Cent. Eur. J. Phys. 8(2) 2010 202-206DOI: 10.2478/s11534-009-0090-0

Central European Journal of Physics

Efficiency enhancement in a microcavity solid-statedye laser with Bragg grating reflectors

Research Article

Sergei Popov1, Rui Zhang12, Sergey Sergeyev3, Ari T. Friberg1451 Royal Institute of Technology (KTH), Department of Microelectronics and applied Physics, SE-164 40 Kista, Sweden

2 Joint Research Center of Photonics (KTH / Zheijang University), Department of Microelectronics and applied Physics,SE-164 40 Kista, Sweden

3 Waterford Institute of Technology, Optics Research Group, Cork Road, Waterford, Ireland

4 Helsinki University of Technology, Department of Engineering Physics, FI-02015 TKK, Finland

5 University of Joensuu, Department of Physics and Mathematics, FI-80101 Joensuu, Finland

Received 10 December 2008; accepted 26 April 2009

Abstract: Bragg grating reflectors placed along microcavity facets can improve the efficiency of a polymer dye laserbuilt with such a microcavity. The impact of different reflector designs on the mode pattern and resonancefrequencies of the microcavity is numerically simulated and analyzed. This rigorous physical model isbased on solving the Maxwell equations and includes such material properties as absorption, dispersion,fluorescence and optical gain. In certain cases, an asymmetrical layout of the reflectors can be morepreferable than the pair of reflectors located on opposite sides of the microcavity as it is implemented fortypical design.

PACS (2008): 42.55.Mv, 42.55.Sa, 42.79.-e, 42.79.Dj

Keywords: microcavity laser Bragg grating reflector polymer dye laser Versita Warsaw and Springer-Verlag Berlin Heidelberg.

1. Introduction

Microcavity lasers have been continually attracting moreand more interest for their potential use in lab-on-a-chiptechnologies, primarily for bio- and nano-science applica-tions, like drug screening, micro-fluidic systems and oth-ers [13]. Dye microlasers can be an effective solution forsuch techniques since they offer much in-demand featuresE-mail: sergeip@kth.se

in these branches: narrow radiation linewidth and broad-band wavelength tunability in the visible part of spec-trum [4]. A microcavity containing gain material embed-ded in a polymeric-based host matrix is possible to fabri-cate with efficient and robust nano-imprinting lithographythat is an essential factor for cheap mass production ofuse-and-dispose components [5]. Although polymer dyemicrolasers cannot yet achieve the same superior perfor-mance demonstrated by other micro-sized devices of sim-ilar class, e.g., very high Q-factors like in photonic crys-tals or micro-ring cavities, they possess advantages notachievable with those competitors. Firstly, this operation202

Sergei Popov, Rui Zhang, Sergey Sergeyev, Ari T. Friberg

in the visible range of the spectrum is difficult to realizein both photonic crystals and micro-ring devices [6]. Sec-ondly, the monolithic (polymer) microcavities offer a betterfill-factor of the lasing modes and have enough physi-cal volume to provide the required optical gain for lasing.This feature is very poor for micro-ring cavities in whichwhispering-gallery modes are mostly localized in a tinyarea along the walls [7].In this report, we discuss the rigorous physical model ofmicrocavity solid-state dye lasers of the size comparableto radiation wavelengths. The simulation is based on solv-ing the wave equation for the cavity field by means of thefinite element method (FEM). The model includes physi-cal properties of the cavity, i.e., dispersion, optical lossesand dye fluorescence to provide the optical gain. A split-coupled cavity consists of parts separated by tiny gaps.The cavity modes are spread in different sections and cou-pled via evanescent waves existing in these gaps. Sucha structure breaks the rectangular symmetry of a classi-cal cavity and allows forming the field modes using totalinternal reflection from the walls. Thus, highly reflect-ing mirrors, e.g., metal layers can be avoided. ApplyingBragg grating reflectors (BGR) placed on certain facetsenhances the efficiency of the microlaser. The remarkablefeature of such a design is that the efficiency improvementis achieved with non-symmetrical positions of the gratings,different from the classical approach in lasers using dis-tributed feedback or back reflection components exploitingthe Bragg gratings. Since the main part of the microcavityand reflectors are made of the same material, such a laseris feasible for one-step nano-imprinting manufacturing. Inthis letter, we mainly focus on the impact of the reflectordesign on the laser output efficiency, whereas the funda-mental physical and operational features of polymeric dyelasers were recently covered elsewhere [8, 9].2. Microcavity laser layout and mod-eling detailsThe geometry of a laser microcavity is based on thesquare-shaped cavity split along the diagonal line, thusforming a split-coupled cavity consisting of two triangleparts (Fig. 1). The gain section, a polymer bar filledwith dye, is inserted between the triangles. Such a de-sign allows the efficient use of total internal reflectionto form a pattern of standing waves inside the microcav-ity. This cutting axis of symmetry breaks a simple rect-angular symmetry and creates preferable conditions forelementary wavelets (from point sources in the gain sec-tion) propagating in up/down directions. This, in turn,defines the direction of efficient wavevectors with inci-

Figure 1. Schematic layout of the microcavity dye laser with Bragggrating reflectors. For modeling, reflector pairs 1+3 and2+3 are investigated. Integration of the output power tocalculate the mode spectra is performed along the dashedline .

dent angles of 45 degrees to the facets rather than per-pendicularly to them [9]. The latter case would requirehighly reflecting mirrors to build up cavity modes. Anexternal prism is placed at a distance smaller than onewavelength from a facet to couple out the laser radia-tion by catching the evanescent waves penetrating out-side the cavity. The triangle sections are modeled withSU-8 polymer and the gain bar contains the mixtureof poly-methylmethacrylate (PMMA) and Rhodamine 6G(Rh6G) dye. Both the PMMA and SU-8 are most com-monly used polymers in nano-imprinting lithography, andPMMA is well-known as a typical host material for solid-state dye lasers because of its good solubility with theRh6G dye [10, 11]. The refractive indices of PMMA andSU-8 are ndp= 1.492 and npol= 1.595 respectively, whilethe thickness of the gain bar is ldp= 0.8 m and the cav-ity base line islpol= 4 m (Fig. 1). The thickness of theout-coupling air gap lair = 0.2 m is found as the opti-mized value to provide the maximum output intensity forone of the lasing modes around 567 nm. This mode cor-responds to the most efficient operation of the Rh6G dye.Values for the refractive indices of PMMA and SU-8 arealso considered for this wavelength.To investigate the improvement of the cavity performanceby a more efficient entrapment of light inside the mate-rial, we add a set of external reflectors based on the Bragggrating structures made from the same material as the tri-angle sections, i.e. SU-8, and placed behind the facetsof the microcavity (Fig. 1). Along with the classical, de-203

Efficiency enhancement in a microcavity solid-state dye laser with Bragg grating reflectors

fined here as face-to-face design (only reflectors 1+3are chosen), we tested the asymmetrical structure whereadjacent sections of the reflector are included (reflectors2+3). The latter variant might be practical in certain casesof manufacturing the lab-on-a-chip devices where micro-cavity lasers can be connected to other micro-photonicscomponents.In many cases, microcavity lasers are assumed to have aplanar structure, thus our model can be safely restricted to2D geometry with in-plane TE waves, so that the electricfield vector has only the z-component Ez (perpendicularto the plane of figure). Although such a model is sim-ple enough, it is still physically realistic to accuratelydescribe the main features and operation performance ofthe device. Electromagnetic wave propagation inside adielectric cavity and its surroundings is described by thewave equation ( 1r Ez

) rk20Ez = 0, (1)where r is the relative permittivity, r is the relative mag-netic permeability, and k0 is the free space propagationconstant. Dye molecules are modeled as 500 excitationpoint sources of spherical waves which is a reasonableapproximation corresponding to modest dye concentration(about 101 -102 mmol/L) at the scales of the microcav-ity geometry. Dispersion, absorption and gain (for thepolymer-dye section) phenomena are included into themodel using the real and imaginary parts of the mate-rial refractive indices. Using a representation of the wavevector k in its complex form, a relation between the opti-cal absorption and imaginary part of the refractive indexis obtained in following form [12]

na = 04pi (m1), (2)where c is the speed of light, f is the light frequency, 0is the light wavelength in free space, and is the opticalabsorption. Absorption values for SU-8 and PMMA arerelatively small in the visible, 1.4 dB/cm and 0.65 dB/cm,respectively. They only marginally contribute to the in-fluence on the output lasing power. However, since thePMMA part contains the Rh6G dye which has both strongabsorption and fluorescence in the visible, the imaginarypart of the refractive index of the gain material is signif-icantly responsible for the output lasing spectrum. Bothcases of the absorption and gain are described with ex-pression (2) using signs - or + in the relation, respec-tively. Thus, the imaginary part of the refractive indexleading to the optical gain inside the cavity is given byng = 04pi g(m1), (3)

where g is the optical gain coefficient, and all other vari-ables are the same as in relation (2). Combining bothreal and imaginary parts of the refractive index, and us-ing known absorption and fluorescence spectra for Rh6G,complete relations for the refractive index are obtained forthe gain sectionnl - d = nPMMA + i (nPMMA + na - dye + ng - dye), (4)

and for the rest of the cavity (triangle sections withoutgain properties)npol = nSU - 8 + i nSU - 8, (5)

where subscripts a-dye and g-dye stand for the ab-sorption and gain (emission) resulting from the presence ofthe Rh6G dye inside the material. The emission spectrumfor the dye is found by applying the mirror image rule torelate the absorption and fluorescence (Fig. 2)1 [13]. Fig. 2also displays the stopband profile of the BGR (green line)implemented in the model. Each section of the reflectorconsists of 10 slabs of 118 nm thickness each. The spec-tral profile of the grating is adjusted to provide maximumreflectance for the wavelengths within the fluorescencerange and diminish it in the absorption region. Assemblingcomplete expressions for refractive indices (4) and (5)) forproper sections of the microcavity and applying them inEq. (1), we have numerically investigated the electric fieldstructure and spectra of the microcavity modes for differ-ent cavity design with BGRs. For the modeling part of theinvestigation, we used the finite element method (FEM)implemented in Comsol Multiphysics.3. Impact of BGRs on the output ef-ficiencyTo investigate the increase of the output efficiency due toBGRs placed behind the microcavity facets, we selected aspectral region around the lasing mode at a wavelength of567 nm. This mode is close to the maximum of the Rh6Gfluorescence profile (blue line in Fig. 2). Even without re-flectors, the microcavity provides noticeable confinementof the electromagnetic field due to total internal reflec-tion from the cavity walls (Fig. 3). However, a consider-able portion of the energy can be noticed leaking outsidethe microcavity. After placing two BGRs around adja-cent facets of the microcavity, a significant decrease in1 http://omlc.ogi.edu/spectra/PhotochemCAD/html/rhodamine6G.html

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Sergei Popov, Rui Zhang, Sergey Sergeyev, Ari T. Friberg

energy leakage outside the microcavity is clearly notice-able (Fig. 4a). Simultaneously, about 6 dB increase inthe output efficiency is achieved for the strongest mode of = 567 nm (blue line in Fig. 4b). Mode spectra in Fig. 4bfor both, the original microcavity without reflectors (redline) and improved design (blue line) are compared andgiven in arbitrary units normalized to the maximum valueof the improved efficiency at 567 nm. BGRs arranged inface-to-face layout have demonstrated similar enhance-ment of the field confinement (Fig. 5a and growth in theoutput efficiency for the laser modes (Fig. 5b. Roughlythe same 6 dB increase in the efficiency for the strongestmode is obtained.

Figure 2. Spectral profiles of the dye absorption (red), dye fluores-cence (blue), and Bragg grating reflectors (green). Allcurves are normalized to their maximum values. Reflec-tors have the following parameters: refractive index con-trast is n = 0.6, thickness of the layers is 118 nm, centralwavelength of the stopband is 631 nm.

Figure 3. Electric field pattern inside the microcavity without reflec-tors for the mode wavelength = 567 nm.

a)

b)Figure 4. a) Comparison of the longitudinal mode distribution for mi-

crocavity without external reflectors (red line) and for theadjacent BGR (combination 2+3 in Fig. 1, blue line).b) Corresponding electric field pattern for the mode wave-length = 567 nm.

On the other hand, a certain difference can be noticed inthe way the mode spectra are changed for the two reflectordesigns. Along with a strong increase in the main mode(567 nm), the adjacent configuration demonstrates ageneral lift of the background signal for about 2-3 dB. Theface-to-face layout does not increase the backgroundlevel. That can be, in a certain sense, treated as the im-provement of the signal-to-noise ratio. On the other hand,such a configuration selectively enhances other modes andcreates new side modes that do not exist in the originalmicrocavity without reflectors (around 550 nm in Fig. 5b).This effect demonstrates a certain trade-off related to theenhancement of the desired and parasitic side modesand should be accounted for in particular applications ofsuch microcavity lasers.205

Efficiency enhancement in a microcavity solid-state dye laser with Bragg grating reflectors

a)

b)Figure 5. a) Comparison of the longitudinal mode distribution for mi-

crocavity without external reflectors (red line) and for theface-to-face BGR (combination 1+3 in Fig. 1, blue line).b) Corresponding electric field pattern for the mode wave-length = 567 nm.

4. ConclusionUsing numerical modeling based on the application of fi-nite element methods, we have investigated the impactof external Bragg grating reflectors on the mode struc-ture of a microcavity polymer dye laser. The main goal ofsuch reflectors, which can be realized in different designs,is to enhance the output efficiency of microcavity lasers.Modeling results demonstrate an expected improvementin the output efficiency. Along with a classical approachbased on face-to-face location of the reflector sections,an asymmetrical combination of two adjacent reflectorswas considered. Providing the same improvement in thelaser efficiency, such a design can be more efficient thanthe face-to-face layout for the fabrication technology ofphotonics components in lab-on-a-chip systems.

AcknowledgementsThis work was financially supported by the Swedish Foun-dation for Strategic Research (S. Popov and A. T. Friberg),the Academy of Finland (A. T. Friberg), and by the Enter-prise Ireland Commercialization Fund (S. Sergeyev).References

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IntroductionMicrocavity laser layout and modeling detailsImpact of BGRs on the output efficiencyConclusionAcknowledgementsReferences