Advanced Design and Fabrication Techniques of Fiber Grating Devices

Transcription

1 Advanced Design and Fabrication Techniques of Fiber Grating Devices Yinchieh Lai 暎 Institute of Electro-Optical Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C. [Outline]. Introduction. Overlap-Step-Scan Exposure Fabrication of Fiber Bragg Gratings 3. True Apodization Achieved by the Polarization Control of UV Beam 4. Evolutionary Programming Design of Optimal Fiber Gratings 5. Conclusions

2 What are Fiber Gratings? Fiber grating: index grating (induced by UV) on the fiber core. Fiber Bragg Grating (FBG) Long Period Grating (LPG) Slanted FBG Reflection Filter Transmission Filter

3 Standard Fiber Gratings and Applications () DWDM OADM Circulator Circulator (4) Fiber sensor λ, λ λ n FBG at λ i λ, λ λ n ASE source FBG FBG FBG Drop λ i () Dispersion Compensation Add λ i wavelength measurement (3) EDFA gain flattening EDFA LPG Slanted FBG Chirped FBG (5) Pump laser stabilization Non-AR coating Pump laser 3% reflectivity diode laser

4 Data source: Southampton Photonics Advantages of FBG OADM

5 Dispersionless FBG Phase (x π rad) Normalized Refractive Index Profile Index envelope Grating Position (mm) DLP method LS fitting Reflection (db) Reflection (db) (a) (b) Index Difference Position Wavelength (nm) Dispersionless FBG by LP Gaussian Apodization Require:. Constant dc-index (True Apodization).. Special ac-index apodization. 3. Multiple phase-shifts Time delay (ps) Time delay (ps)

6 Fiber Bragg Grating (FBG) as -D photonic crystal Exposure Methods FBG (a) (b) (c) Reflection Filter..8 Λ λ Β = n eff Λ..8 Photonic bandgap (d) (e) Reflectivity Transmission.. LPG (f) (g) Wavelength (nm)

7 Double exposure method for achieving true apodization index difference Excimer laser (48 or 93nm wavelength) Ordinary Apodization Position ASE light source UV laser beam Index Difference x coupler Cylindrical lens True Apodization Optical Spectrum Analyzer Multiple exposure by moving the phase mask C. Yang and Y. Lai, Journal of Optics A, 4().. C. Yang and Y. Lai, Electronics Letters, 665() 3. C. Yang and Y. Lai, Optics & Laser Technology, 3, 37(). phase mask Position Reflection(dBm) Optical Spectrum Analyzer Gaussian Apodization db Raised Gaussian Apodization Wavelength(nm) Transmissi on(dbm) Wavelength(nm)

8 Step-Scan Exposure System Reflector Argon Ion Laser ( λ=44nm) Cylindrical Lens Cylindrical Lens Mask Rotatable Reflector Beamsplitter Reflector Mask or Interfer -ometer Reflector OSA Fiber PZT Translation Stage ASE Source Movable Linear Stage Laser Interferometer Require nm accuracy!! Linear Stage and PZT Stage Controllers

9 Lab Picture with Visitors from Duke University

10 Overlap-Step-Scan Exposure indexdifference Position Not True Apodization! n( z) = η m A m S( z z m ) cos πz ( Λ + φm) Typical parameters: Grating period = 535 nm, UV Gaussion beam diameter = - 5 mm Scan step size = beam diameter/, grating length = - cm

11 New method for true apodization and phase-shift 44nm UV Laser 5 (a) Pure apodized FBG Cos apodized FBG Beam Splitter Mirror Shutter Rotatable Mirror Mirror f θ s Reflectivity (db) (b) Wavelength (nm) half-wave plate Reflectivity (db) Transmission (db) -3-3 Fiber He-Ne Laser Interferometer W avelength (nm ) n( z) = m Translation Stage ηs( z z m ) + cos πz (θ m) cos( Λ + φm) To be published On Optics Letters

12 Another new method for true apodization Reflection Mirror Polarization Beam Splitter Rotatable λ/ waveplate s p 44nm UV Laser Can be used with phase mask or two beam inter- Ferometer. Reflection Mirror s Reflection Mirror Phase Mask I Translation Stage Fiber Z I I Z Z To be published on PTL. p

13 Fabricated Dispersionless FBG Phase (x π rad) Normalized Refractive Index Profile..5.. DLP method LS fitting Grating Position (mm) Reflection (db) Reflection (db) (a) (b) Wavelength (nm) Time delay (ps) Time delay (ps)

14 M An interferometric side-diffraction monitoring technique for UV writing of advanced Bragg gratings SL SL He-Ne Laser (a) Iinter Fourier Transform Filter Inverse Fourier Transform Take The Phase δ UV beams Grating θ θ SL BS M Normalized amplitude (%) - (b) Exp. interference fitted interference Phase of interference 4 - Phase (rad) Fiber Translation SL CCD θ 3 BC To be presented in CLEO 4 A M CCD position (pixel) Reflection (db) Wavelength (nm) 5cm FBG Transmission (db)

15 Final Fabrication Goal Reflector Argon Ion Laser (λ=44nm) Cylindrical Lens Cylindrical Lens Mask Rotatable Reflector Beamsplitter Reflector Mask or Interfer -ometer Reflector OSA Fiber PZT Translation Stage ASE Source Movable Linear Stage Laser Interferometer Fabrication of FBGs with Linear Stage and PZT Stage Controllers Arbitrary Profile, Phase-Shifts, and Long Length

16 Final Design Goal: Optimal Inverse Design Synthesis of fiber gratings based on the optimization approach for arbitrary reflection or transmission properties Garting Index profile n(z) [or equivalently κ(z)] Reflection or Transmission Spectrum (Amplitude and Phase) κ () z Analysis based on CME () z z ηπ n 4 exp () ( ) ac πη = j j θ z ndc z dz λ λ

17 Coupled Mode Equation Analysis Anti-directional coupling (FBG) da dz db dz * = iβa + κ ( z)exp[ ik = iβb + κ ( z)exp[ ik () z β k g () z g β z] b g z] a ac index (amplitude and phase)+ dc index κ Coupled mode equations da = iδa + κ ( z) B dz db = iδb + κ ( z) A dz kg δ = β kg a = Aexp i z k = g b B exp i z ηπ n 4 exp () ( ) ac πη = j j θ z ndc z dz λ λ z r = B A dr dz r( L) = r(δ) r( δ ) κ ( z) Ricatti equation = iδr + κ ( z) κ ( z) r For r << = = π FT L κ ( z) e z= r δ = κ(z) iδ z ( δ ) e dz iδ z dδ

18 Design Methodology of Advanced Fiber Gratings. Inverse Methods () GLM inverse scattering method (E. Peral, et al., IEEE JQE, 3, 78, 996.) () Layer-Peeling method (R. Feced, ei al., IEEE JQE 35, 5, 999.). Optimization Methods () Genetic algorithm (J. Skaar and K. M. Risvik, J. Lightwave Tech. 6, 98, 998.) () Evolutionary Programming (C.-L. Lee and Y. Lai, IEEE Photon. Tech. Lett, November,.) (C.-L. Lee and Y. Lai, CLEO 3, USA; also to be published on OC

19 Layer Peeling Method () FBG () LPG τ= τ δ = τ > τ iδ τ κ ( ) = r( δ ) e dδ = h( τ ) π z= τ/ τ= τ= τ > τ τ= z= τ

20 Phase (x π rad) Normalized Refractive Index Profile Dispersionless FBG by the LP Method Index envelope Grating Position (mm) DLP method LS fitting Reflection (db) Reflection (db) (a) (b) Index Difference Position Wavelength (nm) Dispersionless FBG by LP Gaussian Apodization Require:. Constant dc-index (True Apodization).. Special ac-index apodization. 3. Multiple phase-shifts Time delay (ps) Time delay (ps)

21 The Least Square Fitting Method σ id m ({ C }) A ( z) A ( z) m = dz m A m ( z) C exp ( z z ) ( ) = w m m s σ C m = ( z z ) - A ( ) id ( ) m z Am z exp( ) dz = m ws To determine the experimental exposure parameters.

22 PTL 3. Dispersion Compensation Fiber Bragg Grating by Single Period Overlap-Step-Scan Exposure Profile of κ(z) Phase profile Reflection Spectrum Phase-shifted approximation Phase error tolerance

23 Advantages and Disadvantages of Layer Peeling Method. Advantages: () Very fast. () Single solution.. Disadvantages: () Complete spectra information (amplitude and phase) must be provided. () Reconstruction sometimes fails. (3) Can not impose additional constrains. (4) Not necessary optimal solution for applications.

24 Synthesis of advanced FGs using EP (Flow chart of the algorithm) κ will be discretized into m sections κ A new set of N-offspring κ the only operator in EP κ with higher fitness value lower Perturbation factor (vice versa) κ κ κ with higher fitness has higher probability to be chosen

25 Design of Dispersionless Fiber Bragg Grating Reflection Spectrum ) m n s (p / n o r e si D isp Dispersion Spectrum EP(4cm) LP(4cm) LP(cm) Gaussian-apodized(4cm) Wavele ngth (nm) λ, λ λ n Circulator Drop λ i FBG at λ i Circulator Add λ i λ, λ λ n To be published on Optics Communications ) m /c n t( oefic ie C p li n g C ou Grating Le ngth (cm) EP LP Gaussian-apodized

26 Convergence of the Stochastic Search.5 x 5 ) m n (ps / r Ero d ) n a inḇ n ( rs i o D i s pe Generation E D E R 8 E ror y v c ti i t 6 4 R efl e

27 Comparison of the Computation Time Matlab Programming Designed Methods for the designed example CPU time EP (4cm) with sections, ~4 hrs LP (4cm) with N=8, M=6 sec LP (cm) with N=4, M=8 3min sec Obviously the EP Optimization approach should compete with the LP method on the designed flexibility and achieved performance, not on computation time.

28 Transmission Loss(dB) Design of Gain Flattening Long Period Grating Wavelength(nm) Amplitude of Coupling Coefficient(/mm) (a) (c) Filter Response Desired Synthesized Index Profile Amplitude Phase Grating Length(mm) Phase of Coupling Coefficient(rad) Gain(dB) (b) Wavelength(nm) B ) (d n s io m i s Gain Flattening T ran -4-8 Unflatten Flatten Phase Error Tolerance Max. 5nm Exact Error Long Period Grating EDFA Wavelength (nm) (C.-L. Lee and Y. Lai, IEEE Photon. Tech. Lett, November,.). LPG B ) (d E ror

29 Coupling of Modes Co-directional coupling: (LPG) + = + + = = = + = z k i z i A a z k i z i A a k A z A i dz da A z A i dz da g g g exp exp ) ( ) ( β β β β β β δ κ δ κ δ ] )exp[ ( ] )exp[ ( a z ik z a i dz da a z ik z a i dz da g g = + = κ β κ β β β g k Long Period Grating Coupling between the core and cladding modes

30 Comparison of the single- and multi-objective EP algorithms Examples Number of targets Targets Error functions Fitness functions Selection process LPG EDFA Gain Flattening Filters (Single-objective optimization). Desired transmission spectrum E T Roulette wheel selection algorithm FBG Dispersionless Filters for DWDM OADM (Multi-objective optimization). In-band zero-dispersion. Desired reflectivity spectrum n κ i ) = Ttarget, Ti, Etot ( κi ) = [ WR ER ( κi ) + WD ED ( κi )] ( = F( κ i ) = E T ( κ ) i F ( κ ) = i Roulette wheel with elitism selection algorithm:. Keep the best for the next generation. The with higher F has higher probability to be chosen E tot ( κ ) i Mutation process Adaptive with single fitness value Adaptive with multiple actual error values

31 Quantum Effects of Fiber Bragg Grating Solitons Kerr nonlinearity Fiber Grating Amplitude Squeezed R.-K. Lee and Y. Lai, To be published on Phys. Rev. A Rapid Communication.

32 Conclusions Standard Fiber Gratings and Applications are mature technologies. Advanced Fiber Gratings and Applications are under intense development and will find more and more important applications. Precision Fiber Grating Design and Fabrication techniques are the keys for the development of advanced fiber gratings and applications. At IEO/NCTU we have established a firm basis for the design and fabrication of advanced fiber gratings.

33 Acknowledgement Our Lab Members Cheng-Ling Lee Kai-Ping Chuang Dr. Lih-Gen Sheu ( Van Nung Institute of Technology).