Characterization of the Near-FieldProfile of Semiconductor Lasers and the

Spot Size of Tightly Focused LaserBeams from Far-Field Measurements

Jeffrey L. Guttman and John M. FleischerPhoton Inc.

6860 Santa Teresa Blvd.,San Jose, CA 95119

7th International Workshop on Laser Beam and OpticsCharacterization

September 18-19, 2002

ABSTRACT

Characterization of the near field of typical semiconductor lasers and thespot size of tightly focused laser beams poses significant challenges todirect near-field profile measurement techniques. Far-field measurementsare considerably easier to perform and offer an attractive alternative for thischaracterization. To assess this alternative, profiles of edge-emitting laserdiodes and VCSELs, and the spot size of focused laser beams weredetermined from far-field and near-field measurements. In the far field,measurements were made using a 3D-scanning goniometric radiometer thatprovides irradiance profiles with angular extent to approximately ±70°.Indirect measures derived from these data using different methods arereported, including the spot size using the M2 times-diffraction-limitedapproximation, the Hankel transform Petermann II mode-field diameterused for optical fiber characterization, and a measure obtained from 2DFourier transform inversion of the far field using phase retrieval. In thenear field, direct profile measurements were made using scanning slit andknife-edge profilers, and a CCD camera with magnifying lenses.

PRESENTATION OUTLINE

Applications of Near Field CharacterizationMeasurement Techniques

• Direct Near Field• Indirect Far Field

Near and Far Field Data• Focused HeNe• Edge Emitting Laser Diode• VCSEL

Analysis MethodsSummary of ResultsConclusion

Near Field Characterization

ApplicationsTightly Focused Laser BeamsLDs - Modes, GeometryVCSELs - Modes, GeometryFibers - MFD, Aeff

Waveguides - Modes, GeometryTapered Fibers - Spot SizeQuantum Dots - Modes, GeometryOther “μm-subμm” Sources

Direct Near Field SourceMeasurement Techniques

Camera/Magnifying LensDiffraction Limited for “μm-subμm” ResolutionNA, MTF, and λ Dependence of OpticsAccess to Aperture Field

Scanning Slit or Knife-EdgeAccess to Aperture Field

Near Field Scanning Optical Microscopy (NSOM)Speed of MeasurementAccess to Aperture FieldExpensive

Indirect Near Field Characterizationfrom Far Field Measurement

Calculate Near Field quantitiesfrom measured Far FieldMinimal Optics LimitationsNo Access ConstraintsEase of MeasurementProvides “sub-µm” Measures

Indirect Near Field Characterizationfrom Far Field Measurement

Diffraction Limited 1/e2 Diameter• Calculated from Far-Field Divergence (d=4λ/πθ)

Mode-Field Diameter (MFD)• Petermann II Integral

Near Field 1/e2 Diameter• 2D Fourier Transform with Phase Retrieval

Edge-Emitting Laser Diode Near FieldCCD with 100x Objective

Edge-Emitting Laser Diode Far Field3D Rectangular View

Edge-Emitting Laser Diode Far Field3D Logarithmic Rectangular View

Edge-Emitting Laser Diode Far Field3D Polar View

Edge-Emitting Laser Diode Far FieldAnalysis: Fast and Slow Axes

Edge-Emitting Laser Diode Far FieldAnalysis: Fast and Slow Axes

Focused HeNe Laser Beam Near Field - Scanning Slit

Typical Profiles

Focused HeNe Laser Beam Near Field - Camera/40X Lens

Typical Profiles

Focused HeNe Laser Beam Far Field - Goniometric Radiometer

Far Field/Near Field Measurements ofVCSEL Modes

Near Field

Far Field

7mA 15mA 19mA 24mA 29mA

Near Field Profiles of VCSEL: Increasing Drive Current

VCSEL Near Field Profiles

0

50

100

150

200

250

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

POSITION (microns)

AM

PLIT

UD

E (A

rbitr

ary

Uni

ts)

7mA

15mA

19mA

24mA

29mA

Far Field Profiles of VCSEL: Increasing Drive Current

VCSEL Far Field Profiles

1

10

100

1000

10000

100000

-50 -40 -30 -20 -10 0 10 20 30 40 50

ANGLE (degrees)

AM

PLIT

UD

E (A

rbitr

ary

Uni

ts)

4mA5mA6mA7mA15mA19mA24mA29mA

Near Field 1/e2 Diameter fromGaussian Approximation

• Equation for Diffraction Limited Width:

2

2

/1

/1

4

e

eD

πθλ

=

• Near-Field Diameter Calculated Using MeasuredFar-Field Divergence Angle

“Mode-Field Diameter” of Source

θθθθ

θθθθπλ θ

θ

θ

θ

dI

dIMFD

)cos()(sin)(

)cos()sin()(2)/(

3∫

∫

−

−=

Calculated using Petermann II Integral1,2:

1TIA/EIA Standard for Single-Mode Fiber2Integral Limit Adjusted for Background Scatter

VCSEL Far Field MFD Analysis:Principal Axes

Near Field 1/e2 Diameter from 2D FourierTransform of Far Field

Phase Retrieval Technique:“Error-Reduction” Algorithm*

)](exp[)()](exp[)()(

)]([)](exp[)()(

)](exp[)()(

)]([)](exp[)()(

11

1

xixfxixfx

uxixx

uiuFu

xuiuu

kkk

kkkk

kk

kkkk

g

GFgg

G

gFGG

θθ

θ

φ

φ

′

′′′′

′

==

==

=

==

++

−

*J. R. Fienup, “Phase retrieval algorithms: a comparison,”Applied Optics Vol. 21, No. 15, pp. 2758-2769, Aug. 1982.

•Fourier transform estimate

•Substitute measured modulus

•Inverse Fourier transform

•Apply support constraints

Near Field from Far FieldEdge-Emitting Laser Diode

3D View

2D Fourier Transform Camera Near Field

Near Field from Far FieldVCSEL @ 7 mA

3D View

Near Field Profile from 2D FourierTransform of FF with Phase Retrieval

Near Field Profile from Camera with100X Objective Lens

Near Field from Far FieldVCSEL @ 15 mA

3D View

Near Field Profile from 2D FourierTransform of FF with Phase Retrieval

Near Field Profile from Camera with100X Objective Lens

Near Field from Far FieldVCSEL @ 15 mA

3D View

Near Field Profile from 2D FourierTransform of FF with Phase Retrieval

Near Field Profile from Camera with100X Objective Lens

Near Field from Far FieldVCSEL @ 15 mA

Topographic View

Near Field Profile from Camera with100X Objective Lens

Near Field Profile from 2D FourierTransform of FF with Phase Retrieval

Far Field/Near Field Measurements ofFocused HeNe Laser Beam Spot Size

Lens AxisObjective Lens/CCD Camera XY Slit Profiler

"Times Diffraction Limit" Width (µm) MFD (µm) 1/e2 Width (µm) 1/e2 Width (µm)

1 Horizontal 5.46 5.22 5.52 5.671 Vertical 5.68 5.35 5.93 6.252 Horizontal 6.00 5.64 5.96 6.332 Vertical 5.93 5.65 6.34 6.36

Measurement TechniqueGoniometric Radiometer

Summary of Results

Far Field/Near Field Measurements ofEdge-Emitting Laser Diode

Device Axis Near Field

Camera/100X Lens

" Diffraction Limit" 1/e2 Width (µm)

Mode-Field Diameter* (µm)

2D Fourier Transform

1/e2 Width (µm)1/e2 Width (µm)

Laser Diode "Fast" 1.20 1.12 *(40 deg) 1.10 1.10Laser Diode "Slow" 2.96 3.07 *(16 deg) 3.30 3.20

Measurement TechniqueFar Field

Goniometric Radiometer

Summary of Results

Far Field/Near Field Measurements ofVCSEL for Different Modes

Device Axis Near Field

Camera/100X Lens " Diffraction Limit" Width

(µm)Mode-Field Diameter

(µm)2D Fourier Transform

(µm)D4σ Width

(µm)VCSEL @ 7mA 1 7.86 7.83 7.92 7.87

2 7.71 7.52 7.83 7.60VCSEL @ 15mA 1 3.99 4.34 4.47 8.95

2 4.02 4.35 4.67 9.63

Measurement TechniqueFar Field

Goniometric Radiometer

Summary of Results

Conclusion

Measurements of NF and FF• Focused HeNe, LDs, and VCSELs• NF: Camera/Objective Lens, Slit Profiler• FF: Scanning Goniometric Radiometer

Comparison of Results• NF: 1/e2 , d4σ,• FF: Gaussian, MFD, 2D FFT 1/e2

Favorable Comparison ~5-10%• Tends to Validate Far Field Methods

Further Development Recommended

“Mode-Field Diameter”

θθθθ

θθθθπλ θ

θ

θ

θ

dI

dIMFD

)cos()(sin)(

)cos()sin()(2)/(

3∫

∫

−

−=

Far Field Petermann II Integral:

Far Field/Near FieldVCSEL Mode @ 7mA

Far Field/Near FieldVCSEL Mode @ 15mA

Far Field/Near FieldVCSEL Mode @ 19mA

Far Field/Near FieldVCSEL Mode @ 24mA

Far Field/Near FieldVCSEL Mode @ 29mA