Abstract

We used ultrafast laser inscription to fabricate three-dimensional integrated optical transitions that efficiently couple light from a multimode waveguide to a two-dimensional array of single mode waveguides and back. Although the entire device has an average insertion loss of 5.7 dB at 1539 nm, only ≈0.7 dB is due to mode coupling losses. Based on an analysis which is presented in the paper, we expect that our device should convert a multimode input into an array of single modes with a loss of ≈2.0 dB, assuming the input coupling losses are zero. Such devices have applications in astrophotonics and remote sensing.

© 2011 OSA

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References

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  1. J. Bland-Hawthorn and P. Kern, “Astrophotonics: a new era for astronomical instruments,” Opt. Express 17(3), 1880–1884 (2009).
    [CrossRef] [PubMed]
  2. P. Kern, E. Le Coärer, and P. Benech, “On-chip spectro-detection for fully integrated coherent beam combiners,” Opt. Express 17(3), 1976–1987 (2009).
    [CrossRef] [PubMed]
  3. J. Bland-Hawthorn, M. Englund, and G. Edvell, “New approach to atmospheric OH suppression using an aperiodic fibre Bragg grating,” Opt. Express 12(24), 5902–5909 (2004).
    [CrossRef] [PubMed]
  4. S. G. Leon-Saval, T. A. Birks, J. Bland-Hawthorn, and M. Englund, “Multimode fiber devices with single-mode performance,” Opt. Lett. 30(19), 2545–2547 (2005).
    [CrossRef] [PubMed]
  5. D. Noordegraaf, P. M. W. Skovgaard, M. D. Nielsen, and J. Bland-Hawthorn, “Efficient multi-mode to single-mode coupling in a photonic lantern,” Opt. Express 17(3), 1988–1994 (2009).
    [CrossRef] [PubMed]
  6. D. Noordegraaf, P. M. W. Skovgaard, M. D. Maack, J. Bland-Hawthorn, R. Haynes, and J. Laegsgaard, “Multi-mode to single-mode conversion in a 61 port Photonic Lantern,” Opt. Express 18(5), 4673–4678 (2010).
    [CrossRef] [PubMed]
  7. S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: a study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010).
    [CrossRef] [PubMed]
  8. T. A. Birks, A. Diez, J. L. Cruz, S. G. Leon-Saval, and D. F. Murphy, “Fibers are looking up: optical fiber transition structures in astrophotonics,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FTuU1. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2010-FTuU1 .
  9. R. R. Thomson, G. Brown, A. K. Kar, T. A. Birks, and J. Bland-Hawthorn, “An integrated fan-out device for astrophotonics,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPA3. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2010-PDPA3 .
  10. N. Cvetojevic, J. S. Lawrence, S. C. Ellis, J. Bland-Hawthorn, R. Haynes, and A. Horton, “Characterization and on-sky demonstration of an integrated photonic spectrograph for astronomy,” Opt. Express 17(21), 18643–18650 (2009).
    [CrossRef]
  11. E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
    [CrossRef]
  12. B. Martin, A. Morand, P. Benech, G. Grosa, P. Kern, L. Jocou, and E. Le Coarer, “Realization of the compact static Fourier transform spectrometer LLIFTS in glass integrated optics,” Opt. Lett. 34(15), 2291–2293 (2009).
    [CrossRef] [PubMed]
  13. J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
    [CrossRef]
  14. R. R. Thomson, A. K. Kar, and J. Allington-Smith, “Ultrafast laser inscription: an enabling technology for astrophotonics,” Opt. Express 17(3), 1963–1969 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. C. Mauclair, G. Cheng, N. Huot, E. Audouard, A. Rosenfeld, I. V. Hertel, and R. Stoian, “Dynamic ultrafast laser spatial tailoring for parallel micromachining of photonic devices in transparent materials,” Opt. Express 17(5), 3531–3542 (2009).
    [CrossRef] [PubMed]
  19. M. Ams, G. D. Marshall, and M. J. Withford, “Study of the influence of femtosecond laser polarisation on direct writing of waveguides,” Opt. Express 14(26), 13158–13163 (2006).
    [CrossRef] [PubMed]
  20. A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]

2010 (3)

2009 (7)

2007 (2)

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

R. R. Thomson, H. T. Bookey, N. D. Psaila, A. Fender, S. Campbell, W. N. Macpherson, J. S. Barton, D. T. Reid, and A. K. Kar, “Ultrafast-laser inscription of a three dimensional fan-out device for multicore fiber coupling applications,” Opt. Express 15(18), 11691–11697 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (2)

2004 (3)

1996 (1)

Allington-Smith, J.

Ams, M.

Argyros, A.

Audouard, E.

Bado, P.

A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
[CrossRef]

Barton, J. S.

Bellouard, Y.

A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
[CrossRef]

Benech, P.

Betters, C.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

Birks, T.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

Birks, T. A.

Blaize, S.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Bland-Hawthorn, J.

S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: a study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010).
[CrossRef] [PubMed]

D. Noordegraaf, P. M. W. Skovgaard, M. D. Maack, J. Bland-Hawthorn, R. Haynes, and J. Laegsgaard, “Multi-mode to single-mode conversion in a 61 port Photonic Lantern,” Opt. Express 18(5), 4673–4678 (2010).
[CrossRef] [PubMed]

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

N. Cvetojevic, J. S. Lawrence, S. C. Ellis, J. Bland-Hawthorn, R. Haynes, and A. Horton, “Characterization and on-sky demonstration of an integrated photonic spectrograph for astronomy,” Opt. Express 17(21), 18643–18650 (2009).
[CrossRef]

D. Noordegraaf, P. M. W. Skovgaard, M. D. Nielsen, and J. Bland-Hawthorn, “Efficient multi-mode to single-mode coupling in a photonic lantern,” Opt. Express 17(3), 1988–1994 (2009).
[CrossRef] [PubMed]

J. Bland-Hawthorn and P. Kern, “Astrophotonics: a new era for astronomical instruments,” Opt. Express 17(3), 1880–1884 (2009).
[CrossRef] [PubMed]

S. G. Leon-Saval, T. A. Birks, J. Bland-Hawthorn, and M. Englund, “Multimode fiber devices with single-mode performance,” Opt. Lett. 30(19), 2545–2547 (2005).
[CrossRef] [PubMed]

J. Bland-Hawthorn, M. Englund, and G. Edvell, “New approach to atmospheric OH suppression using an aperiodic fibre Bragg grating,” Opt. Express 12(24), 5902–5909 (2004).
[CrossRef] [PubMed]

Bookey, H. T.

Burghoff, J.

Campbell, S.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

R. R. Thomson, H. T. Bookey, N. D. Psaila, A. Fender, S. Campbell, W. N. Macpherson, J. S. Barton, D. T. Reid, and A. K. Kar, “Ultrafast-laser inscription of a three dimensional fan-out device for multicore fiber coupling applications,” Opt. Express 15(18), 11691–11697 (2007).
[CrossRef] [PubMed]

Cheng, G.

Cvetojevic, N.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

N. Cvetojevic, J. S. Lawrence, S. C. Ellis, J. Bland-Hawthorn, R. Haynes, and A. Horton, “Characterization and on-sky demonstration of an integrated photonic spectrograph for astronomy,” Opt. Express 17(21), 18643–18650 (2009).
[CrossRef]

Davis, K. M.

Dugan, M.

A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
[CrossRef]

Edvell, G.

Ellis, S. C.

Englund, M.

Fedeli, J. M.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Fender, A.

Grosa, G.

Haynes, R.

Hertel, I. V.

Hibino, Y.

Hirao, K.

Horton, A.

Huot, N.

Jocou, L.

Jovanovic, N.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

Kar, A. K.

Kern, P.

Kohtoku, M.

Laegsgaard, J.

Lawrence, J.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

Lawrence, J. S.

Le Coarer, E.

B. Martin, A. Morand, P. Benech, G. Grosa, P. Kern, L. Jocou, and E. Le Coarer, “Realization of the compact static Fourier transform spectrometer LLIFTS in glass integrated optics,” Opt. Lett. 34(15), 2291–2293 (2009).
[CrossRef] [PubMed]

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Le Coärer, E.

Leblond, G.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Lederer, F.

Leon-Saval, S.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

Leon-Saval, S. G.

Lérondel, G.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Maack, M. D.

Mabesa, J.

A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
[CrossRef]

Macpherson, W. N.

Marshall, G. D.

Martin, B.

Mauclair, C.

Miura, K.

Morand, A.

B. Martin, A. Morand, P. Benech, G. Grosa, P. Kern, L. Jocou, and E. Le Coarer, “Realization of the compact static Fourier transform spectrometer LLIFTS in glass integrated optics,” Opt. Lett. 34(15), 2291–2293 (2009).
[CrossRef] [PubMed]

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Nasu, Y.

Nielsen, M. D.

Nolte, S.

Noordegraaf, D.

Pertsch, T.

Peschel, U.

Pope, B.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

Psaila, N. D.

Reid, D. T.

Robertson, G.

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

Rosenfeld, A.

Royer, P.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Said, A. A.

A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
[CrossRef]

Scott, A.

A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
[CrossRef]

Skovgaard, P. M. W.

Stefanon, I.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Stoian, R.

Sugimoto, N.

Thomson, R. R.

Tünnermann, A.

Will, M.

Withford, M. J.

Nat. Photonics (1)

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Opt. Express (11)

R. R. Thomson, A. K. Kar, and J. Allington-Smith, “Ultrafast laser inscription: an enabling technology for astrophotonics,” Opt. Express 17(3), 1963–1969 (2009).
[CrossRef] [PubMed]

R. R. Thomson, H. T. Bookey, N. D. Psaila, A. Fender, S. Campbell, W. N. Macpherson, J. S. Barton, D. T. Reid, and A. K. Kar, “Ultrafast-laser inscription of a three dimensional fan-out device for multicore fiber coupling applications,” Opt. Express 15(18), 11691–11697 (2007).
[CrossRef] [PubMed]

C. Mauclair, G. Cheng, N. Huot, E. Audouard, A. Rosenfeld, I. V. Hertel, and R. Stoian, “Dynamic ultrafast laser spatial tailoring for parallel micromachining of photonic devices in transparent materials,” Opt. Express 17(5), 3531–3542 (2009).
[CrossRef] [PubMed]

M. Ams, G. D. Marshall, and M. J. Withford, “Study of the influence of femtosecond laser polarisation on direct writing of waveguides,” Opt. Express 14(26), 13158–13163 (2006).
[CrossRef] [PubMed]

J. Bland-Hawthorn and P. Kern, “Astrophotonics: a new era for astronomical instruments,” Opt. Express 17(3), 1880–1884 (2009).
[CrossRef] [PubMed]

P. Kern, E. Le Coärer, and P. Benech, “On-chip spectro-detection for fully integrated coherent beam combiners,” Opt. Express 17(3), 1976–1987 (2009).
[CrossRef] [PubMed]

J. Bland-Hawthorn, M. Englund, and G. Edvell, “New approach to atmospheric OH suppression using an aperiodic fibre Bragg grating,” Opt. Express 12(24), 5902–5909 (2004).
[CrossRef] [PubMed]

D. Noordegraaf, P. M. W. Skovgaard, M. D. Nielsen, and J. Bland-Hawthorn, “Efficient multi-mode to single-mode coupling in a photonic lantern,” Opt. Express 17(3), 1988–1994 (2009).
[CrossRef] [PubMed]

D. Noordegraaf, P. M. W. Skovgaard, M. D. Maack, J. Bland-Hawthorn, R. Haynes, and J. Laegsgaard, “Multi-mode to single-mode conversion in a 61 port Photonic Lantern,” Opt. Express 18(5), 4673–4678 (2010).
[CrossRef] [PubMed]

S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: a study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010).
[CrossRef] [PubMed]

N. Cvetojevic, J. S. Lawrence, S. C. Ellis, J. Bland-Hawthorn, R. Haynes, and A. Horton, “Characterization and on-sky demonstration of an integrated photonic spectrograph for astronomy,” Opt. Express 17(21), 18643–18650 (2009).
[CrossRef]

Opt. Lett. (5)

Proc. SPIE (2)

J. Bland-Hawthorn, J. Lawrence, G. Robertson, S. Campbell, B. Pope, C. Betters, S. Leon-Saval, T. Birks, R. Haynes, N. Cvetojevic, and N. Jovanovic, “PIMMS: photonic integrated multimode microspectrograph,” Proc. SPIE 7735, 77350N (2010).
[CrossRef]

A. A. Said, M. Dugan, P. Bado, Y. Bellouard, A. Scott, and J. Mabesa, “Manufacturing by laser direct-write of three-dimensional devices containing optical and microfluidic networks,” Proc. SPIE 5339, 194–204 (2004).
[CrossRef]

Other (2)

T. A. Birks, A. Diez, J. L. Cruz, S. G. Leon-Saval, and D. F. Murphy, “Fibers are looking up: optical fiber transition structures in astrophotonics,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FTuU1. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2010-FTuU1 .

R. R. Thomson, G. Brown, A. K. Kar, T. A. Birks, and J. Bland-Hawthorn, “An integrated fan-out device for astrophotonics,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPA3. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2010-PDPA3 .

Supplementary Material (2)

» Media 1: MOV (3701 KB)     
» Media 2: MOV (3733 KB)     

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Figures (4)

Fig. 1
Fig. 1

Sketches of (a) a MM-to-SM integrated PL transition and (b) a MM-to-SM-to-MM transition created by inscribing two of the PLs shown in (a) back-to-back.

Fig. 2
Fig. 2

White light transmission micrographs of (a) the 4 × 4 SM array end of PL-1 and (b) one end of MM-1. (c) Single frame from a near field video recording (Media 1) of the SM array end of PL-1 while adjusting the injection of 1539 nm light into the MM end. (d) Single frame from a near field video recording (Media 2) of MM-1 while adjusting the injection of 1539 nm light into the opposite end. The field of view is 200 μm × 200 μm for (a) and (c), and 100 μm × 100 μm for (b) and (d). In all cases, the inscription laser entered the sample from below.

Fig. 3
Fig. 3

(a) Two-dimensional refractive index profile of one of the SM waveguides of PL-1. The laser entered from the −z direction. (b) & (c) One-dimensional index profiles along z and x respectively, taken at x = 0 and z = 0 respectively in (a).

Fig. 4
Fig. 4

(a) Two-dimensional normalised refractive index profile of MM-1 (the structure shown in Fig. 2(b)). The laser entered from the −z direction. (b) & (c) One-dimensional normalised index profiles along z and x respectively, taken at x = 0 and z = 0 respectively in (a).

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