Generation of quasi-coherent cylindrical vector beams by leaky mirrorless laser

We demonstrate that cylindrical vector beams with radial and azimuthal polarization states can be generated by leaky emission from photoexcited molecules embedded in slab-optical-waveguides which are formed on thin metal films on glass. Mirrorless lasing action in the optical waveguide leads to an order-of-magnitude collapse of the emission energy bandwidth and an emission directionality enhancement exceeding threefold. This leads to the creation of fine rings of quasi-coherent light with radial and azimuthal polarizations. We study the effect of the leakage loss on the amplified spontaneous emission process and on the photon yield. We find a critical value of metal film thickness for the observation of mirrorless lasing action and optimal values for enhancing photon extraction. ©2012 Optical Society of America OCIS codes: (310.6845) Thin film devices and applications; (140.0140) Lasers. References and links 1. B. E. A. Saleh and M. C. Teich, Fundamentals of photonics (Wiley Online Library, 1991). 2. R. W. Boyd, Nonlinear optics (Academic Pr., 2003). 3. T. Ellenbogen, P. Steinvurzel, and K. B. Crozier, “Strong coupling between excitons in j-aggregates and waveguide modes in thin polymer films,” Appl. Phys. Lett. 98(26), 261103 (2011). 4. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. in Opt. and Photon. 1(1), 1–57 (2009). 5. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000). 6. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003). 7. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single Molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001). 8. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008). 9. D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007). 10. F. K. Fatemi, “Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems,” Opt. Express 19(25), 25143–25150 (2011). 11. Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. 31(11), 1726–1728 (2006). 12. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004). 13. S. C. Tidwell, G. H. Kim, and W. D. Kimura, “Efficient radially polarized laser beam generation with a double interferometer,” Appl. Opt. 32(27), 5222–5229 (1993). 14. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000). 15. U. Levy, C. H. Tsai, L. Pang, and Y. Fainman, “Engineering space-variant inhomogeneous media for polarization control,” Opt. Lett. 29(15), 1718–1720 (2004). 16. K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006). 17. Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005). 18. T. Ellenbogen and K. B. Crozier, “Exciton-polariton emission from organic semiconductor optical waveguides,” Phys. Rev. B 84(16), 161304 (2011). #177401 $15.00 USD Received 3 Oct 2012; revised 25 Nov 2012; accepted 26 Nov 2012; published 12 Dec 2012 (C) 2012 OSA 17 December 2012 / Vol. 20, No. 27 / OPTICS EXPRESS 28862 19. G. M. Akselrod, J. R. Tischler, E. R. Young, D. G. Nocera, and V. Bulovic, “Exciton-exciton annihilation in organic polariton microcavities,” Phys. Rev. B 82(11), 113106 (2010). 20. K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5(3), 166–169 (2011). 21. A. E. Siegman, Lasers, (Mill Valley, 1986), Chap. 13. 22. P. Yang, G. Wirnsberger, H. C. Huang, S. R. Cordero, M. D. McGehee, B. Scott, T. Deng, G. M. Whitesides, B. F. Chmelka, S. K. Buratto, and G. D. Stucky, “Mirrorless lasing from mesostructured waveguides patterned by soft lithography,” Science 287(5452), 465–467 (2000). 23. L. W. Casperson and A. Yariv, “Spectral narrowing in high-gain lasers,” IEEE J. Quantum Electron. 8(2), 80–85 (1972).


Introduction
The polarization state of light plays a major role in optical phenomena, ranging from the common, e.g.reflection, transmission and absorption [1], to the complex, e.g.nonlinear interactions [2] and generation of strongly coupled light matter states [3].This is a fundamental consequence of the fact that the interaction between light and matter is mediated through the material's linear and non-linear electric susceptibility, χ , which measures the material polarization response to an applied polarized electromagnetic field.It is therefore important to be able to precisely control the polarization state of light and to create light beams with unique polarization properties.
One class of beams with such unique properties is that of cylindrical vector beams (CVB) which have a cylindrical spatial symmetry of the polarization state [4].It has been shown that radially-polarized CVBs can be focused to smaller spots than linearly-polarized light beams [5,6], can be formed with a strong non-propagating longitudinal polarization component [7,8], and are useful for applications including single molecule spectroscopy [7], electron acceleration [9], manipulation of atomic spins [10], generation of surface plasmon evanescent Bessel distributions [11] and super-resolution imaging [12].As a consequence, recent years have seen a growing number of works aimed at finding new ways to generate CVBs.Examples include coherent combination of cross-polarized Hermite-Gaussian modes in a cavity [13,14], using unique phase plates with sub-wavelength features [15], birefringent intra-cavity elements [16], and conical intra-cavity Brewster prisms [17].These methods rely on special elements that have to be added to the optical systems in order to generate CVBs.Here we use leaky slab waveguides doped with Rhodamine 6G (R6G) molecules to demonstrate that a mirrorless lasing (ML) process in this system leads to the generation of quasi-coherent light with radial and azimuthal polarizations without the need for phase or polarization manipulation.
We recently presented a study on light emission from strongly coupled waveguide exciton polaritons, demonstrating that, with radially-symmetric excitation, waveguide exciton polaritons are converted to radially-and azimuthally-polarized leaky light modes [18].In that work, molecular J-aggregates were chosen for the excitonic material due to their large oscillator strengths.This made it possible to reach the strong coupling regime at room temperature.Stimulated emission or stimulated scattering were not observed, however, due to the low quantum yield of the J-aggregate emission and due to the exciton-exciton annihilation process that provides a major population-dependent loss mechanism [19].A different work recently showed that properly-aligned single molecules in a layered structure, termed a quasiwaveguide, emit light with radial polarization [20].
In this work we study emission characteristics of leaky slab waveguides doped with gain material at different pumping rates.At high pumping rates, the emission collapses in energy and momentum space.This results in the generation of fine rings of narrow bandwidth light with radial and azimuthal polarizations.We show that the coupled wave equations predict that there is a level of leakage optimal for enhanced photon extraction, a consequence of the interplay between gain and leakage.We verify this experimentally by controlling the leakage and observing its effect on the ML process.

Mirrorless laser configuration
The mirrorless laser (Fig. 1(a)) consists of a thin layer of poly(methyl methacrylate) (PMMA) doped with R6G formed on a thin silver film on glass.The PMMA acts as the confining and guiding optical layer for the propagating waveguide modes.The photoexcited R6G molecules emit to these modes which in turn leak to glass radiation modes following momentum conservation ( )sin( ) ( ) β is the momentum of the waveguide mode, m is the mode order, p is its polarization state, i.e. transverse electric (TE) or transverse magnetic (TM), glass k is the momentum of the radiation in the glass and θ is the leakage angle.We find θ for different wavelengths and polarizations by calculating the Fresnel reflection of the multi-layered system from the glass side.Reflection minima occur when the incident light impinges at the values of θ satisfying Eq. ( 1).The results are plotted in Fig. 1(b) for the first four TE and four TM waveguide modes of the system.It can be seen that the largest leakage angle occurs for the lowest order modes and that the modes alternate between being TE and TM as the angle is varied.With a radially-symmetric pump beam, conical emission with angle θ occurs (Fig. 1(a)).TM waveguide modes, which are polarized in the plane of the waveguide cross section of Fig. 1(a), leak to perfectly radially-polarized CVBs.TE waveguide modes, which are polarized perpendicular to the plane of the waveguide cross section of Fig. 1a, leak to perfectly azimuthally-polarized CVBs.

Results and discussions
Sample preparation starts with the evaporation of a thin silver film (20 nm -120 nm thick) onto an indium-tin-oxide-coated glass slide, followed by spin coating PMMA (Microchem 495 A8) doped with R6G molecules to form a waveguide that is  We photoexcite the samples from the PMMA side using either a continuous wave (CW) laser (20 mW, 532 nm) or a pulsed doubled Nd:YAG laser (Continuum Minilite II, 5 ns pulse duration, 532 nm) with a pump density of 2.1 mJ/cm 2 and a diameter of ~2 mm and photograph the leaky emission pattern.This is done using a hemispherical prism to couple the radiation from the glass to air, where it encounters a semi-transparent diffusive screen that is photographed.The maximum emission angle that is captured is ~70°.An emission pattern representative for the CW pump case is shown as Fig. 1(c).Rings of light with different radii can be seen, a result of conical emission into different angles.Adding a polarizing film to the beam path modifies these patterns from being circles to double crescents (Fig. 1(d)), thereby revealing the polarization state of each ring.The innermost ring, corresponding to the smallest value of θ (emission from TM 4 ) supported by the waveguide, is radially-polarized and successive rings alternate in polarization between azimuthal and radial.This is also shown in the schematic diagram of Fig. 1(a) and the calculations of Fig. 1(b).Due to the fact that these rings originate from pure TE and TM waveguide modes, their radial and azimuthal polarization qualities are excellent.We note that the rings can be observed only from the prism side and not from the pump side, as it is the presence of the prism which facilitates their leakage.Some background noise can be seen in the photograph, and originates from light being reflected from the screen back onto the sample and then back onto the screen.This does not, however, obscure the emission pattern from being clearly seen.In the dark regions where the local polarization of the beam is orthogonal to the polarizer the emission intensity drops to the noise level.This was also verified by characterizing the beam locally with a high extinction ratio Glan-Thompson polarizer.
When we pump the sample at a sufficiently high rate using the pulsed source, the emitted rings become highly directional and change in color (Fig. 1(e)).By again placing a polarizer in the emission path, we verify that the emitted rings maintain their polarization states (Fig. 1 (f)).We will show below that these fine rings of radially-and azimuthally-polarized light are the result of a ML process occurring in the doped slab optical waveguide.
We use an objective lens to couple the free space emission into a fiber connected to a spectrometer with a thermoelectrically cooled CCD detector (Synapse, Horiba Scientific).The objective lens and the fiber are placed on a rotating arm, allowing emission spectra to be collected at different angles.The results of the emission from four different modes are presented as Figs.2(a) and 2(b) for pumping the sample with the CW source and with the pulsed source at pump density of 2.1 mJ/cm 2 , respectively.We do not observe emission from modes with higher order as these are not guided by our thin slab waveguide.For the low pumping rate case obtained with CW laser, we observe that the emission is broad in wavelength and in angle.The emission from each mode extends over a range of angles and wavelengths that can be seen to follow the calculated waveguide dispersion shown in Fig. 1(b).For the high pumping rate case obtained with the pulsed laser, we observe a collapse in the emission's spectral content and increased emission directionality for all four modes.It can also be seen that, for the high pump rate, the TE mode emission is significantly brighter than that from the TM modes.This is due to the TE modes being more confined to the waveguide, which leads to stronger amplification.Figures 2(c) and 2(d) show the TE 4 emission spectra and angular dispersion respectively for low and high pumping rates.The emission spectra narrows significantly for high pumping rates and the directionality is improved by a factor exceeding three.for different pump pulse energies.The emission narrows down to 5.9 nm FWHM which is more than an order of magnitude smaller than the spontaneous emission bandwidth (72 nm, Fig. 2(c)).In addition the emission dependence on pump pulse energy shows strong superlinear behavior (Fig. 2(f)).
Since the slab waveguide does not have any end mirrors to form a closed cavity, the emission features shown in Figs.2(b)-2(f) result from a ML action [21,22].Mirrorless lasing is also known as amplified spontaneous emission (ASE) [21,22].We term the emission quasi-coherent since there is a limit to the amount of coherence that can be achieved by ML.The dynamics of the amplification in the ML process can be described by [23] ( ) where ( , ) I z λ is the intensity, λ is the wavelength, z is the distance of light propagation in the photoexcited slab waveguide, α is the loss, η is the spontaneous emission rate, Substituting Eq. ( 2) into Eq.( 3) and integrating then yields: ) We can use Eq. ( 4) to examine the dependence of the emission on the pumping rate by assuming that the gain parameter, g, has a Lorenzian shape in energy with a peak value that increases linearly with the pumping rate.In Fig. 3(a) the calculated ( , ) leak I z λ is presented as a function of pumping rate and wavelength.The inset presents the same data as a normalized intensity plot.It can be seen that in agreement with the measurements shown in Fig. 2 the leakage emission is expected to have a superlinear dependence on the pumping rate, with a narrowing of the emission spectra for high pumping rates.Figure 2(e) shows a spectral emission peak shift with pumping rate.At high pumping rate there is a collapse of the emission spectra (Fig. 2(b)).Therefore if the emission measurement is performed at an angle not exactly corresponding to the peak emission for the high pumping rate case, a spectral emission peak shift will be in general observed.In Fig. 3 I z λ will have a superlinear dependence on g but the photons will be trapped in the guiding layer and the energy will eventually dissipate to other loss pathways of the system instead of leaking to CVBs.In order to study experimentally the effect of the leakage loss on the nonlinear behavior of the system and on the photon extraction efficiency we fabricate samples with varying metal film thicknesses (20 nm to 120 nm).We measure the dispersion relation of each sample at low and high pumping rates, in a similar manner to the measurements of Figs.2(a) and 2(b).The results are shown in Fig. 4(a) for silver thickness ranging from 20 nm to 45 nm in steps of 5 nm, with pumping at 2.1 mJ/cm 2 .It can be seen that the dispersion relations of samples with silver thicknesses below 30 nm do not show the ML signature of narrowing of the emission spectral content and directionality.With increasing silver film thickness, however, the ML signature becomes clearly evident and the differences between the emission to the TE and TM modes becomes more pronounced.Figure 4(b) shows the emission intensity of the TM 4 mode measured over a range of pulse energies from samples with 25 nm and 30 nm thick silver films.The sample with 25 nm silver film shows a sublinear dependence on the pump energy, possibly due to absorption saturation and bleaching effects.The sample with the 30 nm thick silver film, on the other hand, shows the characteristic ML superlinear dependence.The measured TM 4 emission as a function of pumping for samples with silver thickness between 25 nm and 100 nm is shown in Fig. 4(c).Interestingly, it can be seen that the emission is most efficient with film thicknesses in the 45-60 nm range.This also occurs for the TE 4 mode, for which emission efficiency is best for film thicknesses around 45 nm as shown in Fig. 4(d).This phenomenon results from the interplay between confinement and leakage, with the latter being a strong function of silver film thickness.Increasing the film thickness however also improves the photoexcitation rate due to reflection of the pump beam by the silver film.To remove the effect of increased photoexcitation, we therefore normalize the emission intensity at high pumping rate ( 400 J μ ) with the emission intensity at low pumping rate (100 J μ ) which is below the onset of ML and is linearly dependent on the pump intensity.Figure 4(e) presents the emission normalized in this way as a function of silver film thickness for the TE 4 and TM 4 modes.It is seen that, as predicted by Eq. ( 4) and Fig. 3b, there is certain range of silver film thickness for maximizing the normalized emission.(λ 0 ≈610nm) we extracted Δω, the full width at half maximum of the normalized resonance, for different silver film thicknesses.We then found the transient decay by 2 γ ω = Δ .Figure 5 shows the calculated results for the TE where the subscripts show different thicknesses, γ leak is the decay due to leakage output and γ m is the decay due to metal loss.We use the fact that at a silver thickness of 100 nm the decay due to leakage loss is negligible (as seen in Fig. 5).We also use the fact that decay due to metal loss at a silver thickness of 100 nm is greater than that at a silver thickness of 50 nm.From Fig. 5, we find γ 50nm /γ 100 nm .From Eq. ( 5), we then obtain the value of γ leak_50nm / γ 50nm , i.e. a lower theoretical limit on the leakage coupling efficiency to the CVBs at a silver film thickness of 50 nm.This is found to exceed 50% for both the TE and TM modes of the system.

Conclusions
In conclusion we show here that ML action from leaky slab waveguides generates fine quasi coherent rings of light with radial and azimuthal polarizations.We show that this unique emission results from the conversion of TE and TM waveguide modes to leaky radiation following momentum conservation relations.We measure more than an order of magnitude narrower emission spectrum of the CVBs and more than three times smaller angular spread of the rings when pumped in the superlinear regime, compared to the case of spontaneous emission.The trend of the measured results agrees well with our coupled mode analysis of leaky ML process which shows that the photon extraction efficiency has an optimum value of silver film due to the interplay between gain and leakage loss in the system.This work demonstrates a new means for generating quasi coherent CVBs using an extremely thin device which is optically pumped or potentially electrically driven.It does not employ the brute force manipulations of the light performed with additional elements such as phase plates, and could therefore prove useful in applications of CVBs.

Fig. 1 .
Fig. 1.(a) Illustration of the sample and the conical leakage to rings of light with radial and azimuthal polarizations.(b) Calculation of the angular dispersion of TE (red line) and TM (black dashed) waveguide modes in a 1.1 m μ thick PMMA waveguide on top of a silver film.Photograph of leaky emission when the sample is pumped with a CW source without (c) and with (d) polarizer in beam path.(e) and (f) correspond to (c) and (d) respectively when the sample is pumped at high pumping rates.

Figure 2 (
e) shows the normalized emission spectra taken at 49 θ °= for different pump pulse energies and Fig. 2(f) shows the emission counts at 613nm λ = dependent gain where N 1 and N 0 are the concentrations of molecules in the excited and ground states respectively, and e σ and 0 σ are the emission and absorption cross sections respectively which are wavelength dependent.We break the loss parameter into leakage radiation loss leak α $15.00 USD Received 3 Oct 2012; revised 25 Nov 2012; accepted 26 Nov 2012; published 12 Dec 2012 (C) 2012 OSA a function of leakage loss leak α for several gain values.It is interesting to see that, when gain is sufficient, there is optimal value for leakage loss that maximizes leakage radiation.This results from the interplay between total gain, g α − and photon extraction from the system (set by leak α ).When the total gain is dominated by high leakage loss, linear dependence on the pumping rate and no amplification.On the other hand, when the leakage radiation is very low, 0 leak α  , the waveguided modes ( , )

Fig. 3 .
Fig. 3. (a) Calculated leaky emission spectra for different pumping rates.Inset shows the data as intensity plot: spectral narrowing is evident.(b) Dependence of leaky emission on the leakage loss for different gain values.

Fig. 4 .
Fig. 4. (a) Measured emission dispersion characteristics of samples with different silver film thicknesses pumped at 2.1 mJ/cm 2 .(b) Emission from TM 4 for sample with 25 nm silver thickness showing sublinear dependence on pulse energy and with 30 nm silver thickness showing superlinear dependence on the pump energy.Emission from TM 4 (c) and TE 4 (d) vs. pulse energy for samples with different silver thicknesses.(e) Normalized emission at high pumping rate from TE and TM leaky modes from samples with different silver thicknesses showing an optimum value of silver thickness for maximum photon extraction.To estimate the efficiency of the generation of CVBs by the ML process in the slab waveguide we calculated the theoretical values of the transient decay, γ, of the waveguide modes for different silver thicknesses.The transient decay was obtained using the same method that was used to calculate the dispersion relations shown in Fig. 1(b).For the reflection minima at angular frequency 15 0 3.09 10 ω = ×(λ 0 ≈610nm) we extracted Δω, the full width at half maximum of the normalized resonance, for different silver film thicknesses.We then found the transient decay by 2

Fig. 5 .
Fig. 5. Calculated transient decay rate in inverse picoseconds for TE 3 (blue line) and TM 3 (red dashed line) waveguide modes vs. silver film thickness.The inset shows the region where the silver film thickness ranges from 50 to 120 nm in enlarged detail.