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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 13 — Jun. 27, 2005
  • pp: 4931–4938
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Detailed characterization of slow and dispersive propagation near a mini-stop-band of an InP photonic crystal waveguide.

Marcelo Davanço, Aimin Xing, James Raring, Evelyn L. Hu, and Daniel J. Blumenthal  »View Author Affiliations


Optics Express, Vol. 13, Issue 13, pp. 4931-4938 (2005)
http://dx.doi.org/10.1364/OPEX.13.004931


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Abstract

An experimental study of light propagation near a small band gap for a lattice-of-holes InP photonic crystal waveguide is reported. Polarization-resolved measurements of power transmission, reflection and group delay clearly reveal the PC waveguide filtering properties. Group delay enhancement was observed close to the band-edges together with very large dispersion. The test devices were fabricated with a novel technique that allows incorporation of deeply-etched photonic crystals within an InP photonic integrated circuit.

© 2005 Optical Society of America

1. Intoduction

Photonic Crystal (PC) waveguides of the lattice-of-holes type have been shown to offer very interesting light propagation characteristics, given the availability of very slow and dispersive modes in the vicinity of band-gaps [1

1. T. J. Karle, Y. J. Chai, C. N. Morgan, I. H. White, and T. F. Krauss, “Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides,” J. Lightwave Technol. 22514–519 (2004). [CrossRef]

, 2

2. A. Xing, M. Davanço, S. Camatel, D. J. Blumenthal, and E. L. Hu, “Pulse compression in Line Defect Photonic Waveguide,” in Proceedings of the Optical Fiber Communications Conference2005, Paper OWD5.

, 3

3. M. Notomi, K. Yamada, A. Shynia, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett 87253902-1–4 (2001). [CrossRef]

]. Calculated Bloch-mode group velocities do tend to zero very quickly as band gap frequencies are approached. However, inasmuch as finite PC waveguides can be modeled as 1D-periodic systems in the vicinity of certain band-gaps [4

4. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 111490 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490. [CrossRef] [PubMed]

, 5

5. S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, ‘Transmission properties of two-dimensional photonic crystal channel waveguides,” Opt. Quantum Electron. 34171–181 (2002). [CrossRef]

], their transmission characteristics are expected to present only finite group delay peaks near such gaps, accompanying resonances in transmitted and reflected power [6

6. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107 (1996). [CrossRef]

]. In what follows, we present experimental data clearly showing these propagation characteristics near a mini-stop-band of a W3(M) line-defect waveguide [5

5. S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, ‘Transmission properties of two-dimensional photonic crystal channel waveguides,” Opt. Quantum Electron. 34171–181 (2002). [CrossRef]

], such as shown in Fig. 1(a). In order for the characterization to be performed, a novel fabrication platform for photonic integrated circuits incorporating photonic crystals was developed.

2. Description of the tested devices

A series of 20µm×80µm mesas were fabricated, on top of which PC patterns were to be etched. The mesas were accessed via input and output 3-µm wide, 710-µm long weakly-guiding ridge waveguides, as shown in Fig. 1(b). Tilted waveguide designs were used to suppress reflections into the fundamental waveguide mode at the semiconductor/air interface.

Fig. 1. (a) W3(M) waveguide. The first triangular lattice Brillouin zone is displayed underneath. (b) Top-view schematic of fabricated devices.

All measured PC patterns were 80-µm-long W3(M) line-defect waveguides of varying lattice constant a and air-filling fraction; such waveguides are defined by suppressing three lines of holes along the ΓM direction from a triangular-lattice-of-holes PC. The channel widths were on the order of 400nm. As will be shown later, these waveguides display a small band-gap for guided TM modes near the Brillouin-zone boundary. The mechanism responsible for slow and dispersive propagation near this band-gap is the coupling between forward- and backward-propagating waves caused by the periodicity along the waveguide; the same effect takes place at the band-edges near the Brillouin-zone boundary in the PC line-defect waveguides studied in [2

2. A. Xing, M. Davanço, S. Camatel, D. J. Blumenthal, and E. L. Hu, “Pulse compression in Line Defect Photonic Waveguide,” in Proceedings of the Optical Fiber Communications Conference2005, Paper OWD5.

, 3

3. M. Notomi, K. Yamada, A. Shynia, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett 87253902-1–4 (2001). [CrossRef]

, 4

4. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 111490 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490. [CrossRef] [PubMed]

, 5

5. S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, ‘Transmission properties of two-dimensional photonic crystal channel waveguides,” Opt. Quantum Electron. 34171–181 (2002). [CrossRef]

]. On the other hand, the advantages of studying this effect in the present W3(M) waveguides are the following: firstly, the guided TM modes exist in a range of frequencies where only unconfined, very lossy TE modes exist; thus collected light at the output of the device is mostly TM-polarized and the task of discerning TE and TM curves is thereby much facilitated. Secondly, guided-mode propagation losses are expected to be reasonably low in a three-line-defect waveguide, given the lesser interaction with the holes. Indeed, the observed insertion loss (~30dB in the transmission pass-bands) was low enough for the test instruments to yield reliable and repeatable measurements.

The devices were processed on an MOCVD-grown wafer encompassing an n-doped InP substrate, a 1.37Q, 300-nm-thick intrinsic InGaAsP guiding layer, a 1-µm, p-doped InP cladding layer, a 100-nm layer of highly p-doped InGaAs for the formation of ohmic contacts and finally a 50-nm InP cap layer. The approximate refractive index of the guiding layer is 3.45 at λ=1.5µm. Figure 2(a) shows a schematic of an access ridge waveguide, detailing the epitaxial layer-structure. Notice that a p-i-n junction is formed between the top of the ridge and the n-doped substrate.

The upper cladding layer thickness reflects a compromise between achievable etched hole depth and losses at the highly-conductive p-doped InGaAs layer: our dry-etching technique yielded at most 2-µm deep holes, which demanded a thinner upper cladding; as detailed in [7

7. H. Benisty, Ph. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, ‘Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” Opt. Quantum Elec. 34205–215 (2002). [CrossRef]

], PC holes should extend far enough into the substrate in order to keep propagation losses due to out-of-crystal-plane radiation as low as possible. Shallow holes will cause the field to leak considerably into the substrate. On the other hand, it was desired to minimize the interaction of the waveguide mode’s evanescent tail with the top InGaAs layer and p-doped InP, thereby requiring a thicker cladding.

Fig. 2. (a) Schematic cross-section of a ridge waveguide, showing the different waveguide layers. Mesas have the exact same structure. (b) SEM micrograph of a mesa cross section, showing etched photonic crystal holes.

Electrical contacts were defined on the ridge waveguides such that guided light could be detected by measuring current from reverse-biased p-i-n junctions. This facilitated immensely the coupling of ridge waveguides with lens-fibers during the testing process; optimal alignment is in fact achieved in little more than a minute, requiring no equipment other than a voltage-source with a built-in amp meter. An additional reason for the inclusion of the metal contacts was to demonstrate the ability of fabricating devices with electrically-pumped active or passive waveguides, such as described in [8

8. M. L. Mašanović, V. Lal, J. A. Summers, J. S. Barton, E. J. Skogen, L. G. Rau, L. A. Coldren, and D. J. Blumenthal, “Widely-Tunable Monolithically-Integrated All-Optical Wavelength Converters in InP,” J. Lightwave Technol. 231350–62 (2005). [CrossRef]

], that incorporate photonic crystals. The present fabrication platform is in fact an extension of the platform used in the latter cited reference.

3. Test-device fabrication

Following these steps, metallic contacts were defined with contact photolithography followed by Ti/Pt/Au e-beam evaporation. The sample was subsequently thinned-down and metallization of the back-side was performed before cleaving.

4. Device measurement and characterization

The Polarization-Dependent Loss (PDL) of an optical system is defined as 10·log(Imax/Imin), where Imax and Imin are the maximum and minimum output intensities with respect to the input State of Polarization (SOP). The Principal States of Polarization (PSP) are the SOP that produce Imax and Imin and can be obtained from the system’s Müller matrix at each wavelength. When measuring a semiconductor device that carries both TE and TM modes, it is reasonable to assume that the two PSP excite either one of these two polarizations at wavelengths where very high PDL is observed [13

13. K. Yamaguchi, M. Kelly, G. Stolze, and D. Kobasevic, “Polarization-Resolved Measurements using Mueller Matrix Analysis,” Agilent application note 5989-1261EN.

]. As such, in order to obtain the TE and TM transmission and reflection curves presented below, PSP were obtained at wavelengths with large PDL in each case and applied to the corresponding Müller Matrices at all other wavelengths.

Coupling to the fabricated devices was done by aligning lens-fibers to the input and output waveguides; electrical contacts were biased at -2V with a Keithley 2400LV sourcemeter, and the photocurrents produced by a 0.8-mW optical signal at 1520nm were on the order of 15µA. The optical signal absorption for such bias level was below 0.5dB, measured with an optical power-meter. In each measurement, after the alignment was optimized, the bias voltage was set to zero so light would suffer no extra absorption in the waveguide.

The correct correspondence between measured curves and polarization states was primarily verified by infrared imaging of the output waveguide signals through a free-space polarizer. Additionally, we compared experimental results with effective 2D PC band structures, calculated with the 2D Plane-Wave Expansion (PWE) method [14

14. The MIT Photonic-Bands package, http://www.ab-inito.mit.edu/mpb/

]. The effectiveness of this technique has been experimentally demonstrated in various articles, including [4

4. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 111490 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490. [CrossRef] [PubMed]

, 5

5. S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, ‘Transmission properties of two-dimensional photonic crystal channel waveguides,” Opt. Quantum Electron. 34171–181 (2002). [CrossRef]

, 7

7. H. Benisty, Ph. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, ‘Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” Opt. Quantum Elec. 34205–215 (2002). [CrossRef]

]; additionally, it has been detailed in [15

15. M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” App. Phys. Lett. 811163 (2002). [CrossRef]

] that band-structures of 3D lattice-of holes PC with weak vertical confinement and deep holes can be very well approximated by band structures of effective 2D PC. Figure 3(a) shows band diagrams for TM modes of a waveguide with r/a=0.265 (r being the hole radius) and background index nTM=3.26 (equal to the effective index of the epi-wafer’s first TM slab mode at λ=l.55µm). The color scale corresponds to the electric field energy within the line-defect region, normalized to the total power in the unit cell. Well-confined modes (darker dots) with even symmetry yield higher transmitted output power; two bands of such modes are clearly distinguishable, presenting a small band gap at the Brillouin-zone boundary, around a/λ≈0.275. This band-gap clearly corresponds to the stop-band found in the transmission curves shown in Fig. 3(b). Modes on the high-frequency band are well confined, while those on the low-frequency side are more spread out in the crystal region. It is expected that the latter will suffer higher losses, as a result of a larger interaction with holes. Notice that confined modes are of the index-guided type [6

6. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107 (1996). [CrossRef]

], since a bulk-crystal band gap does not exist for TM modes in the present case.

Fig. 3. (a) Band structure for TM modes of a W3(M) waveguide with r/a=0.265 and n=3.26. The yellow shaded area indicates the mini-band-gap position. (b) Corresponding TM transmission curves for devices with a=400nm, a=420nm, and a=440nm. (c) Band structure for TE modes. The bulk-crystal air-band edge is depicted as a continuous line. (d) Corresponding TE transmission curves for the same devices. In both (a) and (c), the color scale relates to the electric field energy confined in the defect region.

Figure 3(c) shows the TE-mode band structure for the same waveguide with background refractive index nTE=3.28 and Fig. 3(d) shows the corresponding transmission curve. A high-confinement band below a/λ≈0.255 in Fig. 3(c) corresponds to the transmission band on Fig. 3(d). The inexistence of highly-confined modes in the region above a/λ≈0.255 explains the low transmitted power in this range in Fig. 3(d). A very small band of highly-confined modes exists near a/λ≈0.275. Transmitted power carried by these is expected to be very low, given their closeness to the Brillouin zone boundary and the narrow width of the band.

It must be pointed out that the substrate light-line in all cases meets the Brillouin-zone boundary at a/λ≈0.09 thus all displayed modes are expected to leak into the substrate.

4.1 TM transmitted and reflected power

The TM transmission PDL is more than 20dB at all wavelengths except within the stop-bands for all measured devices; PSP at λ=1520nm and 1580nm were used to generate transmission curves respectively for a=420nm and a=440nm. For reflection, PSP at λ=1532nm and λ=1610nm were chosen, with PDL≈10dB. The raw reflected signal curve presented a series of 0.4-nm-period oscillations caused by a beating of reflected light from the wafer facet and the PC waveguide input. To suppress this effect, the raw signal was filtered with a 51-sample (500pm) Locally Weighted Scatter Plot Smooth (LOWESS) filter.

Black lines in Fig. 4 show the obtained TM transmittance and reflectance close to the mini-stop-band of representative devices with a=420nm and a=440nm, normalized to their respective maxima. An approximately 10-nm stop-band is observed centered at λ≈1533nm for the first device and at λ≈1607nm for the latter, both corresponding to a/λ ≈0.274. The less pronounced resonances on the right side of the stop-bands can be explained by the predicted higher losses. The wide stop-band in transmission corresponds to a high-reflection band. Also, maxima in the transmission curves coincide with minima in reflection. These resonances are due to the finite extent of the PC waveguide [6

6. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107 (1996). [CrossRef]

].

Fig. 4. Transmission (T), reflection (R) and excess group delay (τg) for waveguides with two different lattice constants. Black curves are experimental, blue and red are fitted. (a) a=400nm. (b) a=420nm.

4.2 Group delay

4.3 Fitting with coupled-mode theory

As in [4

4. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 111490 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490. [CrossRef] [PubMed]

], propagation close to the mini-stop-band can be reasonably well-described with 1D Coupled-Mode Theory (CMT). Details of the theory can be found in a large number of textbooks, a good example of which is reference [18

18. L. A Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley Intersciences), Chap. 6.

]. In its basic form, it describes the evolution of an optical wave as it travels along a medium with periodic refractive index perturbation. The periodicity of the perturbation causes coupling between a forward-propagating wave and a backward-propagating counterpart, at frequencies close to where the Bragg condition is satisfied. A transmission stop-band is observed centered at the Bragg frequency, due to a strong energy transfer from the impinging wave into its backward-traveling counterpart. The propagation characteristics of both waves are clearly dependent on the coupling strength between the two and detuning from the Bragg frequency. The theory predicts the following equations for transmission and reflection coefficients of a finite 1D periodic medium:

t=2σ(z+σ)e+σL(zσ)eσL
(1)
r=2iκsinh(σL)(z+σ)e+σL(zσ)eσL
(2)

In these equations, κ is the coupling coefficient, z=α+i·(β-β 0), σ 2=κ 2+z 2, α and β the loss and propagation constants for both forward- and backward-propagating modes and L is the total length. Also β=2πn/λ, and n is the effective phase index, which describes the spatial phase evolution of the field in an unperturbed medium. Notice that material absorption and out-of plane radiation, either intrinsic or caused by hole imperfections can be phenomenologically modeled by the loss parameter.

In the spirit of [4

4. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 111490 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490. [CrossRef] [PubMed]

], CMT curves were fitted to the experimental data to yield estimates of coupling strength and propagation losses in the waveguides. In the present case, coupling happens between modes of the same order. Bloch modes on the two sides of the stop-band are considerably different, though, and thus require different fitting parameters.

Despite the mild group delay enhancement, calculated GVD from CMT reaches D≈-8.5×106ps/km·nm on the high-frequency band-edge for the device in Fig. 4(b), almost five orders of magnitude that of dispersion-compensating fiber [2

2. A. Xing, M. Davanço, S. Camatel, D. J. Blumenthal, and E. L. Hu, “Pulse compression in Line Defect Photonic Waveguide,” in Proceedings of the Optical Fiber Communications Conference2005, Paper OWD5.

]; this corresponds to a total dispersion of -0.7ps/nm for the 80-µm waveguide. The bandwidth over which the dispersion remains within the same order of magnitude is slightly larger than 1.0nm, pointing towards possible uses of similar PC waveguides in dispersion compensation or pulse-shaping by proper tuning of the coupling coefficient and lattice constant. Considering the same parameters and zero loss, the maximum achievable excess delay and largest total dispersion are respectively 1.06ps, and -1.2ps/nm. On the other hand, it must be noted that the large dispersion figures reported here can in principle be found in any one-dimensional system with very large coupling coefficients. Photonic crystal waveguides naturally offer such characteristic, given the large index discontinuities and very narrow confinement regions.

A very detailed theoretical account on the usage of the described 1D band-edge effects for dispersion compensation, including impairment due to high-order dispersion, is given in references [19

19. P. St. Russel, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” Jour. Modern Optics 381599–1619 (1991). [CrossRef]

, 20

20. N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg Gratings for Dispersion Compensation in Transmission: Theoretical Model and Design Criteria for Nearly Ideal Pulse Recompression,” J. Lightwave Technol. 151303 (1997). [CrossRef]

].

5. Summary and conclusions

A set of InP-based test devices were fabricated to characterize deeply-etched Photonic Crystal structures. The fabrication process is a novel form of integration of deeply-etched PC with standard photonic integrated circuit structures. Etched PC holes were more than 2µm deep, with aspect ratio close to 9. The devices incorporated PC patterns and standard ridge waveguides with electrical contacts. This allowed fast and complete polarization-resolved measurement of transmission, reflection and group delay characteristics of a series of W3(M) PC waveguides.

Waveguide transmission and reflection measurements revealed a small stop-band for TM-polarized modes. Measured excess group delay curves displayed a maximum enhancement of approximately 0.6ps (~60% over that from a ridge waveguide of the same length) at the edge of the stop-band. Group-Velocity Dispersion of almost five orders of magnitude that of dispersion-compensating fiber was observed in the same region. Experimental curves were fitted with coupled-mode theory, yielding estimates for losses and coupling coefficient. Enhancement of group delay and GVD is clearly dependent on propagation losses. Even at zero loss, though, only a mild enhancement of group delay is found. On the other hand, dispersion is found to be extremely large over reasonably wide bandwidths, even when considerable losses are present. This suggests that, by proper tuning of coupling coefficients, very compact dispersion-compensating or pulse-shaping elements could be designed.

Acknowledgments

This work was supported by the Center for Nanosystems Innovation for Defense (CNID) award DMEA90-02-2-0215, jointly funded by DMEA and DARPA

References and links

1.

T. J. Karle, Y. J. Chai, C. N. Morgan, I. H. White, and T. F. Krauss, “Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides,” J. Lightwave Technol. 22514–519 (2004). [CrossRef]

2.

A. Xing, M. Davanço, S. Camatel, D. J. Blumenthal, and E. L. Hu, “Pulse compression in Line Defect Photonic Waveguide,” in Proceedings of the Optical Fiber Communications Conference2005, Paper OWD5.

3.

M. Notomi, K. Yamada, A. Shynia, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett 87253902-1–4 (2001). [CrossRef]

4.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 111490 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490. [CrossRef] [PubMed]

5.

S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, ‘Transmission properties of two-dimensional photonic crystal channel waveguides,” Opt. Quantum Electron. 34171–181 (2002). [CrossRef]

6.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107 (1996). [CrossRef]

7.

H. Benisty, Ph. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, ‘Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” Opt. Quantum Elec. 34205–215 (2002). [CrossRef]

8.

M. L. Mašanović, V. Lal, J. A. Summers, J. S. Barton, E. J. Skogen, L. G. Rau, L. A. Coldren, and D. J. Blumenthal, “Widely-Tunable Monolithically-Integrated All-Optical Wavelength Converters in InP,” J. Lightwave Technol. 231350–62 (2005). [CrossRef]

9.

S. Mankopf, R März, M Kamp, D. Guang-Hua, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser,” IEEE Jour. Quantum Elec. 40, 1306–14 (2004). [CrossRef]

10.

A. Xing, M. Davanço, D. J. Blumenthal, and E. L. Hu, “Fabrication of InP-based two-dimensional photonic crystal membrane,” J. Vac. Sci. Technol. B 2270 (2004). [CrossRef]

11.

T. Jensen, E. Witzel, A. Paduch, P. Ziegler, E.U. Wagemann, and O. Funke, “A new method to determine loss, PDL, GD and DGD of passive optical components”, 18th NFOEC, Dallas, September 2002.

12.

E. Collett, Polarized Light in Fiber Optics (The PolaWave Group, 2003), Chap. 13.

13.

K. Yamaguchi, M. Kelly, G. Stolze, and D. Kobasevic, “Polarization-Resolved Measurements using Mueller Matrix Analysis,” Agilent application note 5989-1261EN.

14.

The MIT Photonic-Bands package, http://www.ab-inito.mit.edu/mpb/

15.

M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” App. Phys. Lett. 811163 (2002). [CrossRef]

16.

L. J. Gamble, W. M. Diffey, S. T. Cole, R. L. Fork, D. K. Jones, T. R. Nelson Jr., J. P. Loehr, and J. E. Ehret, “Simultaneous measurement of group delay and transmission of a one-dimensional photonic crystal,” Opt. Express 5267 (1999), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-11-267. [CrossRef] [PubMed]

17.

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” App. Phys. Lett. 86053108 (2005). [CrossRef]

18.

L. A Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley Intersciences), Chap. 6.

19.

P. St. Russel, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” Jour. Modern Optics 381599–1619 (1991). [CrossRef]

20.

N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg Gratings for Dispersion Compensation in Transmission: Theoretical Model and Design Criteria for Nearly Ideal Pulse Recompression,” J. Lightwave Technol. 151303 (1997). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.7380) Optical devices : Waveguides, channeled

ToC Category:
Research Papers

History
Original Manuscript: May 2, 2005
Revised Manuscript: June 10, 2005
Published: June 27, 2005

Citation
Marcelo Davanco, Aimin Xing, James Raring, Evelyn Hu, and Daniel Blumenthal, "Detailed characterization of slow and dispersive propagation near a mini-stop-band of an InP photonic crystal waveguide," Opt. Express 13, 4931-4938 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-4931


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References

  1. T. J. Karle, Y. J. Chai, C. N. Morgan, I. H. White, and T. F. Krauss, �??Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides,�?? J. Lightwave Technol. 22 514-519 (2004). [CrossRef]
  2. A. Xing, M. Davanço, S. Camatel, D. J. Blumenthal, E. L. Hu, �?? Pulse compression in Line Defect Photonic Waveguide ,�?? in Proceedings of the Optical Fiber Communications Conference 2005, Paper OWD5.
  3. M. Notomi, K. Yamada, A. Shynia, J. Takahashi, C. Takahashi, I. Yokohama, �??Extremely Large Group- Velocity of Line-Defect Waveguides in Photonic Crystal Slabs,�?? Phys. Rev. Lett 87 253902-1-4 (2001). [CrossRef]
  4. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré , �??Coupled-mode theory and propagation losses in photonic crystal waveguides,�?? Opt. Express 11, 1490 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490</a>. [CrossRef] [PubMed]
  5. S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, T. F. Krauss, �??Transmission properties of two-dimensional photonic crystal channel waveguides,�?? Opt. Quantum Electron. 34 171-181 (2002). [CrossRef]
  6. J. M. Bendickson, J. P. Dowling, M. Scalora, �??Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,�?? Phys. Rev. E 53, 4107 (1996). [CrossRef]
  7. H. Benisty, Ph. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, �??Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,�?? Opt. Quantum Elec. 34 205-215 (2002). [CrossRef]
  8. M. L. Mašanoviæ, V. Lal, J. A. Summers , J. S. Barton, E. J. Skogen, Rau, L. G., L. A. Coldren and D. J. Blumenthal, �??Widely-Tunable Monolithically-Integrated All-Optical Wavelength Converters in InP,�?? J. Lightwave Technol. 23 1350-62 (2005). [CrossRef]
  9. S. Mankopf, R März, M Kamp, D. Guang-Hua, F. Lelarge, A. Forchel, �??Tunable photonic crystal coupledcavity laser,�?? IEEE J. Quantum Electron. 40, 1306-14 (2004). [CrossRef]
  10. A. Xing, M. Davanço, D. J. Blumenthal, E. L. Hu, �??Fabrication of InP-based two-dimensional photonic crystal membrane,�?? J. Vac. Sci. Technol. B 22 70 (2004). [CrossRef]
  11. T. Jensen, E. Witzel, A. Paduch, P. Ziegler, E.U.Wagemann and O. Funke, �??A new method to determine loss, PDL, GD and DGD of passive optical components�??, 18th NFOEC, Dallas, September 2002.
  12. E. Collett, Polarized Light in Fiber Optics (The PolaWave Group, 2003), Chap. 13.
  13. K. Yamaguchi, M. Kelly, G. Stolze, D. Kobasevic, �??Polarization-Resolved Measurements using Mueller Matrix Analysis,�?? Agilent application note 5989-1261EN.
  14. The MIT Photonic-Bands package, <a href="http://ab-initio.mit.edu/mpb/">http://www.ab-inito.mit.edu/mpb/</a>
  15. M. Qiu, �??Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,�?? App. Phys. Lett. 81 1163 (2002). [CrossRef]
  16. L. J. Gamble, W. M. Diffey, S. T. Cole, R. L. Fork, D. K. Jones, T. R. Nelson, Jr., J. P. Loehr, J. E. Ehret, �??Simultaneous measurement of group delay and transmission of a one-dimensional photonic crystal,�?? Opt. Express 5 267 (1999), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-11-267">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-11-267.</a> [CrossRef] [PubMed]
  17. G. von Freymann, S. John, S. Wong, V. Kitaev, G. A. Ozin, �??Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,�?? App. Phys. Lett. 86 053108 (2005). [CrossRef]
  18. L. A Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley Intersciences), Chap. 6.
  19. P. St. Russel, �??Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,�?? J. Mod. Opt. 38, 1599-1619 (1991). [CrossRef]
  20. N. M. Litchinitser, B. J. Eggleton, D. B. Patterson, �?? Fiber Bragg Gratings for Dispersion Compensation in Transmission: Theoretical Model and Design Criteria for Nearly Ideal Pulse Recompression,�?? J. Lightwave Technol. 15 1303 (1997). [CrossRef]

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