- Research
- Open Access
Carrier generation using a dual-frequency distributed feedback waveguide laser for phased array antenna (PAA)
- M. R. H. Khan^{1, 2}Email author,
- M. F. Islam^{1},
- G. Sarowar^{1},
- T. Reza^{1} and
- M. A. Hoque^{1}
https://doi.org/10.1186/s41476-017-0058-4
© The Author(s) 2017
- Received: 8 May 2017
- Accepted: 16 October 2017
- Published: 27 October 2017
Abstract
Background
Carrier generation based on optical heterodyning techniques where a beat signal is generated from the mixing of two light sources can be interesting solution due to ease on tunability. The free running heterodyning scheme benefits with a very wide tuning capability and the generated carrier can be freely adjusted. However, the drawbacks come in the form of frequency stability. Heterodyning of two optical frequencies coming from a single laser cavity has shown its potential on improvement of frequency stability.
Methods
The impact of the laser parameters (i.e., optical power and linewidth) on the quality of the generated carrier (i.e., phase/frequency stability and carrier-to-noise ratio) is analyzed for a 25×64 elements PAA system. An optically generated carrier signal using a dual-frequency distributed feedback waveguide laser in ytterbium doped aluminum oxide (Al_{2}O_{3}:Yb^{3+}) is analyzed and experimentally demonstrated in this paper. The carrier signal is used for downconversion of the signal received from a phased array antenna (PAA) of a DVB-S (Digital Video Broadcasting-Satellite) system.
Results
An optical frequency locked loop (OFLL) to stabilize the generated carrier is implemented which results in a microwave frequency at ∼14 GHz with a phase noise of -75 dBc/Hz at 1 MHz offset from the center frequency and gives a loop settling time of 12 μs. By using the proposed OFLL, the long term and the short term frequency stability of the generated carrier has an Allan deviation of more than 1×10^{−10} for an averaging time of 1000 s and a standard deviation of 39.4 kHz, respectively. The lasers linewidth should be in the order of tens of Hz, with a maximum relative intensity noise (RIN) of -107 dB/Hz and a minimum optical power of 0.94 mW.
Conclusions
The optical carrier generation by OFLL using a DFL to comply with the requirements of the standard carrier used in commercial LNBs has been investigated. The detailed analysis of the OFLL scheme is presented. Specifications requirement on carrier power, linewidth and relative intensity noise of the optically generated carrier have been addressed. The optical carrier generation is experimentally demonstrated and the requirements on CNR have been determined by measuring the noise floor and the optical carrier power. The measured values are compared with the calculated values and found to be very close.
Keywords
- Phased array antenna
- Optical heterodyning
- Carrier generation
- K _{ u }-band
- Laser linewidth
- Stability
- Optical frequency locked loop (OFLL)
- Dual frequency laser (DFL)
Background
The application of phase array antennas (PAA) to many satellite services, ranging from digital radio and TV broadcasts to broadband internet services, has been increasingly addressed in the last few years [1, 2]. Potential applications especially regard mobile environments (cars, trains, boats, airplanes). A PAA is a set of multiple antennas, called antenna element (AE). Modern PAA consists of a large number of small antenna elements (AEs) and it can achieve the same gain of a large mechanically steerable antenna [3]. Recently, the use and advantages of PAA system for satellite communications systems have been thoroughly described in literature [4–6]. When installed on a vehicle a PAA system can be an advantageous solution for receiving satellite signals due to the flatness of its shape hence provides low aerodynamic profile [2] and to the fact that it can be electronically beamsteered, not requiring continuous mechanical realignment. Additional to that are the possibilities for beam-shaping, tracking and multi-beam reception [7].
The satellite signal received by the AE of the PAA is downconverted into lower frequency to ease on amplification and further processing. Downconversion is done by mixing the received signal with a carrier signal at an RF mixer placed at each AE. To maintain phase synchronization among the carrier signals, the distribution of carrier signal from a central source is essential. The distribution of carrier signal by means of coaxial cable or waveguide is limited by the transmission line losses and their bulk size. Photonics offer an interesting alternative because these systems take advantage of the extremely low transmission and distribution losses 0.2 dB/km in 1.5 μm and 1 dB/km in 1 μm of the standard single-mode fiber (SMF). In addition to that, optical fiber cables are compact, lightweight and provide wide bandwidth and immunity to electromagnetic interference [8]. This approach has been proven as a successful solution in many deployed systems for instance radio-astronomy [9, 10] and satellites for remote sensing [11]. In order to use an optically generated carrier in a satellite reception system it must meet the criteria of that of the specifications given for commercially available electronic carrier. The crucial challenge for optically generated carrier is to meet the requirements in term of low phase noise, low drift, carrier-to-noise ratio (CNR) and wide tunability [12].
One of the methods to optically generate microwave carriers is to use optical heterodyning. In heterodyning between two separate single frequency lasers, all the phase noise from each laser is directly transferred into the microwave carrier [13]. Moreover, such scheme is rather bulky and suffers from large frequency drift of the microwave carriers. Heterodyning of two optical frequencies coming from a single laser cavity has shown its potential on improvement of frequency stability [14]. In this regard a dual-frequency laser (DFL) is interesting as the relative fluctuations between the two frequencies are low and can be used to generate a low-phase-noise microwave carrier due to the common-mode noise rejection effect [13, 15–17].
In this paper we consider an optically generated carrier based on heterodyning of a dual-frequency laser reported recently [14]. This laser is in ytterbium-doped aluminum oxide (Al_{2}O_{3}:Yb^{3+}) fabricated on a silicon substrate, which shows great potential for the monolithic integration of optically generated microwave sources. Here we present an efficient technique to lock a dual-frequency (Al_{2}O_{3}:Yb^{3+}) DFB channel waveguide laser using an OFLL in order to improve the free-running frequency and power stability of the optically generated carrier, while also reducing the phase noise. This approach is promising in terms of compactness, low phase noise and high stability. This paper demonstrates the feasibility of such a system to provide carrier signals.
The remainder of the paper is organized as follows. In “Methods” section, the proposed optically generated carrier for PAA system using a DFL is described and analyzed for the carrier generation criteria. “Results and discussion” section presents performance of the generated carrier. In the last section, the conclusions of this analysis are stated.
Methods
System description
Since the received signal power density from the satellite is relatively low, the antenna should have a high gain and a low noise temperature to achieve the required CNR for K _{ u }-band satellite signals. This dictates a number of antenna elements of at least 1600 [1]. Those can be placed as 25 tiles of 64 AEs. More details of this PAA system have been described in [1]. In this paper we restrict ourself to the downconversion system of the DVB-S reception. The proposed downconversion system consists of a PAA, an optical distribution network (ODN) and the optical heterodyning scheme.
As a basic building block, we consider an 8 ×8 antenna tile consisting of 64 antenna elements (AEs), shown in Fig. 1 a. The DVB-S signal received by each AE will be amplified by a low noise amplifier (LNA) and downconverted at the mixer using a centrally generated carrier signal.
The carrier is generated optically and also distributed by an optical distribution network (ODN) in order to take advantage of low loss distribution by means of standard single-mode fiber. Shown in Fig. 1 b, the ODN is implemented in conjunction with an individual photodetector (PD) at each antenna tile. The carrier signal at the output of each PD is then distributed to each mixer.
The optical heterodyning system that generates the carrier signal is shown in Fig. 1 c. The DFL laser produces a beat frequency of ≈14 GHz at the output of the PDs. This enables downconvertion of 10.7 GHz to 12.75 GHz DVB-S signal to a required intermediate frequency (IF) of 950 MHz - 2150 MHz. The frequency stabilization of the optically generated carrier is accomplished by an optical frequency lock loop (OFLL) explained in detail in “Stabilization of optically generated carrier signals” section.
Dual frequency laser characteristic
where c is the speed of light, L is the distance between the two phase shifts and n is the effective refractive index of the guided mode. This implies that the beat frequency can be scaled to higher frequencies by reducing L. However, the stop band of the Bragg grating in the device has a width of approximately 30 GHz, which poses an upper-limit to the frequency separation of the two optical carriers, and thus the beat frequency, which can be generated with the current grating design.
When both phase shifts are varied symmetrically from a quarter-wavelength phase shift π/2, such that one has a value of π/2−Δ θ and the other π/2+Δ θ, then the two resonant wavelengths separate symmetrically from each other with respect to the Bragg wavelength, while they remain equivalent in terms of their amplitude and line width. In other words, the value of Δ θ can be used to increase the frequency spacing between the two resonances as compared to the frequency spacing given by Eq. (1).
Making use of standard lithography and a chlorine based reactive ion etching process, 2.5 μm wide waveguides were fabricated in an Al_{2}O_{3}:Yb ^{3+} waveguide layer with an ytterbium concentration of 5.8×10^{2} cm ^{−3}, after which the waveguide layer was overgrown with a plasma enhanced chemical vapour deposited SiO_{2} cladding layer. A 10 mm long surface corrugated Bragg grating was defined by means of laser interference lithography and etched into the top surface of the SiO_{2} layer with reactive ion etching. The detail process of fabricating the waveguide is explained in [14]. In order to realize the two required quarter-wavelength phase shifts, two sections with 2 mm long adiabatic sinusoidal widening of the waveguide width are fabricated [20]. The two quarter-wavelength phase shifts are centered at 4.5 mm and 6.5 mm respectively (as measured from the pumped end facet of the 1 cm long cavity). Based on coupled-mode theory, where the grating reflectivity at the Bragg wavelength is given by R=tanh^{2}(κ L), where κ L is the dimensionless quantity express the grating strength [21]. Each of the bragg reflectors was designed to have a grating coupling coefficient of k=6 cm^{−1}. Fabrication of the waveguide and Bragg gratings is described in detail in [14].
where f _{L} and f _{R} are the relaxation oscillation frequencies of the two respective longitudinal modes with f _{L}<f _{R}. The value of C _{lamb} indicates whether there exists weak (C≈0) or strong (C≈1) mode competition between the two oscillating wavelengths. By using the measured relaxation oscillation frequencies as shown in Fig. 6, the value of C could be determined. Just above threshold of the second mode, (C>0.5), indicating a relatively strong interaction and mode competition between the two longitudinal laser modes close to threshold. However, with increasing pump power C _{lamb} converges to a value of C _{lamb} = 0.23, indicating that the mode competition is rather weak, since each longitudinal mode was being amplified mostly by separate sections of the active medium. The weak longitudinal mode interaction was confirmed by the longitudinal field overlap between the two modes (Fig. 2), which was calculated to be 0.34 [14]. Moreover, for a period of 45 min the power of the microwave signal was stable within ± 0.35 dB [14].
The optical spectrum of the DFL is measured by an optical spectrum analyzer (OSA) (ANDO AQ6317) is shown in Fig. 4 b. This optical spectrum was measured at a pump power of 35 mW.
Optical carrier generation
where the beat linewidth of the optically generated carrier, Δ υ _{LO}=Δ υ _{1}+Δ υ _{2} is equal to the sum of the two linewidths of the lasers [27, 28]. The PSD of the optically generated carrier is a Lorentzian centered at f _{LO}. Due to the laser phase noise, the spectral linewidth of the laser broadens into a Lorentzian shape and ultimately broadens the linewidth of the optically generated carrier.
Criteria for the optically generated carrier
Carrier specifications for DVB-S receiver
Carrier Parameters | Values |
---|---|
Frequency range | 9.75 GHz or 10.6 GHz |
Single sideband | − 50 dBc/Hz @ 1 kHz |
(SSB) phase noise | − 70 dBc/Hz @ 10 kHz |
− 90 dBc/Hz @ 100 kHz | |
− 110 dBc/Hz @ 1 MHz | |
Frequency drift | 5 MHz |
Linewidth criteria of optically generated carrier
Close to the carrier frequency, the performance of the generated carrier is determined by the linewidth of the optical carrier. The ratio between Eqs. (4) and (5) gives the single sideband (SSB) phase noise expressed in dBc/Hz [30]. Calculating the SSB phase noise curve for various offset frequencies and comparing it to the values from Table 1, one can determine the linewidth of the optical carrier to match the DVB-S requirements. It is evident that the parameters in Table 1 shows a Lorentzian decay of the SSB phase noise.
Carrier-to-noise ratio criteria of photonic carrier
Beyond 1 MHz offset frequency from the carrier, it is the noise floor that determines the system performance. To analyze the impact of noise in this heterodyning system, it is useful to consider all noise sources in the photonic system. The system is affected by noise, comprising thermal noise, shot noise and relative intensity noise (RIN).
According to the carrier specifications in Table 1, at 1 MHz offset frequency the generated carrier signal has to have less than -110 dBc/Hz phase noise. To keep this value for the optically generated carrier the noise floor must not exceed this limit. To maintain a noise floor of 110 dB below the carrier power, i.e., CNR, a minimum carrier power is required. Equation 5 shows that the minimum carrier power ultimately sets the minimum laser power in the heterodyning operation.
Stabilization of optically generated carrier signals
Several investigations and experiments show that the beat signal generated by a free-running heterodyning system suffers substantial frequency drift [16]. The frequency of a laser generally drifts hundreds of MHz in an ordinary environment [31]. According to the DVB-S specification [29], the maximum allowable frequency drift of the generated carrier is 5 MHz [32]. Therefore, the optically generated carrier needs to be frequency stabilized.
Optical frequency locked loop schemes
Proposed optical frequency locked loop scheme
The high-frequency terms (2^{nd} and successive terms between the brackets) are eliminated by the cut-off frequency of the current controller, f _{c}, of the pump laser given as 100 kHz^{1} which is lower than that of the 10 MHz of the LPF. In this case the current controller of the pump laser will ultimately dictate the frequency response and bandwidth of the feedback loop.
Characterization of the components
From the schematic of the proposed OFLL (in Fig. 7), one can notice that the dynamics of the loop will be influenced by the characteristics, namely the frequency response and the conversion factor, of the various components used in the loop. In this section the characteristics of the FVC is investigated.
The purpose of the RF discriminator used in the OFLL is to convert the frequency to its input to a proportional voltage. The frequency-to-voltage conversion factor, K _{FVC}, for the frequency discriminator is maximum at the closest nulls to the reference frequency (point A and B in Fig. 8). From Eq. (9), a higher delay will reduce the frequency offset of the null from the reference frequency and will increase the slope at the nulls which ultimately will give a higher conversion of K _{FVC}. The error signal at the output of the low pass filter (LPF) is sent to the pump laser (976.18 nm) in order to control its current and, consequently, the optical pump power. A change in the pump power changes the thermally induced chirp in the Bragg grating, which, in turn, changes the frequency separation between the two laser modes. The commercial pump laser current controller (Thorlabs PRO8000) of the DFL has an external tuning port having a voltage-to-current conversion factor of 200 mA/V. For the pump powers at which the DFL operates, the optically generated microwave carrier increases linearly with pump current at a rate of 180 kHz/mA. This gives a voltage-to-frequency conversion, K _{DFL}, of 36 kHz/mV in Fig. 7.
Various loop parameters
Parameter | Value | Dimension | Notation |
---|---|---|---|
Responsivity of the PD | 0.4 | A/W | r _{pd} |
Conversion loss of the mixer | − 5.5 | dB | K _{mix} |
Total gain of the RF amplifiers | variable | dB | K _{a} |
Frequency-to-voltage conversion | 0.15 | mV/MHz | K _{FVC} |
factor of the RF discriminator | |||
Cut-off frequency of the current | 100 | kHz | f _{c} |
controller of the pump laser | |||
Voltage-to-frequency conversion | 36 | MHz/mV | K _{DFL} |
factor of the current controller |
Optical frequency lock loop analysis
The proposed OFLL in Fig. 7 a can be represented in a generic model for a feedback system and presented as Laplace domain (s-domain) representation [37] of OFLL in Fig. 7 b.
In Fig. 7, the optical and the electrical connections are represented by dotted and solid lines, respectively. The optical field from the DFL is represented by E _{L}. The gain of the PD can be defined as K _{pd}=r _{pd} where r _{pd} is the responsivity of the PD. The output beat frequency from the PD is mixed with a reference frequency, f _{Ref}. The RF mixer has a conversion loss of K _{mix}. The downconverted signal is then amplified by an RF amplifier with a gain of K _{a}. An RF frequency discriminator converts the frequency to its proportional voltage with a conversion factor of K _{FVC}. The error voltage is passed through a LPF to filter out the high frequency components and is then applied to the current controller of the pump laser. The pump laser acts as a current-controlled oscillator and the change in output optical power is a function of the frequency components of the input current modulation. The frequency response of the current controller is indicated by F _{FM}(f) and its Laplace transform is denoted by F _{FM}(s). The external voltage-to-optical power conversion factor is denoted by K _{SL}. As the bandwidth of the current controller will dominate in the loop so its frequency response will be considered in the s-domain model.
Results and discussion
In this section we will present the experimental results on various performance criteria of an optically generated carrier, namely the long term frequency stability, the short term frequency stability, loop response and the phase noise.
Long term frequency stability
where y _{ i } is the i ^{th} of M fractional frequency values averaged over the measurement (sampling) interval, τ.
The Allan deviation for the free-running condition increases from 3.5 ×10^{−10} at an averaging time of τ=1 s to 5 ×10^{−9} at an averaging time of τ=1000 s. However, the long-term frequency stability of the DFL could be improved to a value of 1×10^{−10} for an averaging time, τ, of 1000 s by implementing the OFLL. These results emphasize the effectiveness of using the OFLL for improving the long-term stability of the free-running microwave carrier by a 50 fold improvement in the frequency stability at 1000 s averaging time. The long-term frequency stability of the OFLL shows batter performance than a typical quartz oscillator (Wenzel 501-04623E) having a frequency stability of Allan deviation of 4×10^{−7} [39]. Moreover, this performance is also comparable to recently reported radio frequency (RF) clock signals transmission over 100 m via fiber link results in an Allan deviation of 1.31×10^{−10} for an averaging time of 1 s [40].
Short term frequency stability
In addition to the requirement of long term frequency stability for the application like RF clock/reference signal transmission, radio astronomy or microwave carrier generation and distribution of a PAA, these applications also require very good short-term frequency stability [41]. The improvement of the short-term frequency stability also improves the phase noise performance of the generated carrier [42]
The procedure of producing such a spectrogram is as follows. The microwave carrier at the output of the photodetector was mixed with a high-purity, stable RF reference signal produced by a vector signal generator (Agilent PSG E8267D) with a sub-Hz line width, which was produced by a microwave carrier generator. This reference signal was set within a few MHz offset of the 14.21 GHz microwave beat signal produced by the DFL. Since the reference signal was much narrower than the laser beat signal, mixing of the two signals produced a convoluted signal which was nearly identical in shape to the original microwave beat signal produced by the DFL, but shifted to the MHz range, so that a time trace of this down converted signal could be measured with an oscilloscope (Agilent infinium 54854A). A Discrete Fourier transformation (DFT) over duration of a short time frame (μs) was then performed on that time trace of the down-converted signal [13], This will give the frequency spectrum of the time domain signal, with various center frequency due to short time drift. By plotting these center frequencies as a function of time a graph called spectrogram can be produced.
Loop response
From Eq. (11) and (12) we calculate the natural frequency f _{n}=200 kHz and damping factor ζ=0.7 for a loop gain, K _{a}, of 3 dB. From Eq. (11) and (12) it is noticed that an increase of gain will increase the loop natural frequency but will decrease the damping factor. These phenomena can be observed in Fig. 15. For example, with K _{a}=5 dB and K _{a}=1 dB the natural frequency and the damping factor become f _{n}=350 kHz, ζ=0.4 and f _{n}=50 kHz, ζ=1, respectively.
With the help of Eq. (10) we also calculated the step response of the loop using the above values of natural frequencies and damping factors. As the input of the system is an unit impulse the stabilization can be thought of as the response to a brief external disturbance. As shown in Fig. 15 b, at a brief external disturbance the OFLL stabilizes in 12 μs for ζ= 0.7. With lower and higher damping factor the loop experiences more and less oscillation, respectively, before its stabilizes. For instance, with both ζ= 0.4, and ζ= 1, the OFLL stabilizes in 14 μs as shown in Fig. 15 a and 15 c, respectively. These experimental values are in good agreement with the calculated values. From this result it is clear that the loop response time depends on the value of the damping factor, ζ, and its proper choice depends on the values of gain and natural frequency.
Phase noise of the generated carrier
Besides improving the frequency stability, a degree of phase-noise reduction can be achieved by implementing the OFLL using the DFL. From Leeson’s well known phase noise model for oscillator [43], random walk of frequency noise is usually very close (< 100 kHz offset) to the carrier [44]. It is usually related to the oscillator’s physical environment (mechanical shock, vibration, temperature, or other environmental effects) [44]. It has been reported previously that the low frequency noise (< 100 kHz offset) can be compensated by locking the microwave carrier generated from a laser to an ultra-low noise RF oscillator [45, 46]. Thus an OFLL can optimize this noise effect due to environment [45].
As demonstrated in Fig. 15, the measured and calculated response of the OFLL is found to be optimized for ζ=0.7 and used for frequency stabilization of the OFLL. With ζ=0.7 the loop stabilizes in 12 μs. This provides a loop speed of 80 kHz. This ultimately means that the OFLL could improve the laser phase noise below an offset frequency of 80 kHz from the carrier.
Noise analysis
The optical power from the pump laser was injected into the DFL and then its output was passed through the VOA before inserting into the PD. The VOA was varied from 0 dB to 60 dB with a small step and for each step the total noise power spectral density (PSD) was measured with the RF-SA using the noise marker. The marker was positioned at the frequency of 3.8 GHz^{2} and the noise was measured in a 10 kHz noise bandwidth. The marker gave the measured noise power normalized in 1 Hz bandwidth, i.e., in dBm/Hz. Due to high displayed average noise level (DANL) of the RF-SA used in our noise measurement a low-noise RF amplifier (LNA) was used to overcome the dominate noise of the RF-SA over the noise floor of the DFL. The LNA amplified the noise from the DFL above the DANL. However, the LNA itself contributed to an additional noise to the measurement. As a result, the measured noise power consists of both the amplified noise of the DFL by the LNA gain and noise from the LNA itself.
In the equation above, k is the Boltzmann constant and T=290 K. The noise factor is related to the noise figure via the relation NF _{LNA}=10 log10F _{LNA}.
The optical spectrum of the DFL was measured by an optical spectrum analyzer (OSA) (ANDO AQ6317) with a resolution of 0.01 nm and is shown in Fig. 4 b. This optical spectrum was measured at a pump current of 0.8 A. The two optical modes contain an optical power of P _{L1}=−17.5 dBm (17.8 μ W) and P _{L2}=−6 dBm (251 μ W), respectively. The total measured optical power using an optical power meter was P _{T}=−5.7 dBm (0.27 mW). The photo-current, I _{av}, and the RF carrier power, P _{LO}, can be calculated by using the measured values of optical power using Eq. (5) and (6), such as I _{av}=0.11 mA, P _{LO}=−41 dBm and the total optical power, P _{T}=0.27 mW. The responsivity of the PD (r _{pd}) as 0.4 A/W and R _{L}=50 Ω is considered.
As stated earlier, the phase noise is plotted in the decibel scale. To make better comparison between the phase noise and the noise floor of the heterodyning system, the noise floor needs to be plotted on same scaling as that of the phase noise. In order to express the noise power in decibel scale, the Fig. 18 a is re-plotted with reference to the optically generated LO power (in Fig. 4 a) in Fig. 18 c. Hence, the PSD plot in dBm/Hz of Fig. 18 a will be transformed to PSD plot in dBc/Hz as a function of the average photo-current. Given in Table I, at 1 MHz offset frequency the generated LO should maintain a phase noise of − 110 dBc/Hz, this means the noise floor of the system should be below − 110 dBc/Hz. It is evident from Fig. 18 c that at an average photo-current of 0.03 mA and above, the DFB laser with any RIN value will keep the total noise floor much below of − 110 dBc/Hz.
As the optical power needs to be distributed to each PD of 25 tiles in the PAA, the minimum optical power of each laser required for 25 tiles is 1 mW (0.04 mW ×25). Finally, the RF output of the PD will be distributed to 64 AE’s of each tile, and should be amplified by individual RF amplifier if necessary. Having a minimum optical power of 1 mW from a laser with a RIN of − 122 dB/Hz, the total noise floor will be below -110 dBc/Hz. This will satisfy the minimum CNR of 110 dB. All these parameters will ensure the optically generated LO which will maintain a phase noise of -110 dBC/Hz at 1 MHz offset frequency from the carrier frequency.
Conclusions
In the past years, reports on microwave carrier generation by using a DFL were mainly focused on very low phase noise [48, 49] or large tunability [15, 50]. However, there seems to be very little attention to some crucial requirements of the generated carrier, namely its short term as well as long-term frequency stability. Our OFLL clearly addresses this crucial requirement by achieving a frequency stability of 1×10^{−10} for averaging time of 1000 s. At very short time iteration standard deviation for the OFLL was very low. With increase of iteration duration the locked frequency the standard deviation shows little change and close to within 40 kHz. By employing an OFLL the standard deviation of the frequency stability of the generated carrier was improved by 70 fold. Loop response time (settling time) comparison on calculated and measured values for various damping factors are also presented. These experimental values are in good agreement with the calculated values. The total noise power and individual noise contributions from the stable generated carried is also investigated. It is observed that the total noise floor is dominated by the relative intensity noise (RIN) contribution. A stable carrier of 14.21 GHz is observed with a phase noise of − 75 dBc/Hz at 1 MHz frequency offset. Since our DFL has great potential for integration with generic silicon-based photonic platforms, it paves the way for microwave generation on a hybrid integration platform. An integrated OFLL will be less affected by the overall environmental noise because of its reduced footprint [51], thus promising an even higher stability. The demonstrated system has a great potential to be used in application on generation and distribution of highly stable reference signal such as ALMA or space navigation tracking in the NASA Deep-space Network (DSN).
Endnotes
^{1} This value is taken from the data sheet of commercial current controller (Thorlabs PRO8000) of the pump laser.
^{2} The RF-SA (Agilent MXA N9020A) used in this setup gives the lowest noise floor at this frequency.
Declarations
Acknowledgements
The authors gratefully acknowledge the support of the Smart Mix Programme of the Netherlands Ministry of Economic Affairs and the Netherlands Ministry of Education, Culture and Science.
Funding
Not applicable.
Authors’ contributions
The original idea, mathematical framework, experiment and simulation model were developed by the first author. The second and third authors worked on the simulations and evaluation. The fourth author supervises the experimental and simulation work. The fifth author conducted the characterization of the DFL and helped to draft the manuscript. The progress is a result of common contributions and discussions. The authors also gave final approval of the version to be submitted. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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