Polarization tuning of an H 1 organic-inorganic nano-cavity

We investigate the optical properties of the dipole-like modes of an H 1 nano-cavity consisting of a single missing air hole imbedded into a triangular two-dimensional silicon nitride (Si 3 N 4 ) based photonic crystal coated with a red-fluorescent molecular dye. We modify the size and position of the first six neighboring air holes around the nano-cavity and demonstrate that this allows a control over the energy and separation of two dipole-like optical modes ( M x and M y ). This allows us to produce either linearly polarized optical modes or an unpolarized optical mode composed of degenerate modes having orthogonal polarization. We confirm our findings using three-dimensional finite difference time domain (FDTD) calculations.


I. INTRODUCTION
A photonic crystal nano-cavity is a structure in which a physical defect is deliberately introduced in an otherwise perfect photonic crystal [1][2][3] . In such a structure, light of certain frequencies can become trapped in the defect, with the volume of the cavity being around ( / ) & [4][5][6][7] . Such properties make photonic crystal nanocavities very attractive systems to study light matter interaction at the nanoscale in both weak 8,9 and strong coupling regimes 10,11 . Photonic crystal nano-cavities have been explored for applications as single photon sources 12,13 , sensor devices 14 and quantum cryptography systems. 15,16 Here applications require a close control over the polarization state of the cavity mode; for example in quantum cryptography, an unpolarized optical cavity mode is desirable 17 , whilst single photon light sources generally require a linearly polarized optical mode 18 .
Families of different 2D-photonic-crystal nano-cavities have been explored in which a physical defect is created from a linear array of missing holes in a triangular lattice, with cavities created from 3, 5 and 7 missing holes referred to as L3, L5 and L7 cavities [19][20][21] . Here, larger cavities generally have a higher qualityfactor (Q-factor) with this parameter being important in applications such as low-threshold lasers 22,23 .
However, the optical mode volume (V) of a cavity is also of importance as the Q/V ratio defines the Purcell Factor (enhancement of spontaneous emission rate) that occurs when placing an emitter into the cavity, with large spontaneous emission rates being of importance in single-photon light sources 24,25 . To combine both large Q and small V, researchers have explored so-called 1 nano-cavities that are created by defining a single missing air hole defect into a two-dimensional triangular lattice photonic crystal slab [26][27][28] . Here a number of different types of H1 structures have been created using materials of different refractive index. For example, cavities have been realized based on materials having a high refractive index ( = 3.46) with a maximum (measured) Q-factor determined of around 10 6 based on a structure having a slab thickness = 0.575 27 .
By using a dielectric material of lower refractive index (n = 1.93) it has been predicted 29 that the Q-factor is expected to reduce to around 700 based on a slab-thickness of 1.55a. Q-factor can however be enhanced by modifying the size and position of the first six nearest-neighboring air-holes that surround the nano-cavity defect 28,30 .
In this work we present a modelling and experimental study of the polarization state of an 1 nanocavity that is coated with a red-emitting molecular dye (see Fig. 1 (a)). It is known that an 1 nano-cavity will support a degenerate dipole-like optical mode that in fact corresponds to two modes having the same frequency but with different polarizations 28,31,32 . Here we demonstrate that the Q-factor of an H1 nano-cavity can be enhanced and the polarization state of the cavity mode controlled 4,28,30 by reducing the symmetry of the surrounding holes in the photonic crystal. This reduction in symmetry is realized via modifying the size and position of the first six neighboring air holes that surround the nano-cavity 'missing hole'. We then demonstrate that the degeneracy of the cavity mode can be removed by reducing the structure symmetry, allowing us to tune the polarization of the cavity mode from being -polarized to -polarized or into an unpolarized state.
Our cavities are constructed using the dielectric material silicon nitride (Si3N4) which is coated with a thin film of the molecular dye Lumogen Red, allowing the dipole-like mode to be positioned at optical frequencies (650 -670 nm). We show that our modified cavities can reach a Q-factor of 1875; a value that is almost one order of magnitude compared to an unmodified H1 cavity.

II. MODELING
The structure of the nano-cavities investigated in this work are shown in  26,[33][34][35] . To improve the cavity quality factor and control its polarization state, we have reduced the size of the first two air holes above and below the cavity (parallel to the -axis) to r¢ = 0.23a. The size of the air holes neighboring the cavity were also reduced to r¢¢ = 0.26a and they were displaced by a distance away from their original position. We chose the values of r¢ and r¢¢ based on the fabrication capability and resolution of our electron beam lithography (EBL) system, with − ;; = 10 and ;; − ; = 8 . As we show below, this lowering of cavity symmetry created by reducing the size of the first two air holes above and below the nano-cavity breaks the degeneracy of the cavity mode and splits it into two linearly polarized modes Mx and My.
We have used three-dimensional finite time difference time domain (FDTD) calculations to investigate the optical properties of our nano-cavities. 36 Here, the photonic crystal size was set to be 34 × 19√3 with boundary conditions implemented by introducing a perfect matching layer around the structure. The Q-factor was calculated by imbedding an oscillating dipole emitter of a dipole moment ( , , ) = (1,1,0) at a weak symmetry point that was 10 nm away from the cavity centre. Here, the dipole source was modelled as a Gaussian oscillating pulse centred at 628 nm with a linewidth of 100 nm. The Poynting vector leaving the cavity was then calculated, with emission from a single dipole emitter being sufficient to study the dependence Wavelength (nm) Unmodified H1 cavity Intensity of the Q-factor and mode shift on the displacement (s) of the side air-holes. Here, the cavity Q-factor of the structures was calculated by relating the cavity emission linewidth at half maximum ∆ to the wavelength of the cavity mode via = ∆ ⁄ .
In Fig. 2(a) we plot the FDTD simulated emission spectrum for an unmodified 1 nano-cavity (i.e. r = 0.3a, s = 0). Our calculations also indicate that this mode is a dipole-like cavity mode composed of two degenerate modes having orthogonal polarization. We find as expected that by reducing the symmetry of the 1 nano-cavity (realised by either modifying the size of the air-holes that surround the cavity or by displacing the side air-holes) we create a splitting of cavity mode into two modes having orthogonal polarizations. This is shown in Fig. 2(b), where we plot a series of simulated emission spectra for an H1 nano-cavity having air Our calculations (see Fig. 2(b)) indicate that mode Mx is sensitive to modification of the size of the surrounding air-holes and causes it to undergo a red-shift from 628 nm to 648 nm as air-hole size is reduced from 78 nm to 59.8 nm for the first two air holes above and below the cavity ( ′ ) and from 78 nm to 67.6 nm for air holes neighboring the cavity ( ′′) . This red-shift is accompanied by an increase in cavity Q-factor from 200 to 650. Interestingly however, we find (see Fig. 2

(c) and (d)) that the Q-factor and wavelength of mode
Mx is not apparently dependent on the air-hole side-shift . In contrast, the Q-factor and wavelength position of mode My has a strong dependence on . Indeed, it can be seen that mode My undergoes a 17 nm shift to longer wavelengths as is increased from s = 0 to 0.22 ; a result that we ascribe to an increase in the physical volume of the nano-cavity.
As can be seen in Fig 2(b), our model indicates that mode My undergoes a spectral overlap with mode Mx at = 0.06 forming a degenerate state. It is apparent that the total integrated area under the peaks of both Mx and My is almost constant, however when such modes are close in energy, we see a transfer of area between them. If we simplistically equate the total area of the emission peaks with the amount of energy stored within the cavity, it suggests an effective transfer of electromagnetic energy stored in each mode as they approach degeneracy 37 . Fig. 2(d) also reveals that the Q-factor of mode My has a strong dependence on shifting the side-holes in the x-direction, with a maximum value of 1,500 predicted for = 0.18 ; a value almost 8 times higher than the Q-factor of the unmodified cavity. We attribute this increase in Q-factor to a reduction of radiation losses from guided modes due to the gentle confinement of the field that occurs as a result of the modifications to the cavity structure 4 .
In order to gain further insight into the optical modes identified in Fig. 2, we have calculated the electromagnetic field distribution associated with mode My and Mx respectively. The results of these calculations are plotted in Fig. 3 for = 0.14 . Here it is apparent that both modes Mx and My have a dipolelike field distribution 26,38 . We can use this calculated field distribution to explain the finding (see Fig. 2

(c) and
(d)) that mode My appears most sensitive to changes in displacements of the side holes in the x-direction position, with such changes not apparently affecting mode Mx. It is clear that this sensitivity results from the fact that the Ey component of the My mode electric field distribution is oriented parallel to the x-direction (see Fig. 3). In contrast, it is apparent that the Ex component of the Mx field distribution will be most sensitive to modifications of the upper and lower air-holes (i.e. resulting from structure changes in the y-direction).

III. EXPERIMENTAL RESULTS AND DISCUSSION
To explore the results of our FDTD calculations, we fabricated a series of 1 nano-cavities having a  15 W cm -2 , with the laser incident on the surface at an angle of 45° relative to the surface normal (so-called "dark field" configuration). The resultant PL was collected from the cavity surface at normal incidence using a 50X objective lens with numerical aperture of 0.42. To reject plasma lines from the laser output, a long pass filter having a cut-off at 450 nm was placed just after the objective lens. The PL was then passed through an optical-polarizer oriented either parallel or perpendicular to the cavity x-axis before being imaged into a 0.25 m liquid nitrogen cooled CCD spectrometer. To separate the nano-cavity emission from that of the surrounding region, the spectrometer slit width was reduced to 0.01 mm, with data recorded from the rows that correspond to the cavity image on the CCD.  1(b)). As it can be seen, the nano-cavity supports two optical modes. In order to characterise these modes in more detail, the PL emission was measured as a function of the cavity side air-hole shift and emission polarization (selecting either Mx or My modes) -see typical emission spectra in Fig. 5(b). For the cavity having = 0, the structure is characterised by two optical modes which we identify as Mx and My with lMx > lMy.
Such findings are in good agreement with the FDTD calculations presented in Fig. 2(b). Note that we observe small changes in the wavelength of mode Mx as a function of changing (see Fig. 5(c)); a result most probably caused by uncontrolled variations in the structure of the photonic crystal, rather than from changes in .
Encouragingly we find that as increases, mode My shifts to longer wavelengths as expected. Furthermore, the intensity of the emission peaks become comparable around = 0.04 indicating the formation of a near degenerate unpolarized state.
In Fig. 5(d) we plot the experimentally determined Q-factor of modes Mx and My as a function of .
Here, the cavity Q-factor was deduced by fitting the cavity mode emission to a Lorentzian function. As it can be seen, the Q-factor of mode Mx is approximately constant as a function of . However, the Q-factor of mode My has a clear dependence on and takes a maximum value of 1875 at = 0.14 ; a result in close agreement with our FDTD simulations as presented in Fig. 2(d).
Here it can be seen that the measured Q-factor is slightly higher than the simulated Q-factor; an effect that we again attribute to structural differences between the modelled and fabricated structures.

IV. CONCLUSIONS
In summary, we have fabricated and modelled the optical properties of the dipole-like mode of a H1 silicon nitride nano-cavity that is coated with a red-fluorescent molecular dye. By modifying the size and position of the six air-holes surrounding the cavity, we showed that the Q-factor of a dipole-like mode can be enhanced by almost an order of magnitude compared to an unmodified H1 cavity. We also confirm that it is possible to manipulate the polarization and the energy separation between the dipole-like cavity modes, with the cavity either characterised by spectrally separate modes having orthogonal polarization, or a single unpolarized mode.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.