Transcript
An Efficient time lens for optical pulse compression Taraprasad Chattopadhyay and Sujit Das Presented by: Prof. Taraprasad Chattopadhyay Department of Physics Visva-Bharati University Santiniketan, West Bengal, India.
Why do we need optical pulse compression? • Conventional methods generate optical pulses having widths in the picosec. region. • Femto second pulses find applications in optical time division multiplexed (OTDM) communication system. OTDM is a high capacity, high bit-rate communication system. • High bit-rate requires high repetition rate of the pulse. • To generate high repetition rate pulses we need ultra-short widths of optical pulses. • This is one application – there are other applications as well.
How to generate ultra-short optical pulses? • Normal pulses can be compressed in the time domain Generation of ultra-short optical pulses
How can we produce pulse compression? by using a time lens
What is a time lens? • Ordinary lenses used in geometrical optics are spatial lenses. They compress a light beam in space. • On the other hand, a time lens compresses the light pulse in time reduction of optical pulse width
How to design a time lens ? • Apply phase modulation of the pulse and then pass through a single-mode fiber to exploit group velocity dispersion. • Phase modulation broadens the spectrum of the pulse, while GVD produces a cancellation of pulse broadening. overall pulse compression
Author’s proposal • Use a cascade of phase modulators instead of a single optical phase modulator in the design of the time lens. • Consider the same total drive power for the sake of comparison of the cascade with a single modulator. Proposed time lens produces better pulse compression.
Consider a cascade of N identical optical phase modulators. The phase modulation produced is
N
Δϕ(t)=(π⁄Vπ)∑Vn (t) n=1
…..(1)
Vπ= half-wave voltage of the constituent phase modulators. Take
Vn(t) = Vm0 cos ωmt ….(2)
for all ‘N’. Vm0 = modulating signal voltage, and ωm = modulator drive frequency
Case I. Linear chirping of the pulse Let τd = input pulse half-width Assume ωmτd <<1. Then, cosωmt≈ [1- ωm2t2 /2]
……(3)
Assume Gaussian electric field profile of the input pulse. Then, Ein (t) =Ep exp[-t2 ln2/(2τd2 )] ….(4)
The electric field of the light pulse at the output of the cascade modulator is given by Ein(t) =Ep exp[-t2 ln2/(2τd2 )].exp[-j(φ0 –NFt2 )] …(5) Where φ0 =(πVm0⁄Vπ)N
F=(πVm0⁄Vπ) ωm2 /2
….(6) …(7)
Time-dependent frequency variation of the pulse is Δω(t)=dΔφ(t)/dt =2NFt ….(8)
Linear chirping
When the chirped pulse travels through a single mode fiber it undergoes spreading due to dispersion. It has a half width given by • • • • • •
ΔτL =[d(L/vg ) /dω]Δω = Lβ2Δω ….(9) where Δω = 2NFτd β2 = d(1/vg ) /dω = d2 βp / dω2 vg = group velocity of the light pulse β2 = GVD parameter βp= phase shift constant of the lightwave in the fiber
Dispersion parameter of the single mode fiber is related with GVD parameter as • β2 =-λ2D/2πc ……(11) • λ = vacuum wavelength of light • c= vacuum velocity of light In presence of linear chirping, the resultant half width of the pulse is τR=τd +ΔτL =τd(1+2Lβ2NF) ….(12)
pulse compression since β2 <0 in standard single-mode fiber. Theoretically, τR 0 when 2Lβ2NF 1.
The optimum fiber length is given by
• Lopt=1/(2NF|β2|)=1/[N(πVm0⁄Vπ) ωm2 |β2|] ….(13) • Now, Pin=NPm and Vm0 ∞√Pm = √(Pin/N) ….(14)
• Here, Pin= total drive power input to the cascade • Pm= drive power input to the single constituent modulator. • Eqn.(13) •
Lopt is reduced by √N. One advantage of the cascade
Eqn.(1) •
Δφ(t) is increased √N times in the cascade.
Another advantage of the cascade.
• Taking λ=1.55 μm , D=17 ps/(Km-nm), fm=10 GHz, Vm0⁄Vπ=0.5, we get • Lopt=7.442 Km for N=1, and • Lopt=3.721 Km for N=4. • Taking τd=2.5 ps, fm=10 GHz, L=3.7Km, we get τR=14 fs.
Nonlinear frequency chirping of the pulse • When ωmτd is not very small, we have • Δϕ(t)= N(πVm0⁄Vπ )[1-
…
ωm2t2/2 + ωm4t4/24] ...(15)
• The resultant half-width of the pulse is • τR=τd[1+2Lβ2NF(1-ωm2τd2/12)] …(16)
Conclusion: • Theory and design of an efficient time lens is proposed. • This time lens produces better optical pulse compression.
