Abstract

A spectroscopic technique based on a full four port modeling and measurement is developed and utilized to study a tapered- fiber photonic crystal waveguide coupler. The coupler is made by directly situating the tapered fiber on the defect region of a silicon membrane photonic crystal waveguide. The waveguide is lithographically terminated resulting a Fabry-Perot cavity. It turns out that the line-shape of the resonances is not merely a Lorentzian but can be constructed from that of the unloaded waveguide resonator. By knowing how the resonances broaden the experimental data is then fit and the coupling efficiency is extracted for the entire spectrum.

© 2009 Optical Society of America

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  1. J. Joannopoulos, P. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386,143-149 (1997).
    [CrossRef]
  2. T. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Stat. Sol. (a) 197, 688-702 (2003).
    [CrossRef]
  3. W. Kuang, C. Kim, A. Stapleton, and J. O’Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides," Opt. Lett. 27, 1602-1606 (2002).
    [CrossRef]
  4. P. Barclay, K. Srinivasan, and O. Painter, "Design of photonic crystal waveguide for evanescent coupling to optical fiber tapers and integration with high-Q cavities," Opt. Express 20, 2274-2284 (2003).
  5. P. Barclay, K. Srinivasan, M. Borselli, and O. Painter "Efficient input and output fiber coupling to a photonic crystal waveguide," Opt. Lett. 29, 697-699 (2004).
    [CrossRef] [PubMed]
  6. I.-K. Hwang, G.-H. Kim, and Y.-H. Lee, "Optimization of coupling between photonic crystal resonators and curved microfiber," IEEE J. Quantum Electron. 42, 131-136 (2006).
    [CrossRef]
  7. M. Lee, C . Grillet, C . Poulton, C. Monat, C . Smith, E. Magi, D . Freeman, S . Madden, B. Luther-Davis, and B . Eggleton, "Characterizing photonic crystal waveguides with an extended k-space evanescent coupling technique," Opt. Express 16, 13800-13808 (2008).
    [CrossRef] [PubMed]
  8. J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).
  9. R. Black, S. Lacroix, F. Gonthier, J. Love, "Tapered single-mode fibers and devices; Part2: Experimental and theoretical qualification," IEE Proc. J. 138, 355-364 (1991).
  10. F. Sanchez, "Matrix algebra for all-fiber optical resonators," J. Lightwave Technol. 9, 838-844 (1991).
    [CrossRef]
  11. K. Okamoto, Fundamentals of optical waveguides (Academic Press, 2000)
  12. V. Cooper, "Analysis of Fabry-Perot interferograms by means of their Fourier transforms," Appl. Opt. 10, 525-530 (1971).
    [CrossRef] [PubMed]
  13. B. Hakki, T. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," Appl. Phys. 46, 1299-1306 (1975).
    [CrossRef]
  14. M. Natomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, " Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett.  87, 253902-1-253902-3 (2001).
  15. A. Gomez-Iglesias, D. O’Brien, L. O’Faolain, A. Miller and T. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett.  90, 261107-1-261107-3 (2007).
    [CrossRef]

2008 (1)

2006 (1)

I.-K. Hwang, G.-H. Kim, and Y.-H. Lee, "Optimization of coupling between photonic crystal resonators and curved microfiber," IEEE J. Quantum Electron. 42, 131-136 (2006).
[CrossRef]

2004 (1)

2003 (2)

T. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Stat. Sol. (a) 197, 688-702 (2003).
[CrossRef]

P. Barclay, K. Srinivasan, and O. Painter, "Design of photonic crystal waveguide for evanescent coupling to optical fiber tapers and integration with high-Q cavities," Opt. Express 20, 2274-2284 (2003).

2002 (1)

W. Kuang, C. Kim, A. Stapleton, and J. O’Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides," Opt. Lett. 27, 1602-1606 (2002).
[CrossRef]

1997 (1)

J. Joannopoulos, P. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386,143-149 (1997).
[CrossRef]

1991 (3)

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

R. Black, S. Lacroix, F. Gonthier, J. Love, "Tapered single-mode fibers and devices; Part2: Experimental and theoretical qualification," IEE Proc. J. 138, 355-364 (1991).

F. Sanchez, "Matrix algebra for all-fiber optical resonators," J. Lightwave Technol. 9, 838-844 (1991).
[CrossRef]

1975 (1)

B. Hakki, T. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," Appl. Phys. 46, 1299-1306 (1975).
[CrossRef]

1971 (1)

Barclay, P.

P. Barclay, K. Srinivasan, M. Borselli, and O. Painter "Efficient input and output fiber coupling to a photonic crystal waveguide," Opt. Lett. 29, 697-699 (2004).
[CrossRef] [PubMed]

P. Barclay, K. Srinivasan, and O. Painter, "Design of photonic crystal waveguide for evanescent coupling to optical fiber tapers and integration with high-Q cavities," Opt. Express 20, 2274-2284 (2003).

Black, R.

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

R. Black, S. Lacroix, F. Gonthier, J. Love, "Tapered single-mode fibers and devices; Part2: Experimental and theoretical qualification," IEE Proc. J. 138, 355-364 (1991).

Borselli, M.

Cooper, V.

Eggleton, B

Fan, S.

J. Joannopoulos, P. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386,143-149 (1997).
[CrossRef]

Freeman, D

Gonthier, F.

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

R. Black, S. Lacroix, F. Gonthier, J. Love, "Tapered single-mode fibers and devices; Part2: Experimental and theoretical qualification," IEE Proc. J. 138, 355-364 (1991).

Grillet, C

Hakki, B.

B. Hakki, T. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," Appl. Phys. 46, 1299-1306 (1975).
[CrossRef]

Henry, W.

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

Hwang, I.-K.

I.-K. Hwang, G.-H. Kim, and Y.-H. Lee, "Optimization of coupling between photonic crystal resonators and curved microfiber," IEEE J. Quantum Electron. 42, 131-136 (2006).
[CrossRef]

Joannopoulos, J.

J. Joannopoulos, P. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386,143-149 (1997).
[CrossRef]

Kim, C.

W. Kuang, C. Kim, A. Stapleton, and J. O’Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides," Opt. Lett. 27, 1602-1606 (2002).
[CrossRef]

Kim, G.-H.

I.-K. Hwang, G.-H. Kim, and Y.-H. Lee, "Optimization of coupling between photonic crystal resonators and curved microfiber," IEEE J. Quantum Electron. 42, 131-136 (2006).
[CrossRef]

Krauss, T.

T. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Stat. Sol. (a) 197, 688-702 (2003).
[CrossRef]

Kuang, W.

W. Kuang, C. Kim, A. Stapleton, and J. O’Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides," Opt. Lett. 27, 1602-1606 (2002).
[CrossRef]

Lacroix, S.

R. Black, S. Lacroix, F. Gonthier, J. Love, "Tapered single-mode fibers and devices; Part2: Experimental and theoretical qualification," IEE Proc. J. 138, 355-364 (1991).

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

Lee, M.

Lee, Y.-H.

I.-K. Hwang, G.-H. Kim, and Y.-H. Lee, "Optimization of coupling between photonic crystal resonators and curved microfiber," IEEE J. Quantum Electron. 42, 131-136 (2006).
[CrossRef]

Love, J.

R. Black, S. Lacroix, F. Gonthier, J. Love, "Tapered single-mode fibers and devices; Part2: Experimental and theoretical qualification," IEE Proc. J. 138, 355-364 (1991).

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

Luther-Davis, B.

Madden, S

Magi, E.

Monat, C.

O’Brien, J.

W. Kuang, C. Kim, A. Stapleton, and J. O’Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides," Opt. Lett. 27, 1602-1606 (2002).
[CrossRef]

Painter, O.

P. Barclay, K. Srinivasan, M. Borselli, and O. Painter "Efficient input and output fiber coupling to a photonic crystal waveguide," Opt. Lett. 29, 697-699 (2004).
[CrossRef] [PubMed]

P. Barclay, K. Srinivasan, and O. Painter, "Design of photonic crystal waveguide for evanescent coupling to optical fiber tapers and integration with high-Q cavities," Opt. Express 20, 2274-2284 (2003).

Paoli, T.

B. Hakki, T. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," Appl. Phys. 46, 1299-1306 (1975).
[CrossRef]

Poulton, C

Sanchez, F.

F. Sanchez, "Matrix algebra for all-fiber optical resonators," J. Lightwave Technol. 9, 838-844 (1991).
[CrossRef]

Smith, C

Srinivasan, K.

P. Barclay, K. Srinivasan, M. Borselli, and O. Painter "Efficient input and output fiber coupling to a photonic crystal waveguide," Opt. Lett. 29, 697-699 (2004).
[CrossRef] [PubMed]

P. Barclay, K. Srinivasan, and O. Painter, "Design of photonic crystal waveguide for evanescent coupling to optical fiber tapers and integration with high-Q cavities," Opt. Express 20, 2274-2284 (2003).

Stapleton, A.

W. Kuang, C. Kim, A. Stapleton, and J. O’Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides," Opt. Lett. 27, 1602-1606 (2002).
[CrossRef]

Stewart, W.

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

Villeneuve, P.

J. Joannopoulos, P. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386,143-149 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

B. Hakki, T. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," Appl. Phys. 46, 1299-1306 (1975).
[CrossRef]

IEE Proc. J. (2)

J. Love,W. Henry,W. Stewart, R. Black, S. Lacroix, F. Gonthier,"Tapered single-mode fibers and devices; Part1: Adiabaticity criteria," IEE Proc. J. 138, 343-354 (1991).

R. Black, S. Lacroix, F. Gonthier, J. Love, "Tapered single-mode fibers and devices; Part2: Experimental and theoretical qualification," IEE Proc. J. 138, 355-364 (1991).

IEEE J. Quantum Electron. (1)

I.-K. Hwang, G.-H. Kim, and Y.-H. Lee, "Optimization of coupling between photonic crystal resonators and curved microfiber," IEEE J. Quantum Electron. 42, 131-136 (2006).
[CrossRef]

J. Lightwave Technol. (1)

F. Sanchez, "Matrix algebra for all-fiber optical resonators," J. Lightwave Technol. 9, 838-844 (1991).
[CrossRef]

Nature (1)

J. Joannopoulos, P. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386,143-149 (1997).
[CrossRef]

Opt. Express (2)

P. Barclay, K. Srinivasan, and O. Painter, "Design of photonic crystal waveguide for evanescent coupling to optical fiber tapers and integration with high-Q cavities," Opt. Express 20, 2274-2284 (2003).

M. Lee, C . Grillet, C . Poulton, C. Monat, C . Smith, E. Magi, D . Freeman, S . Madden, B. Luther-Davis, and B . Eggleton, "Characterizing photonic crystal waveguides with an extended k-space evanescent coupling technique," Opt. Express 16, 13800-13808 (2008).
[CrossRef] [PubMed]

Opt. Lett. (2)

P. Barclay, K. Srinivasan, M. Borselli, and O. Painter "Efficient input and output fiber coupling to a photonic crystal waveguide," Opt. Lett. 29, 697-699 (2004).
[CrossRef] [PubMed]

W. Kuang, C. Kim, A. Stapleton, and J. O’Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides," Opt. Lett. 27, 1602-1606 (2002).
[CrossRef]

Phys. Stat. Sol. (a) (1)

T. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Stat. Sol. (a) 197, 688-702 (2003).
[CrossRef]

Other (3)

K. Okamoto, Fundamentals of optical waveguides (Academic Press, 2000)

M. Natomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, " Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett.  87, 253902-1-253902-3 (2001).

A. Gomez-Iglesias, D. O’Brien, L. O’Faolain, A. Miller and T. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett.  90, 261107-1-261107-3 (2007).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

An illustration of the technique used in fabrication of the photonic coupler under study

Fig. 2.
Fig. 2.

Top microscope view of tapered fiber partially overlapping the waveguide defect region.

Fig. 3.
Fig. 3.

SEM image of a fabricated photonic crystal waveguide with lithographically defined facets.

Fig. 4.
Fig. 4.

An illustration of the coupler. The black lines represent the fiber and the red lines represent the waveguide

Fig. 5.
Fig. 5.

Fig. 5. Transmission spectrum of the unloaded waveguide and the fit obtained via expansion by Lorentzians

Fig. 6.
Fig. 6.

Fig. 6. FWHM and group index extracted by fitting the spectrum of the unloaded waveguide resonator

Fig. 7.
Fig. 7.

Measured output power from right waveguide facet when the input light is launched through the left facet.

Fig. 8.
Fig. 8.

Measured output power from the right waveguide facet when the input light is launched via port 3

Fig. 9.
Fig. 9.

Coupling efficiency and the measured output power from port 2 when the input light is launched through the left facet

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

Ea =[κ]Ef,Ef=[R]Ea +[tin] Ein , Eout =[T]((I[κ][R])1[κ][tin]) Ein
[κ] =(0κ120κ14κ210κ2300κ230κ21κ140κ120),[R] = (re2(α+iβg)lg00000000000000re2(α+iβg)lg)
[tin] =(κine2(α+iβg)lg000) , [ T ] = (te(α+iβg)lg0000eiβflf0000eiβflf0000te(α+iβg)lg)
(e3lg(α+iβg)rtκinκ141e4lg(α+iβg)r2κ14e4lg(α+iβg)(κ21eiβflf+eiβflf4lg(α+iβg)r2κ21κ141e4lg(α+iβg)r2κ14)κineiβflf3lg(α+iβg)rκ21κ14κin1e4lg(α+iβg)r2κ14e2lg(α+iβg)tκ14κin1e4lg(α+iβg)r2κ14)
(eiβflf3lg(α+iβg)rtκ12κ141e4lg(α+iβg)r2κ14eiβflf(κ23eiβflf+eiβflf4lg(α+iβg)r2κ21κ12κ141e4lg(α+iβg)r2κ14)e2iβflf2lg(α+iβg)rκ21κ121e4lg(α+iβg)r2κ14eiβflflg(α+iβg)tκ121e4lg(α+iβg)r2κ14)
Iout =t2e2αLgκin1+R22Rcos(x) Iin
22πt2e2αLgκin1R2 (InRx2+(InR)2) * q=+δ(2πqx)
Iout =t2e2αLgκ14κin1+R22Rcos(x+θ14) Iin
A0=11+R22Rcos(x)
A1=2Rcos(x+π2)1!(1+R22Rcos(x))A0
A2=2Rcos(x+2π2)2!(1+R22Rcos(x))A0+2Rcos(x+π2)1!(1+R22Rcos(x))A1
A3=2Rcos(x+3π2)3!(1+R22Rcos(x))A0+2Rcos(x+2π2)2!(1+R22Rcos(x))A1+2Rcos(x+π2)1!(1+R22Rcos(x))A2
H(x)=11+R22Rcos(x)2Rsin(x)(1+R22Rcos(x))2(θ141!θ1433!+θ1455!)
+2 R cos(x)(1+R22Rcos(x))2 (θ1422!+θ1444!θ1466!)
A0=11R2(1+2Rcos(x)+2R2cos(2x)+2R3cos(3x)+)
sin(x)(1+R22Rcos(x))2=0+11R2sin(x)+2R1R2sin(2x)+3R21R2sin(3x)
cos(x)(1+R22Rcos(x))2=2R(1R2)3+1(1R4)+4R2(1R2)3cos(x)+2(1R4)+4R2(1R2)3Rcos(2x)+
h(x˜)=2π(11R24R2(1cos(θ14))(1R2)3)Rx˜Σn=+δ(x˜n)
2π (1R4)(1cos(θ14))(1R2)3 x˜Rx˜Σn=+ δ (x˜n)
2πi sin(x˜)1R2 x˜ Rx˜ Σn=+ δ (x˜n)
(η1[R,θ14](2ln(1R)x2+(ln(1R))2)+η2[R,θ14](2ln(1R)x2+(ln(1R))2)2+η3[R,θ14]x(2ln(1R)x2+(ln(1R))2))
* (2πΣq=+δ(2πqx))
η1[R,θ14]=11R21cos(θ14)(1R2)3(4R2+1R4ln(1R)),η2[R,θ14]=1cos(θ14)(1R2)3(1R4)
η3[R,θ14]=sin(θ14)1R2

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