2.1. GCPW Leaky-Wave UC Analysis
The antenna design begins with a GCPW that has a characteristic impedance of
. A characteristic impedance of
is selected for the GCPW, since it is a standard value that facilitates antenna measurement. The
GCPW is implemented on an InP substrate with a dielectric constant (
) of
and a loss tangent (
) of
at 300 GHz [
19,
20]. Gold (Au) metal layers are provided on both sides of the InP substrate. The thickness of the InP substrate and the Au metal layers are 50 μm and 1 μm, respectively. To determine the signal line width (
w) and slot width (
s) required for achieving a
GCPW, the design parameters are calculated using Advanced Design System (ADS) LineCalc software Version 2023. The calculated values are subsequently optimized based on an EM simulation performed using CST Microwave Studio software Version 2022. The optimized dimensions for an InP-based
GCPW are found to be 70 μm and 71 μm for the signal line and slot width, respectively. The
GCPW is modified to become leaky by incorporating a waveguide discontinuity in the lateral ground planes of the GCPW. The waveguide discontinuity is designed in the form of an L-slot on each of the lateral ground planes of the GCPW. These L-slots are mirrored with respect to both the longitudinal and transverse axes of the GCPW. The mirroring of L-slots is carried out to mitigate the open stopband phenomena of a periodic leaky-wave antenna, which is explained later in this section. This structure represents a single UC of the periodic GCPW leaky-wave antenna demonstrated in this paper, as illustrated in
Figure 1a. The dimensions of the GCPW leaky-wave UC are shown in
Table 1. The length of the UC and hence the periodicity of the leaky-wave antenna is calculated as one guided wavelength (
) at the desired center frequency,
of 272.5 GHz, using Equation (
1).
In Equation (
1), the parameters
and
denote the speed of light and the effective dielectric constant, respectively. The
of an InP-based
GCPW is calculated as
using the ADS LineCalc software. Consequently, the length of the UC, and hence the periodicity (
p) of the leaky-wave antenna, is calculated as 384 μm using Equation (
1). The value of
p is subsequently optimized based on an EM simulation performed using CST Microwave Studio software. The optimized value of
p is found to be 366 μm.
The UC has a leaky nature due to the introduction of L-slots in its lateral ground planes. As a result, a complex propagation constant (
) is associated with the UC, which is composed of a non-zero attenuation constant (
) and a non-zero phase constant (
) as shown by Equation (
2).
The attenuation constant (
) signifies the leakage rate of the periodic leaky-wave antenna, while the phase constant (
) is useful in determining the beam-steering angle of the periodic leaky-wave antenna. Therefore, in order to design a periodic leaky-wave antenna, the values of
and
should be known in the desired frequency range of 220 GHz–325 GHz. For this purpose, the S-parameters of the GCPW leaky-wave UC are simulated using CST Microwave Studio software Version 2022. The simulation model of the UC is shown in
Figure 1b, indicating the position of waveguide ports configured at both ends of the
GCPW. The boundary conditions used for this simulation consist of open boundaries along the x and y axes, an electric boundary along the negative z axis (i.e., at the bottom ground plane of the UC), and an open add space boundary along the positive z axis (i.e., at the top of the UC). The simulated S-parameters are converted to the
A,
B,
C, and
D parameters of the UC. The
A,
B,
C, and
D parameters of the GCPW leaky-wave UC are used to calculate the values of
and
by using Equation (
3). Note that the Equation (
3) assumes an infinite periodic structure, i.e., an infinitely long GCPW composed of a one-dimensional (1D) cascade of the leaky-wave UCs repeated at periodic intervals of
p. According to the Floquet’s theory of periodic structures, Bloch waves propagate on the periodically-loaded GCPW and the Bloch impedance (
) is calculated using the
A,
B, and
D parameters of the GCPW leaky-wave UC as shown in Equation (
4) [
21].
The
obtained from Equation (
3) corresponds to the phase constant of the fundamental GCPW mode, which is a guided mode with a phase velocity (
) less than
. This implies that
1, where
denotes the free space wavenumber (Note,
and
). A 1D periodic array of the leaky-wave UCs leads to the generation of an infinite number of space harmonics, whose phase constants are given by Equation (
5) [
22].
In Equation (
5),
denotes the phase constant of the nth space harmonic. A space harmonic with
(i.e.,
1) is a leaky wave that is capable of radiating into free space. We already know that
1 for a guided GCPW mode; therefore, in order to make
1,
n should be a negative integer. The value of
n is selected as
in order to design a beam-steering antenna with a single main lobe. Consequently, the phase constant of the first leaky wave (
) that causes radiation into free space is calculated by using Equation (
6) [
22].
In Equation (
6), the value of the leaky-wave UC period,
p, is varied in three steps namely, 356 μm, 366 μm, and 376 μm (note that these values are close to the initially calculated value of 384 μm using Equation (
1)). An EM simulation of the GCPW leaky-wave UC is carried out corresponding to all three values of
p. The simulated S-parameters are converted to the
A,
B,
C, and
D parameters, which are used to calculate the first leaky-wave phase constant,
, by using Equations (
3) and (
6). The resultant phase constant curves over the target frequency range of 220 GHz–325 GHz are shown in
Figure 2a. In each of these three cases, the phase constant curve remains below the light line (i.e.,
) and, hence, in all three cases, the first space harmonic or the first leaky wave radiates into free space in the 220 GHz–325 GHz range. The frequency at which the phase constant becomes null corresponds to a broadside radiation. The frequency of broadside radiation decreases with an increase in the value of
p and a broadside radiation at the desired center frequency of 272.5 GHz is obtained for a periodicity of 366 μm. The range of frequencies on the left and right sides of the null point signifies radiation in backward and forward quadrants, respectively. The total length of the L-slot (i.e.,
) should be approximately half of the guided wavelength (i.e.,
, where
p is equal to the optimized
at the desired center frequency). As a result, the L-slot functions as a waveguide discontinuity that leads to leaky-wave radiation. Between these two values, the longitudinal length of the L-slot (
) is kept relatively longer than the transverse length (
). This choice results in a smaller width of the lateral ground-plane of the GCPW structure. As a result, the overall width of the leaky-wave antenna is reduced, allowing the potential formation of a 1D array of such leaky-wave antennas in the future. This array can be created while still maintaining an antenna spacing of less than half of the free-space wavelength. Consequently, the problem of grating lobes could be avoided when configuring a 1D array of these leaky-wave antennas. Taking this rationale into account, and considering the manufacturing constraints of the InP process used in this work,
is set to 41 μm and the initial value of
is calculated as
. Starting with this initial value, the value of
is optimized based on electromagnetic simulations of the GCPW leaky-wave UC. In this case, the derived
A,
B,
C, and
D parameters are used to calculate the leakage rate,
, and the Bloch impedance,
, using Equation (
3) and Equation (
4), respectively. The value of
is varied in steps of 120 μm, 135 μm, and 150 μm (these values are close to the initially calculated value of 142 μm) and the resultant curves of
and
over the target frequency range of 220 GHz–325 GHz are shown in
Figure 2b,c, respectively. For
of 120 μm, a high leakage rate,
, is observed at the starting frequency of 220 GHz, which implies a small effective aperture and, hence, a poor radiation efficiency for a periodic leaky-wave antenna. On the other hand, for
of 150 μm, the leakage rate is quite low; however, the corresponding Bloch impedance,
, shows a larger deviation from the desired
value. Consequently, the optimum value of
is 135 μm, which provides a good trade-off between a sufficiently low leakage rate and a Bloch impedance that stays close to
for most of the target frequency range.
In a periodic leaky-wave antenna, a mismatch between the Bloch wave impedance,
, and the load impedance, (
), of a periodically-loaded waveguide occurs around the broadside radiation frequency, which results in a somewhat reduced efficiency of the broadside radiation, also known as the open stopband phenomenon [
22]. The GCPW leaky-wave UC shown in
Figure 1a uses mirrored L-slots, which help to mitigate the impedance mismatch between
and
and hence mitigate the open stopband phenomenon to a large extent. In order to prove this, a GCPW leaky-wave UC with longitudinally symmetric L-slots is simulated using waveguide ports on either end, as shown in
Figure 3a. The dimensions of this UC are the same as those shown in
Table 1.
The
extracted for both the GCPW leaky-wave UCs, i.e., with the longitudinally symmetric L-slots and the mirrored L-slots, are shown in
Figure 3b. It is observed that the longitudinally symmetric L-slots result in a
of
at the broadside radiation frequency, which will lead to a maximum reflection coefficient (
) of
using a
of
in Equation (
7) [
22]. On the other hand, the mirrored L-slots result in a
, which stays close to
for most of the target frequency range. At the broadside radiation frequency,
shows a maximum jump of
at the broadside radiation frequency. This leads to an improvement of
.
Finally, the distribution of the electric field (E-field) is analyzed to validate the design procedure of the GCPW leaky-wave UC outlined in this section. The simulated E-field of the GCPW leaky-wave UC at the center frequency of 275 GHz and at phase angles of
and
is depicted in
Figure 3c,d, respectively. The location of the waveguide ports used in this simulation is the same as that depicted in
Figure 1b, and the boundary conditions employed are consistent with those detailed in
Figure 1b. It is evident that a GCPW mode propagates along the host signal line, with the maximum absolute value of the E-field observed around the first L-slot at a
phase angle in
Figure 3c, and around the mirrored L-slot at a
phase angle in
Figure 3d. This E-field analysis confirms that the mirrored L-slots function as waveguide discontinuities within the host GCPW structure, leading to leaky-wave radiation. Secondly, the maximum intensity of the E-field observed within the two L-slots aligns with a phase difference of approximately
. In other words, the phase centers of the mirrored L-slot radiators are spaced a quarter of a guided wavelength apart. As mentioned in the design procedure, the total length of the GCPW leaky-wave UC is chosen to match one guided wavelength at the center frequency, and the total length of each of these mirrored L-slots is set to half of the guided wavelength at the center frequency. Consequently, the phase centers of the mirrored L-slots should be a quarter of the guided wavelength apart at the center frequency, confirming that the observed E-field maxima align with the fundamental design concept of this GCPW leaky-wave UC. The H-field analysis of the GCPW leaky-wave UC reaffirms these findings.
2.2. GCPW Leaky-Wave Antenna: Full EM Simulation vs. Ideal Model
After optimizing the GCPW leaky-wave UC design, a total of 16 UCs are cascaded to build the periodic GCPW leaky-wave antenna. A high number of UCs, combined with a low leakage rate (
), ensures that, as the first space harmonic (with phase constant
) propagates along the periodically-loaded GCPW, most of the energy is leaked and radiated into free space by the time the wave reaches the last UC of a 1D cascaded structure. A schematic of the periodic GCPW leaky-wave antenna is shown in
Figure 4a.
In this schematic, besides the GCPW leaky-wave UCs, a GCPW feed structure and a GCPW open circuit termination are added to realize the periodic leaky-wave antenna. The feed structure is designed to enable antenna measurement using a ground signal ground (GSG) probe. The GSG probe used for measurement has a pitch of 100 μm, according to which the signal line width and the slot width of the GCPW feed (
,
) are adjusted to achieve a characteristic impedance of
. This feed is connected to the 1D periodic array of leaky-wave UCs using a tapered transition. The antenna is terminated with a GCPW open circuit. Note that the beam-steering antennas realized at low frequencies, which are measured using coaxial connectors, are terminated with a matched load, whereas the antenna shown here operates at a high frequency of 220 GHz–325 GHz, which is measured with a probe. Moreover, a matched load cannot be realized due to the manufacturing process and the probe-based antenna measurement setup used in this work. In the GCPW open circuit termination of the antenna, the GCPW signal line is tapered to mitigate the parasitic fringing capacitance that exists at the open end of the signal line. This tapering leads to an improvement in the impedance matching at the broadside radiation frequency. The dimensions of the periodic GCPW leaky-wave antenna are shown in
Table 2.
An EM simulation of the antenna is performed using CST Microwave Studio software. The simulated reflection coefficient and beam-steering angle of the antenna are compared with those of an ideal model derived from a single GCPW leaky-wave UC shown in
Figure 1. The ideal model shown in
Figure 4b is built using ADS software. In this model, the simulated S-parameters of a single GCPW leaky-wave UC are imported into ADS software. To replicate the complete radiating structure of the antenna, the S-parameters of a single UC are cascaded 16 times. The cascade of 16 UCs is terminated on either end using an input impedance (
) and an output impedance (
). The ADS simulation is performed using a start frequency of 220 GHz and a stop frequency of 325 GHz. The S-parameter simulations in ADS are performed in steps of 0.1 GHz. Two different simulations are performed using this model. In the first case, matched terminations are used at the input as well as the output (i.e.,
and
). In the second case, a matched termination is used at the input, whereas a very high impedance is used at the output in order to mimic an open circuit termination (i.e.,
and
). The reflection coefficients of the full-wave EM simulation and two different cases of the ideal ADS model derived from the leaky-wave UC are compared in
Figure 4c. In
Figure 4c, the dashed curve (marked as ‘(1)’) shows the simulated reflection coefficient of the ideal ADS model using
and the dotted curve (marked as ‘(2)’) shows the simulated reflection coefficient of the ideal ADS model using
and
. In the former case, the reflection coefficient forms a smooth curve, whereas, in the latter case, the reflection coefficient shows ripples along with some degradation. Furthermore, the reflection coefficient curves of the second case and the full EM simulation model of the leaky-wave antenna exhibit a similar progression over the frequency range of 220 GHz to 325 GHz. The slight discrepancy between the dotted and solid curves in
Figure 4c, specifically the frequency offset in their peaks, can be attributed to the distinct methods of implementing open-circuit termination in the two models. The ADS model shown in
Figure 4b employs a very high output impedance value (
) to mimic an open-circuit termination, whereas the full EM simulation model in CST (see
Figure 4a) employs a modified GCPW open-circuit termination along with a tapered feed structure. Therefore, a minor deviation between these two curves is to be expected.
The beam-steering angle is also compared between the two models. For the EM simulation model, the far-field radiation pattern of the antenna is simulated in the 220 GHz–325 GHz range at 5 GHz intervals. The main lobe direction of each simulated far-field radiation pattern provides the beam-steering angle over the target frequency range shown in
Figure 4d. In the ideal model, the beam-steering angle is calculated using the phase constant of the first space harmonic, causing radiation into free space, as shown in Equation (
8). Furthermore, the procedure of obtaining the value of
from a single leaky-wave UC has already been explained in
Section 2.1.
The beam-steering angle over the target frequency range obtained from the EM simulation of the periodic GCPW leaky-wave antenna and the ideal model derived from a single GCPW leaky-wave UC show a very good match. It is worth noting that the simulation model of the periodic GCPW leaky-wave antenna employs a hexahedral mesh with approximately
million mesh cells, whereas the simulation model of a single leaky-wave UC used to construct the ideal model in ADS software uses a hexahedral mesh with only
million mesh cells. As a result, the significant reduction in mesh cells by nearly 20 times leads to a substantial reduction in computation time. The excellent agreement observed in the results obtained from both approaches shows that the analysis of leaky-wave UCs combined with an ideal simulation in ADS software can expedite the design process of a periodic leaky-wave antenna. The simulated far-field radiation pattern at 300 GHz (see
Figure 4e) shows a realized gain of 13.3 dBi and a total antenna efficiency of ≈
. The radiation pattern has a fan-shaped beam with a narrow half power beam width of ≈
in the beam-steering plane. The fan-shaped beam tilts in the forward and backward quadrant with increasing and decreasing frequency, respectively.