Slow Light in Photonic Crystal Cavity Filled with

Slow Light in Photonic Crystal Cavity Filled with Nematic Liquid Crystal Kaisar Khan, a, b,* Khaled Mnaymneh, a, c, Hazem Awada, Imad Hasana and Trevor Halla a b

University of Ottawa, 800 King Edward Avenue, Ottawa, ON, K1N6N5, Canada

Canino School of Engineering Technology, State University of New York, Canton, USA c

Department of Electrical Engineering, University of Michigan, AnnArbor, USA *

[email protected] Abstract

An innovative technique to tune the slow light propagated through photonic crystal cavity filled with E7 type nematic crystal has been simulated and presented. Observed propagating modes in the previously fabricated photonic crystal indicate that both slow and fast modes propagate in the waveguide. Design efforts were made to adjust the propagating modes as well as their group velocities. Numerical studies show that by inserting nematic liquid crystal, designer can achieve additional degree of freedom to tune the device by using external perturbation such as applying heat or electric field. Comparative studies have also been done to see the performance of the devices fabricated in two deferent material platforms (silicon and InP) with an objective to develop economic and efficient functional material systems for building robust integrated photonic devices that have the ability to slow, store, and process light pulses. Key Words: Slow Light, Photonics Crystal, Liquid Crystal

1. Introduction Photonic crystals (PhCs) have received a great deal of research attention because these structures control the properties of light wave. The existence of photonic bands in the energy spectrum as well as complete or absolute photonic band gaps (PBGs) for all wave vectors resulting from the Bragg scattering of electromagnetic waves, have permitted quite a number of analogies with physical properties of semiconductor physics [1-3]. A great deal of the studies devoted to understand the band gaps are based on non-dispersive and positive electric and magnetic responses [4]. Tunable band gaps along with dispersive response functions of the media which are strongly dependent on external parameters have been given some attention to the researchers [2-5]. Many applications of PhCs that include spontaneous emission control, lasers, waveguides, filters, and optical limiters have been proposed. These applications would be significantly enhanced if the band structure of the crystal could be tuned [6]. By filling the voids of a PhC with nematic liquid crystals one obtains a PBG which may be tuned by applying an external electric field or by changing the temperature [6-9]. Two different types of photonic crystals were fabricated: one on silicon and other one on InP substrate. Experimentally measured propagating modes observed in the regular air filled photonic crystal waveguide show similar wavelength dependent group velocity that was observed in the simulation [10]. In this present paper we numerically demonstrate tunability of group velocity of photonic crystal filled with liquid crystal. The infiltration can be performed in vacuum chamber by submerging the PhC sample into a small volume of E7 heated well into the isotropic phase, utilizing the strong capillary action of the pores to draw up the liquid crystal [11-13]. External perturbation such as applying heat or electric field tuned the device. Numerical results based on eigen mode expansion (EME) show complete PBG for higher order modes and some mode shows slow even negative group velocity in some wavelengths [56]. An all-optical network still relies on the basic ability to create and control data buffers, logic switches and tunable signal delays. Such operations usually achieved by just imposing a fixed delay via fiber optic cable; but rather Photonics North 2013, Pavel Cheben, Jens Schmid, Caroline Boudoux, Lawrence R. Chen, André Delâge, Siegfried Janz, Raman Kashyap, David J. Lockwood, Hans-Peter Loock, Zetian Mi, Eds., Proc. of SPIE Vol. 8915, 89151R · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2036423 Proc. of SPIE Vol. 8915 89151R-1 Downloaded From: http://biomedicaloptics.spiedigitallibrary.org/ on 01/15/2014 Terms of Use: http://spiedl.org/terms

the ability to store, switch and time delay photons controllably [14-16]. The proposed slow light tuning device is primarily aim to develop functional material systems with the target of building robust integrated photonic devices that have the ability to slow, store, and process light pulses. These systems allow for efficient propagation of light in regimes where the refractive index dispersion of the material is large and positive, resulting in ultra-slow group velocities and large effective nonlinearities [1- 2,14-15].

2. Photonic Crystal Waveguide Figure 1 shows both schematic and scanning electron micrographs of possible photonic crystal transmission structures with integrated electrodes for liquid crystal tuning. Using an innovative architecture that combines the slow-light of PhC waveguides coupled to PhC cavities [10, 14-15], it is possible to integrated electrodes near such a cavity to tune this local slow-light engineering using the nematic liquid crystals. Figures 1a and 1b show schematic views of possible electrode positions related to the PhC cavity. The input light is launched through the upper waveguide made by omitting the holes of the PhC. Then the waveguide modes are propagated along the direction of waveguide and some selective wavelengths were coupled to the second waveguide at the bottom by the resonant cavity. The light is collected at the end of the bottom waveguide by a sensor. One can use the liquid crystals to tune the slow light regions of the coupling waveguides to the cavity. This would enhance coupling between the waveguides and cavities [15]. With liquid crystals, this enhancement can be turned on and off. By first tuning the slow light and cavity resonances, light could be strongly coupled to the cavity followed by detuning causing the light in the cavity to be stored. Then the tuning would be applied again releasing the stored light into the other waveguide. Such systems would be ideal for optical storage or delay elements. Figure 1c and 1d shows scanning electron micrographs of the physical design of the schematic and potential electrode placement near a PhC cavity for nematic liquid crystal tuning, respectively. At first numerical simulation was done considering InP substrate for the PhC to compare the propagation characteristics observed in the fabricated devices. Later on same simulation was also done for silicon (Si) substrate to predict the propagation behavior of light through the proposed PhC fabricated on Si substrate. With the current industry trend Si technology will provide us better economy.

' vi_r

.

4

(b)

u

(c)

(d)

Fig.1 L3 photonic crystal resonator: (a) biasing for ordinary wave (b) biasing for extra ordinary wave (c) scanning electron micrograph of system in (a)/(b) and (d) possible gate configuration

Proc. of SPIE Vol. 8915 89151R-2 Downloaded From: http://biomedicaloptics.spiedigitallibrary.org/ on 01/15/2014 Terms of Use: http://spiedl.org/terms

3. Tuning of Photonic Crystal Cavity 3.1 Tuning the photonic band gap by heat Nematic liquid crystal (LC) in the hole of the photonic crystal gives the facility to tune the band gap by changing the temperature due to external heat source. The applied heat causes increases the temperature and that temperature stabilized to a particular value after a while. Usually the refractive index of LC varies significantly with temperature. The temperature effect of the LC refractive indices can be expressed by the average refractive index and birefringence. The four-parameter model for describing the temperature dependence of the E7 type nematic LC refractive indices are [7-9]

ne (T ) ≈ A − BT + 2( Δ3n )o (1 − TTc ) β

(1.a)

no (T ) ≈ A − BT − 2( Δ3n )o (1 − TTc ) β

(1.b)

Here T is the temperature in ok and Tc is the critical temperature. The value of the coefficients [A,B] and [(∆n)o , β ] can be found by two-stage fittings. These were evaluated as A=1.723, B=0.000524, (∆n)o = 0.3485 and β =0.2542, at 1550 nm. Experimentally found refractive index using bulk E-7 LC from Marc Inc. has been used to do this curve fitting [7-9] We designed and fabricate a L3 photonic crystal resonator that has a centre frequency around 1550 nm [10]. 2D and 3D Simulations were carried out using Crystal Wave by Photon Design (http://www.photond.com/) [5, 10]. Simulation results indicated a lattice constant (a) of 0.445 μm and a hole radius (r) of 0.131 μm will open a TE band gap of 0.25 to 0.31 (a/λ). This corresponds to an allowed wavelength range of 1.39 to 1.75 μm [10]. Figure 2(a) shows the effective refractive indices of ordinary and extraordinary waves. LC material anisotropy was considered in the numerical calculation [5]. For both polarizations the n decreases as the temperature increases. From the figure it is evident that the extra ordinary wave is more sensitive to temperature than that of the ordinary wave. Figure 2(b) shows the band diagram of the L3 resonant cavity that has holes filled with E7 type LC. A distinct band gap in is observed in around 1.5 um. 3

1.8 ne

2.8

no

1.75

2.6

1.7

2.4 2.2

n

λ, μm

1.65

1.6

2 1.8 1.6

1.55

1.4

1.5 1.2

280

290

300

310 0

TK

320

330

340

1 O

X

M

O

(b)

(a)

Figure 2(a) Effect of temperature change on the refractive indices of E7 type LC (b) TE band diagram of photonic crystal filled with E7 LC

Fig 3 demonstrates the temperature sensitivity of the PBG in resonance cavities if silica glass is used as a substrate and the holes are filled with E7 LC. We observe the appearance of PBG as the temperature increased. Temperature sensitivity of the LC molecule’s refractive index is primarily responsible for this PBG tuning [6]. As expected the extraordinary waves demonstrate rapid tuning than the ordinary wave.


(a)

(b)

(c)

(d)

Figure 3 Effect of temperature change on the band gap of a resonance cavity with lattice atom filled with LC (a) resonance coupler (b) BG at 100C (c) 200C and (d) 300C

3.2 Tuning the Crystal by Applying External Electric Field Application of an external electric field in the LC-PCF alters the modal characteristics by changing the orientation of the LC molecules’ director angle, φ . Applying dc voltage in the electrode placed along the ordinary or extraordinary axis provides a preferential orientation for the LC molecules in the corresponding axis [9-11]. The stronger the applied voltage, the closer the director gets to the corresponding axis (ordinary/extraordinary). The following equation describes the variation of refractive index with the director angle change [16] nn n= 2 2e o 2 2 (2) ne cos φ + no sin φ 1.75 Z

1.7

Φ

Y

1.65 n

X

1.6

1.55

1.5 0

10

20

30

40

50

60

70

80

90

Director Angleo

Fig. 4 Refractive index of E7 LC with molecular direction changes

Orientation of the LC molecule in a particular director angle determines the refractive index. Two boundaries of director angle φ are: 00 corresponds to ordinary polarization occur when there is strong electric field tries to align the LC


molecules in the direction of propagation ( axis Z in the Fig. 4) and 900 correspond to extra ordinary polarization. Fig 4 also demonstrates the refractive index variation of E7 LC with molecular direction changes. 3.3 Group velocity Photonic crystal allows light to propagate due to multiple scattering of the optical wave [1]. Multiple modes may be propagated through the crystal with different dispersions as well as group velocities (i.e., the total time average energy flux of the guided mode). By definition group velocity is the first derivative of frequency with respect to wave vector

Vg =

dω dK

(3)

Fig. 5 shows the numerically evaluated group velocity of first four modes propagating through the photonic crystal resonant cavity. The figure also shows the effect of changing the properties of the material that fills the hole of the photonic crystal. We simulate for different materials such as air, water, E7 LC (for different biasing ordinary (n=1.51), extra ordinary (n=1.71) as well as in between n=1.61 etc). As the refractive of the filling material increases (for LC material it increases with the director angle increases) the group velocity curve shifted towards the longer wavelengths. For the first two higher order modes the group velocity can be slows down at beyond 1.55 um wavelengths. The group velocity of third order mode in the direction of propagation is even anti parallel to the phase velocity of the guided mode. The group velocity is thus negative (assuming the phase velocity is positive) and this type of guided wave is called backward wave. 0.03

0.03 0o

0o

30o

0.025

30o

0.025

60o

60o 900

0.02

0.02

0.015

0.015

Vg

Vg

900

0.01

0.01

0.005

0 1.65

0.005

1.7

1.75

1.8

1.85

1.9

1.95

0 1.25

2

λ , μm

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

λ , μm

(a)

(b)

0.07

0

0o

o

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30o

0.06

30o

-0.01

60o

60o 0

900

0.05

90

-0.02

0.04

Vg

Vg

-0.03

-0.04

0.03

-0.05

0.02

-0.06

0.01

-0.07 0.9

1

1.1

1.2

λ , μm

1.3

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0 0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

λ , μm

(c)

(d)

Fig 5 Wavelength dependent group velocity variation due to external biasing change for first four propagating modes according to the descending order (a) Mode 1 (b) Mode 2 (c) Mode 3 and (d) Mode 4


3.3 Transmission The device was first fabricated on InP substrate and tested to observe the light propagation characteristics for the PhC without infiltrated LC. A 1550 nm CW laser pulse was launched to that regular air filled PhC through the input guided waveguide and collected by a photo detector placed at the end of the output waveguide. The transmission spectra obtain from this experiment is showing the slow light propagation consistent with our simulation [10]. Now to test the tunability the PhC was filled with E7 LC and simulate for the BG and transmission to observe the propagation characteristics. Transmission curve for 1550 nm optical pulse obtained from the FDTD simulation using the Crystal wave shown in the Fig. 6. The material parameters have been setup in such a way that it follows the equation (2) for the refractive index of LC. The figures show that the normalized transmission peak at the PhC waveguide output varies as the refractive index of the material filling the hole of the crystal varies. As the director angle increases (due to the increased biasing voltage for the extraordinary wave) the peak shift to the longer wavelength. Resonance wavelength of the cavity readjusted due to change of material parameters. Both TE and TM wave behave similarly in response to this external electrical biasing. Detail experimental results for PhC filled with E7 nematic crystal will be reported in the near future. 1

1

90o

0.9

o

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30 0

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90o 60o 30o 00

0.7

Transmission

Transmission

0.8

60o

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0.6 0.5 0.4 0.3

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0 1

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λ, μm

1.8

2

2.2

0 1

1.2

1.4

1.6

1.8

2

2.2

λ, μm

(a)

(b)

Fig 6 Normalized transmission at the output of the waveguide at different biasing for (a) TE wave and (b) TM wave.

4.0 Conclusion Comprehensive studies have been done to observe the performance of the photonic crystal devices fabricated in two deferent material platforms (silicon and InP). Proposed photonic crystals filled with nematic liquid crystal material add the tunability of the device. The numerical results show that the group velocity and the resonance peak can be shifted either by adjusting geometry of the photonic crystal or by tuning the LC material by external perturbation. Also we observe tunable slow light or even posses negative refraction for certain light wave modes propagating through the photonic crystal waveguide.

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