Diode laser emission

Transcription

1 Lecture 9/1 Diode laser emission x Diode laser emission has oblong cross-section. Y-axis with large divergence angle is called fast axis X-axis with smaller divergence angle is called slow axis

2 Lecture 9/ Laser emission: beam divergence and astigmatism from 1 to µm x less than 1µm LASR OUTPUT FACT Side View d X Top View d Y Θ Y Θ X Beam emitted from a small facet is equivalent to the beam emitted b an imaginar point source P. When d X is larger than d Y the distance between P X and P Y can be nonero. This phenomenon is called astigmatism, and the distance between P X and P Y is the numerical description of astigmatism. P X P Y

3 Lecture 9/3 Laser emission: far and near field emission patterns Field emitted from the laser NAR FILD - (x,) x R At distances larger than d i FAR FILD F (Θ X,Θ Y ) Angle distribution of the optical field far from the laser mirror Spatial distribution of the optical field across laser mirror Θ Y Θ X Near field pattern uniquel determines far field pattern

4 Lecture 9/4 x Laser near field Sie of the laser mirror (at least in direction) is comparable with wavelength of light and wave optic analsis techniques must be used. Main result of this analsis is that laser near field pattern can take shapes onl from certain discrete set of special shapes called modes. No other shapes of near field pattern are allowed. This effect is ver similar in nature to quantiation of the energ states of electron in atom. n eff_1 n eff_ n eff_3 ach laser mode is characteried b certain number effective refractive index (n eff ). This number determines mode shape and its group velocit. Number of possible (allowed) near field shapes (modes) is given b laser wavelength, refractive indexes of all laers and actual sies of laers.

5 Lecture 9/5 Nature of discreteness of the possible near field shapes Consider light propagating in between of two perfect mirrors (metallic with 1% reflection) d ~ We used because onl -projection of the light wave vector matters in -direction: π k k _m + k _m, k _m and k _m _m Resulting optical field will look like: (,) ( ) exp( j ( ω t k ) where m ( ) k m _m cos sin π n ( k _m ) ( k ) _m eff_m,, _m m 1+ even number m 1+ odd number, wavelength in vacuum Because of total reflection from the mirror the energ transfer will occur onl in direction and in direction standing wave must be formed. Standing wave condition for perfect mirrors is: d m, m 1,,3... π _m m () _m d m m 1 n eff_1 m n eff_ m 3 n eff_3

6 n Phsical meaning of the effective refractive index θ m k π n k k _m _m π k sin k cos n ( θ ) n sin( θ ) m ( θ ) n cos( θ ) m 1- sin ( θ ) n - n * Mode effective refractive index determines group velocit for a given mode In semiconductor lasers no metallic mirrors are available (huge loss would have appeared). The waveguide is formed b stack of semiconductors with different refractive indexes. Optical field can propagate in semiconductors as opposed to metals. As a result, we will not have the luxur of ero optical field on the phsical surface of the mirrors. n 1 n n 3 m 1 m m 3 n eff_1 n eff_ n eff_3 π m π π m m π eff_m n eff_m Lecture 9/6 Standing wave in -direction will be formed again. Optical field will not be full confined in region with refractive index n but will have exponentiall decaing tails in regions n 1 and n 3. ffective refractive index can be understood as being weighted average between n 1, n and n 3 as soon as field is present in all these regions. ZigZag waves model can still be applied with some care and θ m can be assigned to each mode

7 Possible range of the effective refractive index and maximum number of supported modes. Lecture 9/7 1. Perfect mirror case: ero field on the boundar between n-region and mirrors. n θ m π k n k k π π π π n k k, k m m, _m + _m _m _m d d π π d k, hence m n or m d n ffective refractive index can be found from: _m m 1,... k _m k k _m k n eff_m π n n k _m + k m d _m π d m + π n eff_m Maximum number of modes is equal to number of half waves that can be squeeed in d. Minimum n eff is ero and corresponds to extreme case when k k and no energ transfer occurs in -direction pure standing wave. Maximum n eff n, this corresponds to pure traveling wave when no mirrors present. When d < /n this waveguide supports no modes.

8 d Possible range of the effective refractive index and maximum number of supported modes.. Semiconductor laser: nonero field in all laers n 1, n and n 3. n 1 n n 3 n 1 fundamental mode alwas supported first mode For simplicit consider smmetric waveguide n 1 n 3. In smmetric dielectric waveguide n eff can change between n 1 and n because optical field penetrate into all regions. Actual value of n eff_m can be found numericall about /n * before we plotted absolute value of the electric filed. Here we plot electric field with phase to assist the ee to recognie half wave distance between maximums. In smmetric waveguide single lobe mode alwas exists and is called fundamental mode. Next mode exists if maximums of the field are inside n. d Number of supported modes m is given b: m ( n ) 1 n n Fundamental mode alwas exists in smmetric waveguide The mode is guided if all maximums of the standing wave in -direction are inside the confining region n. For the first mode (see figure) to exist waveguide width d should be larger than half wave in n media to have standing wave maximums inside. For the second larger than two half waves, for the third three, etc. Lecture 9/8 Important correction to perfect mirror case, see appendix for exact solution

9 Single mode lasers. Lecture 9/9 Smmetric dielectric waveguide alwas supports at least one mode called fundamental mode. *Asmmetric dielectric waveguide does not necessar supports this mode For the waveguide not to support an other higher order modes the condition should be satisfied: ( n n ) 1 n d 1 < Single spatial mode operation of semiconductor laser produces current independent single lobe far field pattern. Single spatial mode operation lasers have the highest brightness. Brightness B b definition is: B Pν S Ω, where S emitting area, Ω solid angle into which the power P ν is emitted Near field is spatial distribution of optical field across laser mirror, i.e. S. Far field is angle distribution of the optical field far from laser mirror, i.e. Ω. When laser emits single spatial mode S and Ω are related as Fourier transform pair and: P S Ω, and brightness is maximum Bmax ν High brightness is desired in almost all applications. Single spatial mode operation is ideal operation condition of semiconductor laser. Its advantages have to be sacrificed when high output power level is required. Usuall, semiconductor laser are single mode in -direction (transverse) and can have man spatial modes in x-direction (lateral).

10 x light wave electric field component oscillates in the plane of active laer Transverse-electric (T) and Transverse-magnetic (TM) modes. T lectric and magnetic components of the light wave in isotropic media are orthogonal and are related b: T n H H mirror TM n TM H H H ε µ Lecture 9/1 light wave magnetic field component oscillates in the plane of active laer ε n µ T modes have lower mirror loss than TM modes and laser emission is usuall T polaried. In QW lasers mode gain for T and TM polariation is also different. mirror 377 T and TM polaried light have different reflection coefficients at both waveguide boundaries and laser mirrors.

11 Lecture 9/11 Lateral optical confinement (X-direction) x Gain-guided Weakl Index-guided Strongl Index-guided Oxide-Stripe Ridge CMBH Current Confinement Gain modifies Imε I(x) leads to Imε(x) Multimode Im index step ~.1 *Dependent on pumping level *Antiguiding Current Confinement Optical Confinement Reε(x) & Imε(x) Single mode Refractive index step <.1 *Antiguiding *xpensive Current Confinement Optical Confinement Reε(x) Stable single mode Refractive index step >.1 *Ver expensive

12 Lecture 9/1 Measurements of the laser near field General approach is to amplif image of the laser output facet and project it on video camera. F 1 A M 1 B B A B A + 1 F Magnification of 1-1 times or more is required for well resolved image * Near field microscop is another option: fiber tip is scanned with submicron resolution along laser output facet. This technique is accurate and free from aberrations that could be introduced b imaging optics.

13 Lecture 9/13 Measurements of the laser far field Scanning of the single detector Detector arra (CCD) or Vidicon camera High resolution true far field for all angles Slow and onl one dimension at a time Fast image of the D far field pattern as alignment and adjustment Special optics required due to limited sie of the photosensitive matrix

14 Lecture 9/14 Tpical diode laser transverse (Y) far field pattern Normalied Intensit 1..5 FWHM ~ 4 1.5µ m d6nm n n Transverse Angle (Degree) Θ Approximate expression for full angle at half intensit for small d ( ) ( rad 4 n n ) Single mode operation (diffraction limited beam) Beam divergence is current independent 1 d

15 Lecture 9/15 Lateral (X) far field pattern of wide stripe (µm) gain guided laser Normalied Power µm STRIP µm 17 Multimode operation Beam divergence is current dependent and orders of magnitude higher than diffraction limited Lateral Angle (Degree)

16 Lecture 9/16 Ridge waveguide lasers and effective index technique Isolator n~ Metal contact n 1 n tch depth 1. Find transverse effective indexes in ridge and etched sections, n ridge and n etched. Use n ridge and n etched to find lateral field distribution with effective index n lateral n 1 etched region ridge etched region 3. Use n ridge for transverse near/far field calculations and n lateral for lateral near/far field calculations. *Current spreading and gain guiding are usuall important and should be taken into account. * For CMBH devices lateral and transverse waveguide dimensions are comparable and exact D waveguide problem should be solved numericall.

17 Lecture 9/17 Isolator n~ Design of single mode ridge waveguide laser w n 1 n n 1 t Design parameters: 1. Ridge width w. tching depth - t t defines n etched transverse effective index of the etched region n ridge and n etched define lateral effective index n lateral Lateral single mode condition etched region ridge etched region n n n etched ridge etched () w n ridge netched t <

18 APPNDIX 1 ε 1 ε Laser near field (x,) x Lecture 9 app1/1 ( ) ( ) ( r, t ) r, t µ ε r t ε 1 ε ε 1 Consider T modes in 3 laer smmetric waveguide d/ -d/ For T modes Z Y and d/dx Let's look for the solution in the form X (,,t) ( ) exp( j( ωt - k) ) X + X ( ω µ ε k ) X

19 APPNDIX 1 Lecture 9 app1/ Laser near field (x,) n 1 n n 1 d/ -d/ X x + k ( n n ) i eff X π k ; ni εi; neff k k β n k n eff k Solution for guided modes (n 1 <n eff <n ) 1.. d X1 < < d ( ) A cos( β ) + A sin ( β ); β ( n n ) d > : d < ; X : ( ) Bexp ( γ ) X3 O ( ) Cexp ( γ ); γ ( n eff n1 ) k eff k

20 APPNDIX 1 Laser near field (x,) Lecture 9 app1/3 Mode intensit distribution is defined b values of A, A O, B, C and n eff The can be found from boundar and normaliation conditions 1. Boundar condition: Tangential components of the and H should be continuous at the interfaces. dx1 dx X1 d X d and For T modes it means: d d. Normaliation condition: Total area under the envelope X1 d curve should be equal to unit. - X3 d and ( ) d 1 X d d d X1 d d d d X3 d

21 APPNDIX 1 Laser near field (x,) Lecture 9 app1/4 1. Observation of the boundar conditions obtains the equation: ven T modes (A O ): Odd T modes (A ): βd βd βd tan γd βd cot γd. Observation of the relation between k, γ and β gives: dβ + dγ dk ( n n ) Numerical (graphical) solution of these equations gives discrete values of n eff for guided modes 1

22 APPNDIX 1 Laser near field (x,) Lecture 9 app1/5 7 xample of graphical solution 1. Mode intensit distributions 6 5 m 1.5µ m, dµ m n 1 3.6, n 3.4 red - T even blue - T odd m m3 γd/ 4 3 m1 m Xm.5 m m1 1 π π/ m βd/ Condition of the single mode operation:. 1, µ m d n n1 < * In full analsis, mode loss and confinement should be taken into account