OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 6 — Mar. 20, 2006
  • pp: 2335–2343
« Show journal navigation

Characterization of symmetric [3 × 3] directional couplers fabricated by direct writing with a femtosecond laser oscillator

Kenya Suzuki, Vikas Sharma, James G. Fujimoto, Erich P. Ippen, and Yusuke Nasu  »View Author Affiliations


Optics Express, Vol. 14, Issue 6, pp. 2335-2343 (2006)
http://dx.doi.org/10.1364/OE.14.002335


View Full Text Article

Acrobat PDF (300 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate and characterize symmetric [3×3] three-dimensional directional couplers fabricated in glass using a high-pulse energy femtosecond laser oscillator. The characteristics of the [3×3] directional couplers closely agree with the theoretical prediction, except for small errors caused by the fabrication process. We show that deviations from symmetry are dominated by vertical position errors of the coupling waveguide.

© 2006 Optical Society of America

1. Introduction

Optical, symmetric [3×3] directional couplers [1

1. S. K. Sheem, “Optical fiber interferometers with [3×3] directional couplers: Analysis,” J. Appl. Phys. 52, 3865–3872 (1981). [CrossRef]

] are useful for optical interferometer-based sensors because they enable the detection of the direction of an interferometer arm phase change caused by an analyte. A Michelson interferometer-based low-coherence reflectometer and optical coherence tomography have already been demonstrated by using a symmetric [3×3] directional coupler for optical signal processing [2

2. K. Takada, H. Yamada, and M. Horiguchi, “Optical low coherence reflectometer using [3×3] fiber coupler,” IEEE Photonics Technol. Lett. 6, 1014–1016 (1994). [CrossRef]

, 3

3. M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 × 3 fiber-optic couplers,” Opt. Lett. 28, 2162–2164 (2003). [CrossRef] [PubMed]

]. Although these sensors employ fiberoptic [3×3] couplers, an integrated optic form for these devices is preferable because it offers such advantages as flexibility in photonic circuit configuration and mass production. Even in an integrated optic form, it is important to maintain the symmetry of the waveguide arrangement in the coupling region in order to be able to detect the direction of phase change efficiently in Mach-Zehnder interferometer-based sensors. However, conventional waveguide fabrication techniques based on planar technology that utilize photolithography and dry etching techniques are unsuitable for realizing three-dimensional devices such as symmetric [3×3] directional couplers.

Waveguide fabrication techniques that use femtosecond laser pulses to write waveguides in solid glass are a promising approach for the above purpose. Photosensitivity phenomena in transparent glass materials were first observed and demonstrated by Davis in 1996 [4

4. 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]

]. This material-processing technique utilizes nonlinear or multiphoton absorption of a focused, high-intensity laser beam. Many photonic devices have already been demonstrated that take advantage of three-dimensional structural fabrication, including optical splitters [5

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

], interconnections [6

6. Y. Nasu, M. Kohtoku, Y. Hibino, and Y. Inoue, “Three-dimensional waveguide interconnection formed with femtosecond laser in planar lightwave circuits,” in Proceedings of Optical Fiber Communication Conference, 2005. Technical Digest. OFC/NFOEC , 4, (Anaheim, Calif., 2005), pp. 503–505.

], and WDM couplers [7

7. W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt. Lett. 28, 2491–2493 (2003). [CrossRef] [PubMed]

]. We previously reported a [3×3] directional coupler for the wavelength range of 800 nm [8

8. M. Kowalevicz, V. Sharma, E. P. Ippen, and J. G. Fujimoto, “3D photonic devices fabricated in glass using a femtosecond laser oscillator,” Opt. Lett. 21, 1060–1062 (2005). [CrossRef]

]. In this paper, we provide a detailed characterization and description of a symmetrical [3×3] directional coupler for the wavelength range of 1500 nm and investigate both the origin of fabrication errors and how they change device characteristics.

2. [3×3] directional coupler

Figure 1 shows the schematic configuration of a symmetric [3×3] directional coupler and its typical coupling characteristics. The coupler consists of three input waveguides, a transition region, a coupling region, a second transition region, and output waveguides. The mode coupling equations for [3×3] directional couplers are described in reference [1

1. S. K. Sheem, “Optical fiber interferometers with [3×3] directional couplers: Analysis,” J. Appl. Phys. 52, 3865–3872 (1981). [CrossRef]

]. Here we summarize this formalism and expand it by including the mismatches in the propagation constants between the waveguides in the coupling region, so that we can later analyze the coupler characteristics in detail. The general mode coupling equations of a [3×3] coupler are represented as:

dA1dz+jκ12A2ej2δ21z+jκ13A3e+j2δ13z=0
dA2dz+jκ23A3ej2δ23z+jκ21A1e+j2δ21z=0
dA3dz+jκ31A1ej2δ13z+jκ32A2e+j2δ23z=0
(1)

where, Ai, κ ij, and δ ij are the electromagnetic fields of waveguide i, and the coupling coefficients and propagation constant differences between coupling waveguides i and j, respectively. Derivations are described in more detail in the appendix. In an ideal case, where we can ignore asymmetry in the equations, the parameters satisfy the conditions δ ij = 0, κ ij = κ. Figure 1(b) shows the calculated coupling characteristics of an ideal symmetric [3×3] directional coupler, where an optical signal is launched into input port waveguide 1. It should be noted that the optical power of waveguide 1 gradually couples with waveguides 2 and 3 at the same ratio, but it never falls to zero. This is because part of the input optical signal, which couples with waveguide 2, is transferred back to waveguides 3 and 1. The same is true of the part of the input signal that couples with waveguide 3, and is transferred back to waveguides 2 and 1. In other words, if we launch an optical signal from input port 1 and monitor output 1, then the coupler becomes an asymmetric directional coupler. Therefore, output 1 does not fall to zero.

Fig. 1. (a) Schematic configuration of a [3×3] directional coupler, and (b) characteristics of an optical, symmetric [3×3] directional coupler.

3. Experiment

Fig. 2. Coupling characteristics of a fabricat ed [3×3] directional coupler with an optical signal from input port 1. The separations between the coupling waveguides S are designed to be (a) 25 μm, (b) 20 μm, and (c) 15 μm. The solid lines and dotted lines correspond to TM and TE polarization modes, respectively.

Figure 2 shows the coupling characteristics of the various [3×3] directional couplers at a wavelength of 1530 nm. The solid and dotted lines represent the coupling characteristics for TM and TE polarized modes, respectively. Only a small polarization dependence of 11 % in the coupling ratio is observed in the coupler with a separation of 25 μm and a coupling interaction length of 7200 μm. This fact supports the idea that a waveguide fabricated with a high-repetition-rate ultra short pulse laser does not show polarization dependence [11

11. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Optical property of waveguides written by a 26 MHz stretched cavity Ti:sapphire Femtosecond oscillator,” Opt. Express 13, 612–620 (2005). [CrossRef] [PubMed]

]. The measured losses were 6.6 dB and varied only by 0.2 dB as the separation distance was varied from 25 μm to 15 μm. The excess loss includes propagation loss as well as fiber coupling loss. The small loss variation of 0.2 dB with waveguide separation distance means that the losses from the discontinuities between waveguides. This means that the effect of the nonadiabatic connection along transition waveguide is negligible. As shown in Fig. 2, the separation S between the waveguides in the coupling region clearly affects the coupling characteristics. For 25 μm separation, the measured characteristics are shown on the left-hand side of Fig. 1(b), and starts at almost 0 % coupling for a coupling length of 0 μm. On the other hand, with separations of 20 and 15 μm, a nonzero amount of power has already been transferred when the straight waveguide interaction length is 0 μm. This is because the coupling between the waveguides in the transition region becomes dominant. In either case, the measured coupling characteristics oscillate as a function of the straight waveguide interaction length. This indicates that, despite some errors, it is possible to realize coupled mode functions that are sinusoidal.

Fig. 3. Calculated coupling characteristics of [3×3] directional couplers, when (a) the position of waveguide 1 is not aligned correctly, and when (b) the propagation constant of the waveguide is different from the others.

However, it should be noted that the optical power of waveguide 1 falls to zero for interaction lengths of the straight waveguide of 7000, 3000, and 800 μm in couplers with waveguide separations of 25, 20, and 15 μm, respectively. This tendency appears systematically for all waveguide separations. In the numerical calculation, it is shown that the optical power of waveguide 1 never falls to zero if the coupler is symmetric. This fact suggests that systematic fabrication errors result in coupler asymmetry.

4. Discussion

Femtosecond laser waveguide fabrication techniques provide a unique approach for fabricating devices such as symmetric [3×3] couplers, which can only be realized using a three-dimensional device design. Measurements of the couplers, as a function of coupling interaction length, have been performed and compared to theoretical predictions. Since each data point represents a different device fabrication, the relatively low scatter in the data shows that fabrication parameters can be relatively well controlled and the device characteristics reproducibly measured.

Coupling effects between the waveguides in the transition region contribute to the observed characteristics because the waveguides entering the interaction region are at small angles of 0.43 to 0.36 degrees. These effects can be accounted for if the design objective is to fabricate specific device characteristics. Measurements of transfer characteristics versus coupling interaction length show that there are residual, reproducible fabrication errors in the process. The fabrication errors can be included by adjusting parameters κ ij and/or δ ij. It is natural to anticipate that waveguides 2 and 3 were fabricated identically, because of our fabrication process and the similarity of the measured characteristics of outputs 2 and 3. On the other hand, waveguide 1 is in a different layer from waveguides 2 and 3. This could result in a fabrication error in the vertical position and/or a propagation constant that is different from the other waveguides.

We calculated numerically the effect of asymmetry in waveguide 1 by using the general mode coupling equations of Eq. (1) with the Runge-Kutta method. Figure 3 shows the estimated coupling ratios for asymmetric [3×3] directional couplers. The insets represent arrangements of waveguide 1; that is, in Fig. 3(a), only the vertical position of waveguide 1 is varied, and in Fig. 3(b), the propagation constant of waveguide 1 differs from those of the others. In other words, the calculations assume an asymmetry of 2κ 12 = κ 23 = κ31 and 0.5κ 12 = κ23 = κ 31 in Fig. 3(a) and, 2δ 12 = δ 23 = δ 31 and 0.5δ 12 = δ 23 = δ 31 in Fig. 3(b). As shown in Fig. 3(a), if waveguide 1 comes closer to the others, the minimum optical power in the waveguide will go to zero for some value of the phase shift or coupling interaction length. In contrast, the minimum power moves away from zero when waveguide 1 is further from the others. Meanwhile, in Fig. 3(b), if we assume that waveguide 1 has a different propagation constant from the others, the minimum optical power also does not go to zero. This tendency is similar to that found in [2×2] couplers [12

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

, 13

13. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,” Opt. Express 10, 645–652 (2002). [PubMed]

]. The optical power from output 1 only goes to zero when the waveguide 1 is closer to the others.

Additional supporting evidence for a position error in waveguide 1 is the fact that there is a small refractive index mismatch between the glass substrate and the immersion oil. This mismatch causes a difference between the physical translation of the glass substrate and the focal point of the beam. A simple calculation gives us a relation of

dz1dz0=tanθ0tanθ1
(2)
θ0=arcsin(NA/n0)
(3)
θ1=arcsin(NA/n1)
(4)

where dz 1, dz 0, n 0 and n 1 are the physical translation of the substrate, the displacement of the focal point, and the refractive indices of the immersion oil and the substrate, respectively. By substituting the values of the experimental configuration, n 0 = 1.516, n 1 = 1.515 and NA = 1.25, we can obtain a ratio of the displacement between the physical translation and the focal point of 99.8 %. Therefore, the vertical translation is smaller than the horizontal translation. This would support the hypothesis that waveguide 1 is closer to the others.

5. Conclusion

In this paper, we fabricated and characterized symmetric three-dimensional [3×3] couplers. The waveguides were fabricated in three dimensions by using a direct waveguide writing technique with a high-repetition-rate femtosecond laser oscillator. The effects of varying interaction length were examined by fabricating couplers with different interaction lengths and by characterizing these devices. The fabricated couplers have characteristics that agree well with theory for a symmetric [3×3] coupler. Coupling in the region of the taper was shown to play an important role in the output characteristics as a function of interaction length. The largest polarization dependence of the coupling ratio was 11% and the maximum insertion loss was 6.7 dB. Even though errors were observed in the fabricated couplers that might cause degradation the coupler performance, comparison to theory shows that these errors are due to an error in the position of one of the waveguides in the vertical direction. These results demonstrate the femtosecond laser fabrication of a representative three-dimensional device, the symmetric [3×3] coupler, the characterization of waveguide characteristics, and a comparison to theory. Measurements are in good agreement with theory and suggest approaches for improving future performance.

Fig. 4. Cross-sectional diagram of the optical coupling region of a general [3×3] directional coupler.

Appendix

General mode coupling equations (1) are derived from Maxwell’s equations by following a procedure described in [12

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

] and by expanding it to a situation where three waveguides are arranged closely. Figure 4 shows a cross-sectional diagram of the optical coupling region of a general [3×3] directional coupler.

Maxwell’s equations in each waveguide are

×Ep=μ0Hp
×Hp=ε0Np2Ep
(A-1)

where E p, and H p are the electric and magnetic fields of the p th waveguide. N p, ω, ε 0 and μ0 are the refractive index distribution of the p th waveguide, the angular frequency of the optical signal, the dielectric constant, and the magnetic permittivity in vacuum. Here, p represents the waveguide number, or p = 1, 2, 3. The electromagnetic fields E of the coupled waveguides are

E=A1(z)E1+A2(z)E2+A3(z)E3
H=A1(z)H1+A2(z)H2+A3(z)H3
(A-2)

These fields must satisfy Maxwell’s equations. Therefore,

×E=μ0H
×H=ε0N2E
(A-3)

N denotes the refractive index distribution of the entire coupling region. By using the following formula of vector,

×(AE)=AxE+AxE
=AxE+dAdzuzxE
(A-4)

we obtain the following equations:

(uzxE¯1)dA1dz+(uzxE¯2)dA2dz+(uzxE¯3)dA3dz=0
(A-5)
[(uzxH¯1)dA1dzε0(N2N12)A1E¯]
+[(uzxH¯2)dA2dzε0(N2N22)A2E¯]
+[(uzxH¯3)dA3dzε0(N2N32)A3E¯]=0
(A-6)

Now, by calculating

[E¯1*·(A5)H¯1*·(A6)]dxdy=0
[E¯2*·(A5)H¯2*·(A6)]dxdy=0
[E¯3*·(A5)H¯3*·(A6)]dxdy=0
(A-7)

and by separating the transversal and axial dependencies of electromagnetic fields,

E¯p=Epejβpz
H¯p=Hpejβpz
(A-8)

we obtain general mode coupling equations for a [3x3] directional coupler.

dA1dz+c12dA2dzej(β2β1)+c13dA3dzej(β3β1)+jχ1A1+jκ12A2ej(β2β1)+jκ13A3ej(β3β1)
dA2dz+c23dA3dzej(β3β2)+c21dA1dzej(β1β2)+jχ2A2+jκ23A3ej(β3β2)+jκ21A1ej(β1β2)
dA3dz+c31dA1dzej(β1β3)+c32dA2dzej(β2β3)+jχ3A3+jκ31A1ej(β1β3)+jκ32A2ej(β2β3)
(A-9)

Here,

κpq=ωε0(N2Nq2)EP*·Eqdxdyuz·(EP*×Hp+Ep×HP*)dxdy
cpq=uz·(EP*×Hq+Eq×HP*)dxdyuz·(EP*×Hp+Ep×HP*)dxdy
χp=ωε0(N2Np2)EP*·Epdxdyuz·(EP*×Hp+Ep×HP*)dxdy
(A-10)

Here, the second term, the third term, and cpq represent the butt-coupling terms and the butt-coupling coefficient, respectively. The fourth term represents the propagation of the electromagnetic field of the waveguide itself. The last two terms are the mode coupling between waveguides. κ pq is the coupling coefficient between the p th and q th waveguides. As described in ref [11

11. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Optical property of waveguides written by a 26 MHz stretched cavity Ti:sapphire Femtosecond oscillator,” Opt. Express 13, 612–620 (2005). [CrossRef] [PubMed]

], when there is sufficient distance between the waveguides, we can ignore the effect of χ p and c pq. In addition, the relation between reciprocity of the coupling coefficients is

κ12=κ21*
κ23=κ32*
κ31=κ13*
(A-11)

In most of the directional couplers, κ pq is real. Finally, we obtain

dA1dz+jκ12A2ej2δ21z+jκ13A3e+j2δ13z=0
dA2dz+jκ21A1e+j2δ21z+jκ23A3ej2δ23z=0
dA3dz+jκ31A1ej2δ13z+jκ32A2e+j2δ23z=0
(1)
δ21=β2β12κ12=κ21
δ32=β3β22κ23=κ32
δ13=β1β32κ31=κ13
(A-12)

Acknowledgments

This research is supported in part by the Air Force Office of Scientific Research Contract F9550–040–1–0011 and the National Science Foundation ECS–0501478. We gratefully acknowledge the contributions of Drs. Andrew Kowalevicz and Kaoru Minoshima in the early phases of this research.

References and links

1.

S. K. Sheem, “Optical fiber interferometers with [3×3] directional couplers: Analysis,” J. Appl. Phys. 52, 3865–3872 (1981). [CrossRef]

2.

K. Takada, H. Yamada, and M. Horiguchi, “Optical low coherence reflectometer using [3×3] fiber coupler,” IEEE Photonics Technol. Lett. 6, 1014–1016 (1994). [CrossRef]

3.

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 × 3 fiber-optic couplers,” Opt. Lett. 28, 2162–2164 (2003). [CrossRef] [PubMed]

4.

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]

5.

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

6.

Y. Nasu, M. Kohtoku, Y. Hibino, and Y. Inoue, “Three-dimensional waveguide interconnection formed with femtosecond laser in planar lightwave circuits,” in Proceedings of Optical Fiber Communication Conference, 2005. Technical Digest. OFC/NFOEC , 4, (Anaheim, Calif., 2005), pp. 503–505.

7.

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt. Lett. 28, 2491–2493 (2003). [CrossRef] [PubMed]

8.

M. Kowalevicz, V. Sharma, E. P. Ippen, and J. G. Fujimoto, “3D photonic devices fabricated in glass using a femtosecond laser oscillator,” Opt. Lett. 21, 1060–1062 (2005). [CrossRef]

9.

M. Kowalevicz, Jr., A. Tucay Zare, F. X. Kärtner, and J. G. Fujimoto, “Generation of 150-nJ pulses from a multiple-pass cavity Kerr-lens mode-locked Ti:Al2O3 oscillator,” Opt. Lett. 28, 1597–1599 (2003). [CrossRef] [PubMed]

10.

Kenya Suzuki NTT Photonics Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan, Yusuke Nasu, Vikas Sharma, Takahiro Ikeda, James G. Fujimoto, Erich P. Ippen, and Michael S. Feld are preparing a manuscript to be called “Characteristics of waveguide in soda-lime glass caused by irradiation of femtosecond laser pulses.”

11.

R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Optical property of waveguides written by a 26 MHz stretched cavity Ti:sapphire Femtosecond oscillator,” Opt. Express 13, 612–620 (2005). [CrossRef] [PubMed]

12.

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

13.

K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,” Opt. Express 10, 645–652 (2002). [PubMed]

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(190.4180) Nonlinear optics : Multiphoton processes
(230.7370) Optical devices : Waveguides
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Optical Devices

History
Original Manuscript: December 16, 2005
Revised Manuscript: March 3, 2006
Manuscript Accepted: March 5, 2006
Published: March 20, 2006

Citation
Kenya Suzuki, Vikas Sharma, James G. Fujimoto, Erich P. Ippen, and Yusuke Nasu, "Characterization of symmetric [3 x 3] directional couplers fabricated by direct writing with a femtosecond laser oscillator," Opt. Express 14, 2335-2343 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2335


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. K. Sheem, "Optical fiber interferometers with [3x3] directional couplers: Analysis," J. Appl. Phys. 52, 3865-3872 (1981). [CrossRef]
  2. K. Takada, H. Yamada, and M. Horiguchi, "Optical low coherence reflectometer using [3x3] fiber coupler," IEEE Photonics Technol. Lett. 6, 1014-1016 (1994). [CrossRef]
  3. M. A. Choma, C. Yang, and J. A. Izatt, "Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers," Opt. Lett. 28, 2162-2164 (2003). [CrossRef] [PubMed]
  4. 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]
  5. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing; a new avenue to three-dimensional integrated optics," Appl. Phys. A 77, 109-111 (2003). [CrossRef]
  6. Y. Nasu, M. Kohtoku, Y. Hibino, and Y. Inoue, "Three-dimensional waveguide interconnection formed with femtosecond laser in planar lightwave circuits," in Proceedings of Optical Fiber Communication Conference, 2005. Technical Digest. OFC/NFOEC, 4, (Anaheim, Calif., 2005), pp. 503-505.
  7. W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, "Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses," Opt. Lett. 28, 2491-2493 (2003). [CrossRef] [PubMed]
  8. M. Kowalevicz, V. Sharma, E. P. Ippen and J. G. Fujimoto, "3D photonic devices fabricated in glass using a femtosecond laser oscillator," Opt. Lett. 21, 1060-1062 (2005). [CrossRef]
  9. M. Kowalevicz, Jr., A. Tucay Zare, F. X. Kärtner, and J. G. Fujimoto, "Generation of 150-nJ pulses from a multiple-pass cavity Kerr-lens mode-locked Ti:Al2O3 oscillator," Opt. Lett. 28, 1597-1599 (2003). [CrossRef] [PubMed]
  10. Kenya Suzuki NTT Photonics Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan, Yusuke Nasu, Vikas Sharma, Takahiro Ikeda, James G. Fujimoto, Erich P. Ippen, and Michael S. Feld are preparing a manuscript to be called "Characteristics of waveguide in soda-lime glass caused by irradiation of femtosecond laser pulses."
  11. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Optical property of waveguides written by a 26 MHz stretched cavity Ti:sapphire Femtosecond oscillator," Opt. Express 13, 612-620 (2005). [CrossRef] [PubMed]
  12. K. Okamoto, Fundamentals of optical waveguides, (Academic Press, 2000).
  13. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, "Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing," Opt. Express 10, 645-652 (2002). [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited