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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 6 — Mar. 20, 2006
  • pp: 2256–2262
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Observation of continuous-wave second-harmonic generation in semiconductor waveguide directional couplers

Po Dong, Jeremy Upham, Aju Jugessur, and Andrew G. Kirk  »View Author Affiliations


Optics Express, Vol. 14, Issue 6, pp. 2256-2262 (2006)
http://dx.doi.org/10.1364/OE.14.002256


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Abstract

We report the observation of continuous-wave second-harmonic generation in waveguide directional couplers. We employ a GaAs/AlGaAs system and observe four resonance peaks in a ~15nm spectral range, with a maximal conversion efficiency of 1.6%W-1cm-2. This observation is theoretically explained by the coupled-mode theory. This new configuration has the potential to open a new range of applications for nonlinear frequency conversion.

© 2006 Optical Society of America

1. Introduction

Waveguide directional couplers consist of two closely spaced waveguides. Light intensity modulates periodically between the two waveguides as a function of distance [15

15. A. Yariv, Optical Electronics in Modern Communications (Oxford University Press,1997).

]. The oscillation behavior of directional couplers can be explained by the propagation of multiple supermodes in compound structures. Second harmonic generation in such structures was first demonstrated and explained in the context of phase matching between supermodes [16–17

16. A. A. Maier, “Coupled modes phase matching and synchronous non-linear wave interaction in coupled waveguides,” Kvantovaya Elektronika 7, 1596–1598 (1980).

]. In Refs. [10

10. P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. 93, 133901 (2004). [CrossRef] [PubMed]

] and [18

18. X. G. Huang and M. R. Wang, “A novel quasi-phase-matching frequency doubling technique,” Opt. Commun. 150, 235–238 (1998). [CrossRef]

], the phenomenon was investigated in the frame of coupled-mode theory and the results were interpreted by quasi-phase matching [18

18. X. G. Huang and M. R. Wang, “A novel quasi-phase-matching frequency doubling technique,” Opt. Commun. 150, 235–238 (1998). [CrossRef]

] and resonance between the coupling coefficients of directional couplers and the phase mismatch [10

10. P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. 93, 133901 (2004). [CrossRef] [PubMed]

]. These explanations are certainly equivalent. However, the advantage of using the coupled-mode theory is that it considers all possible conversion processes in a single set of equations. This makes it more accurate when the resonance wavelengths for different conversion processes are close, under which condition different conversion processes may influence each other. In this configuration, the resonance can be understood by the following descriptions. Because the power in each of the two waveguides can oscillate with the propagation length, the directional coupler acts as a harmonic oscillator for the optical wave. The nonlinear polarization P at the frequency of the generated wave has the form P ∝ exp(iΔkz) , where Δk is the phase mismatch and z is the propagation length. The nonlinear polarization is analogous to an external harmonic force applied on the harmonic oscillator. As is well known, a harmonic oscillator driven by an external harmonic force at resonance obtains the largest magnitude of oscillation. A similar resonance phenomenon appears here, and it was shown that the resonance condition is equivalent to the phase-matching condition [10

10. P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. 93, 133901 (2004). [CrossRef] [PubMed]

]. It is to be noted that second harmonic generation (SHG) in directional couplers has also been investigated for the purposes of optical switching [19

19. G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. V. Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett., 62, 1323–1325 (1993). [CrossRef]

] and soliton generation [20

20. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons”, Phys. Rev. Lett. 93, 113902 (2004). [CrossRef] [PubMed]

].

2. Design of experiment

We implemented a directional coupler as an epitaxially grown dual-core channel waveguide on <1, 0, 0> GaAs substrates. The designed epitaxial structure is 1500nm Al0.9Ga0.1As / 140nm Al0.3Ga0.7As / 300nm Al0.5Ga0.5As / 140nm Al0.3Ga0.7As / 500nm Al0.9Ga0.1As / 140nm Al0.3Ga0.7As / 300nm Al0.5Ga0.5As / 140nm Al0.3Ga0.7As / 1500nm Al0.9Ga0.1As. The Al0.9Ga0.1As layers serve as cladding and as the separating layer between the two waveguides. The Al0.3Ga0.7As/Al0.5Ga0.5As/Al0.3Ga0.7As combination acts as the guiding layer and this is a type of “M” waveguide designed for optimizing the field overlap between TE2 mode at the second-harmonic frequency and TE0 and TM0 modes at the fundamental frequencies [21

21. Chowdhury and L. McCaughan, “Continuously phase-matched M-waveguides for second-order nonlinear upconversion,” IEEE Photon. Technol. Lett. 12, 486–488 (2000). [CrossRef]

]. A typical refractive index distribution and intensities for these modes are plotted in Fig. 1.

Fig. 1. (a) Refractive index distribution at 1.55μm (solid line) and 0.775μm (dotted line). (b) Intensity distribution |E|2 of modes TE0 (solid line) and TM0 (dashed line) at 1.55μm, and TE2 at 0.775μm (dotted line).

Using Aωj(z) and Bωj(z) to represent the slowly varying amplitudes in waveguides 1 and 2, respectively, the coupled wave equations are

dA2ωTE2dz=2ωTE2B2ωTE2AωTE0AωTM0exp(iΔkz)
dB2ωTE2dz=2ωTE2A2ωTE2BωTE0BωTM0exp(iΔkz)
(1)

Here, κTE2 is the mode-coupling coefficient of the directional coupler for the second harmonic [15

15. A. Yariv, Optical Electronics in Modern Communications (Oxford University Press,1997).

], η includes the product of the nonlinear optical coefficient and the overlap integral of the fundamental and the second harmonic waves, and Δk = kTE2 - kTE0 ω - kTM0 is the phase mismatch (k is the wave number). The mode-coupling coefficients indicate how rapidly the power in the first waveguide is transferred to the second waveguide. The first terms in the right-hand sides of the above equations describe the coupling effect of the directional coupler and the second terms in the right-hand sides result from the nonlinear effects. Under the non-depletion assumption which implies that the presence of the second harmonic does not influence the motion of the fundamental wave, the amplitudes for the fundamental wave oscillate between the two waveguides:

AωTE0=c1exp(ωTE0z)+c2exp(ωTE0z)
BωTE0=c1exp(ωTE0z)+c2exp(ωTE0z)
AωTM0=c1exp(ωTM0z)+c2exp(ωTM0z)
BωTM0=c1exp(ωTM0z)+c2exp(ωTM0z)
(2)

Substituting Eq. (2) into Eq. (1) results in four resonance conditions at which efficient SHG should be observed

±(κωTE0+κωTM0)+Δk=κ2ωTE2
±(κωTE0κωTM0)+Δk=κ2ωTE2
(3)

Fig. 2. Typical SHG power as a function of the fundamental wavelength. Three curves were obtained by varying the position of input beam. It is evident that four resonance peaks are found, and the relative peak ratio at resonance can be alternated by the change of input location.

3. Experimental results and discussions

In the experimental implementation, ridge structures, oriented along the <0, 1, 1> direction and of width 5 μm, were dry etched in order to provide two-dimensional confinement. The tested directional coupler has a length of 4 mm. Since the optical power oscillates in between two guiding layers, it is difficult to precisely measure the waveguide loss. However, with a Fabry-Perot technique [22

22. T. Reed and A. P. Knights, Silicon photonics (John Wiley & Sons Inc.,2004). [CrossRef]

], we approximately obtained the loss figure as ~1.24cm-1 for TE input and ~2.71 cm-1 for TM input, both at a 1550nm wavelength. We were unable to measure the waveguide loss of the TE2 mode at the second-harmonic frequency.

Fig. 3. Log-log plot of the second-harmonic output power as a function of the input fundamental power. The best fit gives a slope ~2.0 which verifies the quadratic dependence of the SHG on the pumping power.

4. Conclusion

The GaAs/AlGaAs directional coupler that we have demonstrated here has application not only for the SHG process, but also for difference-frequency generation. By incorporating directional couplers in/out of the cavity of quantum-well lasers, tunable compact sources which emit light at around 750nm can be produced. Based on the unique properties of multi-resonance within a small spectral range, multiple wavelength outputs can be generated by a single pulsed pump. Such light sources may be very useful in many areas where two or more lasers are needed, such as optical metrology, optical switching, and four-wave mixing. Furthermore, the directional coupler is intrinsically a two-port device which may be suited to construct two-photon optical parametric down-conversion. Such devices can generate entangled pairs of photons which can find applications in quantum optics experiments, from quantum cryptography and teleportation to the Bell experiment [23–24

23. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on 2-photon interferometry,” Phys. Rev. Lett. 69, 1293–1296 (1992). [CrossRef] [PubMed]

]. The proposed configuration has potential for application in any suitable material system and is not restricted to GaAs/AlGaAs. Directional couplers have very modest fabrication requirements when compared to quasi-phase matching techniques and potentially open the way to a much broader application of nonlinear optical processes across a much wider range of wavelengths.

In summary, we have experimentally demonstrated continuous-wave SHG in Ga/AlGaAs directional couplers. To our knowledge, this is the first experimental proof of frequency conversion in semiconductor directional couplers. We show that four resonance peaks appear in a 15nm spectral range and η=~1.6%W-1cm-2 is obtained experimentally. To our knowledge, this phenomenon has not been shown in bulk materials or single waveguides.

This work was supported by the Natural Science and Engineering Research Council of Canada. We would like to thank N. Bélanger and Dr. J. Laniel for helpful discussions and comments on experiments, V. Logiudice, N. Lemaire, D. W. Berry, R. Gagnon at McGill University, and H. Lee at Toronto University for assistance with waveguide fabrication.

References and Links

1.

R. W. Boyd, Nonlinear Optics (Academic Press Inc.,2003).

2.

M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47, 25–31 (1994). [CrossRef]

3.

J. P. Van der Ziel, “Phase-matched harmonic generation in a laminar structure with wave propagation in the plane of the layers,” Appl. Phys. Lett. 26, 60–61 (1975). [CrossRef]

4.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–465 (1998). [CrossRef]

5.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]

6.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998). [CrossRef]

7.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation-tuning and tolerance,” IEEE J. Quantum Electron. 28, 2631–2654 (1992). [CrossRef]

8.

G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, and A. H. J. Venhuizen, “Efficient modal dispersion phase-matched frequency-doubling in poled polymer waveguides,” Appl. Phys. Lett. 62, 2483–2485 (1993). [CrossRef]

9.

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447–449 (1970). [CrossRef]

10.

P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. 93, 133901 (2004). [CrossRef] [PubMed]

11.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996). [CrossRef]

12.

T. Skauli, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. 27, 628–630 (2002). [CrossRef]

13.

K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, M. Calligaro, V. Ortiz, and V. Berger, “Second-harmonic generation through optimized modal phase matching in semiconductor waveguides,” Appl. Phys. Lett. 83, 620–622 (2003). [CrossRef]

14.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. 84, 2974–2976 (2004). [CrossRef]

15.

A. Yariv, Optical Electronics in Modern Communications (Oxford University Press,1997).

16.

A. A. Maier, “Coupled modes phase matching and synchronous non-linear wave interaction in coupled waveguides,” Kvantovaya Elektronika 7, 1596–1598 (1980).

17.

S. I. Bozhevol’nyi, K. S. Buritskii, E. M. Zolotov, and V. Chernykh, Sov. Tech. Phys. Lett.7, 278 (1981).

18.

X. G. Huang and M. R. Wang, “A novel quasi-phase-matching frequency doubling technique,” Opt. Commun. 150, 235–238 (1998). [CrossRef]

19.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. V. Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett., 62, 1323–1325 (1993). [CrossRef]

20.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons”, Phys. Rev. Lett. 93, 113902 (2004). [CrossRef] [PubMed]

21.

Chowdhury and L. McCaughan, “Continuously phase-matched M-waveguides for second-order nonlinear upconversion,” IEEE Photon. Technol. Lett. 12, 486–488 (2000). [CrossRef]

22.

T. Reed and A. P. Knights, Silicon photonics (John Wiley & Sons Inc.,2004). [CrossRef]

23.

K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on 2-photon interferometry,” Phys. Rev. Lett. 69, 1293–1296 (1992). [CrossRef] [PubMed]

24.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature, 390, 575–579 (1997). [CrossRef]

OCIS Codes
(130.4310) Integrated optics : Nonlinear
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 17, 2006
Revised Manuscript: March 14, 2006
Manuscript Accepted: March 14, 2006
Published: March 20, 2006

Citation
Po Dong, Jeremy Upham, Aju Jugessur, and Andrew G. Kirk, "Observation of continuous-wave second-harmonic generation in semiconductor waveguide directional couplers," Opt. Express 14, 2256-2262 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2256


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References

  1. R. W. Boyd, Nonlinear Optics (Academic Press Inc., 2003).
  2. M. M. Fejer, "Nonlinear optical frequency conversion," Phys. Today 47, 25-31 (1994). [CrossRef]
  3. J. P. Van der Ziel, "Phase-matched harmonic generation in a laminar structure with wave propagation in the plane of the layers," Appl. Phys. Lett. 26, 60-61 (1975). [CrossRef]
  4. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, "Phase matching using an isotropic nonlinear optical material," Nature 391, 463-465 (1998). [CrossRef]
  5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]
  6. V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998). [CrossRef]
  7. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation-tuning and tolerance," IEEE J. Quantum Electron. 28, 2631-2654 (1992). [CrossRef]
  8. G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, and A. H. J. Venhuizen, "Efficient modal dispersion phase-matched frequency-doubling in poled polymer waveguides," Appl. Phys. Lett. 62, 2483-2485 (1993). [CrossRef]
  9. P. K. Tien, R. Ulrich, and R. J. Martin, "Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide," Appl. Phys. Lett. 17, 447-449 (1970). [CrossRef]
  10. P. Dong, and A. G. Kirk, "Nonlinear frequency conversion in waveguide directional couplers," Phys. Rev. Lett. 93,133901 (2004). [CrossRef] [PubMed]
  11. S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, "Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding," Appl. Phys. Lett. 68, 2609-2611 (1996). [CrossRef]
  12. T. Skauli, "Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation," Opt. Lett. 27, 628-630 (2002). [CrossRef]
  13. K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, M. Calligaro, V. Ortiz, and V. Berger, "Second-harmonic generation through optimized modal phase matching in semiconductor waveguides," Appl. Phys. Lett. 83, 620-622 (2003). [CrossRef]
  14. S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, "Continuous-wave second harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84, 2974-2976 (2004). [CrossRef]
  15. A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1997).
  16. A. A. Maier, "Coupled modes phase matching and synchronous non-linear wave interaction in coupled waveguides," Kvantovaya Elektronika 7, 1596-1598 (1980).
  17. S. I. Bozhevol’nyi, K. S. Buritskii, E. M. Zolotov, and V. Chernykh, Sov. Tech. Phys. Lett. 7, 278 (1981).
  18. X. G. Huang and M. R. Wang, "A novel quasi-phase-matching frequency doubling technique," Opt. Commun. 150, 235-238 (1998). [CrossRef]
  19. G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. V. Stryland, "All-optical switching devices based on large nonlinear phase shifts from second harmonic generation," Appl. Phys. Lett.,  62, 1323-1325 (1993). [CrossRef]
  20. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons", Phys. Rev. Lett. 93, 113902 (2004). [CrossRef] [PubMed]
  21. Chowdhury, and L. McCaughan, "Continuously phase-matched M-waveguides for second-order nonlinear upconversion," IEEE Photon. Technol. Lett. 12, 486-488 (2000). [CrossRef]
  22. T. Reed, and A. P. Knights, Silicon photonics (John Wiley & Sons Inc., 2004). [CrossRef]
  23. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, "Practical quantum cryptography based on 2-photon interferometry," Phys. Rev. Lett. 69, 1293-1296 (1992). [CrossRef] [PubMed]
  24. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature,  390, 575-579 (1997). [CrossRef]

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