J. Eur. Opt. Society-Rapid Publ. 21, 2( 2025) 15
T ¼ T 0 � s ¼ L = sin h m � 1 c c ð20Þ
If the beam offset h 0 f is allowed to be less than one fourth of the beam width in the h m direction, and when s < T 0, the beam offset Dh f can be expressed as:
h 0 f 1 4 h 1 = 2ðh m Þ ¼ 1
4 h 1
1 = 2 ð21Þ cos h m
The allowed signal relative bandwidth can also be increased, becoming
f T 0 h 1 = 2 f 0 T 0 � s 1 ð22Þ
4 sin h m
Due to T 0 /( T 0 �s) > 1, using delay compensation can improve the instantaneous bandwidth of the signal, and the bandwidth limitation on the radar can be expressed as
h 0 1 f 10ðT 0 � sÞ ¼ 1 10 c ð23Þ
L sin h m � l
According to the derivation process of equation( 23), the beam pointing offset h 0 f caused by signal frequency changes can be expressed as
h 0 f ¼� f 1 � s tan h m ð24Þ f 0 T 0
According to the above equation, when s = T 0, the instantaneous delay fully compensating for the aperture transition time, the pointing angle shifts h 0 f ¼ 0, that is, there is no aperture effect. The beam direction of phased array antenna is no longer affected by the instantaneous bandwidth of the signal.
The time delay caused by signal over a single transmission line is called true delay [ 23 ], and both true delay and phase shifters are functional devices designed to achieve beamforming. The characteristic of true delay is that its time delay is independent of frequency or the resulting phase shift is linearly related to frequency. The phase response characteristics of phase shifters are generally different from true delay. For example, it does not have linear phase-frequency characteristics like true time delay line. This leads to a fundamental difference between delay lines and phase shifters in practice. In order to achieve broadband wide-angle scanning in phased array radar, TTD should be used instead of the phase shifter in conventional phased array radar. Different from the traditional phase shifters that are only suitable for narrowband operating ranges, TTD can achieve precise control of time delay over a wide operating frequency band.
If microwave signals are modulated onto optical fibers and the fibers are used as TTD, it is called Optical True Time Delay( OTTD). In the optical phased array antenna system based on OTTD, the microwave signal to be transmitted is converted into changes in optical characteristic parameters by an electro-optic modulator firstly. Then, optical methods are used to propagate the optical signal through different optical paths to achieve time delay control. Finally, at the transmitting end, an optoelectronic conversion element is used to restore the optical signal to a
Figure
3. Introducing optical true delay lines does not produce beam squint.
microwave signal. As shown in Figure 3, the introduction of optical true delay lines did not result in beam squint.
Figure 3 shows the directional patterns of the antenna at operating frequencies of 27 GHz, 28 GHz, and 29 GHz, respectively. It can be observed that the beam direction has not changed and there is no beam squint phenomenon. By comparing Figure 2 and Figure 3, we can conclude that using optical true delay lines can achieve broadband microwave photon beamforming without beam squint, and its operating bandwidth is determined by the flat delay bandwidth of the delay line.
Therefore, in broadband systems, Optical Beam Forming Network( OBFN) has more obvious technical advantages and application potential compared to radio beam forming networks using electronic phase shifters. The optically controlled beamforming scheme is shown in Figure 4 [ 24 ].
As is shown in Figure 4, the scheme include five basic units. The first unit is a laser( LD) used to provide an optical carrier for transmitting microwave signals. The second unit is an electro-optic converter( E / O converter), which is used to modulate and convert the input RF signal into an optical carrier signal. The third unit is the Optical Beamforming Network( OBFN), which is used to control the phase delay of modulated optical carrier signals. The fourth unit is the O / E converter, which recovers the optical signal into an electrical signal and obtains multiple coherent microwave signals; The fifth unit is the transmitter / receiver( T / R) component of the antenna unit, which is used to receive and transmit microwave signals.
As mentioned in this section, in broadband systems, OBFN has more obvious technical advantages and application potential compared to radio beam forming networks