Maximizing the Bandwidth from Supercontinuum Generation in Photonic Crystal Chalcogenide Fibers Curtis R. Menyuk based on the PhD dissertation of: Dr. Jonathan Hu now at Princeton University 1
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Maximizing the Bandwidth from Supercontinuum Generation in Photonic Crystal Chalcogenide Fibers With: Dr. L. Brandon Shaw, J. S. Sanghera, and I. D. Aggarwal at the Naval Research Laboratory 2
Project Goal GOAL: GOAL: To make a broadband (2 10 µm) mid-ir source 10 0 Power (a.u.) A mid-ir Light bulb Bandwidth 10 60 2 Wavelength (µm) 8 3
Why mid-ir sources? Many important materials radiate or absorb in this range 1.55 µ m 9.5 µ m 4 Spectral response of ammonia And it is not alone!
Why chalcogenide? Attenuation in silica grows rapidly beyond 2.5 µ m Attenuation in the chalcogenides remains small beyond 10 µm 5 Source: Oxford Electronics www.oxford-electronics.com
What is chalcogenide? glass is based on chalcogens mixed with As losses ~ 0.1 1 db/m Kerr nonlinearity = 1000X silica fiber CW peak power = 50 125 kw/cm 2 pulse peak power = 1 2 GW/cm 2 6
Photonic crystal fiber (PCF) Solid-core PCF Photonic bandgap fiber (PBGF) 7 solid core holey cladding forms effective low-index material Air core periodic cladding forms photonic band gap
Photonic crystal fiber (PCF) Solid-core PCF We focus on solid-core PCFs to make use of the nonlinearity solid core 8 holey cladding forms effective low-index material
Supercontinuum generation Supercontinuum generation Kerr nonlinearity Raman effect Dispersion It is a complicated, incoherent process! 9
Supercontinuum generation Supercontinuum generation Kerr nonlinearity Raman effect Dispersion Supercontinuum generation using photonic crystal fiber (PCF) 1 Wide single-mode region Enhanced nonlinearity Tailored dispersion 10 1 Dudley, et al., Rev. Mod. Phys. 78, 1135 (2006).
Supercontinuum generation Supercontinuum generation in chalcogenide fibers is not the same as in silica fibers! WHY? Different material properties There are no good sources beyond 2.5 3.0 µm Our design goal is to increase the maximum wavelength of the spectrum as rapidly as possible! 11 1 Dudley, et al., Rev. Mod. Phys. 78, 1135 (2006).
Supercontinuum generation Supercontinuum generation in chalcogenide fibers is not the same as in silica fibers! A key finding: supercontinuum generation proceeds in two stages Stage 1: four-wave mixing Stage 2: soliton self-frequency shift Each stage should be as large as possible! 12 1 Dudley, et al., Rev. Mod. Phys. 78, 1135 (2006).
Prior work Delmonte, et al. 1 show experimental supercontinuum generation from 0.9 to 2.5 µm using a tellurite fiber with a wagon-wheel structure. Price, et al. 2 theoretically demonstrate supercontinuum generation from 2 to 4 µm using a bismuth glass fiber with a wagon-wheel structure. Shaw, et al. 3 show experimental supercontinuum generation from 2.1 to 3.2 µm in a As 2 Se 3 based chalcogenide PCF with one ring of air holes. 13 1 Delmonte, et al., CLEO, CTuA4 (2006) 2 Price, et al., J. Sel. Topics Quantum Electron. 13, 738 (2007). 3 Shaw, et al., Adv. Solid State Photonics TuC5 (2005)
Model validation Shaw, et al. 1 show experimental supercontinuum generation from 2.1 to 3.2 µm in a As 2 Se 3 based chalcogenide PCF with one ring of air holes. We use the Shaw, et al. results to validate our model 14 1 Shaw, et al., Adv. Solid State Photonics, TuC5 (2005).
Design criteria Supercontinuum generation is a complicated process BUT there are general design criteria that work well 1. Design the fiber so that it is single-mode increases the effective nonlinearity 2. Ensure that four-wave mixing is phase-matched with the largest possible Stokes wavelength Rapidly moves energy to a large wavelength 3. Make the second zero dispersion wavelength as large as possible Allows the soliton self-frequency shift to go to long wavelengths 15
A specific example Fixed fiber and pulse features As 2 Se 3 fiber Five-ring hexagonal structure A pump wavelength of 2.5 µ m Fiber parameters to vary: Air-hold diameter (d ) Pitch (Λ) Pulse parameters to vary: Peak power Pulse duration Λ 16
A specific example Needed fiber quantities (experimentally determined) Kerr coefficient Raman gain Material dispersion Needed fiber quantities (calculated) Total Raman response calculated once Total dispersion calculated for each set of fiber parameters Λ 17
Generalized nonlinear Schrödinger equation (GNLS) In principle: We can optimize by solving the GNLS for a broad set of fiber and pulse parameters A( z, t) z iift ( + Ω) ( ) Ω '( ) %(, Ω) {[ β ω ] } 0 β ω0 β ω0 A z i t 2 = iγ 1 A( z, t) R( t ') A( z, t t ') dt ' + ω0 t A(z,t) : Electric field envelope β : Propagation constant = n /( ca ) : Kerr coefficient γ ω 2 0 eff R( t) = (1 f ) δ ( t) + f h ( t) R R R 18 Kerr effect Raman effect
Generalized nonlinear Schrödinger equation (GNLS) In practice: We use our design criteria to reduce the labor In any case: We must solve the GNLS for a broad enough parameter set to verify the design criteria 19
Third-order susceptibility Imaginary part 1 1 Real part Silica N N As 2 Se 3 0 0 0 1000 0 Frequency (cm 1 ) Frequency (cm 1 ) 1000 The real part is obtained by a Hilbert transform of the imaginary part (Kramers-Kronig Kronig relation) 20
Raman response function 5 h R (t) (a.u.) Silica As 2 Se 3-5 0 1500 t (fs) Chalcogenide fiber has a longer response time than silica fiber 21
Raman gain and Raman response function R( t) = (1 f ) δ ( t) + f h ( t) R R R Kerr effect Raman effect h R (t) [ ] Ω = f 0.1 g( ) (2 ω / c) n f Im FFT( h ( t)) p 2 R R R Raman gain Pump frequency Raman fraction of the nonlinearity 22 1 Stolen, et al., J. Opt. Soc. Am. B 6, 1159 (1989). 2 Slusher, et al., J. Opt. Soc. Am. B 21, 1146 (2004).
Fiber geometry Experiment 1 Simulation D d 23 Preform PCF 1 Shaw, et al., Adv. Solid State Photonics, TuC5 (2005) Λ D = 10 µm d/λ = 0.8
Dispersion 50 D (ps/nm-km) -100 2 6 Wavelength (µm) Material Fiber d Λ D = 10 µm d/λ = 0.8 24
Supercontinuum generation 10 Power (a.u.) 10 0-8 2 Wavelength (µm) 3.4 Experiment 1 Simulation L = 1 m FWHM = 100 fs Energy = 100 pj λ p = 2.5 µm Measured nonlinear response can completely account for the supercontinuum generation 25 1 Shaw, et al., Adv. Solid State Photonics, TuC5 (2005)
Single-mode analysis Step-index fiber Solid-core PCF 2π 2 2 V = a n co n cl Fundamental space-filling mode λ n FSM 26
Fundamental space-filling mode 3 n FSM 1 0 λ / Λ 10 d / Λ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 27
Endlessly single-mode region λ /Λ 10 1 10 10 1 Endlessly Single-mode region 2 0 Single-mode region Multi-mode region n=2.8 n=2.4 n=1.45 d / Λ 0.9 28
Endlessly single-mode region What we learned: d / Λ = 0.4 When, the fiber is single mode AND We have the best mode confinement. d / Λ = 0.4 We set from this point on. 29
Four-wave mixing (FWM ) 2ω p ω s ω a Phase-matching condition ( n ω + n ω 2 n ω ) / c + 2(1 f ) γ P = 0 s s a a p p R p 30
FWM wavelength P = 0 kw P = 1 kw P = 0.1 kw Λ = 3 µm P = 0.1 kw Λ = 4 µ m Λ = 3 µ m Λ = 2 µ m At P = 0.1 kw, Λ = 3 µ m gives a large Stokes wavelength 31
5Bandwidth (µm) Bandwidth as a function of pitch 0 2 Λ (µm) 4 32
Output spectrum 10 0 Power (a.u.) 10 60 Bandwidth 20 db 1 Wavelength (µm) 8 L = 0.1 m FWHM = 500 fs d/λ= 0.4 Λ = 3 µm 33
34 Spectrogram t (ps) Distance (m) Wavelength (µm)
5Bandwidth ( µm) Bandwidth as a function of input pulse width 35 0 100 FWHM (fs) 1000
6Bandwidth (µm) Bandwidth as a function of input peak power 0 0 Peak power (kw) 1.5 36
Application of this approach to other fibers Weiblen, et al. As 2 S 3 fiber Presented at CLEO 2010 Stay tuned for more! 37
Conclusions We have developed a design approach that allows us to maximize the supercontinuum bandwidth in chalcogenide fibers We showed that a bandwidth of 4 µm can be generated using an As 2 Se 3 PCF with d/λ = 0.4 and Λ = 3 µm at a pump wavelength of 2.5 µm 38 This same approach can be applied to a wide variety of chalcogenide fibers.
39 Thank you!