DEVICE FOR BROADBAND SPECTRAL ANALYSIS OF A SIGNAL

Description

Technical field :

[0001] The invention relates to the field of analog processing of optical and radiofrequency signals, and more particularly to the analog processing of wideband optical and radiofrequency signals using frequency-shifting optical cavities. Previous technique :

[0002] Knowledge of the spectrum of a signal of interest is essential in many applications such as spectrometry, electromagnetic compatibility, transmitter location and signal interception, navigation, and geophysical and astronomical observation.

[0003] In the optical domain, spectral analysis is typically performed by three types of devices.

[0004] A first solution is to diffract the optical signal by a grating. The far-field illumination gives the spectrum. These grating spectrometers are widely used because of their simplicity and low cost. However, their frequency resolution is no better than tens of GHz.

[0005] Another technique providing better spectral resolution (a few GHz) is Fourier Transform (FT) spectral analysis, which uses a Michelson interferometer. The delay of the interferometer varies over time, thanks to a mirror mounted on a moving carriage. The fringes are recorded over time (i.e., the interferogram). A FT operation then provides access to the spectrum. This is the basic principle of commercial OSA ("optical spectrum analyzer"). The limitations of this device are twofold: the spectral resolution is given by the maximum path difference of the interferometer. In practice, this resolution is of the order of GHz. In addition, the time required to measure a spectrum is of the order of a second. The technique is therefore reserved for sufficiently long optical signals, or whose spectrum is constant over time.Indeed, the probability of interception or POI (i.e. the probability that a signal is actually measured by the spectral analyzer) of such a device is low.

[0006] A third technique is heterodyne spectral analysis. This technique has a spectral resolution of a few MHz and allows for the measurement of spectra with high resolution. It involves using a continuous laser with a narrow linewidth (sub MHz) and scanning it in frequency. The amplitude of the heterodyne beat at a given frequency of this laser with the optical signal to be analyzed during the frequency ramp therefore provides the spectrum of the latter. However, this technique is expensive, requires a reference laser, and has a low POI.

[0007] In the field of radio frequency (RF) signals, current commercial solutions for RF signal spectral analysis are of two types: real-time spectrum analyzers and scanning analyzers.

[0008] The scanning analyzer works by comparing (heterodyning) the SUT (signal under test) with a reference signal whose frequency is varied over time (for example, by a frequency ramp). It can measure spectral widths greater than 20 GHz. However, due to the duration of the frequency ramp, this technique only detects a very small part of the spectrum at any given time. For the scanning analyzer, the POI is typically 1%. It is therefore not suitable for analyzing brief signals or signals whose spectrum varies over time.

[0009] Real-time analyzers combine a signal acquisition step, called analog-to-digital conversion, and a digital calculation step (Fourier transform). The first step is particularly critical for the fidelity of the process: the SUT must be sampled twice as fast as its maximum frequency (Nyquist criterion). A sampling rate that is too low therefore results in a loss of information from the SUT's high frequencies. However, the sampling frequency of analog-to-digital converters is intrinsically limited to a few GS / s. Consequently, the best real-time spectrum analyzers cannot achieve spectral widths greater than 1 GHz. They also require very significant computing resources to perform the spectrum calculation in real time. DURAN V ET AL: "Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs", ARXIV.ORG, CORNELL UNIVERSITY LIBRARY, 201 OLINE LIBRARY CORNELL UNIVERSITY ITHACA, NY 14853, March 20, 2018 discloses prior art.

[0010] Furthermore, the paper "Hugues Guillet de Chatellus, Luis Romero Cortés, and José Azaña. "Optical real-time Fourier transformation with kilohertz resolutions." Optics 3.1 (2016): 1-8”, describes a device comprising a frequency shift loop into which a signal of interest is injected. The device described in this document makes it possible to generate at the output a time signal reproducing the spectrum of the input signal, provided that f 1 t 1 is an integer with f 1 the offset frequency of the signal of interest per round trip in the loop and t 1 the duration of a round trip of the signal of interest in the loop. The figure 1schematically represents the device described in the aforementioned document. The device comprises a source S0 generating an optical signal or an RF signal carried by (i.e. amplitude modulated by) an optical signal, so as to form a signal of interest. By "carried by" is meant here and in the remainder of the document that the carrier signal is amplitude modulated by the modulating signal. This signal of interest is injected into the fibered frequency shift loop BDF0 via a fibered coupler C0. The loop BDF0 comprises a frequency shifter AOM0 (for example an acousto-optic modulator) adapted to shift the optical frequency of the signal by a frequency f1 per round trip in the loop. The loop BDF0 further comprises an amplifier EDFA0 (for example a doped fiber amplifier such as an EDFA, for Erbium Doped Fiber Amplifier) ​​to compensate for the losses induced by the loop and an optical bandpass filter BP0 to limit the noise coming from the amplified spontaneous emission of the amplifier and to fix the number of round trips in the loop. The radiation transmitted by the loop is detected by a photodiode PD0 generating a photocurrent which is filtered by an analog low-pass filter LP0 adapted to keep only frequencies of the photocurrent lower than the Nyquist frequency of the signal of interest. A processor UT is configured to calculate the square modulus of the photocurrent. When f 1 t1 is an integer, the time trace obtained after processing the photocurrent by the processor is the power spectrum of the optical signal in the case where the signal of interest is an optical signal or the power spectrum of the RF signal in the case where the signal of interest is an RF signal carried by a coherent optical signal.

[0011] This system has significant technological limitations. First of all, the spectral width of the signal of interest must be less than 1 / t 1 (i.e. of the order of 10 MHz), which severely limits practical applications. Here, it is not possible to increase t 1 in order to achieve a bandwidth of the order of tens of GHz, because of the complexity and propagation losses that this would entail. The other constraint is that the period of the output signal (the spectrum) is worth 1 / f 1, which requires sampling the output signal at Nf1, that is to say a few tens of Gs / s (taking N = 300 and f 1 = 80 MHz).

[0012] Furthermore, the prior art device of the figure 1 allows to calculate the fractional Fourier transform of a signal of interest when f 1 t 1 is close to an integer. This property is described in the paper: Côme Schnébelin and Hugues Guillet de Chatellus, "Agile photonic fractional Fourier transformation of optical and RF signals," Optica 4, 907-910 (2017). The fractional Fourier transform (FFT) is a generalization of the Fourier transform (FT) to any intermediate domain (called fractional) between direct space and Fourier space. This transformation can be thought of as a rotation in the time-frequency domain. By writing the classical Fourier transform of a function f in the form F π 2 f we can generalize this writing for any fractional order α . The fractional Fourier Transform (FFT) of order α will therefore be: F α ( f ). TFFr is relevant for analyzing input signals whose frequency varies linearly with time (linear frequency modulated signals, or "chirps").

[0013] For α = 0, we find the identity operator and the result would give the function f. For α = π / 2, we find the classical Fourier transform. For α ∈ ℝ and with u the variable in the arrival domain called fractional domain, the TFFr of order α of the function f can be expressed in the form: F α f x u = 1 − icot α e iπ cot α u 2 ∫ − ∞ + ∞ e − i 2 π csc α ux − cot α 2 x 2 f x dx

[0014] The invention aims to overcome some of the aforementioned problems of the prior art by proposing a device for spectral analysis of a broadband signal of interest using two frequency-shifted cavities. Summary of the invention :

[0015] For this purpose, an object of the invention is a wideband device for spectral analysis of a signal of interest comprising: a source adapted to generate said signal of interest; an optical splitter element adapted to spatially separate said signal of interest into a first signal and a second signal; a first optical frequency shift cavity comprising a first frequency shifter adapted to shift the optical frequency of the first signal by a first frequency f 1 by round trip in said first cavity, said first cavity having a first travel time t1; a second optical frequency shift cavity comprising a second frequency shifter adapted to shift the optical frequency of the second signal by a second frequency f 2 by round trip in said second cavity, said second cavity having a second travel time t 2; the first and second optical cavities being adapted so that a maximum number of round trips of said signal in the first and second cavities is equal to N predetermined; a detector adapted to coherently detect the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generate a photocurrent proportional to a light intensity detected by said detector, a low-pass filter adapted to filter frequencies of the photocurrent lower than min f 1 2 f 2 2 , a processor configured to calculate a square modulus of the photocurrent filtered by said low-pass filter, from which a temporal representation of frequency information of said signal of interest is determined.

[0016] According to particular embodiments of the invention: said source comprises a monochromatic continuous laser, an RF source adapted to generate an RF signal s(t), and a modulator adapted to modulate in amplitude or in phase, by said RF signal s(t), laser radiation generated by said continuous laser, so as to form said signal of interest; the first cavity and the second cavity are configured to verify the condition f 1 × t 1 ≠ f 2 × t 2, said frequency information then being a real part of a fractional Fourier transform of said signal of interest, an order of said fractional Fourier transform being fixed by the value f1 × t 1 - f 2 × t 2; first cavity and second cavity are configured to check the condition f 1 × t 1 = f 2 × t 2 modulo 1, said frequency information then being a power spectrum of said signal of interest; the analog low-pass filter is adapted to filter frequencies of said photocurrent lower than min[ N × | f 1 - f 2 | ; f 1 / 2 ; f2 / 2]; the first and second cavities respectively comprise a first and a second amplifier adapted to compensate for the losses induced respectively by the first and second cavities, the first frequency shifter is a first acousto-optic modulator excited by a first local oscillator adapted to vary said first offset frequency and in which the second frequency shifter is a second acousto-optic modulator excited by a second local oscillator adapted to vary said second offset frequency; the first cavity comprises a first controllable delay line adapted to vary the first travel time t 1 and wherein the second cavity comprises a second controllable delay line adapted to vary the second travel time t2; the first and second cavities are ring fiber cavities comprising respectively a first and a second doped fiber amplifier and a first and a second optical bandpass filter configured to fix said maximum number N of round trips in the first and second cavities; the device comprises means for stabilizing the first and second cavities adapted to maintain over time the coherence of said first signal transmitted by the first cavity with said second signal transmitted by the second cavity;the device comprising a single ring cavity, said device further comprising: a first coupler adapted to inject said first signal into said single cavity in a first direction, a second coupler adapted to inject said second signal into said single cavity in a second direction, said first cavity corresponding to the single cavity into which the first signal is injected in the first injection direction, said second cavity corresponding to the single cavity into which the second signal is injected in the second injection direction. said single ring cavity comprising: a first circulator adapted to direct the first signal to a first controllable delay line and adapted to vary the first travel time; t1 and comprising said first frequency shifter, a second circulator adapted to direct the second signal to a second controllable delay line and adapted to vary the second travel time t 1 comprising said second frequency shifter, a doped fiber amplifier, a bandpass optical filter configured to fix said maximum number N of round trips, the first and second cavities are configured so that 1 τ 1 − τ 2 ≥ 40 GHz ; the first and second cavities are configured so that N is greater than 200;

[0017] Another object of the invention is a method for spectral analysis of a signal of interest using a first optical frequency-shift cavity comprising a first frequency shifter having a first travel time t 1 and a second frequency-shifting optical cavity comprising a second frequency shifter having a second travel time t2, a maximum number of round trips of said signal of interest in the first and second cavities being equal to N predetermined, said method comprising the following steps: A. generating said signal of interest; B. spatially separating said signal of interest into a first signal and a second signal; C. injecting said first signal into the first optical frequency-shifting cavity and shifting the optical frequency of the first signal by a first frequency f 1 by round trip in said first cavity; D. injecting said second signal into the second optical frequency shift cavity and shifting the optical frequency of the second signal by a second frequency f2 by round trip in said second cavity; E. coherently detecting the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generating a photocurrent proportional to a detected light intensity, F. filtering frequencies of the photocurrent lower than min f 1 2 f 2 2 , G. calculate a square modulus of the filtered photocurrent and determine a temporal representation of frequency information of said signal of interest

[0018] According to particular embodiments of the method of the invention: the method comprises a step prior to step A, denoted step A0, consisting of adjusting the first or the second cavity in order to fix the difference f 1 × t 1 - f 2 × t2 on a desired non-zero value, in order to calculate, in step G, a specific order of a real part of a fractional Fourier transform of the signal of interest, the method comprises a step prior to step A, denoted step A0 consisting of adjusting the first or the second cavity in order to cancel the difference f 1 × t 1 - f 2 × t 2, in order to calculate, in step G, a power spectrum of said signal of interest. Brève description des figures :

[0019] Other characteristics, details and advantages of the invention will emerge from reading the description given with reference to the appended drawings given by way of example and which represent, respectively: There figure 1 , a schematic view of a prior art spectral analysis device, The figure 2 , a schematic view of a broadband spectral analysis device according to the invention, The figure 3, a schematic view of a broadband spectral analysis device according to a first embodiment of the invention. figure 4 , a schematic view of a broadband spectral analysis device according to a third embodiment of the invention. figure 5 , a schematic view of a broadband spectral analysis device according to a fourth embodiment of the invention. figure 6 , spectral analysis method according to the invention

[0020] References to figures, when identical, correspond to the same elements.

[0021] In the figures, unless otherwise indicated, the elements are not to scale. Detailed description:

[0022] There figure 2is a schematic representation of a device D for broadband spectral analysis of a signal of interest according to the invention. As will be specified later, thanks to a first optical frequency-shift cavity BDF1 and a second optical frequency-shift cavity BDF2, the device D of the invention makes it possible to determine a temporal representation of frequency information of the signal of interest. According to certain conditions linking these cavities, this temporal representation of the frequency information is the real part of a fractional transform or a power spectrum of the signal of interest.

[0023] By "broadband" is meant here that the bandwidth of the device is greater than or equal to 20 GHz, preferably greater than or equal to 40 GHz. The parameters controlling the bandwidth of the device will be specified later in the description.

[0024] The device D of the invention comprises a radiation source S adapted to generate the signal of interest Si. An optical splitter element ES of the device is adapted to spatially separate the signal of interest into a first signal V1 and a second signal V2.

[0025] According to one embodiment, the optical path of the signal of interest at the output of the source S is fibered and the element ES is a 1x2 fibered coupler (also called a Y coupler). Alternatively, according to another embodiment, the optical path of the signal of interest at the output of the source S is in free space and the splitter element ES is a splitter blade or a splitter cube.

[0026] The first signal V1 is injected into the first optical frequency-shifting cavity BDF1. This cavity BDF1 has a first travel time t1 (round trip time in the cavity) and comprises a first frequency shifter AOM1 adapted to shift the optical frequency of the first signal by a first frequency f 1 per round trip in the first cavity.

[0027] Similarly, the second signal V2 is injected into the second frequency-shifting optical cavity BDF2 which has a second travel time t 2 and which comprises a second frequency shifter AOM2 adapted to shift the optical frequency of the second signal by a second frequency f 2 per round trip in the second cavity.

[0028] The first optical cavity BDF1 and the second optical cavity BDF2 may be indifferently and without departing from the scope of the invention a linear cavity or a ring cavity, and a free space cavity or a fiber cavity.

[0029] Essentially, the first and second optical cavities are adapted so that a maximum number of round trips of the signal in the first and second cavities is equal to a number N predetermined. Thus, by calling f 0 , the center frequency of the signal of interest, the first and second cavities each generate a frequency comb comprising respectively the frequencies f 0 + n × f 1 and f 0 + n × f 2, with n ∈ [1; N ] . Concretely, the first and second cavities produce replicas of the signal of interest, shifted both temporally (by multiples of τ 1 and τ 2 respectively), and in frequency (by multiples of f 1 and f 2 respectively).

[0030] According to one embodiment, in order to control this maximum number of round trips N, the first and second loops respectively comprise a first and a second bandpass filter BP1, BP2 (not shown in figure 2 but visible in figure 5 And 6 ), of bandwidth adapted to transmit the frequencies respectively f 0 + n × f 1 and f 0 + n × f 2, with n ∈ [1; N ].

[0031] The first frequency shifter AOM1 and the second frequency shifter AOM2 are preferably acousto-optic modulators controlled by a first OL1 and a second local oscillator OL2 (not shown in the figures). The excitation frequency generated by the first local oscillator and the second local oscillator makes it possible to vary the first frequency f 1 and the second frequency f2. Alternatively, the first and second frequency shifters are single sideband electro-optical modulators (or SSB MZM, for single sideband Mach Zehnder modulator).

[0032] The device D further comprises a PD detector adapted to coherently detect the first signal W1 transmitted by the first cavity and the second signal W2 transmitted by the second cavity. The PD detector is typically a photodiode or any other photodetector known to those skilled in the art. Preferably, the PD detector is formed by balanced photodiodes in order to detect very small variations in the light signal.

[0033] This PD detector detects in real time a light intensity which corresponds to the coherent summation of all the replicas of the signal of interest shifted both temporally and in frequency (the frequency penalties) by the first and second cavities and then generates a photocurrent Tr proportional to this detected light intensity. For the device to work, it is essential that the first signal W1 transmitted by BDF1 is coherent with the signal W2 transmitted by BDF2.

[0034] The photocurrent Tr is then filtered by a low-pass analog filter LP adapted to let through photocurrent frequencies lower than the Nyquist frequencies associated with the first signal W1 and the second signal W2, i.e. min( f 1 / 2 ; f 2 / 2)

[0035] Finally, the device D comprises a processor UT configured to calculate a square modulus of the photocurrent filtered by the filter LP, thus generating a time trace TT. By means of this trace TT, the device D makes it possible to determine a time representation of frequency information of the signal of interest.

[0036] In the device D of the invention, the bandwidth is equal to LS in = 1 / ( t 1 - t 2). This feature is very interesting because by minimizing the difference t 1 - t 2, it is possible to maximize the bandwidth of device D.

[0037] The inventors demonstrated that, depending on the value of the difference f 1 × t 1 - f 2 × t2, the TT trace is the real part of the fractional Fourier transform or a power spectrum of the signal of interest. For the sake of clarity, the development of the equations explaining this result are presented at the end of this description

[0038] Thus, according to a first variant of the invention, the first cavity and the second cavity are configured to verify the condition f 1 × t 1 = f 2 × t 2 (modulo 1). In this first variant, the photocurrent Tr is a temporal representation of the real part of the Fourier transform of the signal of interest ( α = π / 2) and the TT trace is then a temporal representation of the power spectrum of this signal. The device D therefore makes it possible to carry out a mapping of the spectrum over time (Frequency-to-time mapping) in real time.

[0039] Preferably, in this first variant, the analog low-pass filter LP is adapted to filter photocurrent frequencies lower than a minimum value[ N × | f 1 - f 2 | ; f 1 / 2 ; f 2 / 2)], before the calculation of the square module of the photocurrent by the UT processor. Filtering of frequencies lower than N × | f 1 - f 2 | allows, if this value is lower than the Nyquist frequencies f 1 / 2 ; f 2 / 2, to process the photocurrent Tr with a processor including slower processing electronics (typically 50 Ms / s).

[0040] In this first variant, the frequency resolution of the device is Δ f = 1 / ( N ( t 1 - t 2 )) = LS in / N. Thus, we understand that, in order to obtain a spectral resolution Δ f suitable while maintaining bandwidth LS in high, it is necessary to maximize the maximum number of round trips in the first and second cavities BDF1, BDF2. Preferably, in order to obtain a suitable spectral resolution, the first and second cavities are configured so that a maximum number of round trips N is greater than 200, preferably greater than 500. Typically, for a bandwidth of LS in = 20GHz, and N=400 the frequency resolution of the device is Δ f = 50MHz.

[0041] In a second variant of the invention, the first cavity and the second cavity are configured to verify the condition f 1 × t 1 ≠ f 2 × t 2, modulo 1. This difference must be much less than 1, that is to say that: f 1 t 1 = f 2 t 2 + uh, (| e| « 1 (see equations at the end of the description). In this second variant, the trace TT is then a temporal representation of the real part of the fractional Fourier transform (TFFr) of the signal of interest. The order of the fractional transform represented by the device D is fixed by the difference f 1 × t 1 - f 2 × t 2. More precisely, when f 1 × t 1 = f 2 × t 2 modulo 1, (first variant of the invention), the photocurrent is a temporal representation of the real part of the Fourier transform of the input signal (i.e. order of the TFFr corresponding to π / 2) while while when f 1 × t 1 - f 2 × t 2 has a value close to 0 (second variant), the photocurrent represents the real part of the TFFr of the signal of interest. Concretely, the order of the TFFr depends on the scale factor (f 2 - f 1 ) / ( t 1 - t 2) (see equations at the end of the description).

[0042] In this second variant of the invention, it is possible to define a frequency resolution by considering two simultaneous linear frequency modulation signals having the same chirp rate (i.e. the same slope in the time-frequency plane). These two signals therefore differ by the starting frequency. By choosing the right order of the TFFr, the TFFr of these chirped signals consists of two peaks, the spacing of which is proportional to the frequency difference between these two chirped signals. The resolution of the device in the second variant of the invention then corresponds to the smallest value of the frequency difference between the two chirps measurable by the device. This definition makes it possible to define a resolution for this system which is a frequency.

[0043] So, depending on the value of the difference f1 × t 1 - f 2 × t 2, the device D of the invention makes it possible to obtain a real-time temporal representation of two different frequency information items of the signal of interest: the real part of the TFFr or the power spectrum.

[0044] The time resolution of the device (i.e. the time taken by the system to calculate and produce the frequency information) is equal to 1 / ( f 2 - f 1). Note that the frequency information is obtained in real time, that is to say that the determined frequency information is updated every period 1 / ( f 2 - f 1 ).

[0045] According to one embodiment, the first cavity comprises a first delay line DL1 (not shown) controllable and adapted to vary the first travel time t1 and / or the second cavity comprises a first delay line DL2 (not shown) controllable and adapted to vary the second travel time t 2. Thus, it is possible to reduce the difference ( t 1 - t 2) to maximize bandwidth LS in of device D. Preferably, the difference ( t 1 - t 2) is such that the bandwidth LS in is greater than or equal to 20 GHz, preferably greater than or equal to 40 GHz. This bandwidth value is not achievable in the device described in the document “de Chatellus, Hugues Guillet, Luis Romero Cortés, and José Azaña. "Optical real-time Fourier transformation with kilohertz resolutions." Optica 3.1 (2016): 1-8”, where the bandwidth of the device is of the order of 10 MHz because fixed by 1 / t 1 .

[0046] An advantage of embodiments of the invention comprising delay lines DL1, DL2 and / or frequency shifters AOM1, AOM2 which allow to vary f 1 and f 2 is to allow control of the difference f 1 × t 1 - f 2 × t 2. Thus, it is possible to switch the operation of the device from the first variant of the invention to the second variant of the invention or vice versa. Furthermore, the control of the difference f 1 × t 1 - f 2 × t 2 allows you to choose the order of the TFFr of the signal of interest.

[0047] It is noted that in the embodiments of the invention in which the first and second cavities BDF1, BDF2 respectively comprise a first and second bandpass filter BP1, BP2, the passband LS in is equal to a spectral width LS BPof the first and second bandpass filters when this spectral width LS BP is less than 1 / ( t 1 - t 2). In other words, the bandwidth is equal to LS in = min(1 / ( t 1 - t 2) ; LS BP ).

[0048] Notably, the device D does not perform any truncation or sampling on the spectrum of the signal of interest reducing the portion of the spectrum analyzed. Thus, unlike some of the prior art devices mentioned above, the device D of the invention has a POI of 100% and the frequency information of the signal of interest represented by the TT trace is representative of the entire spectrum of the signal of interest included in the bandwidth.

[0049] According to one embodiment, the first and second cavities respectively comprise a first and a second amplifier EDFA1, EDFA2 (not shown in figure 1 but visible in figure 4 ) adapted to compensate for the losses induced by the first and second cavities.

[0050] According to a first embodiment of the invention, illustrated in figure 3 , the source S comprises a monochromatic CW continuous laser, an AM RF source adapted to generate an RF signal s(t), and a Mod modulator suitable for modulating in amplitude or in phase, by the RF signal s(t), the laser radiation generated by the continuous laser so as to form said signal of interest. In the first embodiment of the invention, the device D makes it possible to determine a temporal representation of frequency information of the RF signal s(t) carried by the continuous laser. Thus, according to the second variant of the invention, the TT trace is then a temporal representation of the TFFr of the RF signal s(t)and according to the first variant of the invention, the TT trace is then a temporal representation of the convolution product of the power spectrum of the monochromatic CW laser, by the power spectrum of the RF signal s(t). When the CW laser has a coherence time long enough for the radiation to remain coherent within the cavities BDF1, BDF2 (typically of the order of hundreds of µs), then the TT trace is a temporal representation of the real part of the spectrum of the RF signal s(t). This first embodiment is particularly interesting given the bandwidth LS in of the device which can be greater than 40 GHz while having a POI of 100%, these values ​​not being unattainable by prior art devices performing spectral analysis of RF signals.

[0051] In a second embodiment, the source S is a coherent optical source generating a signal of interest Si in the form of light radiation s(t), for example a laser source. In the second embodiment of the invention, the device D makes it possible to determine a temporal representation of frequency information of the signal s(t).

[0052] There figure 4schematically illustrates a third embodiment, compatible with the first and second embodiments, in which the entire optical path of the signal of interest from the source to detection by the photodiode is fibered. The alignment of the device is thus simplified and the device is less sensitive to shocks and vibrations. In this third embodiment, the signal of interest Si is separated, by a Y coupler ES, so as to form the first signal V1 and the second signal V2, both guided in a respective optical fiber. The first and second cavities BDF1, BDF2 are ring fibered cavities comprising respectively a first and a second doped fiber amplifier EDFA1, EDFA2 and a first and a second bandpass optical filter BP1, BP2.The first signal V1 is injected into the first cavity BDF1 via a fiber coupler C1 and the second signal V2 is injected into the second cavity BDF2 via a fiber coupler C2.

[0053] As explained previously, the first and second doped fiber amplifiers EDFA1, EDFA2, for example EDFAs, are adapted to compensate for the losses induced in the cavities BDF1, BDF2. The optical bandpass filters BP1, BP2 are configured to fix said maximum number N of round trips in the first and second cavities and to limit the noise coming from the amplified spontaneous emission of the doped fiber amplifiers.

[0054] Advantageously, in the third embodiment, the device D comprises stabilization means ST (not shown) of the first and second cavities BDF1, BDF2 adapted to maintain over time the coherence between the first signal transmitted by the first cavity and the second signal transmitted by the second cavity. The stabilization device makes it possible to ensure that the radiation transmitted by the two cavities BDF1, BDF2 is mutually coherent. Such a device is well known to those skilled in the art and is for example described in "Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs," Opt. Express 26, 13800-13809 (2018).

[0055] There figure 5schematically illustrates a fourth embodiment, compatible with the first and second embodiments, which constitutes an alternative to the third embodiment. This fourth embodiment aims to overcome the problem of maintaining coherence over time between the first signal W1 and the second signal W2 transmitted by the first and second cavities. For this purpose, the device comprises a single fiber ring cavity BDF configured to form the first and second cavities BDF1, BDF2 according to the injection direction. This configuration with a single counter-propagating ring cavity makes it possible to limit the effects of fiber length fluctuations (vibrations, thermal drifts, etc.) which may be different between the first and second cavities of the third embodiment, and which cause a loss of coherence as the back and forth passes. It also makes it possible to reduce the number of optical components required.

[0056] Similar to the third embodiment, in the device D of the fourth embodiment, the entire optical path of the signal of interest from the source to detection by the photodiode is fibered. The device D comprises a first fibered coupler C1 adapted to inject the first signal V1 into the single cavity BDF in a first direction S 1. In addition, the device D comprises a second fiber coupler C2 adapted to inject the second signal V2 into the single cavity BDF in a second direction. S 2. The BDF cavity includes: a first circulator CO1 adapted to direct the first signal V1 to a first delay line DL1 comprising the first frequency shifter AOM1. a second circulator CO2 adapted to direct the second signal to the second delay line DL2 comprising the second frequency shifter AOM2, a bi-directional EDFA doped fiber amplifier (operating in both directions), a bandpass optical filter BP configured to fix said maximum number N of round trips. Thus, the first cavity BDF1 corresponds to the single cavity BDF into which the first signal V1 is injected according to the first injection direction S 1 and the second cavity BDF2 corresponds to the single cavity BDF into which the second signal V2 is injected according to the second injection direction S 2 .

[0057] Alternatively, according to a variant of the fourth embodiment, instead of a single EDFA amplifier and a single optical bandpass filter BP common to the first signal V1 and the second signal V2, the first delay line DL1 comprises a first amplifier EDFA1 and an optical bandpass filter BP1 and the second delay line DL1 comprises a second amplifier EDFA2 and an optical bandpass filter BP2.

[0058] It is understood that the methods of realizing the figures 3 to 5 are compatible with the first and second variants of the invention according to the value of the difference f 1 × t 1 - f 2 × t 2 .

[0059] Another object of the invention is a method of spectral analysis of a signal of interest Si implemented by the device D of the invention. The figure 6schematically illustrates this method which allows a temporal representation of frequency information (TFFr or power spectrum) of the signal of interest as a function of the value of the difference f 1 × t 1 - f 2 × t 2 .

[0060] The method of the figure 6 includes the following steps: A. generating the signal of interest Si; B. spatially separating the signal of interest into the first signal V1 and the second signal V2; C. injecting the first signal into the first optical frequency-shifting cavity BDF1 and shifting the optical frequency of the first signal by a first frequency f 1 by round trip in the first cavity; D. inject the second signal into the second optical frequency shift cavity BDF2 shift the optical frequency of the second signal by a second frequency f2 by round trip in the second cavity; E. coherently detect the first signal W1 transmitted by the first cavity and the second signal W2 transmitted by the second cavity and generate the photocurrent Tr proportional to the detected light intensity, F. filter photocurrent frequencies lower than min f 1 2 f 2 2 , G. calculate the square modulus of the filtered photocurrent from which a temporal representation of frequency information of said signal of interest is determined.

[0061] The method of the figure 6 has the notable advantage of being wideband, having a 100% POI and good frequency resolution.

[0062] According to a first variant of the method of the figure 6 , the method comprises a step prior to step A), noted step A0) consisting of adjusting the first or the second cavity in order to cancel the difference f 1 × t 1 - f 2 × t2, so as to calculate, in step G, a power spectrum of the signal of interest. This first variant is implemented by the first variant of the device of the invention.

[0063] According to a second variant of the method of the figure 6 , the method comprises a step prior to step A), noted step A0) consisting of adjusting the first or the second cavity in order to fix the difference f 1 × t 1 - f 2 × t 2 on a desired non-zero value, in order to calculate, in step G, a specific order of the real part of a fractional Fourier transform of the signal of interest. This second variant is implemented by the second variant of the device of the invention.

[0064] The equations showing that, depending on the value of the difference f 1 × t 1 - f 2 × t2, the TT trace is the real part a fractional Fourier transform or a power spectrum of the signal of interest are developed below

[0065] We note f 0 the frequency of the injection laser, t 1 , t 2 the travel times in the loops, f 1 , f 2 the shift frequencies per revolution and s(t) the signal of interest.

[0066] The electric fields at the output of the first and second cavities are respectively: E 1 t = ∑ n = 0 N s t − nτ 1 E 0 e i 2 πf 0 t e i 2 πnf 1 t e − iπf 1 τ 1 n 2 E 2 t = ∑ n = 0 N s t − nτ 2 E 0 e i 2 πf 0 t e i 2 πnf 2 t e − iπf 2 τ 2 n 2

[0067] The intensity detected by PD is: I t = w t ∗ E 1 t E 2 ∗ t Or w(t) is a time window centered at t (related to the detection response) and * is the convolution product. Omitting the term E 0 E 0 * , we have I t = w t ∗ ∑ n , m s t − nτ 1 s t − mτ 2 e i 2 π nf 1 − mf 2 t e − iπ f 1 τ 1 n 2 − f 2 τ 2 m 2 I t = ∫ w t − t ' ∑ n , m s t ' − nτ 1 s t ' − mτ 2 e 12 π nf 1 − mf 2 t ' e − iπ f 1 τ 1 n 2 − f 2 τ 2 m 2 dt '

[0068] We choose the frequencies f 1 and f 2 such that Δ f = f 2 - f 1 ≤ f 1 / 2 N ,f 2 / 2 N. The duration of the window w ( t ) is chosen in the order of 1 / N Δ f. It is therefore greater than 2 / f 1 and 2 / f 1. Thus, only pairs of integers ( n, m = n) have a non-zero contribution in the integral. Première variante de l'invention :

[0069] It is assumed here that f 1 t 1 = f 2 t 2. We then have: I t = ∫ w t − t ′ ∑ n s t ′ - nτ 1 s t ′ − nτ 2 e − i 2 πn Δ ft ′ dt ′

[0070] Over the duration of the window, e - i 2 πn Δ ft' < can be likened to e - i 2 πn Δ feet < because the duration of the window is shorter than the period of the functions e - i 2 πn Δ< ft< '.

[0071] We thus have: I t = ∑ n e − i 2 πn Δ ft ∫ w t − t ′ s t ′ − nτ 1 s t ′ − nτ 2 dt ′ I t = ∑ n s t − nτ 1 s t − nτ 2 e − i 2 πn Δ ft where <> represents the average measured over the duration of the window.

[0072] By shifting the origin of time, we have I t = ∑ n s t s t − n Δ τ e − i 2 πn Δ ft where Δ t = t 2 - t 1. We define the correlation function at the instant t for the delay T : C(t, T) =< s(t)s(t - T) >.

[0073] Either I t = ∑ n C t , n Δ τ e − i 2 πn Δ ft

[0074] We write, by defining d ( t ) as the Dirac delta function: and finally: I t = ∑ n C ˜ t , Δ f Δ τ t − n Δ τ Or C̃ ( t, f) = ∫ ( t , t' ) e - i 2< πft< 'dt' is the Fourier transform (FT) of ( t, t') relative to the variable t '.

[0075] I ( t ) is therefore a repetition of the TF of the autocorrelation function at time t projected in time, that is to say, by the Wiener-Khintchine theorem, the power spectrum of the input signal at time t. We note here that the signal actually measured by the PD detector is in reality 2 Re ( I ( t)). The power spectrum is obtained via a Hilbert transformation of the measured signal.

[0076] The period of the output signal is 1 / Δ f. We therefore find the spectrum of the input signal projected into the time domain ("frequency-to-time mapping"). The coefficient of proportionality is simply Δ t / Δ f = ( f 2 - f 1 ) / ( t 1 - t 2).

[0077] The time resolution is given by the duration of the window w(t), i.e. of the order of 1 / N Δ f. Therefore, the spectral resolution is: δf = Δ f Δ τ 1 N Δ f = 1 N Δ τ

[0078] The spectral width of s(t) unambiguously measurable is 1 / Δ t .

[0079] We note that this result is valid when for all f 1 t 1 = f 2 t 2 modulo 1 (see equation 5). By modulo 1, we mean here f 1 t 1 = f 2 t 2 + k, with k ∈ ℕ . Deuxième variante de l'invention :

[0080] We now assume that: f 1 t 1 = f 2 t 2 + e , (| e | “1) we have: I t = ∑ n C t , n Δ τ e − i 2 πn Δ ft e − iπεn 2

[0081] Following the same approach:

[0082] To make a fractional TF appear, we set y = t' / Δ t. We therefore obtain: I t ∝ ∑ n ∫ C t y e − i 2 π Δ ft − n y e − iπεy 2 dy

[0083] We recognize the expression of the fractional TF (TFFr) of the function C (except for a quadratic phase term which would be in e iβt 2< ). Here, the order α of the TFFr is given by: cot α = 2 th. Note that the definition of parameter y here defines the order of the TFFr.

[0084] Eventually, I ( t) is therefore the repetition of the TFFr of the autocorrelation function at time t projected in time, that is to say, by the convolution theorem applied to the TFFr, the square modulus of the TFFr of the input signal.

[0085] As before, the signal actually measured by the detector is actually 2 Re ( I ( t )), which means that the square modulus of the TFFr is obtained via a Hilbert transformation of the measured signal.

[0086] The period of the output signal is 1 / Δ f. We therefore find the TFFr of the input signal projected into the time domain ("fractional frequency-to-time mapping").

Claims

1. A wideband device (D) for the spectral analysis of a signal of interest comprising: - a source (S) designed to generate said signal of interest (Si); - an optical splitter element (ES) designed to spatially split said signal of interest into a first signal (V1) and a second signal (V2); - a first frequency-shifting optical cavity (DBDF, BDF1) comprising a first frequency shifter (AOM1) designed to shift the optical frequency of the first signal by a first frequency f1 per round trip in said first cavity, said first cavity having a first trip time τ1 ; - a second frequency-shifting optical cavity (DBDF, BDF2) comprising a second frequency shifter (AOM2) designed to shift the optical frequency of the second signal by a second frequency f2 per round trip in said second cavity, said second cavity having a second trip time τ2 ; the first and the second optical cavity being designed such that a maximum number of round trips of said signal in the first and the second cavity is equal to predetermined N; - a detector (PD) designed to coherently detect the first signal (W1) transmitted by the first cavity and the second signal (W2) transmitted by the second cavity and generate a photocurrent (Tr) proportional to a luminous intensity detected by said detector, - a low-pass filter (LP) designed to filter frequencies of the photocurrent that are lower than min f 1 2 f 2 2 , - a processor (UT) configured to compute a square modulus of the photocurrent filtered by said low-pass filter, from which a temporal representation of frequency information of said signal of interest is determined, said frequency information being: ∘ a real part of a fractional Fourier transform of said signal of interest, an order of said fractional Fourier transform being set by the value f1 × τ1 - f2 × τ2 when the first cavity and the second cavity are configured to verify the condition f1 × τ1 ≠ f2 × τ2, modulo 1 or ∘ a power spectrum of said signal of interest when the first cavity and the second cavity are configured to verify the condition f1 × τ1 = f2 × τ2 modulo 1.

2. The device as claimed in claim 1, wherein said source comprises a monochromatic continuous-wave laser (CW), an RF source (AM) designed to generate an RF signal s(t), and a modulator (Mod) designed to amplitude-modulate or phase-modulate, using said RF signal s(t), laser radiation generated by said continuous-wave laser, so as to form said signal of interest.

3. The device as claimed in claim 1 or 2, wherein the analog low-pass filter (LP) is designed to filter frequencies of said photocurrent that are lower than min [ N × |f1 - f2 | ; f1 / 2 ; f2 / 2], when the first cavity and the second cavity are configured to verify the condition f1 × τ1 = f2 × τ2 modulo 1.

4. The device as claimed in any one of the preceding claims, wherein the first and the second cavity respectively comprise a first and a second amplifier (EDFA, EDFA1, EDFA2) designed to compensate for the losses induced respectively by the first and the second cavity.

5. The device as claimed in any one of the preceding claims, wherein the first frequency shifter is a first acousto-optic modulator excited by a first local oscillator (OL1) designed to vary said first shift frequency and wherein the second frequency shifter is a second acousto-optic modulator excited by a second local oscillator (OL2) designed to vary said second shift frequency.

6. The device as claimed in any one of the preceding claims, wherein the first cavity comprises a first controllable delay line (DL1) designed to vary the first trip time τ1 and wherein the second cavity comprises a second controllable delay line (DL2) designed to vary the second trip time τ2.

7. The device as claimed in any one of the preceding claims, wherein the first and the second cavity are fiber ring cavities (BDF1, BDF2) comprising respectively a first and a second doped fiber amplifier (EDFA1, EDFA2) and a first and a second optical bandpass filter (BP1, BP2) configured to set said maximum number N of round trips in the first and the second cavity.

8. The device as claimed in the preceding claim, comprising stabilizing means (ST) for stabilizing the first and the second cavity that are designed to maintain, over time, the coherence of said first signal transmitted by the first cavity with said second signal transmitted by the second cavity.

9. The device as claimed in claim 6, comprising a single ring cavity (BDF), said device furthermore comprising: - a first coupler (C1) designed to inject said first signal (V1) into said single cavity in a first direction, - a second coupler (C2) designed to inject said second signal (V2) into said single cavity in a second direction, said first cavity corresponding to the single cavity into which the first signal is injected in the first injection direction, said second cavity corresponding to the single cavity into which the second signal is injected in the second injection direction, said single ring cavity comprising: ∘ a first circulator (CO1) designed to direct the first signal to a first controllable delay line (DL1) designed to vary the first trip time τ1 and comprising said first frequency shifter (AOM1), ∘ a second circulator (CO2) designed to direct the second signal to a second controllable delay line (DL2) designed to vary the second trip time τ1 and comprising said second frequency shifter (AOM2), ∘ a doped fiber amplifier (EDFA), ∘ an optical bandpass filter (BP) configured to set said maximum number N of round trips.

10. The device as claimed in any one of the preceding claims, wherein the first and the second cavity are configured such that 1 τ 1 − τ 2 ≥ 40 GHz.

11. The device as claimed in any one of the preceding claims, wherein the first and the second cavity are configured such that N is greater than 200.

12. A method for the spectral analysis of a signal of interest (Si) using a first frequency-shifting optical cavity (BDF1) comprising a first frequency shifter (AOM1) having a first trip time τ1 and a second frequency-shifting optical cavity (BDF2) comprising a second frequency shifter (AOM2) having a second trip time τ2, a maximum number of round trips of said signal of interest in the first and the second cavity being equal to predetermined N, said method comprising the following steps: A. generating said signal of interest; B. spatially splitting said signal of interest into a first signal (V1) and a second signal (V2); C. injecting said first signal into the first frequency-shifting optical cavity (BDF1) and shifting the optical frequency of the first signal by a first frequency f1 per round trip in said first cavity ; D. injecting said second signal into the second frequency-shifting optical cavity (BDF2) and shifting the optical frequency of the second signal by a second frequency f2 per round trip in said second cavity; E. coherently detecting the first signal transmitted by the first cavity (W1) and the second signal (W2) transmitted by the second cavity and generating a photocurrent (Tr) proportional to a detected luminous intensity, F. filtering frequencies of the photocurrent that are lower than min f 1 2 f 2 2 , G. computing a square modulus of the filtered photocurrent and determining a temporal representation of frequency information of said signal of interest, said method comprising a step prior to step A, denoted step A0, of: • adjusting the first or the second cavity in order to set a difference f1 × τ1 - f2 × τ2 to a desired non-zero value, in order to compute, in step G, a specific order of a real part of a fractional Fourier transform of the signal of interest, or • adjusting the first or the second cavity in order to cancel out a difference f1 × τ1 - f2 × τ2, in order to compute, in step G, a power spectrum of said signal of interest.