Si24 Directly measure blaze angle in reﬂection

A typical grating has 3 blaze angles.

The width of the facet is inversely related

to the breadth of the blaze envelope.

Depending on the illumination angle,

some facets are shadowed.

shadowed

✔

✗

What Astronomers want:

-know the realized* R3 blaze angle and its uncertainty

-a small** uncertainty

-no avoidable*** efﬁciency loss

*the realized blaze angle may differ from the design blaze angle since it depends

intimately on the Si cutting angle (well known) and the anisotropic KOH wet etch

rates (poorly known, variable)

**small means negligible contribution to the overall uncertainty in the alignment of

the spectrograph during integration and testing. Ask Dan Jaffe what X is.

***geometrical efﬁciency loss comes from groove shadowing, which can be

anticipated in the design.

✗

Immersed in Si

GROOVE TOP SHADOWING MEMO

MICHAEL GULLY-SANTIAGO

1. Introduction

This document describes the geometry of micromachined silicon immersion gratings

being developed at the University of Texas Department of Astronomy Silicon Diﬀractive

Optics Group and the MIT Nanoruler Group. Speciﬁcally, we calculate the acceptable

groove top to pitch length ratio above which the eﬃciency of the devices is degraded. This

information is useful for the design of gratings using direct writing systems, where the

groove width is a free parameter. Maintaining a large groove top to pitch length ratio is

important to avoid failures during processing, such as undercutting or over etching.

2. Geometry

Figure 1 shows an overview of a silicon immersion grating. Figure 2 shows a detail of a

single groove, chronicling the relevant geometry; the parameters are listed below.

t is the groove top width

p is the groove spacing (also called the groove pitch)

δ is the blaze angle

a is the silicon etch angle; for this document we adopt a = 70.53

◦

,

the maximum allowable ratio of

t

p is given by:

t

p =

1

1 +

tan(a)

tan(δ)

,

So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have

t

p

∼

= 0.41.

For an R3 echelle, we have

t

p

∼

= 0.51.

References

[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaﬀe, D. T. 2007, Applied Optics, 46, 3400

MICHAEL GULLY-SANTIAGO

1. Introduction

This document describes the geometry of micromachined silicon immersion gratings

being developed at the University of Texas Department of Astronomy Silicon Diﬀractive

Optics Group and the MIT Nanoruler Group. Speciﬁcally, we calculate the acceptable

groove top to pitch length ratio above which the eﬃciency of the devices is degraded. This

information is useful for the design of gratings using direct writing systems, where the

groove width is a free parameter. Maintaining a large groove top to pitch length ratio is

important to avoid failures during processing, such as undercutting or over etching.

2. Geometry

Figure 1 shows an overview of a silicon immersion grating. Figure 2 shows a detail of a

single groove, chronicling the relevant geometry; the parameters are listed below.

t is the groove top width

p is the groove spacing (also called the groove pitch)

δ is the blaze angle

a is the silicon etch angle; for this document we adopt a = 70.53

◦

,

the maximum allowable ratio of

t

p is given by:

t

p =

1

1 +

tan(a)

tan(δ)

,

So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have

t

p

∼

= 0.41.

For an R3 echelle, we have

t

p

∼

= 0.51.

References

[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaﬀe, D. T. 2007, Applied Optics, 46, 3400

Date: May 27, 2009.

1

δ is the blaze angle

a is the silicon etch angle; for this document we adopt a = 70.53

◦

,

the maximum allowable ratio of

t

p is given by:

t

p =

1

1 +

tan(a)

tan(δ)

,

So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have

t

p

∼

= 0.41.

For an R3 echelle, we have

t

p

∼

= 0.51.

References

[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaﬀe, D. T. 2007, Applied Optics, 46, 3400

Date: May 27, 2009.

1

GROOVE TOP SHADOWING MEMO

MICHAEL GULLY-SANTIAGO

1. Introduction

This document describes the geometry of micromachined silicon immersion

being developed at the University of Texas Department of Astronomy Silicon Di

Optics Group and the MIT Nanoruler Group. Speciﬁcally, we calculate the ac

groove top to pitch length ratio above which the eﬃciency of the devices is degrad

information is useful for the design of gratings using direct writing systems, w

groove width is a free parameter. Maintaining a large groove top to pitch length

important to avoid failures during processing, such as undercutting or over etchin

2. Geometry

Figure 1 shows an overview of a silicon immersion grating. Figure 2 shows a de

single groove, chronicling the relevant geometry; the parameters are listed below.

t is the groove top width

p is the groove spacing (also called the groove pitch)

δ is the blaze angle

a is the silicon etch angle; for this document we adopt a = 70.53

◦

,

the maximum allowable ratio of

t

p is given by:

t

p =

1

1 +

tan(a)

tan(δ)

,

So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have

t

p

For an R3 echelle, we have

t

p

∼

= 0.51.

References

[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaﬀe, D. T. 2007, Applied Optics, 46, 3400

Date: May 27, 2009.

1