Broadband polarization angle continuous adjustment antenna based on electronic control metasurface

Abstract

The invention discloses a broadband polarization angle continuous adjustment antenna based on an electric control metasurface. The broadband polarization angle continuous adjustment antenna comprises a linear polarization slot coupling microstrip antenna and an active electric control metasurface capable of continuously adjusting a linear polarization inclination angle. The linear polarization slot coupling microstrip antenna is a feed source, is excited in a slot coupling mode, and can radiate a single linear polarization wave in a broadband. The active electric control metasurface is composed of electromagnetic units arranged in an array mode, an H-shaped metal strip structure and a diode are integrated in the active electric control metasurface, the on resistance of the active electric control metasurface is adjusted by changing the positive bias voltage of the diode, the amplitude of an orthogonal transmission electric field component is driven to change, and therefore the polarization angle of the antenna is adjusted and controlled. According to the invention, the real-time change of the polarization angle of the electromagnetic wave is realized, the antenna shows good working characteristics in a wide frequency band, the compatibility and the integration degree of the linear polarization antenna can be effectively improved, and the antenna has a good application prospect in the fields of airborne communication, electronic countermeasure, polarization imaging and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of linearly polarized reconfigurable antennas, and in particular to a broadband polarization angle continuously adjustable antenna based on an electrically controlled metasurface. Background Art

[0002] In order to improve the functionality and channel capacity of antennas, polarization reconstruction technology has been widely used in antenna design in recent years. The developed antenna samples have the characteristics of high integration, good flexibility, and rich functions. They are used in synthetic aperture radar, satellite communication, polarization coding communication and other occasions, and have effectively improved the communication and imaging quality. Among them, the linear polarization rotating antenna can transmit and receive multi-angle linear polarization waves based on a single channel by switching the functional state in time-sharing mode. It can be used to overcome the polarization mismatch problem of moving targets and realize polarization alignment in the process of point-to-point signal transmission. It is also conducive to reducing the weight, power consumption and cost of the system, and has a good application prospect in satellite-borne, airborne and other platforms.

[0003] At present, domestic and foreign research teams have proposed a variety of linear polarization rotating antenna designs combined with electrically controlled RF components, but generally only 90° steps of polarization angle can be completed, and there are few functional states. In order to achieve continuous and free adjustment of the linear polarization angle, some researchers use phase shifters to adjust the phase difference between the two circularly polarized signals based on orthogonal dual circularly polarized antennas, and realize the synthesis of linear polarized waves with arbitrary inclination angles. However, the working frequency band of this scheme is narrow, and the introduction of phase shifters will increase the size of the antenna and complicate the feeding line. Metasurface is a two-dimensional composite material composed of subwavelength periodic electromagnetic units. It has the advantages of flexible and controllable properties, light and easy integration. In recent years, it has made a series of major progress in the field of electromagnetic control, especially in the design of new antennas, providing an excellent way to build miniaturized and highly integrated antennas. Some researchers have designed an artificial magnetic conductor based on the concept of metasurface, and proposed a polarization reconstruction method based on dipole antennas, but the switching of its polarization state is completed by changing the capacitance. When the capacitance changes, the working frequency shifts accordingly, which makes it difficult for such antennas to obtain a wider overlapping frequency band in different states. In order to adjust the polarization angle of the horn antenna, domestic researchers proposed a reflective polarization rotation metasurface, which also uses the method of controlling the phase of the orthogonal circular polarization component to manipulate the polarization angle of the outgoing wave of the linearly polarized horn antenna. However, this design still has the problem of too narrow working frequency band, which limits its application scope. Summary of the invention

[0004] The purpose of the present invention is to provide a broadband polarization angle continuously adjustable antenna based on an electrically-controlled metasurface, which realizes the real-time change of the polarization angle of electromagnetic waves by loading an electrically-controlled metasurface above a single linearly polarized antenna. At the same time, thanks to the resistive adjustment method, the antenna exhibits good working characteristics in a wide frequency band, which can effectively improve the compatibility and integration of linearly polarized antennas, and has good application prospects in the fields of airborne communications, electronic countermeasures, polarization imaging, etc.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention uses a linearly polarized slot-coupled microstrip antenna as a feed source, and loads an electrically controlled polarization conversion metasurface on top, thereby realizing continuous adjustment of the inclination angle of the outgoing linear polarization wave. The active electrically controlled metasurface proposed in the present invention is composed of periodically arranged electromagnetic units, both sides of which are covered with an H-shaped metal strip structure, and a pin diode is integrated inside. As the amplitude of the forward bias voltage at both ends of the pin diode changes, the on-resistance of the pin diode also changes accordingly. This resistive control mechanism combined with the H-shaped metal strip structure can realize the amplitude control of the orthogonal transmission line polarization electric field component, thereby synthesizing linearly polarized transmission waves with different inclination angles.

[0007] A broadband polarization angle continuous adjustment antenna based on an electrically controlled metasurface includes a linearly polarized slot-coupled microstrip antenna and an active electrically controlled metasurface disposed above the antenna. The active electrically controlled metasurface has the ability to control polarization, and polarization control is to control the amplitude of the orthogonal linear polarization components in the linearly polarized electromagnetic wave, and to rotate the polarization angle by changing the amplitude ratio.

[0008] The active electrically controlled metasurface is composed of a plurality of electromagnetic unit arrays, wherein the electromagnetic unit comprises a dielectric substrate, and the dielectric substrate comprises a first surface and a second surface opposite to each other; the first surface and the second surface are both provided with two symmetrically arranged H-shaped metal strip structures; the H-shaped metal strip structure on the second surface is the same as the H-shaped metal strip structure on the first surface, and the direction is obtained by rotating the H-shaped metal strip structure on the first surface clockwise by 90° and then flipping it horizontally.

[0009] A pin diode is provided in the middle of the H-shaped metal strip structure, and two H-shaped metal strip structures are connected by a DC bias line, and the two ends of the DC bias line are respectively connected to the forward bias end and the reverse bias end of the pin diode. In the forward bias condition, it can be equivalent to a series branch of a resistor and an inductor, and the resistor can be nonlinearly adjusted by changing the voltage across the pin diode.

[0010] In a specific embodiment, there is a gap between the linearly polarized slot-coupled microstrip antenna and the active electrically controlled metasurface, and the active electrically controlled metasurface completely covers the linearly polarized slot-coupled microstrip antenna.

[0011] In a specific embodiment, a feeding wire is provided on the outside of the H-shaped metal strip structure, and the feeding wire is connected to the H-shaped metal strip structure through a DC bias line, and the feeding wire enables the pin diodes in different electromagnetic units to be fed in parallel. The feeding wire enables the pin diodes in different electromagnetic units to be fed in parallel.

[0012] In a specific embodiment, a first inductor is provided on the DC bias line between the two H-shaped metal strip structures, and a second inductor is provided on the DC bias line between the feed thin wire and the H-shaped metal strip structure.

[0013] In a specific embodiment, the linearly polarized slot-coupled microstrip antenna includes a feeding layer and a radiation layer arranged above the feeding layer, and a gap is left between the radiation layer and the feeding layer.

[0014] In a specific embodiment, the radiation layer includes a dielectric substrate and a radiation patch arranged on the surface of the dielectric substrate, and is used to radiate u-polarized waves.

[0015] In a specific embodiment, the feed layer includes: a dielectric substrate, the dielectric substrate includes a first surface and a second surface relative to each other; the first surface is provided with a metal probe microstrip line, the second surface is a metal thin layer, a gap is etched on the metal thin layer, the projection of the metal probe microstrip line on the metal thin layer intersects with the gap, and the metal probe microstrip line is used to couple and feed the gap.

[0016] In a specific embodiment, the metal probe microstrip line is a U-shaped structure, and the projections of two arms of the metal probe microstrip line of the U-shaped structure on the metal thin layer are perpendicular to the gap.

[0017] In a specific embodiment, the ends of the two arms of the U-shaped metal probe microstrip line are both provided with bending portions bent outward.

[0018] In a specific embodiment, the two arms of the metal probe microstrip line are arranged at 45° to the horizontal direction, and the gap is arranged at 135° to the horizontal direction.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] The present invention solves the problem of too narrow bandwidth in the existing design to a certain extent while achieving continuous adjustment of the linear polarization tilt angle. It also has the characteristics of simple configuration and easy promotion, and provides a useful reference for the flexible regulation of antenna polarization parameters and the low-cost multifunctional integration of modern wireless communication systems.

[0021] The linearly polarized slot-coupled microstrip antenna of the present invention can efficiently transmit and receive electromagnetic waves in a wide frequency band, and can also achieve good compatibility with the active electrically controlled metasurface. When the active electrically controlled metasurface is combined with the microstrip antenna, the polarization angle of the radiated wave can be continuously adjusted by an external bias voltage. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a schematic diagram of the overall structure of the present invention;

[0023] Figure 2 It is a schematic diagram of orthogonal decomposition of linear polarized waves in an embodiment of the present invention;

[0024] Figure 3 Schematic diagram of the working mechanism of the polarization angle continuous adjustment antenna in an embodiment of the present invention;

[0025] Figure 4 Schematic diagram of the structure of the electromagnetic unit of the active electrically controlled metasurface in an embodiment of the present invention; (a) is a schematic diagram of the front structure of the electromagnetic unit, and (b) is a schematic diagram of the back structure of the electromagnetic unit;

[0026] Figure 5 Schematic diagram of an equivalent circuit of an electromagnetic unit of an active electrically controlled metasurface in an embodiment of the present invention;

[0027] Figure 6 Schematic diagram of the transmission coefficient and polarization angle of the active electrically controlled metasurface in an embodiment of the present invention; wherein (a) is a schematic diagram of the transmission coefficient in the xy coordinate system, (b) is a schematic diagram of the transmission coefficient in the uv coordinate system, and (c) is a schematic diagram of the polarization angle;

[0028] Figure 7 This is a schematic diagram of the front structure of the radiation layer in an embodiment of the present invention;

[0029] Figure 8 This is a schematic diagram of the front structure of the feed layer in an embodiment of the present invention;

[0030] Fig. 9 This is a schematic diagram of the back structure of the feed layer in an embodiment of the present invention;

[0031] Fig.10 A side view of a linearly polarized slot-coupled microstrip antenna according to an embodiment of the present invention;

[0032] Fig.11 Schematic diagram of reflection coefficient and gain of a linearly polarized slot-coupled microstrip antenna in an embodiment of the present invention;

[0033] Fig.12 Schematic diagram of reflection coefficient of the present invention in various states;

[0034] Fig.13 Schematic diagram of polarization angles in various states of the present invention.

[0035] As shown in the figure:

[0036] 1. Active electrically controlled metasurface, 2. Radiation layer, 3. Feed layer, 4. PIN diode, 5. First inductor, 6. Second inductor, 7. Feed wire, 8. DC bias line, 9. Bend, 10. First sub-microstrip line, 11. Signal input terminal, 12. Second sub-microstrip line, 13. Slit, 14. Radiation patch, 15. Metal probe microstrip line, 16. Third sub-microstrip line. DETAILED DESCRIPTION

[0037] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0038] See also Figure 1 In this embodiment, the S band is used as the target frequency band. A broadband polarization angle continuously adjustable antenna based on an electrically controlled metasurface includes a linearly polarized slot-coupled microstrip antenna and an active electrically controlled metasurface 1 disposed above the linearly polarized slot-coupled microstrip antenna. The active electrically controlled metasurface 1 is formed by 6×6 electromagnetic units arranged in an array to form a metasurface of 120mm×120mm×1mm in size, and the vertical distance between the active electrically controlled metasurface 1 and the linearly polarized slot-coupled microstrip antenna directly below is 41.3mm.

[0039] The process of realizing polarization angle control in the present invention is as follows: Figure 2-Figure 3 As shown, Figure 2 The figure shows the process of orthogonal decomposition of the transmitted electric field. For any inclined linear polarization wave, the electric field E t Can be orthogonally decomposed into components E along the u and v directions u 、E v , the two components are in phase, and the angle θ between the polarization direction of the electromagnetic wave and the u-axis can be obtained by the following formula:

[0040]

[0041] If the metasurface is used to independently control the amplitudes of the two components, the angle θ can be freely adjusted. Based on this method, this embodiment performs polarization control. The specific working process is as follows: Figure 3 The bottom linearly polarized slot-coupled microstrip antenna radiates u-polarized waves along the +z direction, which will excite a part of v-polarized transmission components after interacting with the active electrically controlled metasurface 1, and then synthesize with the u-polarized components to form tilted polarized transmission waves. By adjusting the metasurface with an external bias voltage, the polarization angle can be controlled, and the tilt angle can be continuously adjusted within the range of ±45°.

[0042] like Figure 4 As shown, the electromagnetic unit includes a dielectric substrate made of FR4 material, with a relative dielectric constant of 4.2 and a thickness of 1.6 mm. The upper and lower surfaces of the dielectric substrate are provided with two symmetrically arranged H-shaped metal strip structures; the H-shaped metal strip structure on the lower surface is the same as the H-shaped metal strip structure on the upper surface, and the direction is obtained by rotating the H-shaped metal strip structure on the upper surface 90° clockwise and then flipping it horizontally.

[0043] A pin diode 4 is provided in the middle of the H-shaped metal strip structure, and two H-shaped metal strip structures are connected by a DC bias line 8, and the two ends of the DC bias line 8 are respectively connected to the forward bias end and the reverse bias end of the pin diode 4. The model of the pin diode 4 is Infineon BAR50-02V, which can be equivalent to a series branch of a resistor and an inductor under forward bias. The resistor can be nonlinearly adjusted by changing the voltage across the pin diode 4.

[0044] A feeding wire 7 is provided on the outside of the H-shaped metal strip structure. The feeding wire 7 is located at the edge of the electromagnetic unit dielectric substrate and is connected to the H-shaped metal strip structure through a DC bias line 8. The feeding wire 7 feeds the pin diodes 4 in different electromagnetic units in parallel.

[0045] To prevent the feed wire from causing crosstalk to the electromagnetic structure, a patch inductor is loaded on it for isolation. Therefore, a first inductor 5 of 60nH is provided on the DC bias line 8 between the two H-shaped metal strip structures, and a second inductor 6 of 20nH is provided on the DC bias line 8 between the feed wire 7 and the H-shaped metal strip structure.

[0046] like Figure 4 As shown, w1 = 1.0 mm, w2 = 0.2 mm, l1 = 8.7 mm, l2 = 4.5 mm, l3 = 6.9 mm, g1 = 1.3 mm, g2 = 0.2 mm, p1 = 20.0 mm. The active electrically controlled metasurface 1 has the ability to control polarization, and the polarization control is to control the amplitude of the orthogonal linear polarization components in the linear polarization electromagnetic wave, and the rotation of the polarization angle is achieved by changing the amplitude ratio.

[0047] Since there is no metal plane between the H-shaped metal strip structures on the front and back sides of the dielectric substrate, spatial coupling can be performed, and there is no metal via, so there is no current conduction. The electromagnetic units in the active electrically controlled metasurface 1 are oriented in the same way, and there is no phase gradient, so there is no transmission beam deflection.

[0048] like Figure 5As shown, L0 is the inductance of the lateral metal strip along the x direction, and C0 is the equivalent capacitance of the adjacent metal strip along the x direction. When an x-polarized wave is incident, the H-shaped metal strip structure together with the pin diode 4 can be equivalent to an RLC series resonant circuit. When the resistance of the pin diode 4 changes, the transmission coefficient near the resonant frequency will change significantly, thereby independently regulating the incident x-polarized component. Moreover, the change in resistance value will not affect the resonant frequency, avoiding the frequency band offset caused by switching the working state, which is conducive to obtaining a wider overlapping frequency band. The working mechanism of the lower surface structure of the electromagnetic unit is similar to this, and the y-polarized electric field component can be independently regulated. The transmission characteristics of the electromagnetic unit when the resistance of the pin diode 4 changes are shown as follows. Figure 6 As shown, R x With R y They are the resistances of the pin diodes 4 located on the positive and negative sides of the electromagnetic unit, and R x Take individual regulation as an example, R y Fixed at 12960Ω. First, Figure 6 (a) It can be seen that when R x The x-direction co-polarization transmission coefficient t increases exponentially from 10Ω to 12960Ω. xx The amplitude gradually increases, and t yy At the same time, Figure 6 (b) It can be seen that as the resistance increases, the v polarization component in the transmitted wave gradually increases from 0 until it is equal to the u polarization component, which means that the polarization direction of the transmitted wave gradually rotates clockwise from the u direction to the v direction (electromagnetic wave polarization angle). When the u and v components are equal, the polarization of the transmitted wave will be parallel to the y axis. Figure 6 As shown in (c), improving R x When the polarization angle increases from 0° to 45° within 2.0-4.0 GHz, the polarization angle in the band is stable with frequency. x Fixed at 12960Ω and independently adjustable R y , the polarization angle range can cover 0° to -45°.

[0049] like Fig.10 As shown, the linearly polarized slot-coupled microstrip antenna includes a feeding layer 3 and a radiation layer 2 disposed above the feeding layer 3. The vertical distance h1 between the radiation layer 2 and the feeding layer 3 below is 11.76 mm. The dielectric substrates used by the radiation layer 2 and the feeding layer 3 are both rectangular substrates with a side length of 54 mm.

[0050] like Figure 7As shown, the radiation layer 2 includes a dielectric substrate and a radiation patch 14 arranged on the surface of the dielectric substrate. The radiation patch 14 is a rectangular metal patch, which is arranged at 45 degrees to the dielectric substrate and is used to radiate u-polarized waves.

[0051] like Figure 8-Figure 9 As shown, the feed layer 3 includes: a dielectric substrate, the dielectric substrate includes a first surface and a second surface relative to each other; the first surface is provided with a metal probe microstrip line 15, the second surface is a metal thin layer, a gap 13 is etched on the metal thin layer, the metal probe microstrip line 15 is used to couple and feed the gap 13, and the gap 13 is a rectangular gap.

[0052] The metal probe microstrip line 15 is a U-shaped structure, which excites a radiation field at the gap 13 and can be used to excite the upper rectangular radiation patch 14. The metal probe microstrip line 15 includes two parallel first sub-microstrip lines 10 and second sub-microstrip lines 12, and the same end of the first sub-microstrip line 10 and the second sub-microstrip line 12 is provided with a third sub-microstrip line 16 perpendicular to the first sub-microstrip line 10 and the second sub-microstrip line 12, and the other end of the first sub-microstrip line 10 and the second sub-microstrip line 12 is provided with a bending portion 9 bent outward, and the bending portion 9 is parallel to the third sub-microstrip line 16. The third sub-microstrip line 16 is connected to the signal input terminal 11. There is a bending portion in the middle of the input terminal 11, one end of which is connected to the middle of the third sub-microstrip line 16, and the other end extends to the edge of the dielectric substrate.

[0053] The first sub-microstrip line 10 and the second sub-microstrip line 12 of the metal probe microstrip line 15 are arranged at 45° to the horizontal direction, and the slot 13 is arranged at 135° to the horizontal direction.

[0054] like Figure 7-10 As shown in the figure, the parameters are as follows: l4=28.36mm, l5=11.63mm, l6=38.79mm, w3=2.32mm, w4=0.59mm, w5=2.35mm, g3=2.42mm, p2=54.0mm, t1=1.0mm, t2=1.6mm, h1=11.76mm.

[0055] Fig.11 The reflection coefficient and gain of the antenna are shown in the figure. In the range of 2.43-3.72 GHz, |S11| is lower than -10 dB and the gain is higher than 4 dBi, with a relative bandwidth of 41.6%, proving that the linearly polarized slot-coupled microstrip antenna can provide stable excitation for the active electrically controlled metasurface 1 in a wide bandwidth.

[0056] When the active electrically controlled metasurface and the linearly polarized slot-coupled microstrip antenna work together, the resistance value is selected with the goal of achieving a 10° step in the polarization angle, and simulation calculations are carried out. First, the reflection coefficient of the antenna in each state is as follows: Fig.12 As shown in the figure, within 2.43-3.67GHz, the reflection coefficient of the antenna is always lower than -10dB, and the relative working bandwidth is 40.7%. The polarization angles of the radiation waves corresponding to different resistance values ​​are shown in the figure below. Fig.13 As shown, within 2.9-3.7GHz, the polarization angle can be adjusted continuously and step-by-step by adjusting the resistor, and the range of variation covers ±45°, which proves that the present invention can achieve continuous adjustment of the linear polarization angle within a wide frequency band. Compared with the existing electrically controlled linear polarization rotating antenna, this design has obvious advantages in bandwidth.

Claims

1. A broadband polarization angle continuously adjustable antenna based on an electrically controlled metasurface, characterized in that: It comprises a linearly polarized slot-coupled microstrip antenna and an active electrically controlled metasurface (1) arranged above the linearly polarized slot-coupled microstrip antenna; The active electrically controlled metasurface (1) is formed by an array of multiple electromagnetic units, wherein the electromagnetic units include a dielectric substrate, and the dielectric substrate includes a first surface and a second surface opposite to each other; the first surface and the second surface are both provided with two symmetrically arranged H-shaped metal strip structures; the H-shaped metal strip structure on the second surface is the same as the H-shaped metal strip structure on the first surface, and the direction is obtained by rotating the H-shaped metal strip structure on the first surface clockwise by 90° and then flipping it horizontally; A pin diode (4) is provided in the middle of the H-shaped metal strip structure, and two H-shaped metal strip structures are connected via a DC bias line (8), and two ends of the DC bias line (8) are respectively connected to the forward bias end and the reverse bias end of the pin diode (4).

2. According to claim 1, a broadband polarization angle continuously adjustable antenna based on an electrically controlled metasurface is characterized in that: There is a gap between the linearly polarized slot-coupled microstrip antenna and the active electrically controlled metasurface (1), and the active electrically controlled metasurface completely covers the linearly polarized slot-coupled microstrip antenna.

3. According to claim 1, the broadband polarization angle continuously adjustable antenna based on the electrically controlled metasurface is characterized in that: A feeding thin wire (7) is arranged outside the H-shaped metal strip structure, and the feeding thin wire (7) and the H-shaped metal strip structure are connected via a DC bias line (8). The feeding thin wire (7) enables the pin diodes (4) in different electromagnetic units to be fed in parallel.

4. According to claim 3, the broadband polarization angle continuously adjustable antenna based on electrically controlled metasurface is characterized in that: A first inductor (5) is provided on the DC bias line (8) between the two H-shaped metal strip structures, and a second inductor (6) is provided on the DC bias line (8) between the feed thin wire (7) and the H-shaped metal strip structure.

5. According to claim 1, the broadband polarization angle continuously adjustable antenna based on electrically controlled metasurface is characterized in that: The linearly polarized slot-coupled microstrip antenna comprises a feeding layer (3) and a radiation layer (2) arranged above the feeding layer (3).

6. The broadband polarization angle continuously adjustable antenna based on electrically controlled metasurface according to claim 5, characterized in that: The radiation layer (2) comprises a dielectric substrate and a radiation patch (14) arranged on the surface of the dielectric substrate.

7. The broadband polarization angle continuously adjustable antenna based on electrically controlled metasurface according to claim 5, characterized in that: The feeding layer (3) comprises: a dielectric substrate, the dielectric substrate comprising a first surface and a second surface opposite to each other; the first surface is provided with a metal probe microstrip line (15), the second surface is a metal thin layer, a gap (13) is etched on the metal thin layer, a projection of the metal probe microstrip line (15) on the metal thin layer intersects with the gap (13), and the metal probe microstrip line (15) is used for coupling and feeding the gap (13).

8. The broadband polarization angle continuously adjustable antenna based on electrically controlled metasurface according to claim 7, characterized in that: The metal probe microstrip line (15) is a U-shaped structure, and the projections of two arms of the metal probe microstrip line (15) of the U-shaped structure on the metal thin layer are perpendicular to the gap (13).

9. The broadband polarization angle continuously adjustable antenna based on electrically controlled metasurface according to claim 8, characterized in that: The ends of the two arms of the U-shaped metal probe microstrip line (15) are both provided with bent portions (9) bent outwards.

10. The broadband polarization angle continuously adjustable antenna based on electrically controlled metasurface according to claim 7, characterized in that: The two arms of the metal probe microstrip line (15) are arranged at 45° to the horizontal direction, and the slot (13) is arranged at 135° to the horizontal direction.

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