Abstract

We report both theoretical and experimental results of a slit beam shaping configuration for fabricating photonic waveguides by use of femtosecond laser pulses. Most importantly we show the method supports focussing objectives with a long depth of field and allows the direct-writing of microstructures with circular cross-sections whilst employing a perpendicular writing scheme. We applied this technique to write low loss (0.39 dB/cm), single mode waveguides in phosphate glass.

©2005 Optical Society of America

1. Introduction

Multiphoton absorption in bulk materials using ultra-fast lasers has generated a great deal of activity in the field of photonics. In 1996 it was shown that tightly focussed infrared femtosecond laser pulses induced a refractive index change inside a glass sample [1]. Because the response of the material is nonlinear, the modification is localised in the focal volume, avoiding any damage to the surface and outer layers. This index gradient may be attributed to multi-photon excitation and partial ionisation [2] which lead to the sample melting and eventually cooling giving rise to densification [3]. Refractive index changes of the order of 10-2 have been reported [4]. Thus by moving a polished sample through the focal point of these high-intensity pulses, three-dimensional structures [5] and patterns can be fabricated in a direct-write fashion inside bulk glass. This simple technique raises the potential for fabricating a wide range of arbitrary telecommunication devices for all-optical networks.

Waveguides may be created using two writing regimes whereby samples are translated perpendicularly or parallel to the writing beam. In the parallel writing scheme, waveguides with circular cross-sections can be fabricated, however this method is limited by the working distance of the focussing objective. The perpendicular writing geometry allows one to write waveguides of arbitrary length and design, however when using conventional spherical focussing optics this method produces waveguides with strong core asymmetry and significant losses [2].

Focussing geometries including a high (de)magnification astigmatic cylindrical telescope have been used to overcome this problem [6]. The telescope acts to reshape the beam before focussing thus allowing the waveguide cross section to be made circular and with arbitrary size. Another group, working in a different field, inserted a slit orientated parallel to the writing direction and before the focussing lens in order to reshape the beam near focus [7,8]. This method is much simpler and offers similar control to the astigmatic telescope approach. In this paper we outline the latter method more thoroughly, offering new insight into the underlying physics at work. We also demonstrate the use of this method by fabricating low-loss, circular optical waveguides in phosphate glass with a long working distance microscope objective and discuss the advantages of this technique with respect to fabricating three-dimensional integrated photonic devices.

2. Theory

For all formulations that follow we apply the paraxial approximation and assume the slit is inserted before the focussing objective within the Rayleigh range associated with its dimension. In order to simplify the calculations, we assume that the beam exiting the slit is Gaussian and not top-hat.

The beam waists in the x and y directions (Wx and Wy respectively) of a elliptical Gaussian beam propagating in the z direction and focused by a lens of focal length f are given by

ωx=πWxandωy=πWy.

Knowing that the associated Rayleigh ranges scale as the beam waist squared, then the following ratio at focus holds true

ZRxZRy=Wy2Wx2.

For the case that Wy is significantly larger than Wx, we can perform a simplified analytical investigation of the focussing properties of this elliptical beam. Hence, for a slit such that Wx > 3Wy, then ZRy > 9ZRx. In this regime we assume the beam to be collimated in the y direction. This approximation simplifies the analysis because the axial intensity, Io, versus z is only controlled by the beam size in the x direction. In order to fabricate waveguides with a circular cross-section, we require the focal depth in the z direction to match the transverse width in the y direction. There are a number of ways to approach this problem and we have chosen to use the half-width-half-maximum (HWHM) approach.

The axial intensity drops by a factor of 2 over a distance XIo2 when the spot size in the x direction doubles, i.e.

2ωx=ωx[1+(λXIo2πωx2)2]12
XIo2=3πλωx2.

Note that, after an axial distance XIo2 , the spot size in the y direction increases by a factor of 1.018 (compared to 2 in the x direction) when Wx = 3Wy. Therefore the assumption regarding the beam being collimated in y is sound.

In the transverse y direction the distance from the axis, YIo2 , when the intensity drops by a factor of 2, can be calculated by the following

Io2=Ioexp(YIo22ωy2)
YIo2=In2ωy.

Equating Eq. (4) and Eq. (5) will give us the aspect ratio of the slit required to fabricate waveguides with a circular cross-section, i.e.

XIo2=YIo2
WyWx=NAIn23forWx>3Wy,

where the numerical aperture of the focussing objective NA is given by

NAWxf.

This approximation is not only due to the paraxial approximation, but also to the fact that Wx is a Gaussian radius which is not necessarily the radius of the aperture of the focussing objective. Nonetheless, this is a small discrepancy. So far we have only considered focussing an elliptical beam in vacuum. In order to complete the study, we must take into account focussing the beam into a glass substrate with a refractive index of n. In this regime, λ → λ/n and the resulting cone angle inside the substrate decreases to give NAWx/nf . Therefore, given the numerical aperture of the focussing objective, the refractive index of the glass substrate and knowing the beam radius of the incoming beam, one can then use the following equation to calculate the slit width required to produce circular cross-sectional waveguides:

WyWx=NAnIn23forWx>3Wy,

3. Experimental setup

Optical waveguides were fabricated using a regeneratively amplified, low-repetition rate Ti:sapphire femtosecond laser system (Hurricane) from Spectra-Physics. This system produces 120 fs, 1 kHz pulses and can deliver an average power of 1 W. Laser pulses at 800 nm were fo-cussed through a 20× microscope objective (Olympus UMPlanFL, NA 0.46) and injected into polished 5×5×5 mm phosphate glass samples (Toplent Photonics). The average power of the laser beam was varied by neutral-density filters that were inserted between the laser and the microscope objective. Powers ranging from 0.2 mW to 5 mW, after passing through the slit, were used in the formation of optical waveguides. Using a computer controlled XYZ stage, samples were scanned in the x direction, perpendicular to the direction of beam propagation, at speeds ranging between 40-100 μm/s. In order to probe the fabricated waveguides, a fibre carrying either 635 nm or 1550 nm light was brought into close proximity to the polished end of the sample. Near field mode profile were imaged using a 635 nm wavelength probe, a microscope objective and CCD camera. Refractive index changes were estimated by matching near field profiles to numerical simulations of a step-index waveguide performed by BeamPROP (part of the RSoft Photonics CAD Suite). Images of fabricated waveguides were taken with an Olympus differential interference contrast (DIC) microscope. To measure the waveguide loss, the output power from a single mode fibre carrying 1550 nm light was measured as was the output power after propagation through the waveguide. A microscope objective was used to collect only the light emanating from the guides; the ratio of these two powers gave us an overall insertion loss which included both coupling and waveguide transmission losses.

4. Results and discussion

 

Fig. 1. (a) beam evolution near focus not using slit, (b) energy distribution in YZ plane not using slit, (c) beam evolution near focus using slit, (d) energy distribution in YZ plane using slit where x corresponds with the direction of the beam translation and the waveguide axis.

Download Full Size | PPT Slide | PDF

The beam of our femtosecond laser has a 1/e 2 radius of ≈ 2.2 mm. By applying Eq. (8), we calculated that the width of the slit had to measure 2Wy ≈ 630 μm if we were to fabricate circular cross-sectional waveguides. The plots shown in Fig. 1((a), (c)) were generated using Eq. (3), a numerical aperture of 0.46 and a slit width of 500 μm to show the beam near focus inside phosphate glass of refractive index 1.54. The effect of the slit on the evolution of the beam through focus can be clearly seen; the transverse width in the y direction has become larger. The corresponding energy distribution plots near the focal point, Fig. 1((b), (d)), were generated using a modified version of the equations from [7]. Cheng et al. did not account for the refractive index of the glass substrate which changes the depth of field of focus. Fig. 1(b) shows that the shape of a waveguide written without a slit would have an elliptical shaped core of aspect ratio ≈ 4:1 consistent with previous reports [5]. By introducing a slit of width ≈ 500 μm, before the focussing objective, a waveguide can be written using the circular distribution shown in Fig. 1(d).

 

Fig. 2. DIC microscope images of waveguides fabricated in phosphate (a) without a slit and (b) with a 500 μm slit.

Download Full Size | PPT Slide | PDF

Figure 2(a) shows a waveguide and its cross-section produced in phosphate glass when translating at a speed of 40 μm/s without a slit. The incident pulse energy before focussing was 0.24 μJ. Because of its elliptical cross-section we were unable to couple light into this waveguide. Inserting a slit with width of 500 μm produced the optical waveguide shown in Fig. 2(b). This waveguide was fabricated in phosphate glass using a translation speed of 40 μm/s, and a pulse energy of 1.5 μJ to match the peak power density in the glass as used without the slit. The core of the waveguide is clearly shown in the inset to have a circular diameter less than 15 μm. This waveguide was fabricated when the slit was positioned within the Rayleigh range associated with its dimension to the focussing objective. If the slit was positioned beyond this range then we found that secondary regions of refractive index were induced next to the waveguide core due to the appearance of a second line focus. This secondary region led to additional transmission losses as observed using scanning near-field optical microscopy (SNOM) techniques [9]. Hence the original assumption regarding the position of the slit with respect to its Rayleigh range is crucial in order to minimise transmission losses.

When probing the waveguide in Fig. 2(b), a far field interference pattern in the form of concentric rings together with a bright central spot was observed (Fig. 3(a)). The mode field profile for 635 nm light was consistent with single mode propagation implying the same would be true for 1550 nm. Numerical simulations using BeamPROP showed a best fit to the near field profile Fig. 3(b) when using a step-index change of ∆n = 3.5 × 10-3. The overall loss of the waveguide was measured to be 0.95 dB/cm. Taking into account general Fresnel losses of 0.36 dB, and a theoretical coupling loss estimate of 0.2 dB [10], the propagation loss of our waveguide measured ≈ 0.39 dB/cm at 1550 nm. Although the mode field diameters may differ this value compares extremely well with previous reports of transmission losses in waveguides written using femtosecond lasers [11]. To the best of our knowledge this value is also the lowest reported in phosphate glass thus far.

 

Fig. 3. (a) Far field distribution of the waveguide at 635 nm and (b) near field image of the waveguide mode at 635 nm.

Download Full Size | PPT Slide | PDF

The key advantage of this technique is that it can produce highly symmetric waveguides using a long working distance objective in a very simple optical setup. The 20 × objective used in this study had a working distance of 3.1 mm in air whereas high NA 100× oil-immersion objectives have typical working distances of 100-200 μm at best. We illustrated this feature by fabricating 8 different waveguides, with similar morphology and transmission loss, at 50 μm increments ranging in depth from 50-400 μm. This method has important implications for the fabrication of deep 3-dimensional integrated photonic devices.

5. Conclusion

The theoretical concepts involved in inserting a slit before a focussing objective to control the aspect ratio of the focussed beam was outlined. The position of the slit with respect to the focussing objective was also reported to be crucial in order to remove lossy secondary refractive index changes. Using this knowledge, we demonstrated the fabrication of a circular cross-sectioned waveguide in phosphate glass by ultra-fast pulses from a femtosecond laser. A refractive index contrast of 3.5 × 10-3 was estimated. It was shown that the waveguide was single mode at 635 nm and had a very small transmission loss of 0.39 dB/cm at 1550 nm. Furthermore the use of long working distance objectives and femtosecond lasers for modifying bulk materials may open new possibilities into the world of passive and active integrated optics and three-dimensional optical circuits.

Acknowledgments

This work was produced with the assistance of the Australian Research Council under the ARC Centres of Excellence program.

References and links

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. A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

3. K. Miura, H. Inouye, J. Qiu, T. Mitsuyu, and K. Hirao, “Optical waveguides induced in inorganic glasses by a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [PubMed]  

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

5. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003). [CrossRef]  

6. R. Osellame, S. Taccheo, and M. Marangoniet al., “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20, 1559–1567 (2003). [CrossRef]  

7. Y. Cheng, K. Sugioka, and K. Midorikawaet al., “Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser,” Opt. Lett. 28, 55–57 (2003). [CrossRef]   [PubMed]  

8. S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).

9. D. Little, G. D. Marshall, M. Ams, and M. J. Withford, “Near-field scanning optical microscopy of femtosecond laser written waveguides,” in Advanced Solid State Photonics (ASSP), WB13 (2005).

10. R. Osellame, N. Chiodo, and G. Della Valleet al., “Optical waveguide writing with a diode-pumped femtosecond oscillator,” Opt. Lett. 29, 1900–1902 (2004). [CrossRef]   [PubMed]  

11. S. Taccheo, G. Della Valle, and R. Osellameet al., “Er:Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. 29, 2626–2628 (2004). [CrossRef]   [PubMed]  

References

  • View by:
  • |
  • |
  • |

  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. A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).
  3. K. Miura, H. Inouye, J. Qiu, T. Mitsuyu, and K. Hirao, “Optical waveguides induced in inorganic glasses by a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
    [PubMed]
  4. K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Crys. Sol. 239, 91–95 (1998).
    [Crossref]
  5. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003).
    [Crossref]
  6. R. Osellame, S. Taccheo, and M. Marangoniet al., “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20, 1559–1567 (2003).
    [Crossref]
  7. Y. Cheng, K. Sugioka, and K. Midorikawaet al., “Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser,” Opt. Lett. 28, 55–57 (2003).
    [Crossref] [PubMed]
  8. S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).
  9. D. Little, G. D. Marshall, M. Ams, and M. J. Withford, “Near-field scanning optical microscopy of femtosecond laser written waveguides,” in Advanced Solid State Photonics (ASSP), WB13 (2005).
  10. R. Osellame, N. Chiodo, and G. Della Valleet al., “Optical waveguide writing with a diode-pumped femtosecond oscillator,” Opt. Lett. 29, 1900–1902 (2004).
    [Crossref] [PubMed]
  11. S. Taccheo, G. Della Valle, and R. Osellameet al., “Er:Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. 29, 2626–2628 (2004).
    [Crossref] [PubMed]

2004 (2)

2003 (4)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003).
[Crossref]

R. Osellame, S. Taccheo, and M. Marangoniet al., “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20, 1559–1567 (2003).
[Crossref]

Y. Cheng, K. Sugioka, and K. Midorikawaet al., “Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser,” Opt. Lett. 28, 55–57 (2003).
[Crossref] [PubMed]

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

1998 (1)

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

1996 (2)

Ams, M.

D. Little, G. D. Marshall, M. Ams, and M. J. Withford, “Near-field scanning optical microscopy of femtosecond laser written waveguides,” in Advanced Solid State Photonics (ASSP), WB13 (2005).

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003).
[Crossref]

Cheng, Y.

Y. Cheng, K. Sugioka, and K. Midorikawaet al., “Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser,” Opt. Lett. 28, 55–57 (2003).
[Crossref] [PubMed]

S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).

Chin, S. L.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

Chiodo, N.

Davis, K. M.

Della Valle, G.

Herman, P.

S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).

Hirao, K.

Ho, S.

S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).

Inouye, H.

Little, D.

D. Little, G. D. Marshall, M. Ams, and M. J. Withford, “Near-field scanning optical microscopy of femtosecond laser written waveguides,” in Advanced Solid State Photonics (ASSP), WB13 (2005).

Marangoni, M.

Marshall, G. D.

D. Little, G. D. Marshall, M. Ams, and M. J. Withford, “Near-field scanning optical microscopy of femtosecond laser written waveguides,” in Advanced Solid State Photonics (ASSP), WB13 (2005).

Midorikawa, K.

Y. Cheng, K. Sugioka, and K. Midorikawaet al., “Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser,” Opt. Lett. 28, 55–57 (2003).
[Crossref] [PubMed]

S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).

Mitsuyu, T.

Miura, K.

Nadeau, M. C.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

Nguyen, N. T.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

Nolte, S.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003).
[Crossref]

Osellame, R.

Petit, S.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

Qiu, J.

Saliminia, A.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

Sugimoto, N.

Sugioka, K.

Y. Cheng, K. Sugioka, and K. Midorikawaet al., “Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser,” Opt. Lett. 28, 55–57 (2003).
[Crossref] [PubMed]

S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).

Taccheo, S.

Tünnermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003).
[Crossref]

Vallee, R.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003).
[Crossref]

Withford, M. J.

D. Little, G. D. Marshall, M. Ams, and M. J. Withford, “Near-field scanning optical microscopy of femtosecond laser written waveguides,” in Advanced Solid State Photonics (ASSP), WB13 (2005).

Appl. Phys. (1)

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” Appl. Phys. 93, 3724–3728 (2003).

Appl. Phys. A (1)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003).
[Crossref]

J. Non-Crys. Sol. (1)

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

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

Opt. Lett. (5)

Other (2)

S. Ho, P. Herman, Y. Cheng, K. Sugioka, and K. Midorikawa, “Direct ultrafast laser writing of buried waveguides in Foturan glass,” in OSA Conference on Lasers and Electro-Optics (CLEO), CThD6 (2004).

D. Little, G. D. Marshall, M. Ams, and M. J. Withford, “Near-field scanning optical microscopy of femtosecond laser written waveguides,” in Advanced Solid State Photonics (ASSP), WB13 (2005).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1. (a) beam evolution near focus not using slit, (b) energy distribution in YZ plane not using slit, (c) beam evolution near focus using slit, (d) energy distribution in YZ plane using slit where x corresponds with the direction of the beam translation and the waveguide axis.
Fig. 2.
Fig. 2. DIC microscope images of waveguides fabricated in phosphate (a) without a slit and (b) with a 500 μm slit.
Fig. 3.
Fig. 3. (a) Far field distribution of the waveguide at 635 nm and (b) near field image of the waveguide mode at 635 nm.

Equations (10)

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

ω x = π W x and ω y = π W y .
Z Rx Z Ry = W y 2 W x 2 .
2 ω x = ω x [ 1 + ( λ X I o 2 π ω x 2 ) 2 ] 1 2
X I o 2 = 3 π λ ω x 2 .
I o 2 = I o exp ( Y I o 2 2 ω y 2 )
Y I o 2 = In 2 ω y .
X I o 2 = Y I o 2
W y W x = NA In 2 3 for W x > 3 W y ,
NA W x f .
W y W x = NA n In 2 3 for W x > 3 W y ,

Metrics