This project uses photonic time stretching, photonic components and instruments to implement RF/microwave processing unit functionalities. This can improve the performance of conventional units or to decrease their cost.
This project is based on a novel idea to dramatically increase the resolution of conventional time stretch vibrometry system. This has application in biomedical imaging and remote sensing.
Time-stretch systems are the fastest methods to capture transient events. In this project we would like to add phase recovery to the time stretch system, this has application in biomedical imaging, remote sensing and laser development.
In this project, we plan to build a stable super-continuum laser for biomedical imaging and remote-sensing applications.
In this project, we plan to build a stable super-continuum laser for biomedical imaging and remote-sensing applications.
Current Projects 1. Microwave photonics This project uses photonic time stretch system to implement RF/microwave processing unit functionalities using photonic components and instruments. This can be used to improve the performance of conventional RF/microwave processing units or to decrease their cost. 2. Highly accurate time stretch vibrometry system This project is based on a novel idea to dramatically increase the resolution of conventional time stretch vibrometry system. This has application in biomedical imaging and remote sensing. It is based on using the movement of fringes in time stretch vibrometry system. 3. Amplitude and phase measurement in time stretch systems It is important for a city to know about the quality of its roads. This is typically done by filming the road and then asking an engineer to watch the film and find and analyze the severity of the cracks. This is very time consuming task specially for long roads. In this project we develop a commercial-level software that can process the captured film and automatically find and analyze the severity of the cracks. 4. Development of a stable super-continuum laser In this project, we plan to build a stable super-continuum laser for biomedical imaging and remote-sensing applications. Previous Projects Ultrafast Optical Coherence Tomography (2016) Ultrafast techniques are very important to analyze fast transient phenomena as well as fast capturing in high throughput applications. This includes cancer cell detection from blood monitoring as well as finding new rare physical phenomena that happen in sub-ps time scales at the speed of light. In this project, we develop a new biomedical imaging system with unprecedented performance. This method uses optical coherence tomography combined with an ultrafast optical signal processing technique to capture and analyze images at the rate of million frames per second. This project will put a world record for the speed of such techniques. Using raspberry-pi tower to analyze network-on-chip systems (2016) Network-on-chip is a practical solution to make multi-core processing units more efficient. These techniques are already used in the recent smart phones. Since these techniques are fabricated using integrated circuits, it is difficult to analyze their performance before fabricating the design. In this project, we plan to develop a system that allows researchers to analyze the performance of Network-On-Chip systems without the need to fabricate the design. It is based on using a network of Raspberry-Pis (a popular low cost mini computer platform) to emulate behavior of a Network-On-Chip system. At the same time, the built Raspberry-Pi tower will act as a super computer. Automatic crack detection on the road (2016) It is important for a city to know about the quality of its roads. This is typically done by filming the road and then asking an engineer to watch the film and find and analyze the severity of the cracks. This is very time consuming task specially for long roads. In this project we develop a commercial-level software that can process the captured film and automatically find and analyze the severity of the cracks.
Research contributions (click on each subject to jump): A. Dealing with the Big Data bottleneck in photonic real-time instruments B. Detection of ultrafast transient and dynamical events in real-time and single-shot C. Microwave photonics signal processing
A. Dealing with the Big Data bottleneck in photonic real-time instruments Anamorphic Stretch Transform (AST): Anamorphic Stretch Transform (AST) is a mathematical transform that can be used to engineer the time bandwidth product of the input signal. It is mathematically defined as follow:
where E_{i}(ω) is the input signal spectrum, and β(ω) is called the phase kernel of the AST. Following figure shows the block diagram of a system incorporating the Anamorphic transform for time bandwidth product compression.
Stretched Modulation (S_{M}) Distribution: The Stretched Modulation (S_{M}) Distribution is a complex valued three dimensional plot that allows one to design time bandwidth engineering systems. It describes the information bandwidth and duration of the signal intensity after a transformation that is mathematically described by the kernel of S_{M}. The Distribution can be written as:
S_{M} distribution can be used to design time-bandwidth engineering systems in both near-field (small dispersion) and far-field (large dispersion) regimes. Following figure shows a comparison of S_{M} distribution for conventional time-stretch transform (i.e. a system with linear group delay) and AST operated on an arbitrary signal. The derivative of the AST phase kernel for this simulation is a sublinear function of frequency.
Analysis of SM distribution suggests that for time bandwidth product compression, the derivative of the AST phase Kernel should be a sublinear function of frequency. Time bandwidth product compression using Anamorphic Stretch Transform (AST) has has been experimentally proved. The experimental setup for proof of the concept experiments is shown bellow.
For experimental demonstrations, AST was implemented using a designed nonlinearly chirped fiber Bragg grating. AST was designed to have a phase Kernel with inverse tangent derivative profile (sublinear function). Experimental results are summarized bellow.
Reference: B. Jalali, and M. H. Asghari, “Method for data compression and time-bandwidth product engineering,” International PCT application submitted Dec. 2013, PCT/US13/77969, Supporting provisional application No. 61/867,515; 61/867,519; 61/888,867, Dec. 2012. M. H. Asghari and B. Jalali, “Anamorphic transformation and its application to time-bandwidth compression,” Applied Optics, Vol. 52, pp. 6735-6743 (2013). M. H. Asghari and B. Jalali, “Experimental demonstration of optical real-time data compression,” Applied Physics Letters, Vol. 104, 111101, pp. 1-4 (2014). M. H. Asghari and B. Jalali, “Warped time lens in temporal imaging for optical real-time data compression,” Springer publishing group, Chinese Science Bulletin journal, ISSN: 1861-9541, DOI: 10.1007/s11434-014-0352-0, pp. 1-6 (2014), INVITED. B. Jalali and M.H. Asghari, “Anamorphic Stretch Transform; putting the squeeze on big data,” Optics and Photonics News 25, 24 (February 2014). H. Gao, M. H. Asghari, and B. Jalali, “Time-bandwidth engineering for arbitrary waveform generation,” IEEE Global Signal and Information Processing Symposium (GlobalSIP 2014), Accepted, Atlanta, December 2014. J. Chan, M. H. Asghari, and B. Jalali, “Performance of time bandwidth engineering systems,” IEEE Photonic Conference (IPC 2014), Accepted, San Diego, October 2014. M. H. Asghari, J. Chan, and B. Jalali, “Time-frequency manipulation in real-time instru-ments,” Progress In Electromagnetics Research Symposium (35th PIERS 2014), Accepted, August 2014, Guangzhou, China, INVITED. J. Zhang, M. H. Asghari, J. Yao, and B. Jalali, “Time-bandwidth product expansion of microwave waveforms using Anamorphic Stretch Transform,” Conference on Lasers and Electro-Optics (CLEO 2014), paper: JTh2A.38, June 2014, San Jose, USA. M. H. Asghari, and B. Jalali, “Anamorphic temporal imaging using a warped time lens,” Conference on Lasers and Electro-Optics (CLEO 2014), paper: STu3E.3, June 2014, San Jose, USA. B. Jalali, and M. H. Asghari, “Anamorphic Stretch Transform for Analog and Digital Compression of Big Data,” Novel Optical Systems Design and Optimization, SPIE Optics-Photonics 2014, paper: OP14O-63, August 2014, San Diego, USA, INVITED. M. H. Asghari and B. Jalali, "Demonstration of analog time-bandwidth compression using anamorphic stretch transform," Frontiers in Optics (FIO 2013), Paper: FW6A.2, Orlando, USA, POST-DEADLINE PAPER. M. H. Asghari and B. Jalali, "Anamorphic time stretch transform and its application to analog bandwidth compression," IEEE Global Signal and Information Processing Symposium (GlobalSIP 2013) paper: NSSIMb.PD.2, Austin, USA. M. H. Asghari and B. Jalali, "Warped dispersive transform and its application to analog bandwidth compression," IEEE Photonic Conference (IPC 2013), paper TUG 1.1, Seattle, USA. B. Detection of ultrafast transient and dynamical events in real-time and single-shot Stereopsis-Inspired Time-Stretched Amplified Real-Time Spectrometer (STARS) Measurement of ultrafast single-shot events harbor a wealth of fascinating science that is inaccessible to pump-and-probe measurements. Real-time instruments fueling this field include high-throughput time-stretch imaging, real-time spectroscopy, high-throughput optical coherence tomography and wideband analog to digital conversion. One of the critical bottlenecks of the electronics is the speed of current analog-to-digital converters (ADCs). Current ADCs are limited by their speed to tens of GHz. They are also very costly and can produce a lot of heat. In contrast, photonic-assisted ADCs can operate at THz speeds, they are cheaper, produce much lower heat and require much lower power. As one of my contributions to this subject, I have recently introduced a photonic-assisted data conversion method, called STARS, to capture electrical signals using a digitizer with much lower sampling rate than required by Nyquist sampling rate theorem. STARS stands for Stereopsis-Inspired Time-Stretched Amplified Real-Time Spectrometer. To give an example I demonstrated capturing of 40 GHz streaming telecommunication signals using a digitizer with only 1.5 Gbps sampling rate. To use a conventional ADC to capture this signal, an ADC with 80 Gbps sampling rate would be required (based on Nyquist sampling rate theorem). In this method (i.e. STARS) first the electrical signal to be digitized is modulated on an optical signal. STARS then employs amplified dispersive Fourier transform to slow down the modulated optical signal in time (to measure the signal using a low-speed digitizer). Finally our novel stereopsis reconstruction algorithm inspired by binocular vision in biological eyes is used to recover the signal in both amplitude and phase. The STARS system is shown in Fig. 4.
STARS benefits from a novel dynamic time-stretch concept to enhance the phase accuracy and dynamic range of the system more than 30 times. Fig. 5 shows the experimental demonstration of the huge dynamic range of STARS method to measure input signal's phase profile. STARS holds the world record for input signal phase dynamic range.
We have employed this instrument to capture 40 Gbps electrical signal using a 1.5 Gbps digitizer. The experimental setup is shown in Fig. 6. Experimental results (see Fig. 7) confirms the capability of STARS to capture ultrafast electrical signal suing a low speed backend digitizer.
Reference: Hossein Asghari and Bahram Jalali, "Stereopsis-inspired time-stretched amplified real-time spectrometer (STARS)", IEEE Photonics Journal, Vol. 4, pp. 1693-1701 (2012), Invited. (pdf) Coherent Dispersive Fourier Transform Future progresses in a wide range of fields essentially depend on capturing ultrafast phenomena as they evolve in time. Also in many biomedical applications (e.g. cancer cell detection) or mass material analysis, high-throughput measurement methods are highly demanded. These demands call for development of measurement methods capable of capturing dynamic phenomenon in a high-throughput fashion. The capability of performing such advanced measurements is specifically important for applications in which random (non-repetitive), rapidly-changing ultrafast waveforms need to be fully characterized and evaluated. These include real-time monitoring in ultrahigh-bit-rate optical telecommunication, computing and information processing systems; testing of electronic and photonic materials, devices and sub-systems; and observation and analysis of a large variety of ultrafast dynamic events in physics, biology, chemistry etc. Photonic technologies can be employed to observe dynamic phenomena as they evolve in time at ultrahigh frame rates and ultrahigh throughputs. We have demonstrated an optical measurement technique, called real-time spectral interferometry, capable of detecting dynamic optical phenomenon at 20 million frames per second. Optical measurement methods prior to our technique had update rates of thousands of frames per second range, i.e. more than thousand times slower than our method. Since in our method the captured signals are recorded using a real-time oscilloscope, billions of these frames can be captured and analyzed for ultrahigh throughput detection. Schematic of real time spectral interferometry is shown in Fig. 8. Our method is based on combining conventional spectral interferometry with a dispersion element having a large group velocity dispersion (GVD), e.g. using a linearly chirped fiber grating (LCFG) device. In conventional spectral interferometry the signal under test is interfered with a reference signal in an optical coupler. The resulted spectral interferogram is then measured using a spectrometer. Spectrometers are very slow equipments (thousand of frames per second). The dispersive element in our method is employed to operate real-time optical Fourier transformation, this way the resulted spectral interferogram after the spectral interferometry is mapped to the time domain so it can be measured using a real time oscilloscope. Oscilloscopes are much faster equipments than spectrometers, they can operate at millions of frames per second.
Proof of concept experiments setup is shown in Fig. 9(a). Experimental results are shown in Fig. 9(b) to (d). We demonstrated capturing of dynamical optical waveforms with TH bandwidth as they evolve in time at an unprecedented frame rate of 20 million frames per second.
References: Hossein Asghari, Yongwoo Park and Jose Azana, "Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry," Optics Express, Vol. 18, pp. 16526-16538 (2010). (pdf) Laser Focus World (LFW) magazine review: Click here C. Microwave photonics signal processing Microwaves are radio waves with wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz (0.3 GHz) and 300 GHz. Microwave is basically a field that fills the gap between electronics (<GHz frequencies) and optics (>300 GHz frequencies). Microwave has a wide range of applications including telecommunications, Radar, radio astronomy, navigation, heating and power, spectroscopy etc. Microwave signal processing addresses the devices that can process, measure or manipulate microwave signals for different applications. Microwave signal processing devices at speeds more than GHz become extremely costly, power hungry and challenging to fabricate. Microwave photonics signal processing is a novel field in which photonic technologies are employed to operate microwave signal processing. These photonic-based devices are much cheaper, easier to operate and they require much lower power. Here I provide two examples of my contributions to microwave photonics signal processing, (1) photonic-based microwave reconfigurable differential operators and (2) photonic-based microwave temporal integrator. Microwave Reconfigurable Differential Operators Using Photonic Technologies Differential operators are generally defined as systems that can virtually emulate any operation on the input analog signal by combining different derivatives of the input signal with different weights. To emulate time-variant operations a reconfigurable differential operator system is required. To give an example on applications of differential operator systems, they can model the behavior of resistor-inductor-capacitor (RLC) processing circuits. Another example is to model microwave filter design methods using differential operators. If the differential operator systems is reconfigurable it can be used to implement any kind of filtering or microwave circuit using a single device. Unfortunately making such devices in the microwave domain are very challenging, costly. In this work, we proposed and experimentally demonstrated the design of a reconfigurable microwave arbitrary differential operator using photonic technologies. We showed that any differential operator can be implemented using the same programmable platform. To implement an arbitrary differential operation we use well-known discrete-time Euler's approximation so the differential operation can be represented by finite-difference-time-domain (FDTD) equations. The experimental setup for our proposed method is shown in Fig. 10. Basically in our method the microwave signal is modulated on an optical signal, then it is processed in the photonic domain and finally is converted back to the microwave domain. To understand our method in more details, the microwave signal is first modulated on an incoherent light using an electro optic modulator (MOD). This way photonic methods can be used to operate the same microwave functionality but in the photonic domain. We operate the target differential operator functionality (based on FDTD equations) in the photonic domain using a dispersive element combined with a wavelength division multiplexing (WDM) system. Using the WDM system different frequency bands of the signal are separated and using a multi channel attenuator system different frequency bands are given different weights. This way an arbitrary differential operation can be emulated in the photonic domain. Finally the resulted optical signal is measured using a balanced photo detector (BD) to generate the output microwave signal. Note that using different weights for different frequency bands, arbitrary differential operator system can be emulated using the same platform.
In the first experiment we targeted to use our method to emulate the operation of a microwave RLC circuit in the photonic domain. The schematic of the targeted RLC circuit is shown in Fig. 11. The RLC circuit was described as a linear second-order differential operator.
The experimental results are shown in Fig. 17 confirming the proper operation of the designed microwave RLC with 40 GHz bandwidth (limited by the speed of electro-optic modulator).
In another experiment we implemented first to fourth-order microwave temporal differentiators with the same platform using our method. The processing speeds in tens of GHz was proved experimentally, see Fig. 12.
References: Yongwoo Park, Hossein Asghari, Robin Helsten, and Jose Azana, "Implementation of broadband Microwave arbitrary-order time differential operators using a reconfigurable incoherent photonic processor," IEEE Photonics Journal 2, 1040-1050 (2010). (pdf) Hossein Asghari and Jose Azana, "Proposal and analysis of a reconfigurable pulse shaping technique based on multi-arm optical differentiators ", Optics Communications, Vol. 281, Issue 18, 15, pp. 4581-4588 (2008). (pdf) Microwave Temporal Integrator Using Photonic Technologies A temporal integrator is a block that gets an arbitrary time-domain signal at its input port and generates the cumulative temporal integration of this input waveform at the output port. Temporal integrators are fundamental devices for implementing a wide variety of signal processing operations of interest, e.g., in computing, control, and communication networks. Similar applications can be expected for temporal integrators in the microwave domain. Implementation of microwave temporal integrators for speeds beyond GHz using microwave devices are very costly and challenging to fabricate. Photonic technologies can be employed to operate microwave temporal integrators with tens of GHz bandwidth with much lower cost and better power efficiency. Before going to the details of our work I give some information about how temporal integrators work. It has been proved that temporal integration is nothing but convolution of the input signal with a unit-step function. Unit-step function is a signal that its value is 0 for t<0 and 1 for t>0. We have also proved that if the input signal is convolved with a square-like signal (instead of unit-step function) the output of the convolution is the proper integration of the input signal but in a limited time window given by the duration of the square-like function. Remember that unit-step function is actually a square-like signal with unlimited time duration. We have proposed and experimentally demonstrated a design for implementing a microwave temporal integrator offering high processing speed using photonic technologies. The experimental setup for our proposed method is shown in Fig. 19(a). Basically in our method the microwave signal is modulated on an optical signal, then it is processed in the photonic domain and finally is converted back to the microwave domain. To understand our method in more details, first the microwave signal is modulated on an incoherent optical signal with square-like broadband spectrum. The modulated optical signal is then passed through a dispersive element with specific amount of group velocity dispersion (GVD). We have shown that when the modulated signal passes through the dispersive element, its time domain amplitude (which has the information of the microwave signal) is convolved with the envelope of the incoherent light spectrum (a square-like shape). Based on our discussions in previous paragraph, the output of the dispersive element is the proper integration of the input microwave signal in a limited time window given by the bandwidth of the incoherent light source. To solve the issue of limited operation time window of this microwave integrator, we proposed to cascade this photonic-based time-limited microwave integrator with a discrete-time optical integrator in which its unit-time delay is equal to the operation time window of the time-limited microwave integrator. We have proved mathematically and experimentally that this way the operation time window of the integrator can go to infinity, i.e. ideal temporal integration. The experimental setup for this implementation is shown in Fig. 13(b).
We have successfully implemented and tested this idea. Specifically we implemented a microwave temporal integrator with 36 GHz bandwidth using our photonic method. The measured frequency transfer function of the implemented integrator is shown in Fig. 14. Integration of some microwave signals with tens of GHz bandwidth is also shown in Fig. 15 confirming the accurate operation of this photonic-based microwave integrator.
References: Hossein Asghari, Yongwoo Park, and Jose Azana, "Photonic temporal integration of broadband intensity waveforms over long operation time windows", Optics Letters, Vol. 36, pp. 3557-3559 (2011). (pdf) Optical memory unit High bit-rate telecommunications, switching networks and signal processing units with ever-increasing the required speed of processing and computing calls for novel data computing units operating at THz range speed. Unfortunately electronic solutions cannot operate at such ultrafast speeds. For example, commercially available memory units (see Fig. 5(a)) operate at the speeds of <10 GHz. In scientific laboratories speeds in tens of GHz range have been demonstrated. Photonic solutions in both analog and digital domains are promising candidates for ultrafast signal processing and data computing operations because they have the potential to operate on signals in the THz regime. To give an example, we have proposed and experimentally demonstrated a photonic-based memory unit (see Fig. 16(b)) which is the fastest memory unit in the world, working at the speed of ~700 GHz. This is well beyond the speed of available electronic memory units.
Our proposed photonic-assisted memory unit's operation is based on a conceptually novel design for a 1-bit optical memory unit using an ultrafast photonic time integrator. For proof-of-concept implementation we used the setup shown in Fig. 17. The set and reset pulse were emulated using a photonic pulse shaper (in this example using a free space interferometer). The ultrafast memory unit was build based on a novel design for an ultrafast photonic temporal integrator: cascading three-stage interferometers with a designed fiber grating. Experimental results are shown in Fig. 18 confirming the proper operation of the proposed memory unit with an unprecedented switching time of ~1.4ps, i.e. memory speed of 700 GHz.
References: Hossein Asghari and Jose Azana, "Photonic integrator-based optical memory unit," IEEE Photonics Technology Letters, Vol. 23, pp. 209-211 (2011). (pdf) Hossein Asghari, Yongwoo Park, and Jose Azana, "New design for photonic temporal integration with combined high processing speed and long operation time window," Optics Express, Vol. 19, pp. 425-435 (2011). (pdf) Laser Focus World (LFW) magazine review: Click here Analog signal processing at the speed of light Photonic analog signal processing offers similar functionalities as in electronic signal processing but with speeds in 1,000 GHz range. To implement general and complex photonic signal processing circuits, basic photonic building blocks are demanded to be designed and demonstrated in photonic platforms. This is a primary step toward the practical realization of all-optical photonic signal processing circuits. These analog basic building blocks include photonic temporal integrator, differentiator and Hilbert transformer. A very relevant example of application of these fundamental devices is that of analog computing systems devoted to solving ordinary differential equations (ODEs). These equations play a central role in virtually any field of science or engineering, e.g., physics, chemistry, biology, economics, medical sciences, and the different branches of engineering. It is well known that linear ODEs can be solved in real time using a suitable combination of first- and higher-order temporal integrators, adders, and multipliers (amplifiers/attenuators) (see Fig. 19). The possibility of realizing these computations all-optically translates into potential processing speeds well beyond the reach of present electronic digital or analog computers.
We have pioneered the design and implementation of these photonic signal processing basic building blocks. Here I give more details about two of these devices, namely photonic temporal integrators and photonic Hilbert transformer. 1. Photonic Temporal Integrator An Nth-order temporal integrator (where N = 1, 2, 3 . . . refers to the integration order) is a device that calculates the Nth cumulative time integral of an input signal. Photonic temporal integrators compared with their electronic counterparts can provide much higher processing speeds. Photonic temporal integrators have already been proposed for various interesting applications, including optical signal characterization, ultrafast pulse shaping and all-optical memories. In some consecutive works, we have designed the first and higher-order integrators using fiber grating technology. We have also fabricated and tested these devices. The experimental setup to test these devices is shown in Fig. 20.
Experimental results are shown in Fig. 21. Accurate and efficient first and second-order temporal integrations of optical signals with 500 GHz bandwidth were successfully demonstrated using the fabricated fiber Bragg grating (FBG) devices.
References: Hossein Asghari, Chao Wang, Jianping Yao and Jose Azana, "High-order passive Photonic temporal integrators," Optics Letters, Vol. 35, pp. 1191-1193 (2010). (pdf) Hossein Asghari and Jose Azana, "On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings ," IEEE/OSA Journal of Lightwave Technology, Vol. 27, pp. 3888-3895 (2009). (pdf) Hossein Asghari and Jose Azana, "Proposal and analysis of a reconfigurable pulse shaping technique based on multi-arm optical differentiators ", Optics Communications, Vol. 281, Issue 18, 15, pp. 4581-4588 (2008). (pdf) Hossein Asghari and Jose Azana, "Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings ," Optics Express, Vol. 16, Issue 15, pp. 11459-11469 (2008). (pdf) Hossein Asghari and Jose Azana, "Proposal for arbitrary-order temporal integration of ultrafast optical signals using a single uniform-period fiber Bragg grating ", Optics Letters, Vol. 33, Issue 13, pp. 1548-1550 (2008). (pdf) Laser Focus World (LFW) magazine review: Click here 2. Photonic Hilbert Transformer A time-domain Hilbert transformer also referred to as a quadrature filter or a wide-band π phase shifter, is a device that calculates the Hilbert transform of an arbitrary input temporal signal (see Fig. 22). Hilbert transformers can be routinely implemented in the electronic domain, either as analog or digital filters, and they are fundamental devices for numerous applications, e.g. in communications, computing, information processing, signal analysis and measurement etc.. A similar range of applications could be expected for a photonic implementation of the Hilbert transformer, i.e. photonic Hilbert transformer (PHT), with the essential difference that such a device would enable processing signals directly in the all-optical domain and at speeds (operation bandwidths) well beyond the reach of electronic technologies.
We have proposed and demonstrated the first design for a photonic Hilbert transformer. We showed that a photonic Hilbert transformer can be implemented using a uniform-period fiber Bragg grating (FBG) with a properly designed amplitude-only grating apodization profile. Photonic Hilbert transformers capable of processing arbitrary optical waveforms with bandwidths in THz range can be implemented using readily feasible FBGs. The numerical results confirming the accurate operation of the designed photonic Hilbert transformer (PHT) are shown in Fig. 23.
References: Hossein Asghari and Jose Azana, "All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis ," Optics Letters, Vol. 34, pp. 334-336 (2009). (pdf) |
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