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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 25500–25511
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Mode junction photonics with a symmetry-breaking arrangement of mode-orthogonal heterostructures

Sunkyu Yu, Xianji Piao, Sukmo Koo, Jung H. Shin, Seung Hoon Lee, Bumki Min, and Namkyoo Park  »View Author Affiliations


Optics Express, Vol. 19, Issue 25, pp. 25500-25511 (2011)
http://dx.doi.org/10.1364/OE.19.025500


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Abstract

Junction structures provide the foundation of digital electronics and spintronics today. An equivalent, a photonic junction to achieve systematic and drastic control of photon flow is currently missing, but is mandatory for serious all-optical signal processing. Here we propose a photonic junction built upon mode-orthogonal hetero-structures, as a fundamental structural unit for photonic integrated circuits. Controlling the optical potential of mode-orthogonal junctions, the flow of photons can be dynamically manipulated, to complete the correspondence to the electronic junction structures. Of the possible applications, we provide examples of a photonic junction diode and a multi-junction half-adder, with exceptional performance metrics. Highly directional (41dB), nearly unity throughput, ultra-low threshold-power, high quality signal regeneration at 200Gb/s, and all-optic logic operations are successfully derived with the self-induced, bi-level dynamic mode-conversion process across the junction.

© 2011 OSA

1. Introduction

The ultrafast, distortion-free optical communication of today owes its remarkable success in large part to the time-reversal symmetry of Maxwell’s equations and the charge-less nature of photons, that providing untainted linearity for optical materials and devices. Still at the same time, this very linearity has seriously hindered the development of photonic logic devices or systems. Nonlinearity being the core in the realization of logic devices, serious effort is now in progress to enhance the nonlinearity. Various nonlinear materials [1

1. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009). [CrossRef]

4

4. M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006). [CrossRef] [PubMed]

], means of field enhancement [5

5. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed]

9

9. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

], functional elements [10

10. J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22(5), 1062–1074 (2005). [CrossRef]

12

12. M. F. Yanik, S. Fan, M. Soljacić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28(24), 2506–2508 (2003). [CrossRef] [PubMed]

], signal processors [13

13. P. L. Li, D. X. Huang, X. L. Zhang, and G. X. Zhu, “Ultrahigh-speed all-optical half adder based on four-wave mixing in semiconductor optical amplifier,” Opt. Express 14(24), 11839–11847 (2006). [CrossRef] [PubMed]

17

17. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010). [CrossRef]

], and photonic-specific circuit design algorithms [18

18. Y. J. Jung, C. W. Son, Y. M. Jhon, S. Lee, and N. Park, “One-level simplification method for all-optical combinational logic circuits,” IEEE Photon. Technol. Lett. 20(10), 800–802 (2008). [CrossRef]

] have been suggested to fully exploit the photonic bandwidth advantage, and to fulfill the promise of all-optical signal processing.

Notwithstanding past effort, attempting the success of digital photonics is still in an early stage, with their premature performances. Worth to examine at this phase of stall would be the breakthrough of electronics, especially witnessed after the introduction of junction structures. Providing drastic, systematic and controllable change to the asymmetric electrical potential (or spin orientation) across [19

19. J. H. Scaff and R. S. Ohl, “Development of silicon crystal rectifiers for microwave radar receivers,” Bell Syst. Tech. J. 26, 1–30 (1947).

21

21. A. A. Tulapurkar, Y. Suzuki, A. Fukushima, H. Kubota, H. Maehara, K. Tsunekawa, D. D. Djayaprawira, N. Watanabe, and S. Yuasa, “Spin-torque diode effect in magnetic tunnel junctions,” Nature 438(7066), 339–342 (2005). [CrossRef] [PubMed]

], the junction has enabled highly advanced, non-reciprocal and nonlinear manipulation for the transport of electrons - the core attributes in the realization of diode, transistor, and logic processors in the electronics / spintronics of today.

Here, taking photonics as an example, we propose a junction for wave, built upon mode-orthogonal photonic hetero-structures, as a fundamental structural unit for ‘photo-tronics’. By exploiting the rich and well-defined orthogonal modes which provide abundant degrees of freedom for the choice of junctions (having different spectral mode-overlap and frequency separation), the modular construction of highly nonlinear devices with systematic control of wave propagation is enabled. Of possible applications for the mode junction, here we provide examples of a photonic junction diode and a multi-junction half-adder, of exceptional performance metrics. Highly directional (41dB), nearly unity throughput with orders of magnitude lower threshold power (~103, compared to [22

22. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79(3), 314–316 (2001). [CrossRef]

28

28. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]

]. For [28

28. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]

], external modulation power), a high quality signal regeneration [16

16. R. Slavík, F. Parmigiani, J. Kakande, C. Lundstro¨m, M. Sjo¨din, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gru¨ner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010). [CrossRef]

,29

29. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, 2002).

] at 200Gb/s, and all-optical AND, XOR operations are successfully demonstrated.

2. Mode junction - principles

For example, let us consider the a junction juxtaposed of two structures (Fig. 1(c)), each supporting T- (1, 2, 1) and T0 (-2, 0,2) modes of tri-atomic resonator (the eigenvector component represents the field amplitude of each atom), at the operation frequency. By adjusting the permittivity (optical potential) for a specific region (here, left side of the junction), the dominant eigenmode at the operation frequency of the controlled region then can be dynamically switched between T- and T0, to block (<T- / T0> = 0) or to authorize (<T0 / T0> = 1) the transmission of photons across the junction structure. To note, now onwards we denote; / j > as the eigenmode of the structure, Ψi-j as the potential-controlled region - supporting mode / i > in unbiased state (Fig. 1(c) in yellow), but toggling to / j > with shifted optical potential (pink in Fig. 1(c)) either by external excitation or self-induced manner.

3. Application I – photonic junction diode: principles

Out of the many possible functional devices that a junction can enable, we first consider the case of the photonic diode. For an electrical diode [19

19. J. H. Scaff and R. S. Ohl, “Development of silicon crystal rectifiers for microwave radar receivers,” Bell Syst. Tech. J. 26, 1–30 (1947).

] especially being highly nonlinear and asymmetric in its response providing the key functionality for current flow manipulation, its photonic counterpart, the photonic diode [22

22. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79(3), 314–316 (2001). [CrossRef]

28

28. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]

,30

30. J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005). [CrossRef] [PubMed]

], has also attracted serious attention. Nevertheless, for the past demonstrations of photonic diode extremely costly in threshold power (~W/μm), with the added trouble of limited throughput or directionality, it will be of worth to investigate whether the proposed junction structure could provide any advantages.

As illustrated in Fig. 2(a)
Fig. 2 Operation of a mode junction diode: under (a) Forward bias below threshold, (b) Forward bias above threshold, and (c) Reverse bias. Corresponding field patterns in the photonic crystal realization are shown in (d) ~(f) (details of numerical analysis in Appendix-A). Unidirectional transmission of the signal is evident only for the state 2(e), confirming the diode operation above threshold. For other states of operation, the wave propagation is inhibited; (d), at the odd-mode coupler for forward bias. (f), at the right end barrier of the di-atomic resonator, for reverse bias.
2(c), without loss of generality, let us consider a di-atomic resonator providing even- and odd- modes, separated in its frequencies (ωe and ωo). At the operation frequency ωe the di-atomic resonator in the even mode forms a ψeo mode junction when combined with the ψo odd-mode coupler (an 1 x 2 splitter and a π phase shifter in one arm). Critical to note, compared to the right-side low-Q ψo coupler, for the left-side high-Q di-atomic resonator enjoying a higher density of photons and thus a much enhanced, self-induced optical nonlinearity, the modification of the optical potential for the Ψe-oo junction becomes strongly dependent on the direction of the incident wave, so as to fulfill the directionality required for diode operation. Specifically, the critical consequences are as follows. First, for the forward bias below threshold (Ψeo, Fig. 2(a)), the wave propagation to the other side of the junction is completely prohibited and reflected, as dictated by the mode orthogonality < e / o > = 0. Meanwhile, for the forward bias above threshold, with a strong on-resonance (ωe) build-up of the field in the resonator and a corresponding optical potential shift (n2 I / n0 ~(ωo - ωe) / ωc), the dominant mode in the resonator Ψe-o then gets converted from even to odd mode (Ψoo, Fig. 2(b)), to render full transparency to the ψo coupler region (< o / o > = 1). Finally, for the reverse bias (Fig. 2(c)), the coupling from the odd mode coupler to even mode di-atomic resonator is suppressed by the mode orthogonality. In this case, the weakly-excited resonator will remain in the even mode, blocking the transmission, until the reverse bias reaches the breakdown - determined by the non-zero mode overlap factor (Appendix A).

Meanwhile simple in its principle, the junction diode offers distinctive advantages. First, when compared to past approaches utilizing asymmetric potential barriers for directional operation of the diode (at the expense of severe impedance mismatch, (Fig. 3(e)
Fig. 3 (a) Impedance matched (1/τL = 1/τR1 + 1/τR2) low reflection design is achieved with a junction diode, by adjusting τL. (e) Illustration of impedance imbalance, for the case of single band photonic diode (case of τR = 4τL). Mode-dependent field intensity inside resonators (even: |a1 + a2|2, odd: |a1-a2|2) for structures in (a) and (e) are shown for; (b) and (f) - forward bias before threshold, (c) and (g) - forward bias after threshold, (d) and (h) - under reverse bias. For two-band operation (b) at the operation frequency ωop (dashed line), on resonance feeding and low power excitation of the resonator is achieved. κ = 0.003ωop, and Q = 200. Coupled-mode-theory was used for the calculation.
, 1/τL >> 1/τR) [22

22. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79(3), 314–316 (2001). [CrossRef]

26

26. X. S. Lin, W. Q. Wu, H. Zhou, K. F. Zhou, and S. Lan, “Enhancement of unidirectional transmission through the coupling of nonlinear photonic crystal defects,” Opt. Express 14(6), 2429–2439 (2006). [CrossRef] [PubMed]

], now for the proposed junction diode, it is possible to keep the full symmetry of the potential barrier - by transferring the required diode directionality to the asymmetric arrangement of mode-orthogonal structures. As a result, an impedance-matched design can be constructed, without any sacrifice in directionality or throughput (Fig. 3(a), 1/τL = 1/τR1 + 1/τR2). Furthermore, with the orthogonal, two-band, on-resonance operation of the Ψe-oo junction (Fig. 3(b)3(d), contrast to the expensive off-resonance excitation for single-band diode operation shown in Fig. 3(f)3(h)), it is possible to simultaneously realize; high reverse breakdown (from mode orthogonality), ultra-low threshold power (from the on-resonance feeding to the resonator in the even mode, Fig. 3(b)), and near unity throughput (with the on-resonance releasing of the resonator odd mode, to the ψo mode coupler, as in Fig. 3(c)).

4. Application I – photonic junction diode: implementation and results

Upon assessment of the key parameters, we also investigate the dynamic performance of the junction diode as a passive all-optical regenerator, for the application in errorless, ultra-high-speed signal processing [16

16. R. Slavík, F. Parmigiani, J. Kakande, C. Lundstro¨m, M. Sjo¨din, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gru¨ner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010). [CrossRef]

,29

29. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, 2002).

]. Figure 4(d) and 4(f) show FDTD obtained regenerated optical eyes utilizing the highly limiting regime of the characteristic curve (p2-p3-p4-p5, in Fig. 4(a)), for the 27-1 PRBS (Pseudo Random Bit Sequence) NRZ (Non Return to Zero) noise-contaminated input at 100Gbit/s (Fig. 4(c)) and 200Gbit/s (Fig. 4(e)) respectively. With the all-optical signal regeneration action from the junction diode, a significant enhancement in the signal quality [29

29. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, 2002).

] was observed, from the optical signal quality factor for the input Qis = 3.3 (Qis = 3.9) to the output Qos = 13.5 (Qos = 7.0), at 100Gbit/s (200Gbit/s).

5. Application II – multi-junction half adder

With the success in the ultra-low-power high-speed operation of photonic junction diode and all-optical regeneration using the simplest Ψe-oo junction, we now consider another example for the modular application of mode junction. Half-adder, being the core building block for the Arithmetic Logic Unit (ALU) in the modern Central Processing Unit (CPU), has been often considered in the photonic domain [13

13. P. L. Li, D. X. Huang, X. L. Zhang, and G. X. Zhu, “Ultrahigh-speed all-optical half adder based on four-wave mixing in semiconductor optical amplifier,” Opt. Express 14(24), 11839–11847 (2006). [CrossRef] [PubMed]

,14

14. Q. Liu, Z. Ouyang, C. J. Wu, C. P. Liu, and J. C. Wang, “All-optical half adder based on cross structures in two-dimensional photonic crystals,” Opt. Express 16(23), 18992–19000 (2008). [CrossRef] [PubMed]

], but mostly as the combination of discrete components, and also lacking isolation properties.

For this, we stretch our design strategy one step further, to construct a monolithic, multi-junction half-adder (ψe-Ψe-oo, shown in Fig. 5(a)
Fig. 5 Multi-junction realization of monolithic half-adder; (a) coupling to S (XOR) port with a single logic input (IA or IB) power below the threshold. (b) coupling to C (AND) port under two input signals (IA · IB) for their total power above the threshold. Even (state 1)- / Odd (state 2)- mode excitation for the central di-atomic resonator and couplings to the even- / odd- mode coupler at the S / C port (left / right) of the half-adder is evident from the FDTD generated field amplitude plot. Figure (c) shows the logic operations of AND & XOR, under the two input signals at 50Gbps (de-correlated, PRBS). Figure (d) and (e) show the optical eye patterns for AND & XOR outputs. To note, for the generation of phase / time synchronized two input signals (IA and IB) for the proper logic operation, a single source was assumed, which are power divided and then separately modulated [14].
); with the high-Q nonlinear region Ψe-o sandwiched in-between ψe and ψo structures (in this case, even- and odd- mode couplers). Setting the input power of the logic signal (IA or IB) for Ψe-o resonator slightly below the threshold of mode conversion, resonator even mode coupling only to the XOR output port (OS; supporting even mode) is enabled for a single input source (Fig. 5(a). 1← ψe-Ψe, Ψeo → 0), meanwhile above the threshold with two input signals (IA · IB), the AND operation to the OC port (supporting odd mode) is activated with the nonlinear conversion to the odd mode in the center resonator (0 ← ψe-Ψo, Ψoo → 1. Fig. 5(b)). Figure 5(c)5(e) show the AND, XOR operation and their optical eye for the multi-junction monolithic half-adder, for the input of two PRBS NRZ signals at 50Gbps. Worth to note, under the arrangement of the multi-junction in three-level ψ2-Ψ(1/2/3)-ψ3 structure, for example with Tri-atom molecule states (T0, T-, T + , in Fig. 1(b)), the same functionality with full input-to-output isolation could be achieved.

6. Conclusion

Appendix

A. Details of the device structures and numerical method used in the study

B. Coupled mode theory for the di-atomic photonic junction diode

B.1. Analytical model and coupled mode equations

Temporal coupled mode theory was employed [12

12. M. F. Yanik, S. Fan, M. Soljacić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28(24), 2506–2508 (2003). [CrossRef] [PubMed]

,33

33. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002). [CrossRef] [PubMed]

,38

38. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

40

40. T. Uesugi, B. S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14(1), 377–386 (2006). [CrossRef] [PubMed]

] to assess the behavior of the proposed junction diode. First, we write down the coupled mode equations for Fig. 7
Fig. 7 Analytical model of the di-atomic mode junction diode, used in the temporal CMT analysis.
,

ddt(a1a2a3)=(iω1(1τ1+1τ2)iκ120iκ21iω21τ3000iω3(1τ4+1τ5+1τ6))(a1a2a3)+(2τ1S+1+2τ2S+22τ3S+32τ4S+4+2τ5S+5+2τ6S+6)
(1)
(S1S2)=(S+1S+2)+(2τ12τ2)a1
(2)
S3=S+3+2τ3a2
(3)
(S4S5S6)=(S+4S+5S+6)+(2τ42τ52τ6)a3
(4)
(S+2S+4)=(S4S2)ejθ1
(5)
(S+3S+5)=(S5S3)ejθ2
(6)

B.2. Solution of resonator field (a1, a2, a3)

Solving Eqs. (2)(4) and Eqs. (5) and (6) together we now arrive at the following expressions for the wave components entering to the resonators 1, 2, and 3.

S+2=2τ2eiθ12isinθ1a1+2τ42isinθ1a3α21a1+α23a3
(7)
S+3=2τ3eiθ22isinθ2a2+2τ52isinθ2a3α32a2+α33a3
(8)
S+4=2τ22isinθ1a1+2τ4eiθ12isinθ1a3α41a1+α43a3
(9)
S+5=2τ32isinθ2a2+2τ5eiθ22isinθ2a3α52a2+α53a3
(10)

Substituting Eqs. (7)(10) into Eq. (1), the field amplitudes in resonators a1 ~a3 can be obtained to give,
a1=(c5c6M2c3)2τ1S+1+(c12c2M2c3)2τ6S+6(M1c21c2c3)(c5c6M2c3)(c4c6c21c3)(c12c2M2c3)
(11)
a2=(c4c6c21c3)2τ1S+1+(M1c21c2c3)2τ6S+6(M1c21c2c3)(c5c6M2c3)(c4c6c21c3)(c12c2M2c3)
(12)
a3=c4M2c21c5c3c5c6M2(c5c6M2c3)2τ1S+1+(c12c2M2c3)2τ6S+6(M1c21c2c3)(c5c6M2c3)(c4c6c21c3)(c12c2M2c3)
(13)
where
M1=i(ωω1)(1τ1+1τ2)+2τ2α21
(14)
M2=i(ωω2)1τ3+2τ3α32
(15)
and cij’s are constant values not affected by the nonlinear frequency shift ; c12 = 12, c21 = 21, c2 = (2/τ2)1/2α23, c3 = (2/τ3)1/2α33, c4 = (2/τ4)1/2α41, c5 = (2/τ5)1/2α52, and c6 = i(ωω3) – (1/τ4 + 1/τ5 + 1/τ6) + (2/τ4)1/2α43 + (2/τ5)1/2α53.

B.3. Implementation of Kerr nonlinearity and Calculation of Diode Throughput

The transmitted optical power for the forward and reverse bias condition can then be calculated from Eq. (11) and (13), by using a simple relation, PO = (2 / τ6)|a3|2 for forward feeding boundary condition |S+1|2 = PI, S+6 = 0, and PO = (2 / τ1)|a1|2 for the reverse feeding boundary condition |S+6|2 = PI, S+1 = 0. Specifically, applying boundary conditions for forward bias, the expression for the stored field energy |a3|2 of resonator 3 becomes
|a3|2=|c1c5c4M2|2|c3c5c6M2|2|a1|2
(16)
where for Eq. (16), M1(|a1|2) and M2(|a2|2) can be calculated from Eqs. (14), (15) with resonance shifted frequency ωk = ωk0ρ|ak|2 and for |a1|2 and |a2|2 being

|a1|2=|c5c6M2c3|22τ1PI|(M1c21c2c3)(c5c6M2c3)(c4c6c21c3)(c12c2M2c3)|2
(17)
|a2|2|a1|2=|c3c4c6c21|2|c3c5c6M2|2.
(18)

For reverse bias boundary condition, the stored field energy |a1|2 can be reduced to give,
|a1|2=|c12c2M2c3|22τ6PI|(M1c21c2c3)(c5c6M2c3)(c4c6c21c3)(c12c2M2c3)|2
(19)
where M1(|a1|2) and M2(|a2|2) can be calculated from, by setting ωk = ωk0ρ|ak|2 and using,

|a2|2|a1|2=|c3M1c2c21|2|c3c12c2M2|2.
(20)

The output power thus then can be obtained from PO = (2 / τ6)|a3|2 for forward feeding, or with PO = (2 / τ1)|a1|2 for reverse feeding. Using the FDTD measured resonator parameter sets ωk0, ρ, τi, and θi , the transmission power and response curve of the diode (Fig. 4(a)) can be finally obtained using equation for PO separately for forward bias and reverse bias.

Acknowledgment

We acknowledge helpful discussions with Prof. Kwang Seok Seo, regarding the history / significance of junction structures in electronics. This work was supported by the National Research Foundation (GRL, K20815000003 and SRC 2011-0001054) funded by the Korean government.

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B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]

9.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

10.

J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22(5), 1062–1074 (2005). [CrossRef]

11.

F. Leo, S. Coen, P. Kockaert, S. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010). [CrossRef]

12.

M. F. Yanik, S. Fan, M. Soljacić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28(24), 2506–2508 (2003). [CrossRef] [PubMed]

13.

P. L. Li, D. X. Huang, X. L. Zhang, and G. X. Zhu, “Ultrahigh-speed all-optical half adder based on four-wave mixing in semiconductor optical amplifier,” Opt. Express 14(24), 11839–11847 (2006). [CrossRef] [PubMed]

14.

Q. Liu, Z. Ouyang, C. J. Wu, C. P. Liu, and J. C. Wang, “All-optical half adder based on cross structures in two-dimensional photonic crystals,” Opt. Express 16(23), 18992–19000 (2008). [CrossRef] [PubMed]

15.

S. Yu, S. Koo, and N. Park, “Coded output photonic A/D converter based on photonic crystal slow-light structures,” Opt. Express 16(18), 13752–13757 (2008). [CrossRef] [PubMed]

16.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstro¨m, M. Sjo¨din, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gru¨ner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010). [CrossRef]

17.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010). [CrossRef]

18.

Y. J. Jung, C. W. Son, Y. M. Jhon, S. Lee, and N. Park, “One-level simplification method for all-optical combinational logic circuits,” IEEE Photon. Technol. Lett. 20(10), 800–802 (2008). [CrossRef]

19.

J. H. Scaff and R. S. Ohl, “Development of silicon crystal rectifiers for microwave radar receivers,” Bell Syst. Tech. J. 26, 1–30 (1947).

20.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294(5546), 1488–1495 (2001). [CrossRef] [PubMed]

21.

A. A. Tulapurkar, Y. Suzuki, A. Fukushima, H. Kubota, H. Maehara, K. Tsunekawa, D. D. Djayaprawira, N. Watanabe, and S. Yuasa, “Spin-torque diode effect in magnetic tunnel junctions,” Nature 438(7066), 339–342 (2005). [CrossRef] [PubMed]

22.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79(3), 314–316 (2001). [CrossRef]

23.

S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19(9), 2241–2249 (2002). [CrossRef]

24.

R. Philip, M. Anija, C. S. Yelleswarapu, and D. V. G. L. N. Rao, “Passive all-optical diode using asymmetric nonlinear absorption,” Appl. Phys. Lett. 91(14), 141118 (2007). [CrossRef]

25.

N. Zhao, H. Zhou, Q. Guo, W. Hu, X. Yang, S. Lan, and X. Lin, “Design of highly efficient optical diodes based on the dynamics of nonlinear photonic crystal molecules,” J. Opt. Soc. Am. B 23(11), 2434–2440 (2006). [CrossRef]

26.

X. S. Lin, W. Q. Wu, H. Zhou, K. F. Zhou, and S. Lan, “Enhancement of unidirectional transmission through the coupling of nonlinear photonic crystal defects,” Opt. Express 14(6), 2429–2439 (2006). [CrossRef] [PubMed]

27.

V. Grigoriev and F. Biancalana, “Nonreciprocal switching thresholds in coupled nonlinear microcavities,” Opt. Lett. 36(11), 2131–2133 (2011). [CrossRef] [PubMed]

28.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]

29.

G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, 2002).

30.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005). [CrossRef] [PubMed]

31.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

32.

X. Hu, Q. Zhang, Y. Liu, B. Cheng, and D. Zhang, “Ultrafast three-dimensional tunable photonic crystal,” Appl. Phys. Lett. 83(13), 2518–2520 (2003). [CrossRef]

33.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002). [CrossRef] [PubMed]

34.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997). [CrossRef]

35.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008). [CrossRef]

36.

R. W. Boyd, Nonlinear Optics (Academic Press, 1992).

37.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]

38.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

39.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999). [CrossRef]

40.

T. Uesugi, B. S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14(1), 377–386 (2006). [CrossRef] [PubMed]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(200.4660) Optics in computing : Optical logic
(230.4320) Optical devices : Nonlinear optical devices
(230.4555) Optical devices : Coupled resonators
(230.5298) Optical devices : Photonic crystals

ToC Category:
Integrated Optics

History
Original Manuscript: September 7, 2011
Revised Manuscript: November 9, 2011
Manuscript Accepted: November 17, 2011
Published: November 29, 2011

Citation
Sunkyu Yu, Xianji Piao, Sukmo Koo, Jung H. Shin, Seung Hoon Lee, Bumki Min, and Namkyoo Park, "Mode junction photonics with a symmetry-breaking arrangement of mode-orthogonal heterostructures," Opt. Express 19, 25500-25511 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25500


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References

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  8. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009). [CrossRef] [PubMed]
  9. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010). [CrossRef] [PubMed]
  10. J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B22(5), 1062–1074 (2005). [CrossRef]
  11. F. Leo, S. Coen, P. Kockaert, S. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics4(7), 471–476 (2010). [CrossRef]
  12. M. F. Yanik, S. Fan, M. Soljacić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett.28(24), 2506–2508 (2003). [CrossRef] [PubMed]
  13. P. L. Li, D. X. Huang, X. L. Zhang, and G. X. Zhu, “Ultrahigh-speed all-optical half adder based on four-wave mixing in semiconductor optical amplifier,” Opt. Express14(24), 11839–11847 (2006). [CrossRef] [PubMed]
  14. Q. Liu, Z. Ouyang, C. J. Wu, C. P. Liu, and J. C. Wang, “All-optical half adder based on cross structures in two-dimensional photonic crystals,” Opt. Express16(23), 18992–19000 (2008). [CrossRef] [PubMed]
  15. S. Yu, S. Koo, and N. Park, “Coded output photonic A/D converter based on photonic crystal slow-light structures,” Opt. Express16(18), 13752–13757 (2008). [CrossRef] [PubMed]
  16. R. Slavík, F. Parmigiani, J. Kakande, C. Lundstro¨m, M. Sjo¨din, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gru¨ner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010). [CrossRef]
  17. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics4(3), 182–187 (2010). [CrossRef]
  18. Y. J. Jung, C. W. Son, Y. M. Jhon, S. Lee, and N. Park, “One-level simplification method for all-optical combinational logic circuits,” IEEE Photon. Technol. Lett.20(10), 800–802 (2008). [CrossRef]
  19. J. H. Scaff and R. S. Ohl, “Development of silicon crystal rectifiers for microwave radar receivers,” Bell Syst. Tech. J.26, 1–30 (1947).
  20. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science294(5546), 1488–1495 (2001). [CrossRef] [PubMed]
  21. A. A. Tulapurkar, Y. Suzuki, A. Fukushima, H. Kubota, H. Maehara, K. Tsunekawa, D. D. Djayaprawira, N. Watanabe, and S. Yuasa, “Spin-torque diode effect in magnetic tunnel junctions,” Nature438(7066), 339–342 (2005). [CrossRef] [PubMed]
  22. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett.79(3), 314–316 (2001). [CrossRef]
  23. S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B19(9), 2241–2249 (2002). [CrossRef]
  24. R. Philip, M. Anija, C. S. Yelleswarapu, and D. V. G. L. N. Rao, “Passive all-optical diode using asymmetric nonlinear absorption,” Appl. Phys. Lett.91(14), 141118 (2007). [CrossRef]
  25. N. Zhao, H. Zhou, Q. Guo, W. Hu, X. Yang, S. Lan, and X. Lin, “Design of highly efficient optical diodes based on the dynamics of nonlinear photonic crystal molecules,” J. Opt. Soc. Am. B23(11), 2434–2440 (2006). [CrossRef]
  26. X. S. Lin, W. Q. Wu, H. Zhou, K. F. Zhou, and S. Lan, “Enhancement of unidirectional transmission through the coupling of nonlinear photonic crystal defects,” Opt. Express14(6), 2429–2439 (2006). [CrossRef] [PubMed]
  27. V. Grigoriev and F. Biancalana, “Nonreciprocal switching thresholds in coupled nonlinear microcavities,” Opt. Lett.36(11), 2131–2133 (2011). [CrossRef] [PubMed]
  28. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009). [CrossRef]
  29. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, 2002).
  30. J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005). [CrossRef] [PubMed]
  31. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  32. X. Hu, Q. Zhang, Y. Liu, B. Cheng, and D. Zhang, “Ultrafast three-dimensional tunable photonic crystal,” Appl. Phys. Lett.83(13), 2518–2520 (2003). [CrossRef]
  33. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002). [CrossRef] [PubMed]
  34. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron.33(3), 341–348 (1997). [CrossRef]
  35. X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics2(3), 185–189 (2008). [CrossRef]
  36. R. W. Boyd, Nonlinear Optics (Academic Press, 1992).
  37. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006). [CrossRef]
  38. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  39. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron.35(9), 1322–1331 (1999). [CrossRef]
  40. T. Uesugi, B. S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express14(1), 377–386 (2006). [CrossRef] [PubMed]

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