A photonic beamformer based on complex-valued filtering of wavelength-division multiplexed signals


Ψ 1 Ψ 2 Ψ 3 Ψ 4 a b c
Ψ(t) = A(t) (j (ω (t)t)) , A(t) ω (t) j δt = d/c × (α), d c α Ψ i (t) Ψ i (t) = A (t -iδt) (jω (t -iδt) t) .

ICSO 2020 International Conference on Space Optics

Virtual Conference 30 March-2 April 2021 
A (t -iδt) ≈ A (t) ∀i, (jω (t -iδt) t) ≈ (j (ω (t) t -iδθ)) ∀i, δθ = ω δt Ψ i (t) Ψ i (t) ≈ A (t) (j (ω (t) t -iδθ)) . ω ,i M (t) = N -1 i=0 √ P i 2 (j (ω ,i t + Φ ,i (t))) • [1 + Ψ i (t)] , N P i Φ ,i (t) L 1 L 2 L 1 (t) = N -1 i=0 Γ i (t)Ψ i (t), L 2 (t) = N -1 i=0 Γ i (t), Γ i (t) = √ P i /2 (j (ω ,i t + Φ i (t))) ω L 2, (t) = N -1 i=0 Γ i (t) (j (ω t + Φ )) , Φ Υ(t) = (j (ω t + Φ )) L 2, (t) = N -1 i=0 Γ i (t)Υ(t) (jρ i ) , ρ i ρ i = iδθ L 1 (t) L 2, (t) S 1 S 2 = √ 1 - j √ j √ √ 1 - L 1 (t) L 2, ( t 
E (t) = R Z |S 1 | 2 -|S 2 | 2 , R Z E (t) = R Z √ 1 -L 1 (t) + j √ L 2, (t) 2 -j √ L 1 (t) + √ 1 -L 2, (t) 2 . |x| 2 = xx † E (t) = R Z (1 -2 ) L 1 (t)L † 1 (t) + (2 -1) L 2, (t)L † 2, (t) 
+ ( -1) L † 1 (t)L 2, (t) + L 1 (t)L † 2, (t) . 
= 0.5 
E (t) = -R 4Z L † 1 (t)L 2, (t) + L 1 (t)L † 2, (t) . L 1 (t) L 2, (t) 
P i = P ∀i E (t) = -RP A(t) 16Z N -1 i=0 (j ((ω -ω (t)) t + iδθ + ρ i + Φ )) + (j ((ω (t) -ω ) t -iδθ -ρ i -Φ )) , E (t) = -RP A(t) 8Z N -1 i=0 ((ω (t) -ω ) t -iδθ -ρ i -Φ ) . Φ ,i (t) ρ i = -iδθ E (t) = N -RP A(

Conference on Space Optics Virtual Conference 30 March-2 April 2021 ω

  
	ICSO 2020		
	International		
	d	f	
			E ,1 (t)
			E ,2 (t)
	e	g	h
	Ψi		E ,k

) , ICSO 2020 International Conference on Space Optics Virtual Conference 30 March-2 April 2021

  

Conference on Space Optics Virtual Conference 30 March-2 April 2021

  
	ICSO 2020		
	International		
	8Z	t)	((ω (t) -ω ) t -Φ ) .
	N		
	Φ		

Proc. of SPIE Vol. 11852 118523S-2 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. of SPIE Vol. 11852 118523S-3 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. of SPIE Vol. 11852 118523S-4 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. of SPIE Vol. 11852 118523S-5 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. of SPIE Vol. 11852 118523S-6 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. of SPIE Vol. 11852 118523S-7 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. SPIE Vol. 11852 118523S-8 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. of SPIE Vol. 11852 118523S-9 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 

Proc. of SPIE Vol. 11852 118523S-10 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 24 Sep 2023 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
Rui Oliveira, Rogério N Nogueira, Miguel V Drummond
A photonic beamformer based on complex-valued filtering of wavelength-division multiplexed signals