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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 16749–16759
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Vertical-cavity surface-emitting laser with liquid crystal overlay

Krassimir Panajotov and Hugo Thienpont  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 16749-16759 (2011)
http://dx.doi.org/10.1364/OE.19.016749


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Abstract

We perform a theoretical study of the spectral and polarization threshold characteristics of Vertical-Cavity Surface-Emitting Lasers with Liquid Crystal overlay (LC-VCSEL) in three different configurations of the LC cell. Our model predicts the possibility of selecting between two orthogonal directions of linear polarization (LP) of the fundamental mode (x or y LP) by choosing appropriate LC length. It further predicts very strong polarization discrimination with LP mode threshold gain difference as large as several times the threshold gain of the lasing mode. We also numerically demonstrate an active control of light polarization by electro-optically tuning the LC director and show that either polarization switching between x and y LP modes or continuous change of the LP direction would be possible. Finally, we numerically demonstrate that LC-VCSEL would be capable of efficient wavelength tuning.

© 2011 OSA

1. Introduction

Combining photonic components with liquid crystals (LC) extends their functionality by making use of the LC exceptionally strong electro-optical and nonlinear properties [1

1. I.-C. Khoo, Liquid Crystals (Wiley, 2007). [CrossRef]

]. Examples can be found for one dimensional (1D) photonic crystals and cavities [2

2. S. M. Weiss, H. Ouyang, J. Zhang, and P. M. Fauchet, “Electrical and thermal modulation of silicon photonic bandgap microcavities containing liquid crystals,” Opt. Express 13, 1090–1097 (2005). [CrossRef] [PubMed]

, 3

3. V. Y. Zyryanov, S. A. Myslivets, V. A. Gunyakov, A. M. Parshin, V. G. Arkhipkin, V. F. Shabanov, and W. Lee, “Magnetic-field tunable defect modes in a photonic-crystal/liquid-crystal cell,” Opt. Express 18, 1283–1288 (2010). [CrossRef] [PubMed]

], 2D photonics crystal slabs [4

4. Ch. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, “Tunable photonic crystals fabricated in III–V semiconductor slab waveguides using infiltrated liquid crystals,” Appl. Phys. Lett. 82, 2767–2769 (2003). [CrossRef]

] and fibers [5

5. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

, 6

6. F. Du, Y.-Q. Lu, and S.-T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2004). [CrossRef]

], 3D photonic crystals [7

7. Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001). [CrossRef]

] and metamaterials [8

8. I.-C. Khoo, A. Diaz, J. Liou, M. V. Stinger, J. Huang, and Y. Ma, “Liquid crystal tunable optical metamaterias,” IEEE J. Sel. Top. Quantum Electron. 16, 410–417 (2010). [CrossRef]

]. Added by the LC values are the temperature and/or electric (or magnetic) field wavelength tunability as well as the strong optical anisotropy and nonlinearity. Wavelength tunability of external cavity semiconductor lasers have also been demonstrated by intracavity Lyot-type LC filter [9

9. J. R. Andrews, “Low voltage wavelength tuning of an external cavity diode laser using a nematic liquid crystal-containing birefringent filter,” IEEE Photon. Technol. Lett. 2, 334–336 (1990). [CrossRef]

] and recently by LC-based tunable mirror [10

10. J. De Merlier, K. Mizutani, S. Sudo, K. Naniwae, Y. Furushima, S. Sato, K. Sato, and K. Kudo, “Full C-band external cavity wavelength tunable laser using a liquid-crystal-based tunable mirror,” IEEE Photon. Technol. Lett. 17, 681–683 (2005). [CrossRef]

]. LCs have also been implemented in a feedback-loop of Vertical-Cavity Surface-Emitting Lasers in order to achieve polarization control [11

11. C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Electrical polarization control of vertical-cavity surface-emitting lasers using polarized feedback and a liquid crystal,” IEEE Photon Technol. Lett. 11, 155–157 (1999). [CrossRef]

] and high contrast modulation [12

12. C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Enhancement of a liquid-crystal modulator using an external-cavity VCSEL,” IEEE Photon. Technol. Lett. 11, 940–942 (1999). [CrossRef]

]. In these experiments the external cavity containing the LC is several tens of cm long resulting in a bulky system. We have recently demonstrated polarization control of VCSEL [13

13. K. Panajotov, M. Arizaleta, M. Camarena, and H. Thienpont, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004). [CrossRef]

, 14

14. M. Arteaga, M. Lpez-Amo, H. Thienpont, and K. Panajotov, “Tailoring light polarization in vertical cavity surface emitting lasers by isotropic optical feedback from an extremely short external cavity,” Appl. Phys. Lett. 89, 091102 (2006). [CrossRef]

] and wavelength tuning of edge-emitting semiconductor laser [15

15. M. A. Arteaga, M. Lopez-Amo, J. Hernandez, H. Thienpont, and K. Panajotov, “Spectral properties of edge-emitting semiconductor laser subject to optical feedback from extremely short external cavity,” Opt. Quantum Electron. 40, 69–81 (2008). [CrossRef]

] with optical feedback from piezo-electrically controlled isotropic (air) extremely short external cavity, of the order of a few μm. Filling in this cavity with a LC would form in the case of VCSEL a laser with a LC overlay (LC-VCSEL), in which the normal VCSEL cavity is optically coupled to a cavity containing LC. Such devices can be independently biased using separate electrical contacts for the VCSEL and the LC cell and potentially offer extended functionality than common VCSELs. Monolithic Coupled-Cavity VCSELs (CC-VCSELs) have been first investigated by Stanley et al. [16

16. R. P. Stanley, R. Houdre, U. Oesterle, M. Illegems, and C. Wesbuch, “Coupeld semiconductor microcavities,” Appl. Phys. Lett. 65, 2093–2095 (1994). [CrossRef]

] demonstrating pronounced wavelength anticrossing effect: two different resonant wavelengths appear in the reflectance spectrum with separation that depends on the coupling mirror transmission. Light emission in optically pumped [17

17. P. Pellandini, R. P. Stanley, R. Houdre, U. Oesterle, M. Illegems, and C. Weisbuch, “Dual-wavelength emission from coupled semiconductor microcavity,” Appl. Phys. Lett. 71, 864–866 (1997). [CrossRef]

] or electrically injected [18

18. M. Brunner, K. Gulden, R. Hovel, M. Moser, J. F. Carlin, R. P. Stanley, and M. Illegems, “Continuous-wave dual-wavelength lasing in a two-section vetrical-cavity laser,” IEEE Photon. Technol. Lett. 12, 1316–1318 (2000). [CrossRef]

, 19

19. D. M. Grasso, K. D. Choquette, D. K. Serkland, G. M. Peake, and K. M. Geib, “High slope efficiency measured from a composite-resonator vertical-cavity laser,” IEEE Photon. Technol. Lett. 18, 1019–1021 (2006). [CrossRef]

] CC-VCSELs can occur on a single (short or long) wavelength mode, as well as on the two of them simultaneously. The experimentally measured single and double wavelength threshold characteristics of CC-VCSELs showed good agreement with theory [20

20. V. Badilita, J.-F. Carlin, M. Ilegems, and K. Panajotov, “Rate-equation model for coupled-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 1646–1656 (2004). [CrossRef]

]. The goal of this paper is to provide insight in the operation and design of coupled-cavity LC-VCSELs. To this aim we make use of a simple transfer-matrix method recently applied for studying threshold characteristics of CC-VCSELs [21

21. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

]. We investigate the spectral and polarization characteristics of the LC-VCSELs for the case of electrically modulated LC cavity and fundamental transverse-mode operation. We show that such a LC-VCSEL can act as a voltage-controlled polarization switching or wavelength tuning device that is decoupled from the laser design. When the reflectivity of the coupling mirror is reduced to zero, much enhanced wavelength tuning Δλ is possible as recently suggested for optically pumped VCSEL containing nano polymer dispersed LC material [22

22. V. Verbrugge, J.-L. de Bougrenet de la Tocnaye, and L. Dupont, “C-band wavelength-tunable vertical-cavity laser using a nano polymer dispersed liquid crystal material,” Opt. Commun. 215, 353–359 (2003). [CrossRef]

]. Experimentally, Δλ of 30 and 40 nm has been recently demonstrated for optically pumped 1.5 μm InGaAs/InP quantum well VCSEL with a-Si/a-SiNx and SiO 2/TiO 2 Bragg mirrors [23

23. O. Castany, L. Dupont, A. Shuaib, J. P. Gauthier, C. Levallois, C. Paranthoen, N. Chevalier, O. Durand, and A. Le Corre, “Tunable VCSEL with intracavity liquid crystal layer,” EOS Annual Meeting (October 2010).

, 24

24. O. Castany, L. Dupont, C. Paranthoen, C. Levallois, A. Le Corre, and S. Loualiche, “Liquid crystal micro-cells for tunable VCSELs,” Journes nationales sur les technologies mergentes (November 2010).

].

2. VCSEL with liquid crystal overlay: longitudinal and transversal LC cells

Three LC-VCSEL structures are considered as shown schematically in Fig. 1: one longitudinal and two transversal LC cells with electric field applied to the LC, respectively, along (ELC || Oz), Fig. 1(a) and transverse (ELC || Oy), Figs. 1(b) and 1(c) to the light propagation - or VCSEL cavity. We call hereafter these three types of LC-VCSEL cells L 1, T 1 and T 2, respectively. Nematic LC is considered with planar alignment of the LC molecules close to the glass boundaries (the longer axis of the LC molecules along Oy, Oz and Ox axes in Figs. 1(a)–1(c), respectively). Such alignment could be achieved by depositing and rubbing thin polyimide layers on top of the transparent ITO (indium tin oxide) electrodes of the glass plates forming the LC cell. The length of the LC cell for the case of Fig. 1(a) is determined by the spacer used to separate the glass plate from the plate on which the VCSEL wafer is fixed and can vary from μm-s to hundreds of μm-s, while the transverse sizes can be very large (cm-s). An electric field ELC applied to the LC cell will turn the LC director (the averaged direction of the longer axis of the LC molecules) at an angle θ, which depends on the distance to the anchoring boundary, as schematically illustrated in Fig. 1 [1

1. I.-C. Khoo, Liquid Crystals (Wiley, 2007). [CrossRef]

]. To simplify the calculations, we consider that this angle is constant in the area above the VCSEL aperture where light is propagating. This assumption is quite reasonable for transversal LC cells as the VCSEL aperture of several micrometers is much less the size of the LC cell in x- (and y-) directions: hundred(s) (thousands) of μm. However, it is questionable for the case of thin longitudinal LC cell. Calculations of the distribution of the LC director orientation θ(z) for this case will be presented in section 5 assuming hard-boundary conditions.

Fig. 1 VCSEL with LC overlay: (a) longitudinal (type L 1) and (b)–(c) transversal LC cells with electric field applied to the LC, respectively, along (ELC || Oz) and transverse (ELC || Oy) to the light propagation direction (or VCSEL cavity). Transversal type LC-VCSEL cells T 1 (b) and T 2 (c) are with planar alignment of the LC molecules close to the glass boundaries along Oz and Ox, respectively.

For longitudinal LC cell (Fig. 1(a)) and transversal LC cell with planar alignment along the Oz-axis (Fig. 1(b)) the LC director (along the Oz′ axis) is turned in the yOz plane at an angle θ with respect to the Oz axis; the coordinate transformation matrix being:
[zy]=[cos(θ)sin(θ)sin(θ)cos(θ)][zy].
(1)
Substituting this expression in the equation for the refractive index ellipsoid [1

1. I.-C. Khoo, Liquid Crystals (Wiley, 2007). [CrossRef]

, 25

25. M. Born and E. Wolf, Principles of Optics (Wiley, 1970).

]:
x2no2+y2no2+z2ne2=1,
(2)
gives for the refractive indices for light traveling along Oz axis and linearly polarized along the Ox and Oy axes, respectively:
nx=no,ny=noneno2sin2(θ)+ne2cos2(θ).
(3)
Here no and ne are the LC ordinary and extraordinary refractive indices.

For transversal LC cell with planar alignment along the Ox-axis (Fig. 1(c)) the LC director along Ox′ is turned in the xOy plane at an angle ϕ with respect to the Ox axis, i.e.:
[xy]=[cos(ϕ)sin(ϕ)sin(ϕ)cos(ϕ)][xy].
(4)
Transversely polarized light propagating along the Oz axis will experience the highest birefringence if it is linearly polarized along Ox′ and Oy′, i.e.:
nx=ne,ny=no.
(5)
We consider, without lost of generality, GaAs QW VCSEL lasing around 850nm; the obtained results are generic and would be similar for other VCSEL material compositions providing lasing on different wavelengths. Spectral dependencies of the complex refractive indices of different layers are not taken into account to keep the study simple and easily reproducible; considering material dispersion does not change the basic results of our study. The VCSEL and LC parameters are listed in Table 1. In the following, we use as parameters the number of pairs Ntop of the VCSEL top distributed Bragg mirror (DBR) and the LC length LLC.

Table 1. VCSEL and LC Parameters

table-icon
View This Table

Our procedure of finding the resonant wavelengths and threshold gains of the LC-VCSEL is based on the transfer matrix method [25

25. M. Born and E. Wolf, Principles of Optics (Wiley, 1970).

], by imposing the condition that there is no in-coming field to the whole LC-VCSEL multilayer structure [21

21. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

]. The real and imaginary parts of the so obtained implicit characteristic equation are solved for two variables, namely the resonant wavelength λres and the imaginary part of the quantum well refractive index nQWim [21

21. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

]. The threshold gain is then obtained as Gth=4πnQWim/λres.

3. LC-VCSEL: optical field distribution and threshold gain

In Fig. 2 we present the optical power distributions for two modes of LC-VCSEL with Ntop = 27 in Figs. 2(a)–2(d), which corresponds to a commercial off-shelf VCSEL and with Ntop = 0 in Figs. 2(e)–2(f), i.e. half a VCSEL without the top-DBR. The LC cell length and mirror are: Figs. 2(a) and 2(b) LLC = 5.05μm and ITO/Au mirror; Figs. 2(c) and 2(d): LLC = 5.08μm and ITO/dielectric DBR mirror and Figs. 2(e) and 2(f): LLC = 5.1μm and ITO/dielectric DBR mirror. Refractive index profile of the LC-VCSEL structure is shown by black lines. LC ordinary refractive index is considered, which corresponds to x-linearly polarized (LP) mode in LC-VCSEL type L 1 or T 1.

Fig. 2 Optical power distributions for two modes of LC-VCSEL with: (a) and (b) Ntop = 27, LLC = 5.05μm and ITO/Au mirror; (c) and (d) Ntop = 27, LLC = 5.08μm and ITO/dielectric DBR mirror and (e) and (f) Ntop = 0, LLC = 5.1μm and ITO/dielectric DBR mirror. LC ordinary refractive index is considered, which corresponds to x-LP mode in LC-VCSEL type L 1 or T 1. Refractive index profile of the LC-VCSEL structure is shown by black lines.

For LC cell with ITO/dielectric DBR mirror and off-shelf VCSEL, the calculated resonant wavelengths and threshold gains of such two realistic modes are: Fig. 2(c) λ = 0.85131 μm, Gth = 1357cm −1 and Fig. 2(d) λ = 0.85222 μm, Gth = 4814cm −1. Now, as can be seen from Figs. 2(c) and 2(d), the optical field distributions of the two modes are quite similar, resulting in much smaller difference of the threshold gains. We should mention that modes with very small confinement factors and huge threshold gains, like the one shown in Fig. 2(a) also exist for this LC cell but will not be considered hereafter.

For LC cell with ITO/dielectric DBR mirror and half-VCSEL, the calculated resonant wavelengths and threshold gains are: Fig. 2(e) λ = 0.84092 μm, Gth = 2755cm −1 and Fig. 2(f) λ = 0.86839 μm, Gth = 3371cm −1. The optical field now occupies largely the LC region leading to increased threshold gain in comparison to VCSEL with full top-DBR.

4. LC-VCSEL: polarization control and electro-optic polarization switching

Stand-alone VCSELs emit linearly polarized (LP) fundamental mode oriented along either [110] or [11̄0] crystallographic direction due to small residual-stress birefringence (Δn = |n [110]n [11̄0]| ∼ 10−4) [26

26. A. K. Jansen van Doornen, M. P. van Exter, and J. P. Woerdman, “Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers,” Appl. Phys. Lett. 69, 1041–1043 (1996). [CrossRef]

, 27

27. K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” in Nanoscale Linear and Nonlinear Optics, M. Bertolotti, C. M. Bowden, and C. Sibilia, eds. (American Institute of Physics, 2001), Vol. 560, pp. 403–417.

]. The LC birefringence, (Δn = 0.2 for E7 LC considered here), would easily overcome this small inherent VCSEL birefringence and would therefore determine light polarization orientation, i.e. the LC overlay will make it possible to control the polarization of the emitted light by the VCSEL. We demonstrate this polarization control in Fig. 3, where the resonant wavelengths λ and threshold gains Gth for two LP modes oriented along x and y axes are shown as a function of the LC cell length LLC. The LC cell is with either a metal (Figs. 3(a), 3(b) and 3(e), 3(f)) or a dielectric (Figs. 3(c), 3(d)) LC mirror. The LC refractive index is given by Eq. (3) and we take θ = π/2, corresponding to L 1 cell without electric field ELC applied to it and to T 1 cell with ELC such that the LC molecules are completely turned along it. As can be seen from Fig. 3, the wavelength splitting between the two orthogonal LP modes and their threshold gain difference, ΔGth=|GthxGthy|, strongly increase at certain LC cell lengths where the two cavities, the VCSEL and the LC one, strongly interact with each other. At these resonances the two cavities share the optical field, i.e. much larger than out-of-resonance part of the optical field resides in the LC cavity (see e.g. Fig. 2(d)). This leads to a strong decrease of the QW confinement factor and, therefore, to a huge increase of the threshold gain. Simultaneously, the wavelength splitting between the orthogonal LP modes increases as the LC confinement factor has increased. Quite importantly, the large LC birefringence makes the resonances for the two orthogonal LP modes happen at different LC lengths. Therefore, the threshold gain difference could become very large; for example, at LC length of LLC = 5.2(5.23)μm the threshold gain difference is as large as ΔGth = 2477(1346)cm −1 for the case of metal (dielectric) LC mirror, i.e. several times larger than the threshold gain itself. As can be deduced from Figs. 3(b), 3(d), and 3(f), a continuous change of the LC length would lead to consecutive polarization switching between the x and y LP modes (and eventually mode competition (hoping) at the points where the Gth curves cross). By choosing an appropriate LC length one can therefore control the polarization of the light emitted by the LC-VCSEL. Moreover, a range of LC lengths exists where the threshold gain difference is larger than the threshold gain itself, i.e. where a strong polarization discrimination is possible. Scaling the length of the LC cell does not impact the polarization selection mechanism: it remains nearly the same as can be seen by comparing (a,b) and (e,f) graphs of Fig. 3. The wavelength splitting between successive longitudinal modes of the LC-VCSELs in Figs. 3(a) and 3(b) is about 40nm and 4.5nm, respectively.

Fig. 3 Resonant wavelengths λ and threshold gains Gth for two LP modes oriented along x (green lines) and y (blue lines) axes as a function of the LC cell length LLC. Longitudinal, L 1, and transversal, T 1, LC cells are considered with θ = π/2 and either a metal ((a),(b),(e) and (f)) or a dielectric ((c) and (d)) LC mirror. In (e) and (f) the LC cell is 10 times longer.

Fig. 4 Resonant wavelengths λ (a,c) and threshold gains Gth (b, d) for two LP modes oriented along x (green lines) and y (blue lines) as a function of the LC director angle θ for the case of LC cell with a metal mirror and for two LC lengths: (a,b) LLC = 5.1μm and (c,d) LLC = 50.2μm. Dotted lines in a) and b) are for the case of realistic LC losses of 23 cm −1.

According to Figs. 3(b), 3(d), 3(f), a precise control of the LC length (within 0.1μm) seems necessary in order to achieve gthx>gthy, i.e. a condition that ensures electro-optic polarization control and modulation. We would like to stress that such precise control of the LC length is actually not necessary when considering a practical LC-VCSEL device. A very simple and practical way to easily match the above condition would be to exploit the temperature dependence of the LC refractive index. As an example, let us consider a LC cell length of LLC = 5.2μm such that the green curve is bellow the blue curve (c.f. Fig. 3(b)). Then, taking LC thermooptic coefficient of dn/dT ≈ 1 × 10−3, a temperature change of 40 degrees would bring the green curve above the blue curve, thus making it possible to electro-optically control the LC-VCSEL polarization. Less temperature change would be required for longer LC cells.

We now discuss electro-optical modulation for the case of T 2 LC cell (cf. Fig. 1(c)). As shown in Fig. 3, we can chose appropriate EC length such, that the threshold gain for the y LP mode at ELC = 0 is smaller that the one for the x LP ( Gthx<Gthy). Now, with applying an external electric field ELC the LC director will turn in the xOy plane at an angle ϕ as given by Eq. (3). As a result, the threshold gains for the LP modes oriented along Ox’ and Oy’ axis will not change: Gthx=Gthx<Gthy=Gthy. Therefore, we expect that LC cell type T 2 would allow to electro-optically turn the direction of the LP fundamental mode of the LC-VCSEL at any angle in the xOy plane.

We conclude this section by mentioning that the speed of electro-optical polarization switching depends on the LC dynamical response and the length of the LC cell and is in the millisecond range.

5. LC-VCSELs for wavelength tuning

Fig. 5 Resonant wavelengths λ (a,c) and threshold gains Gth (b, d) for two LP modes oriented along x (green lines) and y (blue lines) as a function of the LC director angle θ for the case of half-VCSEL (without the top DBR) and LC cell with a dielectric mirror and for two LC lengths: (a, b) LLC = 0.64μm and (c, d) LLC = 5.11μm.

So far, we have considered that the LC director angle θ is constant in the area above the VCSEL aperture where light is propagating. As mentioned above, this assumption is questionable for a very thin longitudinal LC cell (c.f. Fig. 1(a)). In order to calculate the longitudinal distribution of the LC director θ (z;E) for a given electric field E, we assume hard-boundary conditions θ (z = 0) = θ (z = LLC) = 0 and solve the boundary-value problem in one-elastic-constant (K) approximation, namely [1

1. I.-C. Khoo, Liquid Crystals (Wiley, 2007). [CrossRef]

]:
Kd2θdz2+ΔɛE2sin(θ)cos(θ)=0,
(6)
where Δɛ is the dielectric anisotropy and ɛ 0 is the vacuum permittivity.

The results for a longitudinal cell of length LLC = 1.2μm filled in with E7 LC (K = 11 × 10−12 Nɛ = 13.8 [28

28. J. A. Yeh, C. A. Chang, C.-C. Cheng, J.-Y. Huang, and S. H. Hsu, “Microwave characteristics of liquid-crystal tunable capacitors,” IEEE J. Dev. Lett. 26, 451–453 (2005). [CrossRef]

]) are presented in Fig. 6(a) for three LC voltages of U = 2, 3 and 10V (dotted,dashed and solid lines, respectively). Once the distribution θ(z;E) is known, we approximate it by a piecewise-constant function, i.e. we divide the LC layer in a number NLC of homogenous layers with fixed but different director angle and calculate the LC-VCSEL resonant wavelength and threshold gain by the transfer matrix method (we take NLC = 40). The results are shown in Figs. 6(b) and 6(c) for two LC lengths: LLC = 0.64μm (blue line) and LLC = 1.2μm (red line) and demonstrate that indeed, electrical wavelength tuning is possible for such very thin LC cells. However, as evident by comparing Fig. 5(a) and Fig. 6(b) (blue curve) the assumption of constant along the LC length θ somehow overestimates the induced wavelength shift. Nevertheless, comparable wavelength span can still be achieved by increasing the length of the LC cell - c.f. Fig. 6(b) (red curve). Figure 6(b) provides further information for the LC voltage necessary for a certain wavelength shift, and also reveals that the LC voltage has to exceed a certain voltage, the so called Freedericksz threshold voltage, before the LC director starts reorienting according to the applied electric field [1

1. I.-C. Khoo, Liquid Crystals (Wiley, 2007). [CrossRef]

].

Fig. 6 (a) Orientation of the LC director θ along the length of the LC cell type L 1 for LC voltage of U = 2V(dotted line), U = 3V(dashed line) and U = 10V (solid line). Resonant wavelength λ (b) and threshold gain Gth (c) for the y LP mode as a function of the voltage U for the case of half-VCSEL and LC cell with a dielectric mirror and for two LC lengths: LLC = 0.64μm (blue line) and LLC = 1.2μm (red line).

6. Conclusions

Acknowledgments

The authors acknowledge the financial support of FWO-Vlaanderen project G.0656.09N and of OZR-VUB. KP acknowledges fruitful discussions with Profs. Kristiaan Neyts, Jeroen Beeckman and Minko Petrov.

References and links

1.

I.-C. Khoo, Liquid Crystals (Wiley, 2007). [CrossRef]

2.

S. M. Weiss, H. Ouyang, J. Zhang, and P. M. Fauchet, “Electrical and thermal modulation of silicon photonic bandgap microcavities containing liquid crystals,” Opt. Express 13, 1090–1097 (2005). [CrossRef] [PubMed]

3.

V. Y. Zyryanov, S. A. Myslivets, V. A. Gunyakov, A. M. Parshin, V. G. Arkhipkin, V. F. Shabanov, and W. Lee, “Magnetic-field tunable defect modes in a photonic-crystal/liquid-crystal cell,” Opt. Express 18, 1283–1288 (2010). [CrossRef] [PubMed]

4.

Ch. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, “Tunable photonic crystals fabricated in III–V semiconductor slab waveguides using infiltrated liquid crystals,” Appl. Phys. Lett. 82, 2767–2769 (2003). [CrossRef]

5.

T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

6.

F. Du, Y.-Q. Lu, and S.-T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2004). [CrossRef]

7.

Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001). [CrossRef]

8.

I.-C. Khoo, A. Diaz, J. Liou, M. V. Stinger, J. Huang, and Y. Ma, “Liquid crystal tunable optical metamaterias,” IEEE J. Sel. Top. Quantum Electron. 16, 410–417 (2010). [CrossRef]

9.

J. R. Andrews, “Low voltage wavelength tuning of an external cavity diode laser using a nematic liquid crystal-containing birefringent filter,” IEEE Photon. Technol. Lett. 2, 334–336 (1990). [CrossRef]

10.

J. De Merlier, K. Mizutani, S. Sudo, K. Naniwae, Y. Furushima, S. Sato, K. Sato, and K. Kudo, “Full C-band external cavity wavelength tunable laser using a liquid-crystal-based tunable mirror,” IEEE Photon. Technol. Lett. 17, 681–683 (2005). [CrossRef]

11.

C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Electrical polarization control of vertical-cavity surface-emitting lasers using polarized feedback and a liquid crystal,” IEEE Photon Technol. Lett. 11, 155–157 (1999). [CrossRef]

12.

C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Enhancement of a liquid-crystal modulator using an external-cavity VCSEL,” IEEE Photon. Technol. Lett. 11, 940–942 (1999). [CrossRef]

13.

K. Panajotov, M. Arizaleta, M. Camarena, and H. Thienpont, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004). [CrossRef]

14.

M. Arteaga, M. Lpez-Amo, H. Thienpont, and K. Panajotov, “Tailoring light polarization in vertical cavity surface emitting lasers by isotropic optical feedback from an extremely short external cavity,” Appl. Phys. Lett. 89, 091102 (2006). [CrossRef]

15.

M. A. Arteaga, M. Lopez-Amo, J. Hernandez, H. Thienpont, and K. Panajotov, “Spectral properties of edge-emitting semiconductor laser subject to optical feedback from extremely short external cavity,” Opt. Quantum Electron. 40, 69–81 (2008). [CrossRef]

16.

R. P. Stanley, R. Houdre, U. Oesterle, M. Illegems, and C. Wesbuch, “Coupeld semiconductor microcavities,” Appl. Phys. Lett. 65, 2093–2095 (1994). [CrossRef]

17.

P. Pellandini, R. P. Stanley, R. Houdre, U. Oesterle, M. Illegems, and C. Weisbuch, “Dual-wavelength emission from coupled semiconductor microcavity,” Appl. Phys. Lett. 71, 864–866 (1997). [CrossRef]

18.

M. Brunner, K. Gulden, R. Hovel, M. Moser, J. F. Carlin, R. P. Stanley, and M. Illegems, “Continuous-wave dual-wavelength lasing in a two-section vetrical-cavity laser,” IEEE Photon. Technol. Lett. 12, 1316–1318 (2000). [CrossRef]

19.

D. M. Grasso, K. D. Choquette, D. K. Serkland, G. M. Peake, and K. M. Geib, “High slope efficiency measured from a composite-resonator vertical-cavity laser,” IEEE Photon. Technol. Lett. 18, 1019–1021 (2006). [CrossRef]

20.

V. Badilita, J.-F. Carlin, M. Ilegems, and K. Panajotov, “Rate-equation model for coupled-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 1646–1656 (2004). [CrossRef]

21.

K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

22.

V. Verbrugge, J.-L. de Bougrenet de la Tocnaye, and L. Dupont, “C-band wavelength-tunable vertical-cavity laser using a nano polymer dispersed liquid crystal material,” Opt. Commun. 215, 353–359 (2003). [CrossRef]

23.

O. Castany, L. Dupont, A. Shuaib, J. P. Gauthier, C. Levallois, C. Paranthoen, N. Chevalier, O. Durand, and A. Le Corre, “Tunable VCSEL with intracavity liquid crystal layer,” EOS Annual Meeting (October 2010).

24.

O. Castany, L. Dupont, C. Paranthoen, C. Levallois, A. Le Corre, and S. Loualiche, “Liquid crystal micro-cells for tunable VCSELs,” Journes nationales sur les technologies mergentes (November 2010).

25.

M. Born and E. Wolf, Principles of Optics (Wiley, 1970).

26.

A. K. Jansen van Doornen, M. P. van Exter, and J. P. Woerdman, “Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers,” Appl. Phys. Lett. 69, 1041–1043 (1996). [CrossRef]

27.

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” in Nanoscale Linear and Nonlinear Optics, M. Bertolotti, C. M. Bowden, and C. Sibilia, eds. (American Institute of Physics, 2001), Vol. 560, pp. 403–417.

28.

J. A. Yeh, C. A. Chang, C.-C. Cheng, J.-Y. Huang, and S. H. Hsu, “Microwave characteristics of liquid-crystal tunable capacitors,” IEEE J. Dev. Lett. 26, 451–453 (2005). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(160.3710) Materials : Liquid crystals
(250.7260) Optoelectronics : Vertical cavity surface emitting lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 17, 2011
Revised Manuscript: April 10, 2011
Manuscript Accepted: June 9, 2011
Published: August 15, 2011

Citation
Krassimir Panajotov and Hugo Thienpont, "Vertical-cavity surface-emitting laser with liquid crystal overlay," Opt. Express 19, 16749-16759 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-16749


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References

  1. I.-C. Khoo, Liquid Crystals (Wiley, 2007). [CrossRef]
  2. S. M. Weiss, H. Ouyang, J. Zhang, and P. M. Fauchet, “Electrical and thermal modulation of silicon photonic bandgap microcavities containing liquid crystals,” Opt. Express 13, 1090–1097 (2005). [CrossRef] [PubMed]
  3. V. Y. Zyryanov, S. A. Myslivets, V. A. Gunyakov, A. M. Parshin, V. G. Arkhipkin, V. F. Shabanov, and W. Lee, “Magnetic-field tunable defect modes in a photonic-crystal/liquid-crystal cell,” Opt. Express 18, 1283–1288 (2010). [CrossRef] [PubMed]
  4. Ch. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, “Tunable photonic crystals fabricated in III–V semiconductor slab waveguides using infiltrated liquid crystals,” Appl. Phys. Lett. 82, 2767–2769 (2003). [CrossRef]
  5. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]
  6. F. Du, Y.-Q. Lu, and S.-T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2004). [CrossRef]
  7. Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001). [CrossRef]
  8. I.-C. Khoo, A. Diaz, J. Liou, M. V. Stinger, J. Huang, and Y. Ma, “Liquid crystal tunable optical metamaterias,” IEEE J. Sel. Top. Quantum Electron. 16, 410–417 (2010). [CrossRef]
  9. J. R. Andrews, “Low voltage wavelength tuning of an external cavity diode laser using a nematic liquid crystal-containing birefringent filter,” IEEE Photon. Technol. Lett. 2, 334–336 (1990). [CrossRef]
  10. J. De Merlier, K. Mizutani, S. Sudo, K. Naniwae, Y. Furushima, S. Sato, K. Sato, and K. Kudo, “Full C-band external cavity wavelength tunable laser using a liquid-crystal-based tunable mirror,” IEEE Photon. Technol. Lett. 17, 681–683 (2005). [CrossRef]
  11. C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Electrical polarization control of vertical-cavity surface-emitting lasers using polarized feedback and a liquid crystal,” IEEE Photon Technol. Lett. 11, 155–157 (1999). [CrossRef]
  12. C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Enhancement of a liquid-crystal modulator using an external-cavity VCSEL,” IEEE Photon. Technol. Lett. 11, 940–942 (1999). [CrossRef]
  13. K. Panajotov, M. Arizaleta, M. Camarena, and H. Thienpont, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004). [CrossRef]
  14. M. Arteaga, M. Lpez-Amo, H. Thienpont, and K. Panajotov, “Tailoring light polarization in vertical cavity surface emitting lasers by isotropic optical feedback from an extremely short external cavity,” Appl. Phys. Lett. 89, 091102 (2006). [CrossRef]
  15. M. A. Arteaga, M. Lopez-Amo, J. Hernandez, H. Thienpont, and K. Panajotov, “Spectral properties of edge-emitting semiconductor laser subject to optical feedback from extremely short external cavity,” Opt. Quantum Electron. 40, 69–81 (2008). [CrossRef]
  16. R. P. Stanley, R. Houdre, U. Oesterle, M. Illegems, and C. Wesbuch, “Coupeld semiconductor microcavities,” Appl. Phys. Lett. 65, 2093–2095 (1994). [CrossRef]
  17. P. Pellandini, R. P. Stanley, R. Houdre, U. Oesterle, M. Illegems, and C. Weisbuch, “Dual-wavelength emission from coupled semiconductor microcavity,” Appl. Phys. Lett. 71, 864–866 (1997). [CrossRef]
  18. M. Brunner, K. Gulden, R. Hovel, M. Moser, J. F. Carlin, R. P. Stanley, and M. Illegems, “Continuous-wave dual-wavelength lasing in a two-section vetrical-cavity laser,” IEEE Photon. Technol. Lett. 12, 1316–1318 (2000). [CrossRef]
  19. D. M. Grasso, K. D. Choquette, D. K. Serkland, G. M. Peake, and K. M. Geib, “High slope efficiency measured from a composite-resonator vertical-cavity laser,” IEEE Photon. Technol. Lett. 18, 1019–1021 (2006). [CrossRef]
  20. V. Badilita, J.-F. Carlin, M. Ilegems, and K. Panajotov, “Rate-equation model for coupled-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 1646–1656 (2004). [CrossRef]
  21. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]
  22. V. Verbrugge, J.-L. de Bougrenet de la Tocnaye, and L. Dupont, “C-band wavelength-tunable vertical-cavity laser using a nano polymer dispersed liquid crystal material,” Opt. Commun. 215, 353–359 (2003). [CrossRef]
  23. O. Castany, L. Dupont, A. Shuaib, J. P. Gauthier, C. Levallois, C. Paranthoen, N. Chevalier, O. Durand, and A. Le Corre, “Tunable VCSEL with intracavity liquid crystal layer,” EOS Annual Meeting (October 2010).
  24. O. Castany, L. Dupont, C. Paranthoen, C. Levallois, A. Le Corre, and S. Loualiche, “Liquid crystal micro-cells for tunable VCSELs,” Journes nationales sur les technologies mergentes (November 2010).
  25. M. Born and E. Wolf, Principles of Optics (Wiley, 1970).
  26. A. K. Jansen van Doornen, M. P. van Exter, and J. P. Woerdman, “Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers,” Appl. Phys. Lett. 69, 1041–1043 (1996). [CrossRef]
  27. K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” in Nanoscale Linear and Nonlinear Optics , M. Bertolotti, C. M. Bowden, and C. Sibilia, eds. (American Institute of Physics, 2001), Vol. 560, pp. 403–417.
  28. J. A. Yeh, C. A. Chang, C.-C. Cheng, J.-Y. Huang, and S. H. Hsu, “Microwave characteristics of liquid-crystal tunable capacitors,” IEEE J. Dev. Lett. 26, 451–453 (2005). [CrossRef]

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