Wide-band device for measuring the cross-correlation of signals
A wideband device for measuring the cross-correlation of a first signal and a second signal, includes a first frequency-shifting optical cavity comprising a first frequency shifter designed to shift the optical frequency of the first signal by a first frequency f 1 per round trip in the first cavity, the first cavity having a first trip time τ 1 ; a second frequency-shifting optical cavity comprising a second frequency shifter designed to shift the optical frequency of the second signal by a second frequency f 2 per round trip in the second cavity, the second cavity having a second trip time τ 2 ; the first and the second optical cavity being designed such that a maximum number of round trips of the first and the second signal in the first and the second cavity is equal to predetermined N, a detector designed to coherently detect the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generate a photocurrent (Tr) proportional to a luminous intensity detected by the detector, a low-pass filter designed to filter frequencies of the photocurrent that are lower than min (I), a processor configured to compute a Fourier transform of the photocurrent, so as to generate an output signal that is representative (II).
1. A wideband device (D) for measuring the cross-correlation of a first signal and a second signal, comprising:
a first source (S 1 ) designed to generate said first signal s 1 (t) (Si 1 );
a second source (S 2 ) designed to generate said second signal s 2 (t) (Si 2 );
a first frequency-shifting optical cavity (DBDF, BDF 1 ) comprising a first frequency shifter (AOM 1 ) designed to shift the optical frequency of the first signal by a first frequency f 1 per round trip in said first cavity, said first cavity having a first trip time τ 1 ;
a second frequency-shifting optical cavity (DBDF, BDF 2 ) comprising a second frequency shifter (AOM 1 ) designed to shift the optical frequency of the second signal by a second frequency f 2 per round trip in said second cavity, said second cavity having a second trip time τ 2 ;
the first and the second optical cavity being designed such that a maximum number of round trips of the first and the second signal in the first and the second cavity is equal to predetermined N
a detector (PD) designed to coherently detect the first signal transmitted by the first cavity and the second signal 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 Fourier transform of said photocurrent filtered by said low-pass filter, so as to generate an output signal (SS) representative, in the frequency space, of a real-time cross-correlation between the first signal and the second signal, C(τ)= s 1 (t)s 2 *(t−τ) , with τ=n(τ 1 −τ 2 ), n∈[1, N].
2. The device as claimed in claim 1 , wherein the device comprises a monochromatic laser (CW), the first and the second sources respectively comprising: a first and a second RF source (AM 1 , AM 2 ) designed to generate a first and a second RF signal s 1 ( t ), s 2 ( t ) and a first and a second modulator (Mod 1 , Mod 2 ) designed to amplitude-modulate, using said first and said second RF signal s 1 ( t ), laser radiation generated by said continuous-wave laser, so as to form said first and said second signal.
3. The device as claimed in claim 1 , wherein the first source is configured to generate a plurality of i∈[1, p] first sub-signals s 1,i (t) that are spatially and temporally superposed so as to form the first signal, each i first sub-signal having a first center frequency f 1,i different from the others, and wherein the second source is configured to generate a plurality of j∈[1, q] second sub-signals s 2,j (t) that are spatially and temporally superposed so as to form the second signal, each j second sub-signal having a second center frequency f 2,i different from the others,
said output signal then being representative of a cross-correlation of each first sub-signal with each second sub-signal, C i,j (τ)= s 1,i (t)s 2,j *(t−τ , with τ=n(τ 1 −τ 2 ), n∈[1, N].
4. The device as claimed in claim 1 , wherein the first and the second cavity are designed to verify the condition f 1 ×τ 1 =f 2 ×τ 2 modulo 1, said output signal (SS) then corresponding to the real part of a real-time cross-correlation between the first signal and the second signal, C(τ)= s 1 (t)s 2 *(t−τ) , with τ=n(τ 1 −τ 2 ), n∈[1, N].
5. The device as claimed in claim 1 , wherein the first and the second cavity are designed such that f 1 ×τ 1 ≠f 2 ×τ 2 modulo 1, said processor furthermore being configured to compute a square modulus of a Fourier transform of said photocurrent, the output signal (SS) then corresponding to a square modulus of a real-time cross-correlation between the first signal and the second signal, |C(τ)| 2 =| s 1 (t)s 2 (t−τ) | 2 , with τ=n(τ 1 −τ 2 ), n∈[1, N].
6. The device as claimed in claim 1 , wherein the first and the second cavity respectively comprise a first and a second amplifier (EDFA, EDFA 1 , EDFA 2 ) designed to compensate for the losses induced respectively by the first and the second cavity.
7. The device as claimed in claim 1 , wherein the first frequency shifter is a first acousto-optic modulator excited by a first local oscillator (OL 1 ) 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 (OL 2 ) designed to vary said second shift frequency.
8. The device as claimed in claim 7 , comprising a single ring cavity (BDF), said device furthermore comprising:
a first coupler (C 1 ) designed to inject said first signal (V 1 ) into said single cavity in a first direction,
a second coupler (C 2 ) designed to inject said second signal (V 2 ) 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 (CO 1 ) designed to direct the first signal to a first controllable delay line (DL 1 ) designed to vary the first trip time τ 1 and comprising said first frequency shifter (AOM 1 ),
a second circulator (CO 2 ) designed to direct the second signal to a second controllable delay line (DL 2 ) designed to vary the second trip time τ 1 and comprising said second frequency shifter (AOM 2 ),
a doped fiber amplifier (DFA),
an optical bandpass filter (BP) configured to set said maximum number N of round trips.
9. The device as claimed in claim 1 , wherein the first cavity comprises a first controllable delay line (DL 1 ) designed to vary the first trip time τ 1 and wherein the second cavity comprises a second controllable delay line (DL 2 ) designed to vary the second trip time τ 2 .
10. The device as claimed in claim 1 , wherein the first and the second cavity are fiber ring cavities (BDF 1 , BDF 2 ) comprising respectively a first and a second doped fiber amplifier (DFA 1 , DFA 2 ) and a first and a second optical bandpass filter (BP 1 , BP 2 ) configured to set said maximum number N of round trips in the first and the second cavity.
11. The device as claimed in claim 10 , 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.
12. The device as claimed in claim 1 , wherein the first and the second cavity are configured such that
1
❘
"\[LeftBracketingBar]"
τ
1
-
τ
2
❘
"\[RightBracketingBar]"
≥
40
GHz
.
13. The device as claimed in claim 1 , wherein the first and the second cavity are configured such that N is greater than 200.
14. A method for measuring the cross-correlation of a first and a second signal (Si 1 , Si 2 ) using a first frequency-shifting optical cavity (BDF 1 ) having a first trip time τ 1 and a second frequency-shifting optical cavity (BDF 2 ) comprising a second frequency shifter (AOM 1 ) having a second trip time τ 2 , a maximum number of round trips of the first signal and of the second in the first and the second cavity being equal to predetermined N, said method comprising the following steps:
F. generating said first signal s 1 (t) and said second signal s 2 (t);
G. injecting said first signal into the first frequency-shifting optical cavity (BDF 1 ) and shifting the optical frequency of the first signal by a first frequency f 1 per round trip in said first cavity, injecting said second signal into the second frequency-shifting optical cavity (BDF 2 ) and shifting the optical frequency of the second signal by a second frequency f 2 per round trip in said second cavity;
H. coherently detecting the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generating the photocurrent (Tr) proportional to the detected luminous intensity, a maximum number of round trips of the first and the second signal respectively in the first and the second cavity before they are transmitted being equal to predetermined N, and
I. filtering frequencies of the photocurrent that are lower than
min
(
f
1
2
;
f
2
2
)
,
J. computing a Fourier transform of said filtered photocurrent, so as to generate an output signal (SS) that is representative of a real-time cross-correlation between the first signal and the second signal, C(T)= s 1 (t)s 2 *(t−τ , with τ=n(τ 1 −τ 2 ), n∈[1, N].