A biefingent etalon as single-mode selecto in a lase cavity Kyle S. Gadne, Richad H. Abam and Eling Riis Depatment of Physics, Univesity of Stathclyde, Glasgow, G4 NG, Scotland e.iis@stath.ac.uk Abstact: A novel technique is demonstated fo stabilizing an inta-cavity etalon used fo single-mode selection in a lase cavity. By appopiate polaization analysis of the eflection fom an etalon designed as a quatewave plate an electonic signal can be deived, that enables the implementation of an electonic stabilization scheme. This scheme obviates the need fo any modulation of the etalon in ode to ensue stable single mode opeation of a cw tunable lase. 4 Optical Society of Ameica OCIS codes: (4.36) Lases, tunable; (6.44) Biefingence Refeences and Links. A.L. Schawlow, Spectoscopy in a new light, Rev. Mod. Phys. 54, 697-77 (98). C.S. Adams and E. Riis, Lase cooling and tapping of neutal atoms, Pog. Quantum Electon., -79 (997). 3. E. A. Conell and C. E. Wieman, Nobel Lectue: Bose-Einstein condensation in a dilute gas, the fist 7 yeas and some ecent expeiments, Rev. Mod. Phys. 74, 875-893 (). 4. W. Kettele, Nobel lectue: When atoms behave as waves: Bose-Einstein condensation and the atom lase, Rev. Mod. Phys. 74, 3-9 (). 5. C.E. Wieman and L. Hollbeg, Using diode lases fo atomic physics, Rev. Sci. Instum. 6, - (99). 6. G. Holtom and O. Teschke, Design of a biefingent filte fo high-powe dye lases, IEEE J. Quantum Electon. QE-, 577-579 (974). 7. S.A. Collins and G.R. White, Intefeomete lase mode selecto, Appl. Opt., 448-449 (963). 8. C.G. Aminoff and M. Kaivola, High powe single-mode cw dye lase with Michelson mode selecto, Opt. Commun. 37, 33-37 (98). 9. W. Vassen, C. Zimmeman, R. Kallenbach, and T.W. Hänsch, A fequency-stabilized titanium sapphie lase fo high-esolution spectoscopy, Opt. Commun. 75, 435-44 (99).. C.S. Adams and A.I. Feguson, Tunable naow linewidth ulta-violet light geneation by fequency doubling of a ing Ti:Sapphie lase using lithium ti-boate in an extenal enhancement cavity, Opt. Commun. 9, 89-94 (99).. T.W. Hänsch and B.J. Couillaud, Lase fequency stabilization by polaization spectoscopy of a eflecting efeence cavity, Opt. Commun. 35, 44-444 (98).. A. Yaiv, Optical Electonics, fouth edition (Saundes 99). 3. R.H. Abam, K.S. Gadne, E. Riis, and A.I. Feguson, Naow linewidth opeation of a tunable optically pumped semiconducto lase, To be published.. Intoduction The single fequency tunable lase has been a key technology in the development of high esolution lase spectoscopy [] and in paticula the ecent spectacula advances in lase cooling of atoms and ions [-4]. Any such applications, howeve, ely heavily on the ability to select a single mode of the lase cavity and maintain it fo an extended peiod of time. Fo one of the most popula lases on the spectoscopy maket today, the extended cavity diode lase [5], this is achieved by a combination of a shot cavity and theeby lage cavity mode spacing and a wavelength dependent feedback fom a gating. The selected mode can be tacked by adjusting the gating angle as the lase cavity length is scanned in ode to change the output fequency. The stongly wavelength dependent feedback fom a gating, howeve, (C) 4 OSA 3 May 4 / Vol., No. / OPTICS EXPRESS 365
is too weak to povide sufficient feedback fo the lowe gain tunable lases such as the dye lase and the Ti:Sapphie lase. These souces ae based on an inheently low-loss cavity, whee the mode selection is nomally caied out with a combination of optical elements inseted into the cavity. These may include biefingent filtes [6], etalons [7], Michelson mode selectos [8] o a combination of these. The equiements fo the selection elements ae paticulaly stingent in the case of widely tunable lases. Fistly, the desied mode is one of a geat numbe of possible ones. Secondly, the need to tune the lase fequency implies that the selecting element has to be tuned as well, typically otated aound one of its axes. This nonsolid mounting subsequently makes it pone to difts. The dye lase and the Ti:Sapphie lase offe tuning anges fom tens to moe than a hunded THz. The lase cavity modes of which a single one has to be selected ae spaced by typically a few hunded MHz. The inseted optical elements each intoduce a loss, which is a peiodic function of lase fequency, whee the peiod is efeed to as the fee spectal ange (FS of the element. The elements chosen fo the single fequency selection have successively smalle fee spectal anges coesponding to successively naowe egions of low insetion loss, until only one lase mode is capable of oscillating at a fequency coesponding to a loss minimum of all inseted elements. The exact equiements fo the mode selecting elements depend on the amount of inhomogeneous to homogeneous boadening in the gain medium as well as any spatial hole buning effects. In a tunable single fequency lase a coase selection is typically achieved using a biefingent filte. This may consist of one o moe plates made of a biefingent mateial and is otated to select a lase bandwidth of typically GHz. At this point it is often sufficient just to inset a fused silica etalon with a fee spectal ange of appoximately GHz and a eflectivity of -3% in the cavity to ensue single-mode opeation [9-]. Howeve, the stability equiements ae extemely stingent. The otation of the etalon by an angle of ode one thousandth of a degee is sufficient fo the lase to jump to the next cavity mode. Two main methods have taditionally been employed to pevent this mode jumping: ) a passive technique involves the addition of yet anothe etalon with an even smalle fee spectal ange and ) an active technique wheeby a feedback is applied to the otation of the etalon so as to keep it locked to the lase mode. This is achieved by modulating the angle of the etalon aound the eflection minimum and deiving a suitable eo signal by demodulating the detected eflection fom the etalon. While offeing the clea advantages of a simple optical layout this technique caies with it a numbe of significant penalties. Fistly, the modulated etalon intoduces a loss in the cavity at twice the modulation fequency and hence an undesiable intensity modulation. Secondly, the etalon sets up acoustic vibations in the cavity, which, if not compensated fo electonically, will lead to a substantial fequency modulation of the lase. In this pape we pesent new technique fo deiving a obust electonic eo signal fo stabilizing a single etalon to a lase cavity mode. A biefingent etalon is inseted with a slight angle between one of its axes and the lase polaization and an eo signal is deived fom the diffeential eflection and phase shift of the polaization components along the two axes. The technique has some similaities with a standad technique fo stabilizing an extenal cavity to a lase [].. The biefingent etalon The eflection coefficient A (δ, fo an electic field incident on a solid etalon is given by the expession [] exp ( iδ ) A δ, R = R () R exp iδ whee R is the intensity eflection coefficient and δ = 4π d n cos θ is the phase etadation fo a oundtip of the light of wavelength λ in the etalon with thickness d and λ (C) 4 OSA 3 May 4 / Vol., No. / OPTICS EXPRESS 366
efactive index n, which is tilted at an angle θ to the incident beam. This eflection epesents a peiodic loss with a peiod of c ( nd cos( θ )). Fo an etalon made of a biefingent mateial thee ae two efactive indices n and n coesponding to the two pincipal axes of the mateial. Hence thee ae two diffeent values δ and δ fo the phase delay. In geneal this will esult in diffeent eflectivities fo the two polaizations. Specifically, if the diffeence δ δ is π modulo π one polaization will expeience a eflection maximum when the othe has a minimum. This is equivalent to the etalon being designed as a quate-wave plate. α β λ/4 plate λ/4 etalon Polaising beamsplitte otated 45 o I Fig.. The pinciple of opeation of the biefingent etalon demonstated in an exta-cavity setup. The input light is polaized at a slight angle to one of the optic axes of the quate-wave etalon. An intensity component α is diected along axis and a component β along axis. The fequency of the lase o the tilt angle of the etalon ae chosen such that the α component is close to a eflection minimum fo the etalon. At exact esonance the eflection of the component along axis vanishes and the eflected light is linealy polaized along axis (indicated by geen aow). Away fom exact esonance the eflection is elliptically polaized with opposite helicity fo fequencies above and below esonance (indicated by ed and blue ellipses). A quate-wave plate is inseted with its axes aligned with those of the etalon. The tansmitted light is now linealy polaized. The polaization is along axis at exact esonance and changes clockwise and counte-clockwise espectively above and below esonance. This linea polaization is analyzed with a polaizing beamsplitte, which is otated by 45 with espect to the axes of the analyzing waveplate. On esonance an equal amount of light is tansmitted to both detectos while the split is asymmetic fo fequencies above and below esonance. The essence of this technique is to inset the etalon in such a way that the diection of the lase polaization foms a slight angle, α, with one of the optic axes as shown in Fig.. Specifically, the majoity of the light (intensity of this component popotional to α ) is polaized along this axis while a component popotional to β has othogonal polaization (α + β = ). We shall efe to these components as the and component espectively. The incident electic field can be esolved in its two components along these two axes E( t) = ( α E exp( iωt), β E exp( iωt) ) () whee E is the amplitude and ω the optical fequency. The eflected electic field is then E t δ, δ, R α E A δ, R exp iωt, β E A δ, R exp iωt (3) ( ), = I At esonance fo the -component (δ = modulo π) the eflected light is linealy polaized along the -axis. At eithe side of this point it is elliptically polaized with opposite helicity. This polaization can be analyzed by the combination of a quate-wave plate and a polaizing beamsplitte. A numbe of implementations of this ae possible, but the conceptually simplest one is shown in Fig.. If the analyzing quate-wave plate is aligned with the axes of the biefingent etalon, the light will be linealy polaized afte the waveplate. The diection of the polaization will depend on the fequency of the mode elative to the etalon tansmission fequency. The vaying linea polaization can now be analyzed with a (C) 4 OSA 3 May 4 / Vol., No. / OPTICS EXPRESS 367
polaizing beamsplitte set at an angle of 45 elative to the axes of the analyzing quatewave plate. The two output electic fields fom the beamsplitte ae: E E t, δ, δ, R = [ α A ( δ, + i β A ( δ, ] exp( iωt) (4a) E E t, δ, δ, R = [ α A ( δ, i β A ( δ, ] exp( iωt) (4b) Fom the qualitative aguments egading the polaizations we expect the coesponding intensities I ( δ, δ, and I ( δ, δ, detected by a pai of photo detectos to show an asymmetic imbalance aound the minimum loss point of the etalon. Thus, the quantity S ( δ, δ, ( δ, δ, I( δ, δ, ( δ, δ, + I ( δ, δ, * Im[ A ( δ, A ( δ, ] ( δ, + β A ( δ, I αβ = = (5) I α A will coss zeo at the etalon esonance and povide an ideal disciminant fo an electonic stabilization cicuit. Futhemoe, it is insensitive to lase intensity fluctuations and elatively easy to compute electonically eithe by using analogue cicuits o digitally. Using Eq. () and the fact that δ δ is π modulo π fo an ideal quate-wave plate we can now plot the signal S(δ,. Fig (a) shows this function plotted ove a fee spectal ange of the etalon fo eflectivities fom 4% to %. It is woth noting that the geneal shape of the signal does not vay and that the slope though zeo only depends weakly on the eflectivity as shown in the inset in Fig. (a). This is a paticulaly useful featue fo a pactical implementation as the etalon eflectivity can then be optimized with only the optical pefomance of the lase in mind. Nomalised eo signal Gadient 8 7 6 5 4 5 5 5 3 Etalon eflectivity, % - -.5.5 - Phase, π (a) R = 4% R = 8% R = % R = 6% R = % Fig.. The calculated signal S fo an etalon with (a) quate-wave etadation and vaying eflectivities R and (b) a % eflectivity and a etadation vaying fom λ/8 to 3 λ/8. The inset in (a) shows the dependence on the eflectivity of the gadient though the zeo-cossing. Geneally waveplates ae only exact fo a paticula wavelength. Fo applications in a tunable lase system it is theefoe elevant to conside the effect on the signal S of a deviation fom an exact quate-wave etadation of the etalon. The widest bandwidth fo an etalon (i.e., the slowest vaiation of the phase etadation with espect to wavelength) is obtained with a tue zeo-ode plate. That is a waveplate, whee the diffeence in optical thickness expeienced by light polaized along the two optic axes is exactly a quate of a wavelength. Fo a waveplate made of quatz this coesponds to an extemely thin plate (tens of micons), which will typically be too thin fo an etalon. Assuming that a thickness of ode.5 mm is equied fo the etalon to pefom its pupose in the lase cavity we need to use a highe-ode plate, i.e. one whee the optical thickness diffeence is qλ ± λ/4, whee q is an intege. Fo a quatz waveplate the etadation will way by less than ±λ/8 when the lase wavelength is vaied by ± nm aound the design wavelength. Figue (b) shows the calculated signals fo a vaiation of ±λ/8 and a eflectivity of %. The signal develops a slight asymmety, but the Nomalised eo signal - -.5.5 - Phase, π (b) /8 3/6 /4 5/6 3/8 (C) 4 OSA 3 May 4 / Vol., No. / OPTICS EXPRESS 368
zeo-cossing emains at the coect point and the slope at the zeo-cossing emains unaffected. 3. Exta-cavity expeiment The eflection fom an uncoated quate-wave plate was fist investigated in the output beam fom a cw Ti:Sapphie lase with the set-up shown in Fig.. In this case the etalon, the analyzing waveplate and the polaize wee fist aligned with the lase polaization, which was subsequently otated by ~5 with a half-wave plate. The two photo detecto signals I and I wee ecoded as a function of lase wavelength fo a fixed tilt angle. Fig. 3 shows the measued sum and diffeence signals togethe with thei atio: I I S = (6) I + I ove about thee fee spectal anges of the etalon. The steep positive slopes though zeo would povide an ideal disciminant fo stabilizing the lase wavelength to the maximum etalon tansmission. The atio data show the same geneal shape as the theoetical pediction based on Eq. (5) although with a slightly lowe amplitude. This is most likely due to a less than complete extinction of the eflection of the esonant polaization due to walk-off in the tilted waveplate and the less than ideal optical quality a waveplate athe than an etalon. This manifests itself as an offset in the sum signal. If we abitaily assume that /3 of the signal obseved on esonance is due to this wong polaization and compensate fo this in deiving the expeimental values fo S, the ageement between theoy and expeiment is significantly bette. Signal, ab. units.5 778 779 78 78 78 -.5 - Wavelength, nm Diffeence Sum Ratio Sine fit Cos fit Theoy Fig. 3. Expeimental esults obtained with an uncoated waveplate in an exta-cavity configuation as shown in Fig.. The sum and diffeence signals fom the two detectos as well as the atio of the diffeence and sum ae shown as a function of the lase wavelength. The solid cuves shown with the sum and diffeence signals ae sinusoidal fits to the data, which ae expected to povide good fits to the expeimental data fo a low eflectivity etalon. The solid cuve shown with the atio data is the theoetical pediction fo an etalon with a 4% eflectivity. 4. Inta-cavity expeiment The compaison of theoy and expeiment ae slightly less staightfowad in an inta-cavity configuation. As the etalon is tuned, fo instance, by tilting it the lase will jump between successive cavity modes. We would theefoe expect a signal of the type given by Eq. (6) to be a sequence of smooth cuves though zeo sepaated by a sign changing jumps. We have demonstated this using a cw tunable vetical extenal cavity suface-emitting lase (VECSEL). The details of this system ae descibed elsewhee [3]. Fo the pesent discussion it suffices to note that the lase opeates with a linea thee-mio cavity fomed by a Bagg mio immediately below the semiconducto gain egion, a cuved folding mio and a flat output couple. The oveall cavity length is appoximately.5 m leaving ample space (C) 4 OSA 3 May 4 / Vol., No. / OPTICS EXPRESS 369
fo inta-cavity elements in the segment between the folding mio and the output couple. Single-fequency opeation ove a tuning ange of ~ nm is obtained by the insetion of a single-plate biefingent filte and a GHz FSR etalon with % eflecting coatings. A cystalline quatz etalon designed as a 7λ/4 plate at the lase wavelength of 975 nm is mounted on a galvanomete with a hoizontal otation axis. The etalon is walked off slightly in the hoizontal diection as shown in Fig. to enable an aluminum coated pick-off mio mounted at appoximately 45 to sepaate the eflected light fom the path of the cavity. The lase polaization is hoizontal and the etalon axes ae otated by ~ elative to hoizontal/vetical. The polaization analyze is set up as descibed above. The atio S of the diffeence and sum of the detecto signals is geneated by an analogue multiplie and ecoded as the etalon is tilted. Fig. 4 shows an example. Electonic stabilization is achieved by feeding back to the galvanomete otation angle a signal deived fom the time integal of S. With the addition of a sevo system fo the cavity length a fequency stability of bette than khz has been achieved with this system [3]. Ratio signal, ab. units 5-5 Lase FSR Etalon tuning Fig. 4. Expeimental esults fo a 5% eflecting etalon inseted in the cavity of a VECSEL. The atio signal S defined by Eq. 6 is deived fom the measued outputs of the polaization analyze and shown as function of etalon tuning. The discontinuities coespond to longitudinal lase mode jumps. 5. Conclusion A new technique has been demonstated fo stabilizing an inta-cavity solid etalon to a cavity mode to ensue long-tem single-mode opeation. The technique is based on the use of a quate-wave plate as the etalon. By analyzing the polaization eflected fom the etalon a signal can be deived enabling electonic stabilization of the single-mode selection. One of the optic axes of the etalon is at a slight angle with espect to the lase polaization. It is woth noting that the insetion of the biefingent etalon in the lase cavity does not appea to have a detimental effect on the lase tuning o output polaization. The technique has been demonstated on a lase system with a tuning ange of ~ nm, which has allowed us to use a elatively high ode waveplate. Fo a lase system with a wide tuning ange, such as that offeed by the Ti:Sapphie gain medium, a low-ode (pefeably zeo-ode) plate would be equied. The equied thickness fo the opeation as an inta-cavity etalon can be achieved eithe by using a low-biefingence mateial of by optically contacting togethe two plates with a λ/4 thickness diffeence. This scheme is elated to the familia stabilization scheme developed by Hänsch and Couillaud fo stabilizing the fequency of a lase to passive cavity containing a polaizing element []. In thei case the polaization of the light impinging on the cavity is otated slightly elative to the plane of the polaize. This esults in a fequency dependent polaization of the light eflected fom the cavity, which enables the implementation of an electonic locking scheme. Acknowledgments This wok was suppoted by the UK Engineeing and Physical Sciences Reseach Council (EPSRC) and by Scottish Entepise unde the Poof of Concept Scheme. (C) 4 OSA 3 May 4 / Vol., No. / OPTICS EXPRESS 37