RU2777799C1 - Integrated optical system for spatial separation of scalar beams with orbital angular moments (oam) - Google Patents

Abstract

FIELD: microelectronics.

SUBSTANCE: invention relates to microelectronics, namely to integral optical elements, in particular to dielectric metasurfaces with a complex geometric profile, which can be used in the field of quantum communications to protect data during transmission over broadband communication channels by increasing the dimension of Hilbert space through the use of scalar beams with orbital angular momentum (OAM). The system for spatial separation of scalar beams with OAM is based on the use of two dielectric metasurfaces with a certain surface morphology and consisting of silicon nanoresonators: nanodiscs with magnetodipole resonance in the IR range. Under these conditions, the optical system will perform a camphor coordinate transformation (a transformation by which polar coordinates turn into linear coordinates) and phase correction of electromagnetic radiation transmitted through this system from the OAM.

EFFECT: invention provides spatial separation of scalar beams with different values of OAM without violating the dimension of Hilbert space (meaning N-dimensional Hilbert space, where N depends on the values of OAM), while the system implementing such separation is CMOS-compatible with modern optical integrated circuits.

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Description

The field of technology to which the invention belongs

The invention relates to microelectronics, namely, to integral optical elements, in particular, to dielectric metasurfaces with a complex geometric profile, which can be used in the field of quantum communications to protect data during transmission over broadband communication channels by increasing the dimension of the Hilbert space through the use of scalar beams with orbital angular momentum (OAM). The dielectric metasurface consists of resonant silicon nanostructures - nanodisks, can be compatible with CMOS technology and implemented on an optical microcircuit.

State of the art

Over the past decade, a large number of works have appeared aimed at increasing the degree of protection of broadband communication channels in the implementation of quantum communications based on the management and control of quantum radiation propagating in a communication channel and carrying encoded information. The task of controlling the main parameters of quantum radiation (phase, amplitude and polarization) through the use of additional degrees of freedom of electromagnetic radiation - radiation with different values of the orbital angular momentum (OAM) is currently relevant. In 1992, L. Allen and his colleagues demonstrated that Laguerre-Gauss vector beams, which are analytically described by the azimuthal phase term, have a pronounced OAM [L. Allen, M. Beijersbergen, R, Spreeuw, J. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian modes, Phys. Rev., 8185-8189, 1992], due to which the dimension of the Hilbert space can be increased [X. Wang, Z. Nie, Y. Liang, J. Wang, T. Li, B. Jia, Recent advances on optical vortex generation, Nanophotonics, 2018]. Such scalar Laguerre-Gauss beams, which have orbital angular momentum (OAM) and phase distribution at each point in space, are of particular interest for quantum cryptography. This is due, first of all, to the creation of reliable and secure broadband communication channels for the transmission and processing of information. In addition, it has been proven that increasing the dimension not only contributes to an increase in the density of information encoding in one channel, but also increases the secrecy of communication, making the channel more stable [J. O'brien, A. Furusawa, J. Vuckovic, Photonic quantum technologies, Nature Photonics, 2009]. In this regard, it is topical to search for solutions aimed at increasing the dimension of the Hilbert space, which can be implemented through the spatial separation of scalar light beams with different OAM values. The solution of this problem consists of two successive stages: the 1st stage consists in the transformation of polar coordinates into linear ones; The 2nd stage consists in compensating the phase of electromagnetic radiation. This can be implemented on the basis of planar metasurfaces, which are two-dimensional resonant nanostructures with a specially designed surface topology for efficient generation and control of high-dimensional entangled quantum photon states. At the same time, the size that makes it possible to place them in photonic chips and fabricate using the means and methods of modern microelectronics (CMOS-compatible technologies) is essential for such metasurfaces.

Optical polarization elements are known from the prior art, such as an integrated optical polarization splitter (patent RU 92205 U1) capable of separating TE and TM polarized waveguide modes in optical transmission and information processing systems. The optical element is a metal-dielectric multilayer structure, which is applied to the surface of the optical waveguide of one of the arms of the integrated optical Mach-Zehnder interferometer. Thus, on the basis of the plasmon resonance effect, mode anisotropy is formed in the waveguide channel and there is a difference in the transit time of the TE and TM modes in the optical system. The disadvantage of such a device is its narrow scope - the ability to spatially separate electromagnetic radiation only in polarization modes. This device does not provide spatial separation of electromagnetic radiation and depends on the phase of the input signal. This, in turn, does not allow the use of the known device in integrated optical circuits, including for protecting communication channels during data transmission, in which mixed phase and polarization states are realized.

In addition, optical metasurfaces are known, on the basis of which the process of spatial separation of electromagnetic radiation can be implemented [K. Wang, G. Titchener, Sergey S. Kruk, A. Sukhorukov, et al., "Quantum metasurface for multiphoton interference and state reconstruction", Science, 14, 361, 1104-1108, (2018)]. The metasurface is a four-inch quartz substrate 500 μm thick with a set of silicon nanoresonators placed on it, 800 nm high, with varying dimensions (height and diameter), phase, and orientation relative to each other (with a different arrangement period). The substrate is made with the possibility of spatial separation of the radiation incident on it according to the state of polarization, i.e. this structure is capable of separating certain states of elliptical polarization of photons. The use of light with different degrees of polarization makes it possible to form only a two-dimensional Hilbert space. The disadvantage of such optical structures is their polarization dependence, the ability to spatially separate nonclassical light entangled only in spin angular momentum.

Closest to the claimed invention is an optical system based on the use of optical elements - spatial light converters - SLM (Selective Laser Melting) (hereinafter referred to as SLM), to set the phase profile of electromagnetic radiation of a certain type. Thus, to solve the problem of spatial separation of scalar beams with different OAM, it is known to use three optical elements: SLM No. 1 to form a scalar beam with OAM; SLM No. 2 for "log-pol" coordinate transformation - polar to linear; SLM No. 3 for correcting the phase of electromagnetic radiation [Gregorius C.G. Berkhout, Martin P. J. Lavery, Johannes Courtial, Marco W. Beijersbergen, and Miles J. Padgett, Efficient Sorting of Orbital Angular Momentum States of Light Phys. Rev. Lett. 105, 153601 (2010)]. SLMs from manufacturers such as Fourth Dimension Displays, Santec Corporation, Jenoptik, Hamamatsu Photonics, Perkin Elmer, Holoeye Photonics, American Electric Power, Meadowlark Optics, Laser 2000 (UK), Texas Instruments, etc. can be used as optical elements. For example, SLM-200 - Full HD spatial light modulator manufactured by Santec is characterized by the following parameters: operating wavelength range 450-1600 nm, display size 15.5 × 10 mm, display resolution 1920 × 1200 pixels, pixel size 8 μm, overall dimensions of the device 122 ×122×40 mm. Thus, the disadvantage of this optical element and the system based on them is significant dimensions, which do not allow integrating this system into a photonic microcircuit, while planar metasurfaces, due to their small dimensions (of the order of 100–200 μm), make it possible to integrate them and compatible with optical chip.

The technical problem solved by the present invention is the elimination of the above disadvantages, typical for analogs and prototype.

Disclosure of the essence of the invention

The technical result is the development of a CMOS-compatible system for implementation in an integrated optical microcircuit with the possibility of spatial separation of scalar beams with orbital angular momentum (OAM), capable of interacting with the radiation of an N-dimensional Hilbert space at the entrance to the system while maintaining its dimension at the exit from the system .

The technical result is achieved by an integrated optical system for spatial separation of scalar beams with OAM, including three optical elements, where the first optical element is made in the form of a spatial light modulator with the possibility of forming scalar beams with different OAM, the second optical element is configured to convert the polar coordinates of the radiation into linear coordinates, and the third optical element is made with the possibility of correcting the phase of the radiation that has passed through the second optical element, the second and third optical elements are located in the Fourier plane of two lenses, according to the invention, the second and third optical elements are made in the form of dielectric metasurfaces formed by located on dielectric substrates silicon nanoresonators - nanodisks with magnetic dipole resonance (Mi-resonance) in the IR range, while the period of the nanodisks is determined by relations (1) and (2)

where u and υ are polar coordinates, x and y are linear coordinates,

и υ = a arctan(y/х), λ - длина волны падающего излучения (скалярного пучка), ƒ - фокусное расстояние линз, а - коэффициент преобразования координат (а=d/2π), d - ширина преобразованного пучка, а параметр b переводит преобразованное изображение в направлении u и может быть выбран независимо от а.

and υ = a arctan(y/x), λ is the wavelength of the incident radiation (scalar beam), ƒ is the focal length of the lenses, a is the coordinate transformation coefficient (a=d/2π), d is the width of the transformed beam, and the parameter b translates the transformed image in the u direction and can be chosen independently of a.

In one of the embodiments of the invention, the nanodisks are made of the same height and diameter, and differing in the value of the location period. Nanoresonators are subwavelength silicon nanodisks. The substrate is made of silicon dioxide or glass. The number of different periods for nanocavities that describe the phase profile of the surface is 4, 8, or 16.

The advantage of such an integrated optical system is that the second and third optical elements of the system are made in the form of dielectric metasurfaces formed by silicon nanoresonators located on dielectric substrates - nanodisks having a magnetic dipole resonance in the IR range, while the period of the nanodisks is determined by the relations ( 1) and (2), which mathematically describe the spatial separation of scalar beams with OAM. These geometric phase transformations are associated with each point in space (region on the metasurface) with the value of the radiation phase, which makes it possible to perform a camphor transformation of coordinates, i.e. convert polar coordinates to linear ones with subsequent correction of the radiation phase. In addition, these optical metasurfaces are CMOS compatible with modern integrated optical circuits. All this allows efficient separation of scalar beams with orbital angular momentum (OAM) in space. Also, it is worth noting that such an interaction of the incident quantum radiation with OAM with these optical elements does not change (in particular, does not reduce) the dimension of the N-dimensional Hilbert space at the output of such a system.

Thus, the claimed invention, in comparison with the prototype, is aimed at realizing the possibility of spatial separation of a scalar light beam with an orbital angular momentum while maintaining the TV-dimensional Hilbert space (which depends on the value of the orbital angular momentum). The developed system is based on phase control and is polarization independent.

Brief description of the drawings

The invention is illustrated by drawings, where in Fig. 1 schematically shows one of the options for the implementation of a resonant metasurface (M1 and M2 have an identical structure, differing in the geometry of the surface - the relative position of the dielectric resonators relative to each other, which is specified using geometric transformations), consisting of silicon nanodisks (2), through which electromagnetic radiation passes with OUM. Each metasurface device is made on a substrate (1) of silicon oxide; in fig. 2 - a diagram of the metasurface M1 and a table of geometric parameters for creating a phase mask for M1 are presented: the geometry of pixelation, where each number is assigned a lattice period Pi; in fig. 3 is a diagram of the M2 metasurface and a table of geometric parameters for creating a phase mask for M2: the geometry of pixelation, where each number is assigned a lattice period Pi; in fig. 4 is a diagram of the proposed system, demonstrating the propagation of electromagnetic radiation with OAM through a system of metasurfaces M1 and M2 located in the focal plane of the lens system L1 and L2; in fig. 5 shows: (a) The dependence of the coefficient and (b) the dependence of the phase profile on the wavelength and period between silicon nanodisks; (c) plot of transmittance and (d) phase profile versus period for silicon nanodiscs for a wavelength of 810 nm; in fig. 6 - phase surfaces showing the change in the phase profile according to the geometric transformations (1) and (2), respectively; in fig. 7 shows the phase masks of partitions into quadrants M1 and M2, respectively, where the numbers indicate the average phase values in each quadrant according to the tables in FIG. 2 and FIG. 3; in fig. Figure 8 shows the phase profiles of radiation transmitted through the resonant system, demonstrating the separation of different OAM values in space.

Implementation of the invention

The inventive integrated optical system for demultiplexing scalar beams with OAM (Fig. 4) is designed for spatial separation of scalar beams (Lugger-Gauss type) with OAM and is polarization independent.

The system contains three optical elements, the first of which is made in the form of a spatial light modulator (SLM) with the possibility of forming scalar beams with different OAMs. The second and third optical elements are made in the form of mat surfaces M1 and M2, located in the Fourier plane of two lenses, while M1 is configured to convert the polar coordinates of the radiation into linear coordinates, and M2 is configured to correct the phase of the radiation passed through the second optical element. Variants of realization of metasurfaces M1 and M2 are shown in Fig. 1-3. In FIG. 4 shows a diagram of the implementation of the proposed system, where the lens L1 is located between the metasurfaces M1 and M2, and the lens L2 is located behind the metasurface M2. Two lenses Thorlabs LA1039-B N-BK7 Piano-Convex Lens, d=3 mm, f=9 mm can be used as lenses, as the first optical element - SLM HOLOEYE PLUTO-2.1-NIR-015, the operating range of which is 650-1100 nm with low phase jitter.

Dielectric metasurfaces are formed by silicon nanoresonators - subwavelength nanodisks located on a silicon dioxide or glass substrate and having a magnetic dipole resonance in the IR range. In this case, the period of nanodisk arrangement (or the geometric distribution of phases - phase masks) is determined by relations (1) and (2), where formula (1) determines the period of nanodisk arrangement on the M1 metasurface, formula (2) - on the M2 metasurface.

where u and υ are polar coordinates, x and y are linear coordinates,

и υ = a arctan(y/х), λ - длина волны падающего излучения (скалярного пучка), ƒ - фокусное расстояние линз, а - коэффициент преобразования координат (а=d/2π), d - ширина преобразованного пучка, а параметр b переводит преобразованное изображение в направлении u и может быть выбран независимо от а.

and υ = a arctan(y/x), λ is the wavelength of the incident radiation (scalar beam), ƒ is the focal length of the lenses, a is the coordinate transformation coefficient (a=d/2π), d is the width of the transformed beam, and the parameter b translates the transformed image in the u direction and can be chosen independently of a.

Preferably, the number of periods for nanocavities that differ in dimension and describe the phase profile of the surface is 4, 8, or 16. The choice of a specific value of the periods is determined by the required accuracy of the spatial separation of the output radiation.

The profile of the second and third optical element of the system (metasurfaces) has a certain surface design, namely, it consists of pixels, for example, 20×20 µm; wherein each pixel consists of an array of silicon Mie-resonant nanoresonators, for example, of the same height and diameter, but differing in the value of the period within a particular pixel. Moreover, it is worth noting that these parameters are selected in such a way that the transmittance of nanocavities with such a geometry is maximum (close to 1) and constant (with small fluctuations from the average value of the transmittance).

In one of the embodiments of the invention (Fig. 2 and 3) the design of the surface profile M1 consists of 4 areas - diagonally oriented bands, characterized by four period values within each pixel. The 1st area, geometrically oriented in the upper left corner, is a triangle with legs of 20 pixels and 16; the 2nd region is a diagonally oriented strip 4 pixels wide; 3rd area - a stripe 11 pixels wide; The 4th area looks like a triangle located in the lower right corner, with legs of 10 pixels and 7 pixels. The design of the M2 surface profile also consists of 4 areas: the 1st and 2nd areas are identical rectangles dividing the surface profile in half; The 3rd and 4th regions are semicircles located in the center of the structure.

The proposed system works as follows.

Electromagnetic radiation - a scalar beam with OAM, for example, Lugger-Gaus modes, falls on metasurface No. 1 (M1). Due to the complex phase profile M1, a conformal mapping of polar coordinates into linear ones takes place, and the phase profile of the initial beam changes. Further, to correct the beam and spatially separate the various values of the orbital angular momenta, the beam is directed to the metosurface No. 2 (M2), located in the Fourier plane of the lens system (L1) and (L2), the focal length of which, for example, is 9 mm (this value is determined according to the phase transformations (1) and (2), where the focal length of the lens system appears in the first factor of the formulas). Then the radiation passed through the optical system hits the screen (E), which can be a camera or highly sensitive detectors.

The surface profile of the silicon metasurfaces used in the proposed system was obtained from the results of model experiments, which included geometric transformations (1) and (2) that correct the phase of the transmitted radiation. Transformation (1) performs a log-pol coordinate transformation, translating polar coordinates (u, υ) into linear ones (x, y), i.e. (u, u)→(x, y); transformation (2) corrects the radiation phase, which changes during transformation (1).

In particular, the following algorithm was used when developing the design of metasurfaces M1 and M2.

Model experiments were carried out to determine the dependences of the transmittance of FIG. 7(a) and the phase profile of FIG. 5(b) for silicon nanodisks with a height of 131 nm and a diameter of 220 nm with a wide range of periods and wavelengths of incident electromagnetic radiation. Then, at the chosen wavelength - 810 nm (the choice of this wavelength is justified by the geometry of the experiment and the possibility of its implementation), four period values were chosen so that they corresponded to the maximum value of the transmittance of Fig. 7(c) and covered the change in the phase profile in the range from 0 to 2π - fig. 7(d).

In the Wolfram Mathematica software package, a numerical calculation was made for the surface profile of dielectric metasurfaces based on geometric phase transformations (1) and (2). In FIG. Figure 6 (a, b) presents the results of the numerical calculation of the phase surfaces corresponding to the transformations for M1 and M2, respectively.

At the next step, the obtained phase profiles for M1 and M2 were divided into areas - quadrants of the same size 20 × 20 μm (the size of the quadrant is determined by the possibility of manufacturing optical elements) with subsequent averaging of the phase value within each quadrant. Due to the fact that nanocavities with the same height, diameter, and four different periods between them were chosen as the initial conditions for the formation of metasurfaces, the phase profile discretization (from 0 to 2π) was carried out with a step of π/2, i.e., e. the resulting pixels correspond to the phase values: π/4, 3π/4, 5π/4 and 7π/4. In FIG. 2, fig. 3 and FIG. 7 shows the design of the metasurfaces corresponding to the obtained phase profiles for M1 and M2 after the pixelization described above, where in FIG. 7, the numerals respectively designate the pixels characterized by the average value of the phase, according to the above.

One of the main conditions for the spatial separation of scalar beams with different OAM values is the change in the phase profile of optical prototypes in the range from 0 to 2π. To do this, each of the dielectric structures is divided into equal quadrants (for example, 20 by 20 micrometers in size), and averaging is performed over the phase value within each such quadrant. Then, for each quadrant, according to the obtained phase profile in Fig. 5(d), a certain value of the period for silicon nanodisks is put in correspondence, which best describes the average value of the phase in this quadrant.

In one of the examples of the implementation of the invention at a wavelength of 810 nm, the optimal geometric parameters of the metasurfaces M1 and M2 were selected - the height, diameter and period of the silicon nanodisks; Transmission spectra were obtained for silicon nanodisks with a height of 131 nm and a diameter of 220 nm for various periods between nanodisks. At a wavelength of 810 nm, bands with the maximum transmittance are observed. Based on the results obtained, four values of the lattice period of silicon nanodisks were chosen, which made it possible to provide a series of phase shifts differing from each other by π/2 for the nanodisc quadrant.

Example

The described system of resonant metasurfaces and the principle of its operation is illustrated by a specific example, which is one of the possible implementations of the invention under consideration. At the same time, this example illustrates well the possibility of achieving the claimed technical result.

Each of the two resonant metasurfaces is a dielectric structure 200×200 micrometers in size, the surface of which is conditionally divided into quadrants 20×20 micrometers in size. The metasurfaces are made on the basis of a silicon-insulator structure, where the insulator layer plays the role of a substrate and consists of silicon dioxide with a refractive index of 1.445 and a thickness of 5 µm. The upper layer, from which arrays of resonant nanodisks were made, is a silicon layer 131 nm high and with a refractive index of 3.5. The phase mask of resonant nanoresonators is made by nanostructuring the upper layer of silicon by electron-beam lithography followed by plasma etching.

The resonant system (PC) included two silicon metasurfaces M1 and M2 (200 × 200 μm in size) located in the Fourier plane of a system of lenses with a focal length of 9 mm. Each of the metasurfaces is divided into 400 pixels (quadrants) 20×20 µm in size. Each pixel is filled with silicon nanodisks 220 nm in diameter, 131 nm high, and is characterized by a certain period value consistent with the phase mask of a specific metasurface (see Figs. 2 and 3). The period values for M1 and M2 are (436, 595, 350, 387) nm and (501, 515, 538, 453) nm, respectively. Electromagnetic radiation at a wavelength of 810 nm falls on the PC. The principle of operation of the PC is illustrated by a specific example shown in FIG. 4. Radiation of a tunable (in the wavelength range from 680 nm to 1080 nm) femtosecond Coherent Chameleon Vision II laser at a wavelength of 810 nm, passing through a spatial light converter - SLM-HOLOEYE PLUTO-2.1-NIR-015, as the first optical element - SLM, which set a scalar beam with OAM, hit the PC of the M1 and M2 metasurfaces and L1 and L2 lenses Thorlabs LA1039-B N-BK7 Piano-Convex Lens (d=3 mm, f=9 mm), after which the transmitted radiation spatially separated and fell on the appropriate COUNT-100N-FC Laser Components detectors. As a result of the interaction of the incident electromagnetic radiation with OAM with such an optical system, which has certain phase profiles and consists of systems of nanodisks with magnetic dipole Mie resonances, the radiation was spatially separated according to different OAM values. Phase profiles demonstrating the spatial separation of scalar beams with an OAM resonant optical system were obtained for OAM values of ±1; ±3 and are shown in Fig. 8. A shift of the maxima of the radiation intensities with OAM along the Y coordinate is observed for all beams with OAM. Moreover, for scalar beams with OAM with different signs, the displacement occurs in different directions from the origin of coordinates (the central optical axis passing through the centers of the metasurfaces). So, for negative OAM values (l=-3 and l=-1), this shift occurs above zero along the OY axis, and for positive OAM values (l=3 and l=1) - below zero along the OY axis. It can also be seen that with an increase in the OAM value in absolute value, the offset relative to zero along the OY axis also increases.

PC has a compact size due to the use of sub-wavelength nanoparticles and CMOS-compatible technologies, which allows such an optical system to be implemented on an integrated circuit.

Claims (10)

1. Integrated optical system for spatial separation of scalar beams with OAM, including three optical elements, where the first optical element is made in the form of a spatial light modulator with the possibility of forming scalar beams with different OAM, the second optical element is configured to convert polar radiation coordinates into linear ones. coordinates, and the third optical element is configured to correct the phase of the radiation passed through the second optical element, while the second and third optical elements are located in the Fourier plane of the two lenses, characterized in that the second and third optical elements are made in the form of dielectric metasurfaces formed silicon nanoresonators located on dielectric substrates - nanodisks with magnetic dipole resonance (Mi-resonance) in the IR range, while the period of the nanodisks is determined by relations (1) and (2):

where u and υ are polar coordinates, x and y are linear coordinates,

and υ = a arctan(y/x), λ is the wavelength of the incident radiation (scalar beam), ƒ is the focal length of the lenses, a is the coordinate transformation coefficient (a=d/2π), d is the width of the transformed beam, and the parameter b translates the transformed image in the u direction and can be chosen independently of a. 2. The integrated optical system according to claim 1, characterized in that the nanodisks are made of the same height and diameter and differ in the value of the location period. 3. An integrated optical system according to claim 1, characterized in that the nanocavities are subwavelength silicon nanodisks. 4. Integrated optical system according to claim 1, characterized in that the substrate is made of silicon dioxide or glass. 5. The integrated optical system according to claim 1, characterized in that the number of different periods for nanocavities describing the phase profile of the surface is 4, 8 or 16. 6. Integrated optical system according to claim 1, characterized in that it is polarization-independent.

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