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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 23 — Nov. 13, 2006
  • pp: 11312–11317
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Photonic switching in waveguides using spatial concepts inspired by EIT

Pavel Ginzburg and Meir Orenstein  »View Author Affiliations


Optics Express, Vol. 14, Issue 23, pp. 11312-11317 (2006)
http://dx.doi.org/10.1364/OE.14.011312


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Abstract

Optical waveguide switches based on spatial arrangements inspired by electromagnetic induced transparency (EIT) concepts are presented. Interferometric control of optical signal by an optical gate is accomplished in three configurations. The first is employing a direct spatial version of EIT, the second is exploiting space reciprocity to accomplish performance not achievable in the time domain EIT and finally a novel version of EIT, using tunneling, is transformed into the spatial domain. For all configurations – closed form analysis as well as actual device simulation are presented.

© 2006 Optical Society of America

1. Introduction

We took one step further and encountered also situations that are not feasible in the EIT framework – taking into advantage the reciprocity of the spatial domain vs. the forbidden time reversal. Finally – we exploited a novel EIT scheme – where the coupling field effect is replaced by a level splitting effect stemming from resonant tunneling [5

5. P. Ginzburg and M. Orenstein, “EIT with Tunneling for Slow Light Generation,” (QMD6), Quantum Electronics and Laser Science Conference, Long Beach, California21–26 May, 2006

] and proposed its spatial version as a switch without “external force” (gratings) namely a three waveguides coupler based switch. We would like to emphasize that we are not attempting here to tailor, by the spatial structure, a dispersion response that resembles that of atomic EIT, as reported before by employing periodic structures[6

6. J. Khurgin, “Light slowing down in Moire′ fiber gratings and its implications for nonlinear optics,” Phys. Rev. A 62, 013821 (2000). [CrossRef]

], coupled cavities[7

7. L. Maleki, A. Matsko, A. Savchenkov, and V. Ilchenko, “Tunable delay line with interacting whisperinggallery-mode resonators,” Opt. Lett. 29, 6 (2004). [CrossRef]

] etc. We are just transforming the dynamics of the EIT quantum system to an equivalent propagation in waveguide structure, gaining interesting novel concepts for optical switching.

2. A switch based on Double-period gratings in a slab dielectric waveguide

Fig. 1. (a). Coherent EIT configuration (b) Schematics of an equivalent spatial switching device (c) The propagation constants diagram in the interaction region. m and k are the corresponding coupling coefficients.

zA=jkC2B=jmCzC=jkA+jmB
(1)

where A, B and C are the respective complex amplitudes (integrated over a gratings period) of mode #1 (signal), #2 (gate) and #3 (drain) modes; k and m are the coupling coefficients as depicted in Fig. 1(c). We solve this equation with an input signal in mode #1 and zero initial power at the drain mode #3:

A(0)=1C(0)=0
(2)

The initial amplitude of the gate mode (#2): B(0) will determine the output of the device (on or off).

The solution of Eq. (1) is:

A(z)=1+jC0kn(1cos(nz))B(z)=kmjC0(k2mn+mncos(nz))C(z)=C0sin(nz)
(3)

where n2=(k2+m2) and C0 is a constant depending on the initial excitation of the gate mode, which determines the switch state. We define the states as:

“On” state:

kA(z=0)+mB(z=0)=0
(4a)
C0=0
(4b)
A(z)=1B(z)=kmC(z)=0
(4c)

Under these initial conditions a steady-state solution is obtained, where the input signal propagates through the device with virtually constant amplitude – equivalent to the so called “dark” state of the atomic system. The required ratio between the signal and gate amplitudes is determined by the ratios of the coupling coefficients.

“Off” state

kA(z=0)mB(z=0)=0
(5a)
C0=2jkn
(5b)
A(z)=12k2n2(1cos(nz))B(z)=km+2kn(k2mn+mncos(nz))C(z)=2jknsin(nz)
(5c)

Here, by flipping the initial relative signal – gate phase, the input signal can be completely blocked (periodically), which is equivalent to the “bright” state of the atomic. The maximum signal to gate amplitude ratio for completely blocking the signal is 3 as obtained by:

A(Ldevice)=01cos(nLdevice)=k2m22k21
(6a)
B(Ldevice)=k2m2km,C(Ldevice)=jk2m2kn
(6b)

To validate the results, a slab waveguide device was simulated, using full vectorial beam propagation method (FVBPM) [12

12. W. Huang, C. Xu, S. Chu, and S. Chaudhuri, “The finite-difference vector beam propagation method. analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992). [CrossRef]

]. The interaction zone is comprised of Silicon-Nitride slab ncore=2 surrounded by glass plates with nclad=1.44; the core width is 1.6µm and it supports 3 guided modes at λ0=1.55µm. Two spatial sinusoidal gratings with refractive index modulation (~2.5% depth) – with periods matching the intermodal propagation constant difference were imposed on the waveguide core [Fig. 2(a)]. The simulation results are depicted in Figs. 2(b)–2(c). Although slight oscillations of the amplitude are observed in the “on state” (absent in the equation due to the slowly varying amplitude assumption), the signal is almost completely transferred to the output port in the “on state”, while almost completely eliminated in the “off” one, for signal/gate input power ratio of ~ 3 (for MZI this power ratio is 1). The extinction ratio of this non optimized switch is 16dB, which is accepted for practical modulators. The imperfect light stopping of the “off” state is due to the oscillations and background scattering by the gratings.

Fig. 2. Simulation results (a) Schematic top view of the simulated device; The total electric field amplitude and the power at the three modes are depicted for (b) “off” – no output signal.; (c) “on” – signal out

3. Back reflection switch with double-period slab dielectric waveguide

An important variant of the above inverse lambda scheme is when one of the modes is selected to be a backward propagating mode (Fig. 3). In this figure we represent by solid lines the propagation constants of the “signal” “gate” and “drain” modes which are the first and second forward propagating modes and third backward mode respectively. These modes are participating in our switching scheme, while the complimentary modes (dashed line in Fig. 3), are propagating in the opposite direction and do not interact with the participating modes even when we apply the proper k and m couplings, as outlined in Fig. 3. This scheme does not have a quantum atomic analog due to the fact that back propagation is equivalent to time reversal which is forbidden.

Fig. 3. Level diagram of the back reflection switch (non participating modes – dashed lines)

In this scheme the periodicity does not exist, allowing for a definite and robust switching device without requiring length precision. The signal is reflected, while the gate is in the “off” state and transmitted while the gate is “on”.

The set of coupled mode equations are:

zA=jkCzB=jmCzC=jkAjmB
(7)

where A, B and C are the respective complex amplitudes (integrated over a gratings period) of first and second forward and third backward modes. We solve this equation for the following initial conditions:

A(0)=1C(L)=0
(8)

where L is the device length. The initial phase of the gate mode will be determined according to the requested state of the device. The general solution of set Eq. (7) is:

A(z)=1+jC0kn(cosh(n(zL))cosh(nL))
(9a)
B(z)=km+jC0n(mcosh(n(zL))+k2mcosh(nL))
(9b)
C(z)=C0sinh(n(zL))
(9c)

where n2=(k2+m2) and C0 is a constant determined by the initial conditions.

The “On” state:

kA(z=0)+mB(z=0)=0;C0=0
(10a)
A(z)=1B(z)=kmC(z)=0
(10b)

exhibits perfect transmission of the input signal to the output port.

Flipping the phase of the gate generates the “Off” state:

kA(z=0)mB(z=0)=0;C0=2jkn1cosh(nL)
(11a)
A(z)=1+2k2n2(cosh(n(zL))cosh(nL))cosh(nL)
(11b)
B(z)=k(k2m2)mn2+2kmn2cosh(n(zL))cosh(nL)
(11c)
C(z)=2jknsinh(n(zL))cosh(nL)
(11d)

For a vanishing transmission, the required signal to gate amplitude ratio is bounded by 1:

A(z=L)=0m2k2n2=0k=m
(12a)

Fig. 4. (a). “off” – all signal reflected. (b) “on”- signal transmitted

4. Switch based on “unmotivated” coupling

We simulated by FVBPM the propagation in the interaction zone, comprised of three identical slab dielectric waveguides with dcore=0.5µm and ncore=2 surrounded by a substrate nclad=1.44. The waveguides spacing are d1=0.5µm and d2=0.375µm. The required Signal to Gate power ratio of this device is 3 independently on the absolute signal power. The performance of the switch is shown in Figs. 5(b)–5(c). The extinction ratio of this actual switch according to the simulation is ~16dB.

Fig. 5. Simulation results (a) Schematics top view of the simulated device; the total electric field amplitude and the power at the three waveguides are depicted for (b) “off” – no output signal; (c) “on” – signal out

It is worthwhile to note that this configuration is the one which is similar to an MZI based switch – the output combiner of the latter is based on two waveguides directional coupler, and yet it provides a generalization and broadening of the MZI concept – providing a new dimension of design flexibility.

5. Conclusions

We presented optical waveguide devices inspired by the atomic EIT configuration, and showed that transitions between modes can be controlled linearly, similarly to atomic transitions, enabling a broad family of photonic switching configurations.

References and links

1.

A. Yariv, Optical electronics in modern communications (Oxford University Press, New York, c1997).

2.

G. P. Agrawal, Fiber-optic communication systems (Wiley-Interscience, New York, c2002). [CrossRef]

3.

S. E. Harris, “Electromagnetically induced transparency,” Physics Today 5036–42 (1997). [CrossRef]

4.

A. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 10 pp. 1321–1328 (2001). [CrossRef]

5.

P. Ginzburg and M. Orenstein, “EIT with Tunneling for Slow Light Generation,” (QMD6), Quantum Electronics and Laser Science Conference, Long Beach, California21–26 May, 2006

6.

J. Khurgin, “Light slowing down in Moire′ fiber gratings and its implications for nonlinear optics,” Phys. Rev. A 62, 013821 (2000). [CrossRef]

7.

L. Maleki, A. Matsko, A. Savchenkov, and V. Ilchenko, “Tunable delay line with interacting whisperinggallery-mode resonators,” Opt. Lett. 29, 6 (2004). [CrossRef]

8.

M. Greenberg and M. Orenstein, “Multimode add-drop multiplexing by adiabatic linearly tapered coupling,” Opt. Express 13, 9381–9387 (2005). [CrossRef] [PubMed]

9.

H. Schmidt and R. Ram, “All-optical wavelength converter and switch based on electromagnetically induced transparency,” App. Phys. Lett. 76, 3173–3175 (2000). [CrossRef]

10.

A. Brown and M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption grating,” Opt. Lett. 30, 699–701 (2004). [CrossRef]

11.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

12.

W. Huang, C. Xu, S. Chu, and S. Chaudhuri, “The finite-difference vector beam propagation method. analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992). [CrossRef]

OCIS Codes
(020.1670) Atomic and molecular physics : Coherent optical effects
(050.2770) Diffraction and gratings : Gratings
(200.4660) Optics in computing : Optical logic
(230.3120) Optical devices : Integrated optics devices
(230.7400) Optical devices : Waveguides, slab

ToC Category:
Optical Devices

History
Original Manuscript: September 26, 2006
Revised Manuscript: October 22, 2006
Manuscript Accepted: October 23, 2006
Published: November 13, 2006

Citation
Pavel Ginzburg and Meir Orenstein, "Photonic switching in waveguides using spatial concepts inspired by EIT," Opt. Express 14, 11312-11317 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11312


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References

  1. A. Yariv, Optical electronics in modern communications (Oxford University Press, New York, 1997).
  2. G. P. Agrawal, Fiber-optic communication systems (Wiley-Interscience, New York, 2002). [CrossRef]
  3. S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50,36-42 (1997). [CrossRef]
  4. A. Kenis, I. Vorobeichik, M. Orenstein and N. Moiseyev, "Non-evanescent adiabatic directional coupler," IEEE J. Quantum Electron. 37, 1321-1328 (2001). [CrossRef]
  5. P. Ginzburg and M. Orenstein, "EIT with Tunneling for Slow Light Generation," (QMD6), Quantum Electronics and Laser Science Conference, Long Beach, California 21-26 May, 2006.
  6. J. Khurgin, "Light slowing down in Moire´ fiber gratings and its implications for nonlinear optics," Phys. Rev. A 62, 013821 (2000). [CrossRef]
  7. L. Maleki, A. Matsko, A. Savchenkov, and V. Ilchenko, "Tunable delay line with interacting whispering-gallery-mode resonators," Opt. Lett. 29, 6 (2004). [CrossRef]
  8. M. Greenberg and M. Orenstein, "Multimode add-drop multiplexing by adiabatic linearly tapered coupling," Opt. Express 13, 9381-9387 (2005). [CrossRef] [PubMed]
  9. H. Schmidt, and R. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000). [CrossRef]
  10. A. Brown, and M. Xiao, "All-optical switching and routing based on an electromagnetically induced absorption grating," Opt. Lett. 30, 699-701 (2004). [CrossRef]
  11. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).
  12. W. Huang, C. Xu, S. Chu, and S. Chaudhuri, "The finite-difference vector beam propagation method. analysis and assessment,' J. Lightwave Technol. 10, 295-305 (1992). [CrossRef]

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