Abstract

A series of waveguides was inscribed in a borosilicate glass (BK7) by an 11MHz repetition rate femtosecond laser operating with pulse energies from 16 to 30nJ and focused at various depths within the bulk material. The index modification was measured using a quantitative phase microscopy technique that revealed central index changes ranging from 5×103 to 102, leading to waveguides that exhibited propagation losses of 0.2dB/cm at a wavelength of 633nm and 0.6dB/cm at a wavelength of 1550nm with efficient mode matching, less than 0.2dB, to standard optical fibers. Analysis of the experimental data shows that, for a given inscription energy, the index modification has a strong dependence on inscription scanning velocity. At higher energies, the index modification increases with increasing inscription scanning velocity with other fabrication parameters constant.

© 2010 Optical Society of America

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References

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  1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729-1731 (1996).
    [CrossRef] [PubMed]
  2. K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239, 91-95 (1998).
    [CrossRef]
  3. A. M. Streltsov and N. F. Borrelli, “Study of femtosecond-laser-written waveguides in glasses,” J. Opt. Soc. Am. B 19, 2496-2505 (2002).
    [CrossRef]
  4. D. M. Krol, “Femtosecond laser modification of glass,” J. Non-Cryst. Solids 354, 416-424 (2008).
    [CrossRef]
  5. A. H. Nejadmalayeri and P. R. Herman, “Rapid thermal annealing in high repetition rate ultrafast laser waveguide writing in lithium niobate,” Opt. Express 15, 10842 (2007).
    [CrossRef] [PubMed]
  6. T. Allsop, M. Dubov, A. Martinez, F. Floreani, I. Khrushchev, D. J. Webb, and I. Bennion, “Bending characteristics of fiber long-period gratings with cladding index modified by femtosecond laser,” J. Lightwave Technol. 24, 3147-3154 (2006).
    [CrossRef]
  7. T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
    [CrossRef]
  8. V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
    [CrossRef]
  9. S. M. Eaton, M. L. Ng, J. Bonse, A. Mermillod-Blondin, H. Zhang, A. Rosenfeld, and P. R. Herman, “Low-loss waveguides fabricated in BK7 glass by high repetition rate femtosecond fiber laser,” Appl. Opt. 47, 2098-2102 (2008).
    [CrossRef] [PubMed]
  10. FEMTOLASERS, Produktions GmbH, Fernkorngasse, Vienna, Austria, http://www.femtolasers.com/.
  11. S. M. Eaton, H. Zhang, M. L. Ng, J. Li, W-J. Chen, S. Ho, and P. R. Herman, “Transition from thermal diffusion to heat accumulation in high repetition rate femtosecond laser writing of buried optical waveguides,” Opt. Express 16, 9443-9458 (2008).
    [CrossRef] [PubMed]
  12. M. Kalal and K. A. Nugent, “Abel inversion using fast Fourier transforms,” Appl. Opt. 27, 1956-1959 (1988).
    [CrossRef] [PubMed]
  13. A. Roberts, E. Ampem-Lassen, A. Barty, K. A. Nugent, G. W. Baxter, N. M. Dragomir, and S. T. Huntington, “Refractive-index profiling of optical fibers with axial symmetry by use of quantitative phase microscopy,” Opt. Lett. 27, 2061-2063(2002).
    [CrossRef]
  14. M. Ams, G. D. Marshall, and M. J. Withford, “Study of the influence of femtosecond laser polarization on direct writing of waveguides,” Opt. Express 14, 13158 (2006).
    [CrossRef] [PubMed]
  15. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, and P. Laporta, “Optical properties of waveguides written by a 26 MHz stretched cavity Ti:sapphire femtosecond oscillator,” Opt. Express , 13, 612-620 (2005).
    [CrossRef] [PubMed]
  16. J. F. Power, “Pulsed mode thermal lens effect detection in the near field via thermally induced probe beam spatial phase modulation: a theory,” Appl. Opt. 29, 52-63 (1990).
    [CrossRef] [PubMed]
  17. R. Brückner, “Properties and structure of vitreous silica. I,” J. Non-Cryst. Solids 5, 123-175 (1970).
    [CrossRef]
  18. http://www.uqgoptics.com
  19. E. R. G. Eckert and R. M. Drake, Heat and Mass Transfer (McGraw-Hill, 1959).
  20. M. Dubov, T. D. P. Allsop, S. R. Natarajan, V. K. Mezentsev, and I. Bennion, “Low-loss waveguides in borosilicate glass fabricated by high-repetition-rate femtosecond chirp-pulsed oscillator,” in Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference (IEEE, 2009), paper CE.P.4 MON.
  21. A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman & Hall, 1991).

2008 (4)

2007 (1)

2006 (2)

2005 (2)

R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, and P. Laporta, “Optical properties of waveguides written by a 26 MHz stretched cavity Ti:sapphire femtosecond oscillator,” Opt. Express , 13, 612-620 (2005).
[CrossRef] [PubMed]

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

2002 (2)

1998 (1)

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239, 91-95 (1998).
[CrossRef]

1996 (1)

1990 (1)

1988 (1)

1970 (1)

R. Brückner, “Properties and structure of vitreous silica. I,” J. Non-Cryst. Solids 5, 123-175 (1970).
[CrossRef]

Allsop, T.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

T. Allsop, M. Dubov, A. Martinez, F. Floreani, I. Khrushchev, D. J. Webb, and I. Bennion, “Bending characteristics of fiber long-period gratings with cladding index modified by femtosecond laser,” J. Lightwave Technol. 24, 3147-3154 (2006).
[CrossRef]

Allsop, T. D. P.

M. Dubov, T. D. P. Allsop, S. R. Natarajan, V. K. Mezentsev, and I. Bennion, “Low-loss waveguides in borosilicate glass fabricated by high-repetition-rate femtosecond chirp-pulsed oscillator,” in Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference (IEEE, 2009), paper CE.P.4 MON.

Ampem-Lassen, E.

Ams, M.

Barty, A.

Baxter, G. W.

Bennion, I.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

T. Allsop, M. Dubov, A. Martinez, F. Floreani, I. Khrushchev, D. J. Webb, and I. Bennion, “Bending characteristics of fiber long-period gratings with cladding index modified by femtosecond laser,” J. Lightwave Technol. 24, 3147-3154 (2006).
[CrossRef]

M. Dubov, T. D. P. Allsop, S. R. Natarajan, V. K. Mezentsev, and I. Bennion, “Low-loss waveguides in borosilicate glass fabricated by high-repetition-rate femtosecond chirp-pulsed oscillator,” in Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference (IEEE, 2009), paper CE.P.4 MON.

Bhardwaj, V. R.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Bonse, J.

Borrelli, N. F.

Brückner, R.

R. Brückner, “Properties and structure of vitreous silica. I,” J. Non-Cryst. Solids 5, 123-175 (1970).
[CrossRef]

Cerullo, G.

Chen, W-J.

Chiodo, N.

Corkum, P. B.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Davis, K. M.

Dragomir, N. M.

Drake, R. M.

E. R. G. Eckert and R. M. Drake, Heat and Mass Transfer (McGraw-Hill, 1959).

Dubov, M.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

T. Allsop, M. Dubov, A. Martinez, F. Floreani, I. Khrushchev, D. J. Webb, and I. Bennion, “Bending characteristics of fiber long-period gratings with cladding index modified by femtosecond laser,” J. Lightwave Technol. 24, 3147-3154 (2006).
[CrossRef]

M. Dubov, T. D. P. Allsop, S. R. Natarajan, V. K. Mezentsev, and I. Bennion, “Low-loss waveguides in borosilicate glass fabricated by high-repetition-rate femtosecond chirp-pulsed oscillator,” in Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference (IEEE, 2009), paper CE.P.4 MON.

Eaton, S. M.

Eckert, E. R. G.

E. R. G. Eckert and R. M. Drake, Heat and Mass Transfer (McGraw-Hill, 1959).

Floreani, F.

Herman, P. R.

Hirao, K.

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239, 91-95 (1998).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729-1731 (1996).
[CrossRef] [PubMed]

Hnatovsky, C.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Ho, S.

Huntington, S. T.

Kalal, M.

Kalli, K.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

Khrushchev, I.

Kluge, M.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Krol, D. M.

D. M. Krol, “Femtosecond laser modification of glass,” J. Non-Cryst. Solids 354, 416-424 (2008).
[CrossRef]

Lai, Y.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

Laporta, P.

Li, J.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman & Hall, 1991).

Marshall, G. D.

Martinez, A.

Maselli, V.

Mermillod-Blondin, A.

Mezentsev, V. K.

M. Dubov, T. D. P. Allsop, S. R. Natarajan, V. K. Mezentsev, and I. Bennion, “Low-loss waveguides in borosilicate glass fabricated by high-repetition-rate femtosecond chirp-pulsed oscillator,” in Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference (IEEE, 2009), paper CE.P.4 MON.

Miura, K.

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239, 91-95 (1998).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729-1731 (1996).
[CrossRef] [PubMed]

Natarajan, S. R.

M. Dubov, T. D. P. Allsop, S. R. Natarajan, V. K. Mezentsev, and I. Bennion, “Low-loss waveguides in borosilicate glass fabricated by high-repetition-rate femtosecond chirp-pulsed oscillator,” in Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference (IEEE, 2009), paper CE.P.4 MON.

Nejadmalayeri, A. H.

Ng, M. L.

Nugent, K. A.

Osellame, R.

Power, J. F.

Rayner, D. M.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Roberts, A.

Rosenfeld, A.

Schreder, B.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Simova, E.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Smith, G.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman & Hall, 1991).

Streltsov, A. M.

Sugimoto, N.

Taylor, R. S.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Webb, D. J.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

T. Allsop, M. Dubov, A. Martinez, F. Floreani, I. Khrushchev, D. J. Webb, and I. Bennion, “Bending characteristics of fiber long-period gratings with cladding index modified by femtosecond laser,” J. Lightwave Technol. 24, 3147-3154 (2006).
[CrossRef]

Withford, M. J.

Yin, A.

Zavelani-Rossi, M.

Zhang, H.

Zhou, K.

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

Zimme, J.

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

Appl. Opt. (3)

J. Appl. Phys. (1)

V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimme, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Non-Cryst. Solids (3)

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239, 91-95 (1998).
[CrossRef]

D. M. Krol, “Femtosecond laser modification of glass,” J. Non-Cryst. Solids 354, 416-424 (2008).
[CrossRef]

R. Brückner, “Properties and structure of vitreous silica. I,” J. Non-Cryst. Solids 5, 123-175 (1970).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

T. Allsop, K. Kalli, K. Zhou, Y. Lai, G. Smith, M. Dubov, D. J. Webb, and I. Bennion, “Long period gratings written into a photonic crystal fibre by a femtosecond laser as directional bend sensors,” Opt. Commun. 281, 5092-5096 (2008).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Other (5)

FEMTOLASERS, Produktions GmbH, Fernkorngasse, Vienna, Austria, http://www.femtolasers.com/.

http://www.uqgoptics.com

E. R. G. Eckert and R. M. Drake, Heat and Mass Transfer (McGraw-Hill, 1959).

M. Dubov, T. D. P. Allsop, S. R. Natarajan, V. K. Mezentsev, and I. Bennion, “Low-loss waveguides in borosilicate glass fabricated by high-repetition-rate femtosecond chirp-pulsed oscillator,” in Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference (IEEE, 2009), paper CE.P.4 MON.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman & Hall, 1991).

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Figures (17)

Fig. 1
Fig. 1

Optical and mechanical schematic of the inscription apparatus. (a) Overhead view of the light source and diagnostics. (b) Side view of the focusing and inscription equipment.

Fig. 2
Fig. 2

Microscope images of example fabricated waveguides. (A) Examples of the overhead views of three waveguides with the same inscription energy of 16.4 nJ and with scanning speeds of (1) 25 and (2)  30 mms 1 inscribed from top to bottom, and (3)  30 mms 1 inscribed from bottom to top at a depth of 45 μm . (B) Example of the cross section of a waveguide with an inscription energy of 29.4 nJ with a scanning speed of 25 mms 1 . (C) Close-up of the waveguide in (B). (D) Waveguide written with the same sample inscription conditions, but with opposite scan direction. (E1), (E2), (E3) examples of the various modes of a fabricated waveguide observed in the near field at a wavelength of 633 nm . Fabrication conditions for this waveguide were inscription energy 19.6 nJ , depth of waveguide 72 μm , scan velocity 45 mms 1 , with measured waveguide characteristics of maximum Δ n , 1.2 × 10 3 ; V parameter, 2.4; and attenuation coefficient, 0.5 dB cm 1 at 633 nm .

Fig. 3
Fig. 3

(a) Typical cumulative phase profile obtained from QPM defining the measurements taken from the data. The waveguide was written with X-polarized light, an energy of 19.6 nJ , scanning velocity of 55 mms 1 , and at an approximate depth of 55 μm . (b) Calculated radial index profile of the waveguides using an Abel inverse transform.

Fig. 4
Fig. 4

Example of the comparison of the radial diameter of the index modification as a function of scanning inscription velocity: (a) the inner section and (b) the outer section of the waveguide. The inscription energy was 29.4 nJ , the depth was 43 μm , and both polarization states are shown (X-polarization, ♦; Y-polarization, ▴).

Fig. 5
Fig. 5

pi twb 0.3w Peak index modification estimated by the use of QPM and the inverse Abel transform for (a) inner regions and (b) outer regions for all waveguides fabricated with both polarization states of the inscribing beam (black shapes for Y-polarization, gray shapes for X-polarization), at a depth of 70 μm and various inscription pulse energy groups (*, 16.4 nJ ; ×, 19.6 nJ ; ▴, 22.9 nJ ; ▪, 26.1 nJ ; ♦, 29.5 nJ ). Within each energy group, the results are presented in order of increasing inscription scanning velocity with increasing sample number.

Fig. 6
Fig. 6

Examples of the peak index change as a function of inscription depth at an inscription energy of 22.9 nJ for both (a) X- and (b) Y-polarization states at three different depths: (a) depths of 68, 87, and 106 μm , and (b) depths of 68, 84, and 100 μm .

Fig. 7
Fig. 7

Rate of index change ( Δ n ) with respect to scanning velocity ( Δ V ) as a function of inscription energy (♦, the inner index feature; ▴, the outer index feature. (a) Y-polarization and (b) X-polarization. The lines are simply added to link together points relating to the same index feature as an aid to the eye.

Fig. 8
Fig. 8

Rate of change of the size of the index feature ( Δ R ) with respect to scanning velocity ( Δ V ) as a function of inscription energy (♦, the inner index feature; ▴, the outer index feature). (a) Y-polarization and (b) X-polarization.

Fig. 9
Fig. 9

Theoretically calculated temperature distribution of glass along the z axis in a heat wave for two Péclet numbers, assuming a Gaussian heat distribution with 2 μm being at the e 1 of the maximum value.

Fig. 10
Fig. 10

Cooling rate of the sample at the glass transition temperature ( T g = 570 ° C ) as a function of the Péclet number for BK7 glass, varying only the scanning velocity.

Fig. 11
Fig. 11

Experimentally observed variation of modified index as a function of dosage for the laser operating in the Y-polarization state (♦) and the X-polarization state (▴), including all depths of inscription.

Fig. 12
Fig. 12

Schematic of the apparatus used to obtain an estimate of the attenuation coefficient of the waveguides

Fig. 13
Fig. 13

Attenuation coefficient of the waveguides fabricated in a sample of BK7 with X-polarized femtosecond laser light as a function of their V parameters, indicating their inscription energy: black ♦, 16.4 nJ ; gray ♦, 19.6 nJ ; black ▴, 22.9 nJ ; gray ▴, 26.1 nJ ; and black ▪, 29.5 nJ .

Fig. 14
Fig. 14

Attenuation coefficient of the waveguides fabricated in a sample of BK7 with Y-polarized femtosecond laser light as a function of their V parameters, indicating their inscription energy: black ♦, 16.4 nJ ; gray ♦, 19.6 nJ ; black ▴, 22.9 nJ ; gray ▴, 26.1 nJ ; and black ▪, 29.5 nJ .

Fig. 15
Fig. 15

(a) Effects of depth and dose on the overall attenuation coefficient of the waveguides at 633 nm for (a) Y-polarized inscription light and (b) X-polarized inscription light.

Fig. 16
Fig. 16

Comparison of the measurements of the low-loss waveguides at 633 nm and at 1550 nm : ♦, losses at 633 nm and ▴, losses at 1550 nm . Fabrication conditions for this waveguide inscription energy 22.9 nJ , depth of waveguide 55 μm .

Fig. 17
Fig. 17

Dependence on pulse energy and scanning speed of two sets of waveguide attenuation coefficients at a wavelength of 633 nm written with the femtosecond laser at a depth of 55 μm . (a) Y-linearly polarized and (b) X-linearly polarized.

Equations (4)

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c ρ T t κ Δ T = q ( z v t , r , t ) ,
c ρ v T z κ Δ T = q ( z , r ) .
Pe T z Δ T = R 2 κ q ( z , r ) .
Energy Dose = E pulse R p A V ,

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