Topic report 2012 March 15 Raman gain & stimulated emission gain

Topic report 2012 March 15 Raman gain & stimulated emission gain
張俊霖 Solid-State Laser Crystal and Device Laboratory Institute of Photonics and Optoelectronics National Taiwan University

Outlines Model SRS & signal in an pulsed Yb:fiber amplifier
Know the different contributed behaviors between Raman & signal Definition of stimulated emission gain & Raman gain Know the difference between them and then hard to compare with each other Define a SRS threshold to estimate SRS influence Introduce the classic model & the modification of LMA core & propagation distance Strategy of suppressing SRS in fiber amplifier Basically, optimize active & passive length, pumping scheme by trade-off between Signal & Raman In advance, pulse shaping & LP-FBG by stripping the Raman signal during amplification. 2017/10/5

Motivation of this talk
Turning point Turning point (1) Now in our third amplifier 15/130 DC PM, we have far enough seed energy but the 1064-nm output energy is limited by signal depletion of 1115-nm SRS generation. (2) We want to find the strategy to move the turning point right as can as possible. For 15/130, target is 600 uJ For 30/250, target is > 2mJ 2017/10/5

Signal & Raman in pulsed fiber amp simulation
線寬效應 Upper population CW pump CW ASE Pulsed signal Stoke 光纖損耗 SRS Stoke受激放大 Ith Stoke Raman 反向瑞里散射擷取前一order能量給予後一order能量 Ith Anti-Stoke Raman 反向瑞里散射擷取前一order能量 2017/10/5

Signal stimulated gain for two doped conc.
30/250 Conc.=8.5E25 m-3 15/130 Conc.=4E25 m-3 By South Ampton Univ. 2017/10/5

Raman gain spectrum Measured Raman gain spectrum
Raman gain coefficient vs. wavelength 2017/10/5

Equation of Raman gain coefficient (m/W)
Generalized equation of Raman Gain (From Agrawal : Nonlinear fiber optics 2007) Three kinds of model to determine the transfer function : Instantaneous & single-damped harmonic oscillator & Multi-vibrational-mode mode 2017/10/5

Two model for transfer function for gR
2017/10/5

Instantaneous model by Stolen et al.
Exp Remove structured 640 cm-1 750 cm-1 Lorentizian-fit 2017/10/5

Single-damped-oscillator model
Original 2017/10/5

Intermediate-broadening model (1)
2017/10/5

Intermediate-broadening model (2)
2017/10/5

Raman threshold at Forward
In fact, there is no SRS threshold physically. In practice, we define a SRS threshold to identify the SRS influence. The first work to define the SRS threshold is R.G. smith at 1972 AO. Small core & long length fiber for application of optical communication for forward wave interaction 2017/10/5

Raman threshold at Backward
Two orders lower than SRS typically 2017/10/5

Modification of propagation length effect
2017/10/5

SRS threshold modified by LMA fibers
(high power fiber laser, not opt. comm.) In Smith’s work, SRS intensity threshold is independent on core size, it is not true in real. Start from Smith relation 2017/10/5

Rewrite analytical equation by new assumption
2017/10/5

1.65 times SRS threshold in 30/250 LMA fiber
2017/10/5

It can improve the output energy by suppressing peak power for signal saturation & Raman (~20% improvements)

(~50% improvements of output energy)

Third amplifier 15/130 – SRS-limited energy
轉折點轉折點目前到20A約10W, 1115-nm SRS nm signal 約各占一半, 但我發現量測平均功率時, fluctuation並沒有很大的差別,波形也是, 我非常確定現在能作的事只有減短active fiber, 試著將轉折點儘量往右移 2017/10/5

Third amplifier 15/130 – Raman spectra
2017/10/5

Third amplifier 15/130 – Raman spectra
轉折點 energy >100 uJ, peak power 約> 20 kW 2017/10/5

Backward-pumped 15/130 & 30/250 2017/10/5 Old New Splices
Passive length after 15/19 before After 15 1 16 0.75 17 0.5 18 19 1.5 20 3 Total 12 /5 Splices Passive length after 15/19 Active fibers length before After 15 1 6/125-1 1.6 16 2 6/125-2 17 0.5 15/130 5 18 Total 8.2 19 1.5 20 10.5 /3.5 2017/10/5

MOPA configuration 2012/02/16 2017/10/5 準直的部份有達到2.4mm (2) 無光纖旋轉夾具,
30/250 – 35A x4 (95.8W) 準直的部份有達到2.4mm (2) 無光纖旋轉夾具, 先用HWP解決 (3) 15/130功率不敢開太高, 現在沒有BPF, 沒法濾掉Raman, 故不敢開高功率 (4) 好消息Semrock BPF 下周到可解決此問題 (5) 有看到30/250出口有光, 預計明天才會well optimize好與製作30/250 出口的end cap (6) 第4級30/250已架好, 預計下星期可試低功率的30/250初步放大成果, 該需要free-space isolator了 30./250-- gain fiber 30/250 – 143W 30/250 – 10A x2 (47.1W) 15/130 – gain fiber 15/130 – 10A x2 (39.8 W) 15/130 – 39.4W 15/130- end cap 30/250- passive 30/250- 8deg. endfacet Measure coupling efficiency 15/130- PCX lens 15/130- HWP 15/130- PCX lens 30/250- 0-deg. endfacet 2017/10/5

Nonlinear optics in Fiber (2)
For intense electromagnetic fields, the response of any dielectric to light becomes nonlinear, including optical fiber. On a fundamental level, the origin of the nonlinear response is related to anharmonic motion of bound electrons under the influence of an applied field. As a result, the dipole moment per unit volume P (polarization) induced by electric dipole (charge separation) is not linear in the electric field E, but satisfies the more general relation in one-dimensional isotropic medium : Vacuum permittivity 1st order optical susceptibility (linear) 2nd order optical susceptibility 3rd order optical susceptibility 2017/10/5

Fiber nonlinear optics (3)
1st order susceptibility － linear propagation giving rise to propagation speed through medium (real part : refractive index) and absorption in medium (imaginary part : attenuation coefficient) 2nd order and even order susceptibility is ~ 0 for silica glass because SiO2 is a symmetric molecule. 3rd order susceptibility is the lowest-order nonlinear effect in an optical fiber as an isotropic glass medium, . Amorphous silicon (a-Si or α-Si) is the non-crystalline allotropic form of silicon. The amorphous structure of glassy Silica (SiO2) in two dimensions. No long range order is present, however there is local ordering with respect to the tetrahedral arrangement of Oxygen (O) atoms around the Silicon (Si) atoms Local ordering Nonlinearity limits the performance of rare-earth-doped fiber lasers ! 2017/10/5

Fiber nonlinear effect induced by χ(3) (4)
There are three categories of nonlinear process for χ(3) Phase matching condition is poor in fiber rather than that in crystal . Define what we care in nanosecond fiber MOPA here (1) Frequency mixing process – (phase matching) Third harmonic generation (THG) : poor phase matching Optical Kerr effect – (Intensity dependent refractive index) Self-phase modulation (SRS) : short duration & pulse shape & chirp Self-focusing (SF) : bulk damage threshold Four-wave mixing (FWM) : poor phase matching Degenerate four-wave (or Three-wave) mixing (DFWM or TWM) : poor phase matching Cross-polarized wave generation (XPW) : Not femtosecond time scale Cross-phase modulation (XPM) : Not femtosecond time scale Optical solitons : No GVD issue for long-distance propagation Light scattering – (Active process without phase matching) Stimulated Raman scattering (SRS) : peak power threshold Stimulated Briilouin scattering (SBS) : peak power & linewidth threshold Stimulated Rayleigh scattering (SRS) : ? Two Photon aborption – (simultaneous absorption of two photons for single electron) Two photon absorption (TPA) : explain well for the green light from active fiber 2017/10/5

Nonlinear effect & Photo-darkening effect to limite C & L
When the signal parameters is beyond the nonlinear threshold, especially SRS in our case, SRS effect is dominant by peak power x fiber interaction length. For this condition, we must choose short highly-doped length with tolerant incomplete pump absorption. For power amplifier, the length need artificially short, doapnt conc. as high as possible without nonlinear & photo-darkening and with enough heat dissipation. 2017/10/5

SRS Stokes threshold for Yb-doped LMA fiber
2017/10/5

Outlines Saturation no real amplifier operating without saturation limit. We need to find it. Extractable energy Use saturation as utilized unit to find the maximum extractable energy you can achieve. FDTD rate equation for repetition rate issue If quantitative results to compare with experimental results is necessary, it can not be avoided. Fiber nonlinear optics In fiber, it cannot be avoided. It is advantage/disadvantage to enhance/suppress it. 2017/10/5

Signal saturation for gain reduction
CW regime Pulse regime CW & pulse are totally different stories by definition quantitatively. CW pump & ASE becomes important during energy storage period and NOT important during signal depletion period. Let’s examine all kinds of saturation effect. 2017/10/5

Signal saturation fluence (1)
Why do we use fluence & energy instead of intensity & power. 1. When does gain saturation set in during pulse build-up (signal depletion period)? 2. Many people believe that saturation becomes strong when the optical intensity in the gain medium reaches the saturation intensity. 3. For most pulsed lasers, however, this guess is far off, since the used rule holds only for the steady state, and the time during pulse build-up is far too short for the steady state to be reached. 4. In reality, saturation in pulse regime sets when the time-integrated intensity reaches the saturation fluence. Therefore the upper-state lifetime is not relevant: it does not influence the saturation fluence, being the relevant quantity for saturation in that situation. 5. Finally, it is material property function of wavelength. 2017/10/5

Signal saturation fluence (2)
Signal saturation fluence in Yb-doped silica vs. wavelength 2017/10/5

Signal saturation energy
Saturation energy of a laser gain medium is defined as the pulse energy of a short signal pulse which leads to a reduction in the gain to 1/e (~37%) of it initial value. (2) For fiber laser or amplifier, the light is guided stably in the waveguide (fiber). Therefore we can directly use “fluence x MFD” to obtain “signal saturation energy” (3) Therefore, we need to obtain the MFD in different fibers function of wavelength. 2017/10/5

Mode field diameter in fiber
Marcuse equation V parameter 2017/10/5 Marcuse, J. Opt. Soc. Am 68, 103 (1978).

Signal saturation energy
When your input pulse energy starts to approach this value, it can be considered as saturated input to exhaust “Gain” during signal depletion period to decrease to “Gain” threshold after this period. For larger MFD, high saturation energy can be obtained. Beyond the signal saturation energy, pulse shape will be deformed. (3) Signal saturation energy is limited by material & geometry. 2017/10/5

Pump saturation power (1)
Definition : For fixed mode field along the gain fiber, this is the pump power that pumps one-half of population in a three- or four-level system, and about one-half in a quasi-two-level system, to upper laser level. At this level and above, absorption of pump power is significantly saturated due to depletion of the ground-state population by pumping when pump rate is equal to fluorescence transition rate . Pump saturation occurs when pumping rate = spontaneous emission rate (1/s) In this way, we can describe “pump saturation intensity” by lifetime Moreover, for CW pumped fiber laser and amplifier, the light is guided stably in the waveguide (fiber). Therefore we can directly use “intensity x pump area” to obtain “signal saturation energy”. For single-clad fiber, pump area is MFD by Marcuse equation. For double-clad fiber (clad NA is >0.46), pump area can be considered as clad area directly. (wave optics -> geometrical optics) 2017/10/5

Launched pump power in clad for pump saturation Ytterbium-doped fiber amplifier pumped at 975 nm can operated far above its pump saturation power and the particularly strong pumping phenomena occurs in cases where both the absorption cross sections and the applied pump power are rather high. It can lead to peculiar saturation behavior: the pump power decays about linearly rather than exponentially in the fiber, and the slope of this decays can be substantially increased if the signal power is also high. Furthermore, the saturation characteristics for signal wave can also be strongly modified because ions undergoing stimulated emission can be quickly returned to the upper laser level. 2017/10/5

For extracted energy from amplifier as possible as we can “efficiently”, basically we need to make “the utilized pump power” to approach the “pump saturation power to reach “strongly pumping”. It is very easy for Yb-doped fiber. If the fiber SPEC can not be chosen and you still want to extract more energy from this fiber, you may use pump power much higher than saturated one but you will loss the efficiency. In this way, core-pumped pre-amp can use it. However, clad-pumped power amp is not preferred unless pulse pumping. 2017/10/5

Transparent Pump power
(1) Transparency pump power is the required minimum pump power when the GAIN COEFFICIENT is ZERO. 2017/10/5

Optimized fiber length
CW-pump definition : Therefore in end-pump scheme, the residual pump power at another fiber end should be higher than transparent pump power for no negative GAIN COEFFICIENT along the entire fiber as completely absorption. Pulsed operation definition : At the fiber end, the population is fixed at threshold. For pulsed amplifier, the optimal fiber length is a range depending on operation parameters. = (1) 1064-nm Yb-doped fiber or amplifier is quasi-four level system, length is not critical. (2) Choose a set of concentration & length to completely absorb pump power along fiber. (3) However, too high Conc. makes Photodarking effect easy to happen. Too low Conc. needs longer fiber length and it makes nonlinear threshold (SRS & SBS) decrease. 2017/10/5

Outlines Saturation no real amplifier operating without saturation limit. We need to find it. Extractable energy Use saturation as utilized unit to find the maximum extractable energy you can achieve FDTD rate equation for repetition rate issue If quantitative results to compare with experimental results is necessary, it can not be avoided. Fiber nonlinear optics In fiber, it cannot be avoided. It is advantage/disadvantage to enhance/suppress it. 2017/10/5

Model of pulsed amplification
We start from the signal depletion period only. 2017/10/5

Frantz-Nodvick model (1)
We can use FDTD to solve these two rate equations. Give the two initial conditions (1) You can obtain temporal shape & pulse energy by (2) You can obtain gain coefficient along the fiber & Amp GAIN by (3) You can obtain signal amplification along fiber by (4) No spectrum in this model 2017/10/5

To know the relation between input & output energy with small-signal gain, F-N assume a square shape and solve it analytically as follows: (2) Assume square pulse shape (3) Analytical solution of signal peak power (4) Define the amplifier gain (5) Integrate it and obtain the amplifier gain 2017/10/5

Arrange the GAIN solution by energy fluence, saturated fluence and small signal gain, you may obtain the well-know F-N equation. (3) For fiber laser, signal propagates in a light waveguide. Therefore, we can transform the fluence into energy directly as follows: (4) Finally, The derivation shows there is no pump & ASE & repetition rate and considers signal depletion only. The G0 can not be known in this model (If you want G0, calculation of energy storage period is necessary). (5) According to the model, F-N results are usually considered as the upper limit. 2017/10/5

Maximum extractable energy (A)
(1) According to F-N curve, the max extractable energy can be obtained by letting (2) In practice, small signal gain will be limited by the onset of parasitic lasing or amplified spontaneous emission to < ~30dB. It means the maximum extractable energy is (3) Moreover, there is a journal paper on JOSA B to use a definition to solve analytically and obtain max. extractable energy during energy storage period only under the assumption of clad-pumped scheme and saturated input. In this way, the repetition rate issue can be considered in it also. 2017/10/5

Maximum extractable energy (B-1)
Assume the signal is beyond the saturation level and then the threshold population can be assumed at the beginning of the energy storage period. (Blue point) We focus on the population at the end of energy storage period (red point) to obtain the max energy where the ASE is just saturated (yellow point) in terms of fiber spec, pump & ASE. Assume NO ASE depletion duration signal depletion period. An analytical model for high energy YDFA to calculate the maximum extractable energy & optimal length before ASE is saturated and depletes the inversion. 2017/10/5 Y. Sintov et al., J. Opt. Soc. Am. B 23, 218 (2005).

Assume the time of pump passage through the fiber << energy storage period Pump power distribution along the fiber with existed inversion is : ASE power evolution in vASE band along the fiber during energy storage period is In the absence of spurious reflections at both fiber ends, copropagating ASE signal vASE band at the fiber end is (the same form for counter-propagating ASE signal) 2017/10/5

The rate equation describes the evolution of the upper-state population density 1. (pump absorption & depletion) Beyond a certain inversion, pump will be lost as ASE. 2. (ASE spontaneous emission) 3. (ASE stimulated emission) 4. (ASE absorption) ASE becomes dominant to deplete inversion when ASE stimulated emission is comparable to ASE spontaneous emission. 2017/10/5

The max. allowed upper-state population integral at the end of energy storage period is The upper-state population at which the net gain at ASE wavelength is 0 We can use numerical solution to obtain in terms of fiber SPEC, pump & rep. rate Finally, the maximum extractable energy can be transformed by the following relation, Where the saturation energy is 2017/10/5

Example for 3rd amp, 30/250 DC (1)
Optimal fiber length is 2.95 meter. Pump is150 W at 20 kHz When seed energy is> 250 uJ, pulse energy of > 3 mJ can be obtained. In real launched should be~130 W, input energy of approaching 400 uJ is safe after energy raiser stage. 2017/10/5

To approach saturated input signal , 150-W pump power can obtain 40% efficiency. 2017/10/5

Due to CW pumping, lower repetition rate will decrease amplifier efficiency but raise the output energy. 20 kHz is Mid-Low repetition rate, the amplifier efficiency is ~40% (2) Due to stimulated amplification, to increase seed energy will make amp efficiency better under unsaturated input. 2017/10/5

Dispersion in fiber Index vs. wavelength Time lag vs. fiber length
For pulse broadening in 1~20 ns duration & 1~3 meter long fiber, (1) Group-Velocity Dispersion (GVD) above is small (<0.01% duration). (2) Polarization-Mode Dispersion (PMD) is relative small compared with GVD effects If pulse duration is < 50 ps, the dispersion length decreases and becomes comparable to both the fiber length and nonlinear length. G. P. Agrawal, “Nonlinear fiber optics” 4 ed. Academia Press. (2007) 2017/10/5

Final-version rate equations (1)
Pump受激吸收增加 N2 Signal & ASE 受激放射消耗N2 ASE 自發輻射消耗N2 Raman受激放射消耗N2 2017/10/5

Pump 隨時空propagation Pump受激吸收 Pump光纖傳播損耗考慮ASE光纖傳播損耗 ASE受激放大考慮線寬所造成的受激與自發輻射貢獻反向Rayleigh 散射的貢獻 ASE 隨時空propagation 2017/10/5

Signal受激放大 Signal隨時空propagation Signal光纖傳輸損耗考慮線寬所造成的受激與自發輻射貢獻反向Rayleigh 散射的貢獻拉曼損耗signal作非線性轉換 2017/10/5

Add considerations step by step
1. Rate equation considering N2 vs. Ps+ only (Step 1) 只考慮signal depletion period 2. Rate equation including pump (Step 2) 以下都需同時考慮energy storage與signal depletion period (重覆頻率) 3. Rate equation including ASE (Step 3) 4. Rate equation including linewidth (Step 4) 5. Rate equation including fiber propagation loss & Rayleigh scattering contribution (Step 5) 6. Rate equation including SRS Stoke (Step 6) 7. Rate equation comparing SRS Anti-Stoke & SBS (Step 7) PS. Step 1 將Seed改成Multi-wavelength 可驗證parasitic stimulated emission 2017/10/5

Topic report 2012 March 15 Raman gain & stimulated emission gain

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