Apparatus for wideband spectral analysis of a signal of interest

Abstract

A broadband device (D) for performing spectral analysis on a signal of interest includes: - a source (S) designed to generate the signal of interest (Si); - a beam splitter element (ES) designed to spatially split the signal of interest into a first signal (V1) and a second signal (V2); - a first frequency-shifting optical cavity (DBDF, BDF1) including: a first frequency shifter (AOM1) designed to shift the optical frequency of the first signal by a first frequency f1 per round trip in the first cavity, the first cavity having a first travel time τ1; - a second frequency-shifting optical cavity (DBDF, BDF2) including: a second frequency shifter (AOM2) designed to shift the optical frequency of the second signal by a second frequency f1 per round trip in the second cavity. Rate f2, the second cavity has a second travel time τ2; the first and second optical cavities are designed such that the maximum number of round trips of the signal in the first and second cavities is equal to a predetermined N; - detector (PD) is 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 the light intensity detected by the detector; - analog low-pass filter (LP) is designed to filter the photocurrent at frequencies below a certain threshold; - processor (UT) is configured to calculate the square modulus of the photocurrent filtered by the low-pass filter, and determine a time representation of the frequency information of the signal of interest based on the square modulus.

Description

Technical Field

[0001] This invention relates to the field of analog processing of optical and radio frequency signals, and more specifically, to analog processing of broadband optical and radio frequency signals using a frequency-shifting optical cavity. Background Technology

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

[0003] In the field of optics, spectral analysis is typically performed using three types of equipment.

[0004] The first solution involves using gratings to diffract the light signal. Far-field illumination provides the spectrum. These grating-based spectrum analyzers are widely used due to their simplicity and low cost. However, their frequency resolution does not exceed 10 GHz.

[0005] Another technique that allows for better spectral resolution (several GHz) is Fourier Transform (FT) spectrum analysis, which involves using a Michelson interferometer. The interferometer's delay varies over time due to mirrors mounted on a moving carriage. Fringes (i.e., interferograms) are recorded over time. The FT operation then makes access to the spectrum possible. This is the basic principle behind commercial OSA ("spectrum analyzer"). This device has two limitations: the spectral resolution is given by the maximum path difference of the interferometer. In practice, this resolution is on the order of GHz. Furthermore, the time required to measure the spectrum is on the order of seconds. Therefore, this technique is reserved for sufficiently long optical signals, or optical signals whose spectrum is constant over time. In fact, the probability of interception, or POI (that is, the probability that the signal is actually measured by the spectrum analyzer), is very low with such a device.

[0006] The third technique is heterodyne spectral analysis. This technique has a spectral resolution of several MHz, allowing for high-resolution measurement of the spectrum. This involves using a continuous-wave laser with a narrow linewidth (sub-MHz) and scanning its frequency. The spectrum is thus provided by the amplitude of the heterodyne beat frequency of the optical signal to be analyzed during the frequency ramp at a given frequency of the laser. However, this technique is expensive, requires a reference laser, and has a low point of interest (POI).

[0007] In the field of radio frequency (RF) signals, there are currently two commercially available RF signal spectrum analysis solutions: real-time spectrum analyzers and scanning analyzers.

[0008] A scanning analyzer operates by comparing the SUT (“signal under test”) with a reference signal whose frequency varies over time (e.g., via a frequency ramp) (heterodyne). It can measure spectral widths greater than 20 GHz. However, due to the duration of the frequency ramp, this technique can only detect a small fraction of the spectrum at a given time. For scanning analyzers, the point of interest (POI) is typically 1%. Therefore, it is not suitable for analyzing short signals or signals whose spectrum varies over time.

[0009] Real-time analyzers combine a signal acquisition step known as analog-to-digital conversion (ADC) with a digital computation step (Fourier transform). The first step is particularly critical for the reliability of the process: in fact, it is necessary to sample the SUT at twice its maximum frequency (Nyquist criterion). Therefore, too low a sampling rate will result in the loss of high-frequency information from the SUT. Currently, the sampling frequency of analog-to-digital converters is essentially limited to several gigabits per second. Therefore, even the best real-time spectrum analyzers cannot achieve a spectral width greater than GHz. They also mobilize a very large amount of computational resources to calculate the spectrum in real time.

[0010] In addition, the document “Hugues Guillet de Chatellus, Luis Romero Cortés and José” "Optical real-time Fourier transformation with kilohertz resolutions" (Optica 3.1 (2016): 1-8) describes a device containing a frequency-shifting loop into which the signal of interest is injected. The device described in this document can generate a time signal at the output that reproduces the spectrum of the input signal, provided that f1τ1 is an integer, where f1 is the frequency shift of the signal of interest for each round trip in the loop, and τ1 is the duration of the round trip of the signal of interest in the loop. Figure 1The apparatus described in the aforementioned document is illustrated schematically. The apparatus includes a source S0 that generates an optical signal or an RF signal carried by an optical signal (i.e., amplitude modulated by the optical signal) to form a signal of interest. "Carried by" is understood here and throughout this document to mean that the carrier signal is amplitude modulated by the modulated signal. This signal of interest is injected via an optical fiber coupler C0 into an optical fiber frequency-shifting loop BDF0. Loop BDF0 includes a frequency shifter AOM0 (e.g., an acousto-optic modulator) designed to shift the optical frequency of the signal by a frequency f1 with each round trip in the loop. Loop BDF0 also includes an amplifier EDFA0 (e.g., a doped fiber amplifier, such as an EDFA, i.e., an erbium-doped fiber amplifier) ​​to compensate for losses caused by the loop, and an optical bandpass filter BP0 to limit noise generated by the amplified spontaneous emission of the amplifier and to set the number of round trips in the loop. The radiation transmitted through the loop is detected by a photodiode PD0 that generates a photocurrent, which is filtered by an analog low-pass filter LP0. This filter is designed to retain only the photocurrent frequency below the Nyquist frequency of the signal of interest. The processor UT is configured to calculate the square modulus of the photocurrent. When f1τ1 is an integer, if the signal of interest is an optical signal, the time trace obtained by the processor after processing the photocurrent is the power spectrum of the optical signal; or if the signal of interest is an RF signal carried by a coherent optical signal, the time trace obtained by the processor after processing the photocurrent is the power spectrum of the RF signal.

[0011] This system has significant technical limitations. First, the spectral width of the signal of interest must be less than 1 / τ1 (on the order of 10 MHz), which greatly limits its practical application. Increasing τ1 to achieve a bandwidth on the order of 10 GHz is not feasible due to the added complexity and propagation loss. Another limitation is that the period of the output signal (spectrum) is 1 / f1, meaning the output signal must be sampled at Nf1 times, or tens of gigabits per second (assuming N = 300 and f1 = 80 MHz).

[0012] also, Figure 1 The existing technology allows for the computation of the fractional Fourier transform of the signal of interest when f1τ1 is close to an integer. This property is described in the following document: Schnébelin and Hugues Guillet deChatellus, “Agile photonic fractional Fourier transformation of optical and RF signals,” Optica 4, 907-910 (2017). The fractional Fourier transform (FrFT) is a generalization of the Fourier transform (FT) to any intermediate domain (called the fractional domain) between the direct space and the Fourier space. This transform can link rotations in the time and frequency domains. The ordinary Fourier transform of a function f can be written as... The form allows this notation to be generalized to any fractional order α. Therefore, the fractional Fourier transform (FrFT) of order α will be: F α (f). The FrFT is related to the analysis of input signals whose frequency changes linearly with time (signals with linear frequency modulation or "chirp").

[0013] For α = 0, find the identity operator, which will give the function f. For α = π / 2, find the regular Fourier transform. And u is a variable in the target domain (called the fractional domain), the α-order FrFT of the function f can be expressed in the following form:

[0014]

[0015] The present 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-shifting cavities. Summary of the Invention

[0016] Therefore, one aspect of the present invention is a broadband device for performing spectral analysis on a signal of interest, comprising:

[0017] - A source, which is designed to generate the signal of interest;

[0018] - A beam splitter element, which is designed to spatially split the signal of interest into a first signal and a second signal;

[0019] - A first frequency-shifting optical cavity, comprising: a first frequency shifter configured to shift the optical frequency of the first signal by a first frequency f1 with each round trip in the first cavity, the first cavity having a first travel time τ1;

[0020] - A second frequency-shifting optical cavity, comprising: a second frequency shifter configured to shift the optical frequency of the second signal by a second frequency f2 with each round trip in the second cavity, the second cavity having a second travel time τ2;

[0021] - The first and second optical cavities are designed such that the maximum number of round trips of the signal in the first and second cavities is equal to a predetermined N;

[0022] - A detector designed to coherently detect the first signal transmitted by the first cavity and the second signal transmitted by the second cavity, and to generate a photocurrent proportional to the light intensity detected by the detector.

[0023] - A low-pass filter, designed to filter photocurrent below... Filter the frequency.

[0024] - A processor configured to calculate the square modulus of the photocurrent filtered by the low-pass filter, and determine a time representation of the frequency information of the signal of interest based on the square modulus.

[0025] According to certain specific modes of the present invention:

[0026] - The source includes a monochromatic continuous-wave laser, an RF source designed to generate an RF signal s(t), and a modulator designed to use the RF signal s(t) to amplitude-modulate or phase-modulate the laser radiation generated by the continuous-wave laser to form the signal of interest;

[0027] - The first cavity and the second cavity are configured to verify the condition f1×τ1≠f2×τ2, and then the frequency information is the real part of the fractional Fourier transform of the signal of interest, the order of which is set by the value f1×τ1-f2×τ2.

[0028] - The first and second cavities are configured to verify the condition f1×τ1=f2×τ2modulo 1, and then the frequency information is the power spectrum of the signal of interest;

[0029] - The analog low-pass filter is designed to filter the photocurrent at frequencies below min[N×|f1-f2|;f1 / 2;f2 / 2];

[0030] The first cavity and the second cavity each include a first amplifier and a second amplifier, respectively, which are designed to compensate for losses caused by the first cavity and the second cavity, respectively.

[0031] - The first frequency shifter is a first acousto-optic modulator excited by a first local oscillator, the first local oscillator being designed to change the first frequency shift, and wherein the second frequency shifter is a second acousto-optic modulator excited by a second local oscillator being designed to change the second frequency shift;

[0032] - The first cavity includes a first controllable delay line designed to change the first travel time τ1, and wherein the second cavity includes a second controllable delay line designed to change the second travel time τ2;

[0033] - The first cavity and the second cavity are fiber ring cavities, each including a first and a second doped fiber amplifier and a first and a second optical bandpass filter configured to set the maximum round-trip number N in the first cavity and the second cavity, respectively.

[0034] - The device includes a stabilization device for stabilizing the first cavity and the second cavity, the stabilization device being designed to maintain the coherence of the first signal transmitted by the first cavity and the second signal transmitted by the second cavity over time;

[0035] - A device comprising a single annular cavity, the device further comprising:

[0036] A first coupler, designed to inject the first signal into the single cavity in a first direction,

[0037] • A second coupler, designed to inject the second signal into the single cavity in a second direction.

[0038] The first cavity corresponds to a single cavity in which the first signal is injected in the first injection direction.

[0039] The second cavity corresponds to a single cavity in which the second signal is injected in the second injection direction.

[0040] The single annular cavity includes:

[0041] A first circulator, designed to direct the first signal to a first controllable delay line and including a first frequency shifter, wherein the first controllable delay line is designed to change the first travel time τ1.

[0042] A second circulator, designed to direct the second signal to a second controllable delay line and including a second frequency shifter, the second controllable delay line being designed to change the second travel time τ1.

[0043] doped fiber amplifier,

[0044] An optical bandpass filter is configured to set the maximum round-trip number N.

[0045] -The first and second cavities are configured such that

[0046] - The first and second cavities are configured such that N is greater than 200.

[0047] Another subject of the present invention is a method for performing spectral analysis on a signal of interest using a first frequency-shifting optical cavity and a second frequency-shifting optical cavity, wherein the first frequency-shifting optical cavity includes a first frequency shifter and has a first travel time τ1, and the second frequency-shifting optical cavity includes a second frequency shifter and has a second travel time τ2, wherein the maximum number of round trips of the signal of interest in the first and second cavities is equal to a predetermined N, and the method includes the following steps:

[0048] A. Generate the signal of interest;

[0049] B. Spatially divide the signal of interest into a first signal and a second signal;

[0050] C. Inject the first signal into the first frequency-shifting optical cavity, and shift the optical frequency of the first signal by a first frequency f1 each time it travels back and forth in the first cavity;

[0051] D. Inject the second signal into the second frequency-shifting optical cavity, and shift the optical frequency of the second signal by a second frequency f2 each round trip in the second cavity;

[0052] E. 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 the detected light intensity.

[0053] F. For those below The frequency of the photocurrent is filtered.

[0054] G. Calculate the square modulus of the filtered photocurrent and determine the time representation of the frequency information of the signal of interest.

[0055] Some specific modes of the method according to the present invention:

[0056] The method includes a step preceding step A, denoted as step A0, adjusting the first or second cavity to set the difference f1×τ1-f2×τ2 to a desired non-zero value, so that in step G, a specific order of the real part of the fractional Fourier transform of the signal of interest can be calculated.

[0057] - The method includes a step prior to step A, denoted as step A0, adjusting the first cavity or the second cavity to cancel the difference f1×τ1-f2×τ2 so that the power spectrum of the signal of interest can be calculated in step G. Attached Figure Description

[0058] Other features, details, and advantages of the invention will become apparent from the description given with reference to the accompanying drawings, which are illustrated by way of example and are as follows:

[0059] Figure 1 This is a schematic diagram of a spectrum analysis device using existing technology.

[0060] Figure 2 A schematic diagram of a broadband spectrum analysis device according to the present invention is shown.

[0061] Figure 3 A schematic diagram of a broadband spectrum analysis device according to a first embodiment of the present invention is shown.

[0062] Figure 4 A schematic diagram of a broadband spectrum analysis device according to a third embodiment of the present invention is shown.

[0063] Figure 5 A schematic diagram of a broadband spectrum analysis device according to a fourth embodiment of the present invention is shown.

[0064] Figure 6 A spectral analysis method according to the present invention is shown.

[0065] References to the accompanying drawings, when they are identical, correspond to the same elements.

[0066] Unless otherwise stated, the components in the figure are not drawn to scale. Detailed Implementation

[0067] Figure 2 This is a schematic diagram of a device D according to the invention for broadband spectral analysis of a signal of interest. As will be explained later, with the aid of a first frequency-shifting optical cavity BDF1 and a second frequency-shifting optical cavity BDF2, the device D of the invention makes it possible to determine the time representation of the frequency information of the signal of interest. Depending on certain conditions connecting these cavities, this time representation of the frequency information is the fractional transform or the real part of the power spectrum of the signal of interest.

[0068] "Broadband" here is understood to mean that the device's bandwidth is greater than or equal to 20 GHz, preferably greater than or equal to 40 GHz. The parameters controlling the device's bandwidth will be explained in the following description.

[0069] The device D of the present invention includes a radiation source S designed to generate a signal of interest Si. The beam splitter element ES of the device is designed to spatially split the signal of interest into a first signal V1 and a second signal V2.

[0070] According to one embodiment, the optical path of the signal of interest at the output of source S is an optical fiber path and the element ES is a 1x2 optical fiber coupler (also known as a Y-coupler). Alternatively, according to another embodiment, the optical path of the signal of interest at the output of source S is a free-space optical path and the beam splitter element ES is a beam splitter or a splitting cube.

[0071] A first signal V1 is injected into a first frequency-shifted optical cavity BDF1. The cavity BDF1 has a first travel time τ1 (round trip time in the cavity) and includes a first frequency shifter AOM1, which is designed to shift the optical frequency of the first signal by a first frequency f1 with each round trip in the first cavity.

[0072] Similarly, the second signal V2 is injected into the second frequency-shifting optical cavity BDF2, which has a second travel time τ2 and includes a second frequency shifter AOM2, which is designed to shift the optical frequency of the second signal by a second frequency f2 with each round trip in the second cavity.

[0073] Without choice and without departing from the scope of the invention, the first optical cavity BDF1 and the second optical cavity BDF2 may be linear cavities or ring cavities, or free space cavities or fiber optic cavities.

[0074] Essentially, the first and second optical cavities are designed such that the maximum number of round trips for the signal in the first and second cavities equals a predetermined number N. Therefore, f0 is called the center frequency of the signal of interest, and the first and second cavities each generate a frequency comb containing frequencies f0 + n × f1 and f0 + n × f2, respectively, where n ∈ [1; N]. Specifically, the first and second cavities generate copies of the signal of interest, both of which are time-shifted (multiples of τ1 and τ2, respectively) and frequency-shifted (multiples of f1 and f2, respectively).

[0075] According to one embodiment, in order to control the maximum number of round trips N, the first loop and the second loop respectively include a first bandpass filter and a second bandpass filter BP1, BP2 ( Figure 2 Not shown in the image, but... Figure 5 and Figure 6 As can be seen in the text, they have bandwidths suitable for transmission frequencies f0+n×f1 and f0+n×f2, respectively, where n∈[1;N].

[0076] The first frequency shifter AOM1 and the second frequency shifter AOM2 are preferably acousto-optic modulators controlled by a first local oscillator OL1 and a second local oscillator OL2 (not shown in the figure). The excitation frequencies generated by the first and second local oscillators allow for the alteration of the first frequency f1 and the second frequency f2. Alternatively, the first and second frequency shifters are single-sideband electro-optic modulators (or SSB MZM, used for single-sideband Mach-Zehnder modulators).

[0077] Device D also includes a detector PD, which is designed to coherently detect a first signal W1 transmitted from the first cavity and a second signal W2 transmitted from the second cavity. The detector PD is typically a photodiode or any other photodetector known to those skilled in the art. Preferably, the detector PD is formed from a balanced photodiode to detect very small changes in the optical signal.

[0078] The detector PD detects the light intensity in real time, which corresponds to the coherent sum of all copies of the signal of interest, time-shifted and frequency-shifted (frequency combed) by the first and second cavities, and then generates a photocurrent Tr proportional to the detected light intensity. For the device to operate, the first signal W1 transmitted by BDF1 must be coherent with the signal W2 transmitted by BDF2.

[0079] Then, the photocurrent Tr is filtered by a low-pass analog filter LP, which is designed to allow the photocurrent frequency, which is lower than the Nyquist frequency associated with the first signal W1 and the second signal W2, to pass through, i.e., min(f1 / 2; f2 / 2).

[0080] Finally, device D includes a processor UT, which is configured to calculate the square modulus of the photocurrent filtered by filter LP, thereby generating a time trace TT. Through this trace TT, device D enables the determination of a time representation of the frequency information of the signal of interest.

[0081] In device D of the present invention, the bandwidth is equal to LS. in = 1 / (τ1-τ2). This property is of great interest because the bandwidth of device D can be maximized by minimizing the difference τ1-τ2.

[0082] The inventors have demonstrated that, based on the difference f1×τ1-f2×τ2, the trace TT is the real part of the fractional Fourier transform or the power spectrum of the signal of interest. For clarity, the derivation of the equations illustrating this result is given at the end of this specification.

[0083] Therefore, according to a first variant of the invention, the first and second cavities are configured to verify the condition f1×τ1=f2×τ2 (modulo 1). In this first variant, the photocurrent Tr is the time representation of the real part (α=π / 2) of the Fourier transform of the signal of interest, and the trace TT is the time representation of the power spectrum of the signal. Thus, device D can map the spectrum (frequency-to-time mapping) that varies with time in real time.

[0084] Preferably, in this first variant, the analog low-pass filter LP is designed to filter frequencies of photocurrent below the value min[N×|f1-f2|;f1 / 2;f2 / 2)] before the processor UT calculates the square modulus of the photocurrent. Filtering frequencies below N×|f1-f2| allows the photocurrent Tr to be processed using a processor with slower processing electronics (typically 50 M samples / second) when this value is below the Nyquist frequencies f1 / 2;f2 / 2.

[0085] In this first variant, the frequency resolution of the device is Δ f =1 / (N(τ1-τ2))=LS in / N. Therefore, it will be understood that in order to maintain high bandwidth LS in At the same time, obtain a suitable spectral resolution Δ f It is necessary to maximize the maximum round-trip count in the first cavity BDF1 and the second cavity BDF2. Preferably, to obtain a suitable spectral resolution, the first and second cavities are configured such that the maximum round-trip count N is greater than 200, preferably greater than 500. Typically, for LS... in = 20GHz bandwidth, N = 400, the device's frequency resolution is Δ f =50MHz.

[0086] In a second variant of the invention, the first and second cavities are configured to verify the condition f1×τ1≠f2×τ2, modulo 1. This difference should be much less than 1, that is: f1τ1=f2τ2+ε,|ε|<<1 (see the equation at the end of the description). In this second variant, the trace TT is the time representation of the real part of the fractional Fourier transform (FrFT) of the signal of interest. The order of the fractional transform, represented by device D, is set by the difference f1×τ1-f2×τ2. More specifically, when f1×τ1=f2×τ2 modulo 1 (first variant of the invention), the photocurrent is the time representation of the real part of the Fourier transform of the input signal (that is, the order of the FrFT corresponding to π / 2), while when the value of f1×τ1-f2×τ2 is close to 0 (second variant), the photocurrent represents the real part of the FrFT of the signal of interest. Specifically, the order of FrFT depends on the scaling factor (f2-f1) / (τ1-τ2) (see the equation at the end of the description).

[0087] In a second variant of the invention, frequency resolution can be defined by considering two signals with linear frequency modulation, which are simultaneous and have the same linear modulation rate (i.e., the same slope in the time-frequency plane). Therefore, the two signals differ in their starting frequencies. By choosing the correct FrFT order, the FrFT of these linearly modulated signals consists of two peaks, the spacing of which is proportional to the frequency difference between the two linearly modulated signals. In this second variant, the resolution of the device corresponds to the minimum frequency difference between the two linearly modulated signals that the device can measure. This definition makes it possible to define the frequency resolution for this system.

[0088] Therefore, based on the difference f1×τ1-f2×τ2, the device D of the present invention enables the acquisition of the real-time representation of two different frequency information items of the signal of interest: the real part or power spectrum of the FrFT.

[0089] The device's time resolution (i.e., the time spent by the system to calculate and generate frequency information) is equal to 1 / (f2-f1). It should be noted that the frequency information is acquired in real time, meaning that the determined frequency information is updated every 1 / (f2-f1) cycles.

[0090] According to one embodiment, the first cavity includes a first controllable delay line DL1 (not shown) designed to change a first travel time τ1 and / or the second cavity includes a first controllable delay line DL2 (not shown) designed to change a second travel time τ2. Therefore, the difference (τ1-τ2) can be reduced to maximize the bandwidth LS of device D. in Preferably, the difference (τ1-τ2) makes the bandwidth LS in Greater than or equal to 20 GHz, preferably greater than or equal to 40 GHz. This bandwidth value is described in the document "de Chatellus, Hugues Guillet, Luis Romero Cortés and José". The device described in "Optical real-time Fourier transformation with kilohertz resolution" Optica 3.1 (2016): 1-8" is not feasible, as the device's bandwidth is on the order of 10 MHz because it is set by 1 / τ1.

[0091] An advantage of embodiments of the invention that include delay lines DL1, DL2 and / or frequency shifters AOM1, AOM2, which allow for changes in f1 and f2, is that the difference f1×τ1-f2×τ2 can be controlled. Therefore, the operation of the device can be switched from a first variant of the invention to a second variant, and vice versa. Furthermore, controlling the difference f1×τ1-f2×τ2 allows selection of the order of the FrFT of the signal of interest.

[0092] It should be noted that, in this embodiment of the invention, the first cavity BDF1 and the second cavity BDF2 respectively include a first bandpass filter BP1 and a second bandpass filter BP2, when the spectral width LS BP When it is less than 1 / (τ1-τ2), this bandwidth is LS in Equal to the spectral width LS of the first and second bandpass filters BP In other words, bandwidth equals LS. in =min(1 / (τ1-τ2);LS BP ).

[0093] It is worth noting that device D does not perform any truncation or sampling on the spectrum of the signal of interest, thereby reducing the portion of the spectrum being analyzed. Therefore, unlike some of the aforementioned devices in the prior art, device D of the present invention has 100% POI and the frequency information of the signal of interest represented by the trace TT represents the entire spectrum of the signal of interest within the bandwidth.

[0094] According to one embodiment, the first cavity and the second cavity respectively include a first amplifier and a second amplifier EDFA1 and EDFA2. Figure 1 Not shown in the text but Figure 4 (As can be seen in the image), they are designed to compensate for the losses caused by the first and second cavities.

[0095] According to a first embodiment of the present invention, such as Figure 3As shown, source S includes a monochromatic continuous-wave laser CW, an RF source AM designed to generate an RF signal s(t), and a modulator Mod. The modulator is designed to amplitude-modulate or phase-modulate the laser radiation generated by the continuous-wave laser using the RF signal s(t) to form the signal of interest. In a first embodiment of the invention, device D allows for the determination of the time representation of the frequency information of the RF signal s(t) carried by the continuous-wave laser. Therefore, according to a second variant of the invention, trace TT is the time representation of the FrFT of the RF signal s(t), and according to a first variant of the invention, trace TT is the time representation of the convolution of the monochromatic laser continuous-wave power spectrum with the power spectrum of the RF signal s(t). When the coherence time of the laser CW is sufficient to keep the radiation coherent within cavities BDF1 and BDF2 (typically approximately 100 μs), trace TT is the time representation of the real part of the spectrum of the RF signal s(t). Considering the bandwidth LS of the device... in This first embodiment is particularly interesting because it can be greater than 40 GHz while having 100% POI, values ​​that are not impossible to achieve using existing equipment for RF signal spectrum analysis.

[0096] In the second embodiment, the source S is a coherent light source, such as a laser source, that generates a signal of interest Si in the form of optical radiation s(t). In the second embodiment of the invention, the device D makes it possible to determine the time representation of the frequency information of the signal s(t).

[0097] Figure 4 A third embodiment, compatible with the first and second embodiments, is schematically illustrated, wherein the entire optical path from the source to the signal of interest detected by the photodiode is fiber-optic. This simplifies device alignment and makes the device less sensitive to shock and vibration. In this third embodiment, the signal of interest Si is split by a Y-coupler ES to form a first signal V1 and a second signal V2, both guided in their respective optical fibers. The first BDF1 and the second cavity BDF2 are fiber ring cavities, each comprising first and second doped fiber amplifiers EDFA1 and EDFA2, and first and second optical bandpass filters BP1 and BP2, respectively. The first signal V1 is injected into the first cavity BDF1 via fiber coupler C1, and the second signal V2 is injected into the second cavity BDF2 via fiber coupler C2.

[0098] As described above, the first and second doped fiber amplifiers EDFA1 and EDFA2, such as EDFA, are designed to compensate for losses in cavities BDF1 and BDF2. Optical bandpass filters BP1 and BP2 are configured to set the maximum round-trip number N in the first and second cavities and to limit noise generated by the amplified spontaneous emission of the doped fiber amplifiers.

[0099] Advantageously, in the third embodiment, device D includes a stabilizing device ST (not shown) for stabilizing the first BDF1 and the second cavity BDF2, which is designed to maintain the coherence between the first signal transmitted by the first cavity and the second signal transmitted by the second cavity over time. The stabilizing device makes it possible to ensure that the radiation transmitted by the two cavities BDF1, BDF2 is mutually coherent. Such devices are well known to those skilled in the art and are described, for example, in "Coherent multi-heterodyne spectroscopy using acousto-opticfrequency combs", Opt. Express 26, 13800-13809 (2018).

[0100] Figure 5 A fourth embodiment, compatible with the first and second embodiments, is schematically illustrated and constitutes an alternative to the third embodiment. This fourth embodiment aims to overcome the problem of maintaining coherence between the first signal W1 and the second signal W2 transmitted by the first and second cavities over time. For this purpose, the device includes a single-fiber annular cavity BDF configured to form a first BDF1 and a second cavity BDF2 in the injection direction. This configuration with a single backpropagation annular cavity can limit the effects of fiber length fluctuations (vibration, thermal drift, etc.), which may differ between the first and second cavities in the third embodiment and cause loss of coherence with round trips. It also reduces the number of optical components required.

[0101] Similar to the third embodiment, in device D of the fourth embodiment, the entire optical path of the signal of interest from the source to the photodiode detection is fiber optic. Device D includes a first fiber coupler C1, which is designed to inject a first signal V1 into a single-cavity BDF in a first direction S1. Furthermore, device D includes a second fiber coupler C2, which is designed to inject a second signal V2 into the single-cavity BDF in a second direction S2. The cavity BDF includes:

[0102] • The first circulator CO1 is designed to direct the first signal V1 to the first delay line DL1, which includes the first frequency shifter AOM1.

[0103] • The second circulator CO2 is designed to direct the second signal to the second delay line DL2, which includes the second frequency shifter AOM2.

[0104] • Bidirectional doped fiber amplifier (EDFA) (bidirectional operation)

[0105] The optical bandpass filter BP is configured to set the maximum round-trip number N. Therefore, the first cavity BDF1 corresponds to a single cavity BDF in which the first signal V1 is injected along the first injection direction S1, and the second cavity BDF2 corresponds to a single cavity BDF in which the second signal V2 is injected along the second injection direction S2.

[0106] As an alternative, according to a variant of the fourth embodiment, the first delay line DL1 includes a first amplifier EDFA1 and an optical bandpass filter BP1, and the second delay line DL1 includes a second amplifier EDFA2 and an optical bandpass filter BP2, instead of a single amplifier EDFA and a single optical bandpass filter BP shared by the first signal V1 and the second signal V2.

[0107] Will understand, Figures 3 to 5 The embodiments are compatible with the first and second variants of the present invention based on the difference f1×τ1-f2×τ2.

[0108] Another subject of the present invention is a method for spectral analysis of a signal of interest Si, implemented by the device D of the present invention. Figure 6 This method is illustrated schematically, allowing for a time representation of the frequency information (FrFT or power spectrum) of the signal of interest based on the difference f1×τ1-f2×τ2.

[0109] Figure 6 The method includes the following steps:

[0110] A. Generate the signal of interest Si;

[0111] B. Spatially divide the signal of interest into a first signal V1 and a second signal V2;

[0112] C. Inject the first signal into the first frequency-shifting optical cavity BDF1, and shift the optical frequency of the first signal by the first frequency f1 each round trip in the first cavity;

[0113] D. Inject the second signal into the second frequency-shifting optical cavity BDF2, and shift the optical frequency of the second signal by the second frequency f2 each round trip in the second cavity;

[0114] E. 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 that is proportional to the detected light intensity.

[0115] F. For those below The frequency of the photocurrent is filtered.

[0116] G. Calculate the square modulus of the filtered photocurrent, and determine the time representation of the frequency information of the signal of interest based on the square modulus.

[0117] Figure 6 The method has the following significant advantages: wide bandwidth, 100% POI, and good frequency resolution.

[0118] according to Figure 6 A first variant of the method, comprising a step prior to step A), denoted as step A0): adjusting the first or second cavity to cancel the difference f1×τ1-f2×τ2, so that the power spectrum of the signal of interest can be calculated in step G. This first variant is implemented by a first variant of the device of the present invention.

[0119] according to Figure 6 A second variant of the method, comprising a step preceding step A), denoted as step A0): adjusting the first or second cavity to set the difference f1×τ1-f2×τ2 to a desired non-zero value, so that a specific order of the real part of the fractional Fourier transform of the signal of interest can be calculated in step G. This second variant is implemented by a second variant of the device of the present invention.

[0120] The equation shows that, based on the difference f1×τ1-f2×τ2, the trace TT is the real part of the fractional Fourier transform or the power spectrum of the signal of interest, as derived below.

[0121] f0 represents the frequency of the injected laser, τ1 and τ2 represent the travel time in the loop, f1 and f2 represent the offset frequency of each travel, and s(t) represents the signal of interest.

[0122] The electric fields at the output terminals of the first and second cavities are respectively:

[0123]

[0124]

[0125] The intensity detected by PD is:

[0126]

[0127] Where w(t) is the time window centered at t (correlated with the detected response), and * represents the convolution product. (Omitted terms) get

[0128]

[0129]

[0130] Choose frequencies f1 and f2 such that Δf = f2 - f1 ≤ f1 / 2N, f2 / 2N. The duration of the window w(t) is chosen to be on the order of 1 / NΔf. Therefore, the duration is greater than 2 / f1 and 2 / f2. Thus, only integer pairs (n, m = n) contribute non-zero to the integral.

[0131] First variant of the invention:

[0132] Here we assume f1τ1 = f2τ2. Then we give:

[0133] I(t)=∫w(tt′)∑ n s(t′-nτ1)s(t′-nτ2)e -i2πnΔft′ dt′ (6)

[0134] During the duration of the window, e -i2πnΔft′ It can be assimilated into e -i2πnΔft Because the duration of the window is longer than the function e -i2πnΔft′ The cycle is short.

[0135] This therefore gives:

[0136] I(t)=∑ n e -i2πnΔft ∫w(tt′)s(t′-nτ1)s(t′-nτ2)dt′ (7)

[0137] I(t)=∑ n <s(t-nτ1)s(t-nτ2)> e -i2πnΔft (8)

[0138] Where <> represents the average value measured over the window duration.

[0139] The origin of the moving time is given

[0140] I(t)=∑ n <s(t)s(t-nΔτ)> e -i2πnΔft (9)

[0141] Where Δτ = τ² - τ¹. The correlation function of delay T at time t is defined as: C(t,T) =<s(t)s(t-T)> .

[0142] That is to say, I(t) = ∑ n C(t,nΔτ)e -i2πnΔft (10)

[0143] According to records, δ(t) is defined as the Dirac delta function:

[0144]

[0145] at last:

[0146]

[0147] in yes Fourier transform (FT) of variable t′.

[0148] Therefore, I(t) is the repetition of the Fourier Transform (FT) of the autocorrelation function at time t over time; that is, the power spectrum of the input signal at time t, using the Wiener-Khintchine theorem. It's important to note that the signal actually measured by the detector (PD) is 2Re(I(t)). The power spectrum is obtained by applying the Hilbert transform to the measured signal.

[0149] The period of the output signal is 1 / Δf. Therefore, this gives the spectrum of the input signal projected into the time domain ("frequency-to-time mapping"). The scaling factor is Δτ / Δf = (f2-f1) / (τ1-τ2).

[0150] The temporal resolution is given by the duration of the window w(t), which is on the order of 1 / NΔf. Therefore, the spectral resolution is:

[0151] The spectral width of s(t) that can be clearly measured is 1 / Δτ.

[0152] It should be noted that this result is valid for all values ​​of f1τ1=f2τ2modulo 1 (see Equation 5). Here, modulo 1 is understood as f1τ1=f2τ2+k, where

[0153] Second variant of the invention:

[0154] Now assume: f1τ1=f2τ2+ε, (|ε|<<1) and give:

[0155]

[0156] Follow the same process:

[0157]

[0158] To give the fractional Fourier transform, set y = t′ / Δτ. Therefore, this gives:

[0159]

[0160] The expression for the fractional FT (FrFT) of function C is recognized (except for the form: (The second phase term). Here, the order α of the FrFT is given by: cotα = 2πε. Note that the definition of the parameter y here defines the order of the FrFT.

[0161] Finally, I(t) is therefore a repetition of the FrFT projected by the autocorrelation function at time t over time, that is, the square modulus of the FrFT of the input signal using the convolution theorem applied to the FrFT.

[0162] As mentioned earlier, the signal actually measured by the detector is 2Re(I(t)), which means that the square modulus of the FrFT is obtained through the Hilbert transform of the measured signal.

[0163] The period of the output signal is 1 / Δf. Therefore, this gives the FrFT ("fractional frequency to time mapping") of the input signal projected into the time domain.

Claims

1. A broadband device (D) for performing spectral analysis on a signal of interest, comprising: A source (S) is designed to generate the signal of interest (Si); A beam splitter element (ES) is designed to spatially split the signal of interest into a first signal (V1) and a second signal (V2). A first frequency-shifting optical cavity (DBDF, BDF1) includes a first frequency shifter (AOM1), the first frequency shifter being designed to shift the optical frequency of the first signal by a first frequency with each round trip within the first frequency-shifting optical cavity. The first frequency-shifting optical cavity has a first travel time. ; The second frequency-shifting optical cavity (DBDF, BDF2) includes a second frequency shifter (AOM2), which is designed to shift the optical frequency of the second signal by a second frequency with each round trip within the second frequency-shifting optical cavity. The second frequency-shifting optical cavity has a second travel time. ; The first and second frequency-shifting optical cavities are designed such that the maximum number of round trips of the signal in the first and second frequency-shifting optical cavities is equal to a predetermined value. N ; A detector (PD) is designed to coherently detect the first signal (W1) transmitted by the first frequency-shifted optical cavity and the second signal (W2) transmitted by the second frequency-shifted optical cavity, and generate a photocurrent (Tr) proportional to the light intensity detected by the detector. A low-pass filter (LP) is designed to filter the photocurrent at a frequency lower than 100 Hz. Filter the frequency. A processor (UT) is configured to calculate the square modulus of the photocurrent filtered by the low-pass filter, and determine a time representation of the frequency information of the signal of interest based on the square modulus, wherein the frequency information is: The real part of the fractional Fourier transform of the signal of interest, when the first and second frequency-shifting optical cavities are configured as verification conditions. When modulo 1, the order of the fractional Fourier transform is determined by the value Settings, or When the first and second frequency-shifting cavities are configured as verification conditions The power spectrum of the signal of interest when modulo 1.

2. The device as claimed in claim 1, wherein, The source includes a monochromatic continuous-wave laser (CW) designed to generate RF signals. The RF source (AM) and modulator (Mod), the modulator being designed to use the RF signal. The laser radiation generated by the continuous wave laser is amplitude-modulated or phase-modulated to form the signal of interest.

3. The device as described in claim 1 or 2, wherein, The low-pass filter LP is designed such that when the first and second frequency-shifting cavities are configured as verification conditions... When modulo 1, the photocurrent is lower than The frequency of the filter is used for filtering.

4. The device as described in claim 1 or 2, wherein, The first frequency-shifting optical cavity and the second frequency-shifting optical cavity each include a first amplifier and a second amplifier (EDFA, EDFA1, EDFA2), and the first amplifier and the second amplifier are designed to compensate for the losses caused by the first frequency-shifting optical cavity and the second frequency-shifting optical cavity, respectively.

5. The device as described in claim 1 or 2, wherein, The first frequency shifter is a first acousto-optic modulator excited by a first local oscillator (OL1) designed to change the first frequency shift, and wherein the second frequency shifter is a second acousto-optic modulator excited by a second local oscillator (OL2) designed to change the second frequency shift.

6. The device as claimed in claim 1 or 2, wherein, The first frequency-shifting optical cavity includes components designed to change the first travel time. The first controllable delay line (DL1), and wherein the second frequency-shifting cavity includes components designed to change the second travel time. The second controllable delay line (DL2).

7. The device as claimed in claim 1 or 2, wherein, The first and second frequency-shifting optical cavities are fiber ring cavities (BDF1 and BDF2), each comprising a first doped fiber amplifier and a second doped fiber amplifier (EDFA1 and EDFA2), and configured to set the maximum round-trip number in the first and second frequency-shifting optical cavities. N The first optical bandpass filter and the second optical bandpass filter (BP1, BP2).

8. The device of claim 7, further comprising a stabilization device (ST) for stabilizing the first frequency-shifting optical cavity and the second frequency-shifting optical cavity, the stabilization device being designed to maintain the coherence of the first signal transmitted by the first frequency-shifting optical cavity and the second signal transmitted by the second frequency-shifting optical cavity over time.

9. The device of claim 6, comprising a single annular cavity (BDF), the device further comprising: A first coupler (C1) is designed to inject the first signal (V1) into the single annular cavity in a first direction. A second coupler (C2) is designed to inject the second signal (V2) into the single annular cavity in a second direction. The first frequency-shifting optical cavity corresponds to the single annular cavity in which the first signal is injected in the first injection direction. The second frequency-shifting optical cavity corresponds to the single annular cavity in which the second signal is injected in the second injection direction. The single annular cavity includes: A first circulator (CO1) is designed to direct the first signal to a first controllable delay line (DL1) and includes a first frequency shifter (AOM1), the first controllable delay line being designed to change the first travel time. , The second circulator (CO2), designed to direct the second signal to the second controllable delay line (DL2) and including the second frequency shifter (AOM2), the second controllable delay line being designed to change the second travel time. , Doped fiber amplifier (EDFA). An optical bandpass filter (BP) is configured to set the maximum round-trip number. N .

10. The device as claimed in claim 1 or 2, wherein, The first frequency-shifting optical cavity and the second frequency-shifting optical cavity are configured such that .

11. The device as claimed in claim 1 or 2, wherein, The first frequency-shifting optical cavity and the second frequency-shifting optical cavity are configured such that N Greater than 200.

12. A method for performing spectral analysis on a signal of interest (Si) using a first frequency-shifting optical cavity (BDF1) and a second frequency-shifting optical cavity (BDF2), wherein the first frequency-shifting optical cavity (BDF1) includes a first frequency shifter (AOM1) and has a first travel time. The second frequency-shifting optical cavity (BDF2) includes a second frequency shifter (AOM2) and has a second travel time. The maximum number of round trips of the signal of interest in the first and second frequency-shifting optical cavities is equal to a predetermined value. N The method includes the following steps: A. Generate the signal of interest; B. Spatially divide the signal of interest into a first signal (V1) and a second signal (V2); C. Inject the first signal into the first frequency-shifting optical cavity (BDF1), and shift the optical frequency of the first signal by a first frequency with each round trip in the first frequency-shifting optical cavity. ; D. Inject the second signal into the second frequency-shifting optical cavity (BDF2), and shift the optical frequency of the second signal by a second frequency with each round trip in the second frequency-shifting optical cavity. ; E. Perform coherent detection on the first signal (W1) transmitted by the first frequency-shifting optical cavity and the second signal (W2) transmitted by the second frequency-shifting optical cavity, and generate a photocurrent (Tr) that is proportional to the detected light intensity. F. For the photocurrent below Filter the frequency. G. Calculate the square modulus of the filtered photocurrent and determine the time representation of the frequency information of the signal of interest. The method includes a step preceding step A, denoted as step A0, wherein step A0 is: Adjust the first or second frequency-shifting optical cavity to reduce the difference. Set to the desired non-zero value so that in step G, the specific order of the real part of the fractional Fourier transform of the signal of interest is calculated, or Adjust the first or second frequency-shifting optical cavity to compensate for the difference. This is so that the power spectrum of the signal of interest can be calculated in step G.

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