-dependent tunability and can operate in the visible regime. The mechanism of all-optical SPP modulation characteristics within the visible regime for the proposed heterostructure is investigated in details. Results show that by simply adjusting the incident light angle of black phosphorus, large extinction ratio (ER) from 25 dB to 55 dB can be obtained within the visible regime. This proposed plasmonic modulator may find great applications in realizing tunable and angle-dependent devices based on 2-D materials in future nanophotonics.