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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 17141–17153
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Stopping of Light by the Dynamic Tuning of Photonic Crystal Slow Light Device

Yuji Saito and Toshihiko Baba  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 17141-17153 (2010)
http://dx.doi.org/10.1364/OE.18.017141


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Abstract

We propose a simple technique of stopping light pulses using a slow-light device based on photonic crystal coupled waveguide (PCCW). Dynamically tuning the material index chirp in the PCCW adiabatically transforms slow-light pulses into stopped ones. We demonstrate this in finite-difference time-domain simulation assuming ideal and actual tuning of the index chirp. In the ideal case, the group velocity of the almost stopped pulse is reduced to 190 times smaller than that of simple slow light pulse. The smallest limit is affected by the timing error of the tuning between wavelengths. Re-ordering and stopping of a pulse train are possible by optimizing the device length and timing. As a practical tuning method, we discuss carrier effects induced by photo-excitation. Taking into account carrier distribution and free carrier absorption, the actual behaviors of stopped light are estimated. We define and evaluate an effective delay-bandwidth product, which is affected by free carrier absorption.

© 2010 OSA

1. Introduction

The slowing and stopping of light pulses have been studied extensively for optical buffer memory and advanced time-domain signal processing in future photonic networks, interconnects, and instrumentations. Photonic nanostructures, which show large first-order dispersion dk/dω (k: wave number, ω: angular frequency), generate on-chip slow light with a group velocity υ g of typically a hundred times smaller than the light velocity c in vacuum [1

1. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

]. So far, coupled-resonator waveguides [2

2. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]

,3

3. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2, 741–747 (2008). [CrossRef]

], all pass filters [2

2. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]

,4

4. F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16(12), 8395–8405 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8395. [CrossRef] [PubMed]

], photonic crystal (PC) waveguides [5

5. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

9

9. J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]

], and metamaterials [10

10. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]

,11

11. Q. Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 101, 169903 (2008). [CrossRef]

] have been exploited as device structures. Those except for metamaterials are made of transparent dielectric media and can be low loss devices. The delay-bandwidth product (DBP) is evaluated as an essential performance factor for these devices [1

1. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

]. It indicates that large dk/dω is obtained only in a narrow frequency bandwidth, and it constrains the maximum buffering capacity, i.e. the number of pulses buffered in the device, when the pulses are not broadened by group velocity dispersion (GVD). We have succeeded in experimentally demonstrating a high DBP of 110 in PC coupled waveguide (PCCW) of 800 μm length [8

8. T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Sci. Academy Ser. B 85, 443–453 (2009). [CrossRef]

]. However, it is difficult to further enhance the DBP without increasing the length. The stopping of light, obtained by dynamically tuning photonic nanostructures, relaxes this constraint [12

12. M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92(8), 083901 (2004). [CrossRef] [PubMed]

14

14. R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers – capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005). [CrossRef]

]. Here, dk/dω is enhanced instantaneously by locally changing the material index of the device in the presence of light pulses. Then, the device and pulses simultaneously narrow their bandwidths, and consequently the pulses almost stop. Some studies experimentally demonstrated similar operation by controlling the Q factor in a single cavity or coupled cavities [15

15. Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater. 6(11), 862–865 (2007). [CrossRef] [PubMed]

18

18. T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102(4), 043907 (2009). [CrossRef] [PubMed]

].

In this paper, we propose a simple dynamic tuning in chirped PCCW. In a uniform PCCW, the photonic band of a waveguide mode becomes flat at a single frequency and dk/dω diverges to infinity, resulting in zero υ g [19

19. D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13(23), 9398–9408 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9398. [CrossRef] [PubMed]

]. When some structural parameters are gradually changed along the device (i.e. chirped structure), the flat band frequency is shifted so that the slow light effect is averaged over a finite bandwidth and slow light pulses can transmit with a moderate delay. The large DBP mentioned above is obtained in such a chirped PCCW. If the chirp range is changed instantaneously from an initial value to zero, slow light pulses with a wide spectrum are converted to stopped ones at a single frequency. Such dynamic tuning is possible by some practical methods. In comparison with other methods, it downsizes the device footprint because incident pulses are pre-compressed in space by the slow light effect before the tuning. Also, it allows subsequent pulses to pass through and stop in the device, which enable the re-ordering and stopping of a pulse train, respectively.

This paper first explains the principle of the tuning process in detail in Section 2. Then, the stopping of a single pulse is demonstrated in finite-difference time-domain (FDTD) simulation in Section 3, assuming ideal tuning of material index. Here, we discuss some fundamental properties and limiting factors. In Sections 4 and 5, the re-ordering and stopping of a pulse train are demonstrated, respectively. Finally in Section 6, a real operation is discussed, assuming photo-excited carriers to change the chirp in a semiconductor device. Here, we take into account nonlinear carrier distribution, carrier plasma and band filling effects, and free carrier absorption (FCA), and discuss an effective DBP restricted by the FCA.

2. Principle

Figure 1(a)
Fig. 1 Principle of stopping light pulse in chirped PCCW. (a) Structure of PCCW. Dashed lines show the original position of airholes in a triangular lattice. (b) Photonic band diagram. Thick black line shows the band of the even mode. Two white dots on this line indicate the range of flat band. Thick gray region indicate the range of shifted bands due to the initial, fixed chirp. (c) Schematic of dynamic tuning. Pump light is used to form the dynamic chirp.
shows a schematic of the PCCW consisting of two line defects in a triangle lattice PC slab, with lattice constant a and background airhole diameter 2r. The diameter 2r' of the center row of airholes and the position of other airholes are modified. Figure 1(b) shows the corresponding photonic band calculated by two-dimensional (2D) FDTD method with the periodic and absorbing boundary condition. We assume an equivalent slab index n eq of 2.917, normalized hole diameters 2r/a = 0.59, 2r'/a = 0.20, normalized shifts s 1/a = 0.10 and s 2/a = 0.20, and a polarization parallel to the 2D plane. Two coupled modes appear, and the even mode exhibits the target flat band at a normalized frequency ωa/2πca/λ = 0.257 (λ: wavelength in vacuum). Here we define the flat band as that sandwiched by two white dots in Fig. 1(b), which are separated by the spectral resolution in this calculation i.e. Δωres a/2πc = 6.7 × 10−5. The band shifts to higher frequencies as n eq decreases along the device. When a light pulse is incident on the device, each frequency component of the pulse reaches the slow light condition of the flat band at a different position. This means that, under the slow light condition, the pulse profile is transformed into a Fourier spectral distribution. Before and after passing through this condition, it passes GVD(1) and GVD(2) in Fig. 1(b), respectively. Thus, the total GVD is compensated and the profile of the incident pulse is recovered at the output end. The bandwidth of slow light is proportional to the chirp range. On the other hand, the effective length of slow light for each frequency component is inversely proportional to the chirp range. In consequence, the delay and bandwidth are constrained by the DBP [1

1. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

,14

14. R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers – capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005). [CrossRef]

].

Now we propose the dynamic tuning, as shown in Fig. 1(c). Here, the initial, fixed chirp is formed so that n eq decreases along the device. A control pulse is incident on the device behind the signal pulse with an appropriate delay and velocity. The control pulse chases the signal pulse, and successively catches up with each frequency component that is slowing down. By means of index change induced by the pump pulse, (such as carrier effects, optical Kerr effect), n eq at this position is instantaneously reduced. The amount of index change Δn eq ' slopes along the device because the control pulse decays due to some propagation losses. In the ideal case, such dynamic chirp Δn eq ' cancels the initial fixed chirp Δn eq, and all frequency components of the situation when light at the flat-band frequency enters a chirp-less PCCW. Therefore, the delay is extended dramatically. In the reverse process, Δn eq ' is removed from the input to output side, and the initial pulse profile is recovered.

3. Simulation

Figures 2(a)-(d)
Fig. 2 FDTD simulation of dispersion-compensated slow light (a) without and (b)-(d) with dynamic tuning. Here, cΔt d/a = (b) 420, (c) 720, and (d) 1020. Chirped structure is lying at z = 0 − 125a and n eq is constant outside of this area. (e)-(h) Corresponding light propagation of each frequency component estimated from photonic band in Fig. 1(b). Colors indicate different frequencies. Gray region indicates the slow light condition. (i)-(l) Animations corresponding to (a)-(d), respectively. (Media 1) (Media 2) (Media 3) (Media 4)
compare the propagation of slow light pulse without and with the dynamic tuning. ((i)-(l) are their animations, respectively.) Without tuning (a), the pulse enters the slow light region and pauses at ct/a = 300, and exit at 1200. With the tuning at the best timing (c), the slow light pulse transforms into a stopped pulse, almost maintaining its profile at least until ct/a = 3000. We notice through careful observation that a small amount of light escapes from the stopped pulse in the forward direction. This is dues to slight timing error of the tuning between different wavelengths against the constant tuning velocity. When the tuning is early (b), the pulse propagates without pause because the tuning takes place before the light (particularly high frequency components) reaches the slow light condition. With late tuning (d), the pulse propagates with dispersion before the dispersion compensation of GVD(1) and GVD(2) is completed.

From (2), the delay due to slow light, Δt s, is given as
Δts=(L/ω c)Δk
(3)
where Δk s is the shift of k at the flat band (distance between white dots in Fig. 1(b)). To achieve the stopping of light, the gray region must be opened by the condition Δt s – Δt p > 0. For a Gaussian pulse satisfying Δt p(Δωp/2π) = 0.44, this condition is rewritten as
(Δω p/Δω c)(Δks/2π)L>0.44
(4)
From Fig. 1(b) and parameters assumed above, Δωp/Δωc = 0.18, Δk s/2π = 0.028/a and L = 125a, which lead to (Δωp/Δωc)(Δk s/2π)L = 0.63 > 0.44. Here, the spectral efficiency Δωp/Δωc will be enhanced up to 0.5 by narrowing the signal pulse and/or the chirp range. Δk s increases slightly when the structure is optimized; the maximum Δk s/2π would be limited to around 0.04/a [19

19. D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13(23), 9398–9408 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9398. [CrossRef] [PubMed]

]. Then, the shortest L satisfying (4) is derived as 22a, which is 9 μm for a = 0.40 μm.

Figure 3
Fig. 3 Velocities at three different parts of slow light pulse after dynamic tuning, which is calculated with normalized delay of the tuning against signal light.
summarizes velocities at three different parts of the pulse. White circles show the velocity at the weighted center, which is equivalent to υ g. Blue and red circles show those at front and back ends whose intensity is 10% of the pulse peak. Dispersion can be evaluated from their difference. For example, dispersion is minimum and υ g = 4.2 × 10−4 c (group index n gc/υ g = 2400) at cΔt d/a = 720 when the pulse looks to be almost stopped in Fig. 2(c). From this value, the normalized DBP, defined as n g(Δωpp) [1], is evaluated to be 14. For slow light without tuning, it is evaluated from the delay inside the device in Fig. 2(a) and the spectral FWHM Δωp to be 0.075. Thus, the tuning provides 190-fold enhancement. Since the spectral FWHM Δωp is 5.4 times narrower than the slow light band Δωc in this simulation, the normalized DBP without tuning can be enhanced by expanding Δωp and/or narrowing Δωc. The spectra should be optimized similarly for the stopped pulse to maintain its advantage. However, if Δωp is comparable to Δωc, the timing error at low frequencies increases and the stopped pulse is dispersed more severely. If the tuning velocity is not constant but changes along the device so that the blue line in Fig. 2(e)-(h) is always included inside the gray region, the error will be neglected and υ g will be minimized closer to zero.

4. Re-ordering of pulses

If the dynamic tuning is performed with cavities, the transmission is limited inside the resonant spectrum. Therefore, when multiple pulses with the same spectrum are incident on the device, subsequent pulses cannot pass through the device after an earlier pulse is stopped by the tuning. In contrast, our method maintains continuous pass-bands around the frequency of stopped light, and so subsequent pulses can pass while earlier pulses are stopped. The order of pulses can be changed by releasing the earlier pulse after the subsequent pulses pass by, as demonstrated in Fig. 4
Fig. 4 Re-ordering of pulses demonstrated in FDTD simulation. (a) Profile of input pulses. (b) Time evolution of pulse intensity distribution. (c) Profile of output pulses. (d) (Media 5) Animation corresponding to (b).
. Here, four Gaussian pulses of cΔt p/a = 290 are successively launched with a peak-to-peak interval of cΔt i/a = 960. The tuning is performed for the second pulse with cΔt d/a = 720 and a duration equal to the interval. (b) shows a complicated light intensity profile due to overlap of pulses, but the corresponding animation (d) displays counterchange of the second and third pulses. The third pulse incident during the tuning propagates with a constant υ g. As observed in (c), the slow light pulses (first, last), the stopped pulse (second), and the non-stop pulse (third) almost maintain their initial shape at the output end. Such pulse re-ordering will be meaningful for some signal processing if each pulse has its own intensity, phase, quantum information, etc.

5. Stopping of pulse train

For optical buffering, it is particularly important to stop an entire pulse train simultaneously. When cavities are used for stopping pulses, it requires many cavities each assigned to one pulse, and complicated tuning process. Here, we show two different approaches to achieve this using our simple tuning process.

As noted in Section 2, the pulse incident on chirped PCCW is expanded into a Fourier spectral distribution due to GVD(1). When a pulse train is incident, pulses do not pause separately but their spectral distributions overlap and slow down, keeping their initial time differences. If timing of the tuning is optimized for one pulse, the timing error occurs for other pulses, resulting in severe dispersion. The key is the blue line of the tuning overlapping with the gray region Δt s – Δt p. In Fig. 2(e)-(h), the gray region is opened for the FWHM of one pulse. For densely-packed return-to-zero pattern of M pulses, Δt p is extended to (2M−1)Δt p. Therefore, Δt s must be extended similarly to keep the gray region still opening. Such a situation is obtainable by elongating the device (2M−1) times without changing the chirp range Δn eq, so that the pulses decelerate and accelerate more slowly. For example, let us consider two pulses and a three-fold longer device, i.e. L = 375a. The second pulse is incident with an interval of cΔt i/a = 720. Then, the optimum delay of the tuning becomes cΔt d/a = 2520. Figure 5
Fig. 5 FDTD simulation of stopping two pulses in three-fold longer PCCW. (a) Light intensity profile. (b) Light propagation of each frequency component estimated from photonic band. (c) (Media 6) Animation corresponding to (a).
shows the FDTD simulation of stopping two pulses. Incident pulses overlap and exhibit a complex interference pattern under the slow light condition, which is almost fixed and stopped after the tuning. It goes into action but does not separate into two pulses again after the tuning is removed. This is due to the incomplete dispersion compensation of the first structure. When the interval is slightly extended to cΔt i/a = 720, clear separation was confirmed in the same simulation. In Section 3, we discussed the shortest length of the device required for stopping one pulse with ideal parameters to be 22a. Therefore, M (>>1) pulses can be buffered in the device of approximately 44aM length, e.g. 1.8 mm with a = 0.4 μm for 100 pulses if the incomplete dispersion compensation is improved.

The other method for stopping a pulse train is to divide areas, each of which stop one pulse. Figure 6
Fig. 6 Schematic of dynamic tuning against two pulses in a two-step chirped structure
shows the case of stopping two pulses in a double-step chirped structure. Here, two chirped PCCWs are simply connected in series. Without tuning, pulses repeat slowing and moving in the PCCWs. If a moderate interval is set between the pulses, they slow simultaneously. If the tuning is performed at this moment, the pulses are equally stopped. Ideally, the tuning should cancel Δn eq in each PCCW. But it is difficult to form a multi-step dynamic chirp. Here we use the single-step dynamic chirp with twice larger Δn eq ', i.e. 0.186. Then, the index slope of each chirp is flattened although their indices after the tuning are not the same. In the FDTD simulation, delays of the second pulse and tuning are set to be cΔt d/a = 1440 and 2580, respectively. Figure 7(a)
Fig. 7 FDTD simulation of stopped two pulses in two-step chirped PCCW. (a) Light intensity profile for Δn eq = 0.093 and (b) 0.0093.
shows the light propagation in a two-step chirped structure with Δn eq = 0.093. The tuning at the first chirping does not operate as expected; strong reflection occurs at the boundary with the index discontinuity. To confirm the expected operation, the same simulation was performed for a smaller Δn eq of 0.0093, as shown in Fig. 7(b). Here, two pulses stop simultaneously although weak reflection still remains. After removing Δn eq ', the two pulses appear at the output end. This approach can be applied to M pulses using M-step chirp. Two drawbacks are the reflection at the boundary particularly for pulses with a short interval and N-fold Δn eq ' required.

6. Practical dynamic tuning using photo-excited carriers

So far, we presented the dynamic tuning with an ideal index change. To realize such index change, let us discuss carrier effects induced by photo-excitation, i.e. carrier plasma dispersion and band filling effects. As discussed in Section 2, pump light is incident on the device in the same manner as signal pulse. We can consider linear inter-band absorption and nonlinear two-photon absorption [20

20. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

] of pump light at frequencies higher and lower than the bandgap frequency of the slab material, respectively. Let us discuss the linear absorption as it generates a carrier slope closer to a linear one, which is suitable for canceling the initial linear chirp. It should be noted that FCA cannot be neglected to estimate the real propagation of signal pulse in this approach.

Δneq'(z)neq[Γn+Δn(z)n+(1Γ)]neq=ΓΔn(z)neq/n
=γe2τcneqΓ2αexeΓαexzPex2n2ε0ωexωp 2S(1me *+1mh *)
(8)

The equivalent FCA coefficient αeq(z) is
αeq(z)=ΓαFCA(z)=e3τcΓ2αexeΓαexzPexnε0cωabωp 2S(1μeme*2+1μhmh*2)
(9)
Now, let us consider a GaInAsP PC slab with m e* = 0.045m 0, m h* = 0.47m 0, μe = 1100 cm2/Vs, μh = 70 cm2/Vs [21

21. S. Adachi, Physical properties of III–V semiconductor compounds: InP, InAs, GaAs, GaP, InGaAs, and InGaAsP (Wiley-VCH, 1992).

,22

22. B. R. Bennet, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990). [CrossRef]

], τc = 100 ps [23

23. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15(12), 7506–7514 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7506. [CrossRef] [PubMed]

], γ = 3 [22

22. B. R. Bennet, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990). [CrossRef]

], n = 3.45, Γ = 0.89, S = 0.3 μm2 (typical values for GaInAsP and PCCW at λ ~1.55 μm), Δn eq = 0.0093, a = 0.4 μm and L = 500 μm ( = 1250a). We can consider αex and P ex as externally controllable parameters; αex can be controlled by changing the composition of GaInAsP and/or pump frequency near the bandgap. These parameters are chosen so that the dynamic chirp cancels the initial chirp, i.e. Δn eq '(0) – Δn eq '(L) = 0.0093. We ignored the scattering loss caused by the disordering in actual devices to investigate the influence of FCA. Fig. 8
Fig. 8 Distributions of photo-excited carrier density, index change by carrier effects, and FCA.
shows the calculated distributions of N(z), Δn eq '(z) and αeq(z). When αex is small, a high P ex is needed to generate the above difference in Δn eq ', while a linear distribution is easily formed. But in this case, the carrier density becomes higher, resulting in large FCA. When αex is large, a small P ex is sufficient to obtain the difference, and so the FCA is small. However, the distribution becomes nonlinear.

The FDTD simulation is performed, assuming Δt p = 3.9 ps and λp = 1.521 μm. For the long device of L = 500 μm, however, a long computation time is necessary even in 2D. To reduce this load, actual calculation is done by scaling L and t to 1/10 times and αex, αeq, Δn eq, and Δn eq ' to 10 times. The results are summarized after scaling back, as shown in Fig. 9
Fig. 9 FDTD simulation of stopped pulse assuming photo-excited carriers in GaInAsP PCCW. (a) αex = 25, (b) 50, and (c) 100 cm−1.
. At αex = 50 cm−1, the pulse stops without dispersion because almost linear distribution in Δn eq ' is formed. However, the pulse severely decays due to the large FCA; the photon lifetime τph after the tuning is as short as 36 ps. At αex = 100 cm−1, the pulse dispersed due to nonlinear distribution while propagation extends due to the small FCA. A solution for suppressing both dispersion and FCA is to modify αex with z so that a linear distribution is formed even for minimal carrier excitation. Such αex is obtainable when using the selective-area growth of GaInAsP in metal-organic vapor-phase epitaxy [24

24. M. Aoki, H. Sano, M. Suzuki, M. Takahashi, K. Uomi, and A. Takai, “Novel structure MQW electroabsorption modulator/ DFB-laser integrated device fabricated by selective area MOCVD growth,” Electron. Lett. 27, 2138–2140 (1991). [CrossRef]

]; a sloped bandgap frequency is formed by shaping the growth mask. If dispersion disappear for αex = 50 cm−1, τph will double. To extend τph drastically, the initial chirp Δn eq must be much smaller than the assumed value. As noted in Section 2, Δn eq determines the slow light band before the tuning; Δn eq = 9.3 × 10−3 corresponds to a bandwidth of 760 GHz for the assumed parameters. If a narrower bandwidth such as 76 GHz is sufficient for one’s purpose, Δn eq can be reduced to 9.3 × 10−4. In proportion to this, the FCA is suppressed and τph will extend by 10 times. This discussion suggests that the product between the bandwidth limited by Δn eq and the photon lifetime limited by the FCA can be defined as an effective DBP for stopping light using carrier effects. It is calculated to be 27 for the above values. Let us consider a situation that some amount of loss in the device can be compensated by integrated or external amplifiers. These days, standard erbium-doped optical fiber amplifiers used for pre-amplification provide a 25 dB gain. If a −25 dB decay of stopped light is recoverable by such amplification, τph extends to 0.2 ns and the effective DBP will be 152. In the case without tuning, the maximum DBP in experiments is 110 for 800-μm long PCCW, suggesting that it will be 69 for 500-μm long device from the linear dependence on L. Therefore, the effective DBP for stopping light can be larger than simple slow light if such decay is acceptable.

7. Conclusion

We proposed and theoretically demonstrated a method of stopping slow light pulse by dynamically cancelling the index chirp in photonic crystal coupled waveguide. In the FDTD simulation, the group velocity of subpicosecond optical pulse is drastically reduced to at least 190 times lower than that of simple slow light when the tuning is performed with the best timing. The complete stopping will be possible by optimizing the velocity of the pump pulse. It was also shown that this method allows the stopping of two continuous pulses by elongating the device to three times. This discussion can be extended to stopping M pulses in (2M−1) times longer device. Therefore, it has a potential of buffering arbitrary optical signals. Finally, carrier plasma and band filling effects induced by photo-excited carriers were considered for real tuning. The stopping of light is observed for real parameters of GaInAsP device. Here, the nonlinear distribution of carriers and free carrier absorption enhance the dispersion and loss, respectively. From their exclusive relation, the effective delay-bandwidth product was defined and estimated to be 27 (or 152 if a recoverable loss is acceptable). This value is comparable or slightly larger than that of simple slow light. To improve this value essentially, investigation of some other tuning mechanisms such as nonlinear optical Kerr effect and electro-optic effect, which do not use carrier excitation, will be necessary.

This work was partly supported by The FIRST Program “Innovative technology for Photonics- Electronics integrated systems”.

References and links

1.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

2.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]

3.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2, 741–747 (2008). [CrossRef]

4.

F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16(12), 8395–8405 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8395. [CrossRef] [PubMed]

5.

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J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6227. [CrossRef] [PubMed]

7.

T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16(12), 9245–9253 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-12-9245. [CrossRef] [PubMed]

8.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Sci. Academy Ser. B 85, 443–453 (2009). [CrossRef]

9.

J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]

10.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]

11.

Q. Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 101, 169903 (2008). [CrossRef]

12.

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92(8), 083901 (2004). [CrossRef] [PubMed]

13.

J. Khurgin, “Adiabatically tunable optical delay lines and their performance limitations,” Opt. Lett. 30(20), 2778–2780 (2005). [CrossRef] [PubMed]

14.

R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers – capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005). [CrossRef]

15.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater. 6(11), 862–865 (2007). [CrossRef] [PubMed]

16.

Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3, 406–410 (2007). [CrossRef]

17.

L. Yosef Mario and M. K. Chin, “Optical buffer with higher delay-bandwidth product in a two-ring system,” Opt. Express 16(3), 1796–1807 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-3-1796. [CrossRef] [PubMed]

18.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102(4), 043907 (2009). [CrossRef] [PubMed]

19.

D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13(23), 9398–9408 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9398. [CrossRef] [PubMed]

20.

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

21.

S. Adachi, Physical properties of III–V semiconductor compounds: InP, InAs, GaAs, GaP, InGaAs, and InGaAsP (Wiley-VCH, 1992).

22.

B. R. Bennet, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990). [CrossRef]

23.

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15(12), 7506–7514 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7506. [CrossRef] [PubMed]

24.

M. Aoki, H. Sano, M. Suzuki, M. Takahashi, K. Uomi, and A. Takai, “Novel structure MQW electroabsorption modulator/ DFB-laser integrated device fabricated by selective area MOCVD growth,” Electron. Lett. 27, 2138–2140 (1991). [CrossRef]

OCIS Codes
(230.3120) Optical devices : Integrated optics devices
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Slow and Fast Light

History
Original Manuscript: June 9, 2010
Revised Manuscript: July 22, 2010
Manuscript Accepted: July 22, 2010
Published: July 28, 2010

Citation
Yuji Saito and Toshihiko Baba, "Stopping of light by the dynamic tuning of photonic crystal slow light device," Opt. Express 18, 17141-17153 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-17141


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References

  1. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]
  2. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]
  3. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2, 741–747 (2008). [CrossRef]
  4. F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16(12), 8395–8405 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8395 . [CrossRef] [PubMed]
  5. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]
  6. J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6227 . [CrossRef] [PubMed]
  7. T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16(12), 9245–9253 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-12-9245 . [CrossRef] [PubMed]
  8. T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Sci. Academy Ser. B 85, 443–453 (2009). [CrossRef]
  9. J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]
  10. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]
  11. Q. Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 101, 169903 (2008). [CrossRef]
  12. M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92(8), 083901 (2004). [CrossRef] [PubMed]
  13. J. Khurgin, “Adiabatically tunable optical delay lines and their performance limitations,” Opt. Lett. 30(20), 2778–2780 (2005). [CrossRef] [PubMed]
  14. R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers – capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005). [CrossRef]
  15. Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater. 6(11), 862–865 (2007). [CrossRef] [PubMed]
  16. Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3, 406–410 (2007). [CrossRef]
  17. L. Yosef Mario and M. K. Chin, “Optical buffer with higher delay-bandwidth product in a two-ring system,” Opt. Express 16(3), 1796–1807 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-3-1796 . [CrossRef] [PubMed]
  18. T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102(4), 043907 (2009). [CrossRef] [PubMed]
  19. D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13(23), 9398–9408 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9398 . [CrossRef] [PubMed]
  20. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]
  21. S. Adachi, Physical properties of III–V semiconductor compounds: InP, InAs, GaAs, GaP, InGaAs, and InGaAsP (Wiley-VCH, 1992).
  22. B. R. Bennet, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990). [CrossRef]
  23. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15(12), 7506–7514 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7506 . [CrossRef] [PubMed]
  24. M. Aoki, H. Sano, M. Suzuki, M. Takahashi, K. Uomi, and A. Takai, “Novel structure MQW electroabsorption modulator/ DFB-laser integrated device fabricated by selective area MOCVD growth,” Electron. Lett. 27, 2138–2140 (1991). [CrossRef]

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