User:Pranav Rathi/Notebook/OT/2010/08/18/CrystaLaser specifications - Revision history

Pranav Rathi: /* Beam propagation factor M2 */

Pranav Rathi — Fri, 08 Feb 2013 20:39:04 GMT

Beam propagation factor M2

←Older revision		Revision as of 20:39, 8 February 2013
Line 113:		Line 113:
	My experimental beam waist is:		My experimental beam waist is:

-	w<sub>R</sub>=.63mm with a divergence of .~~54mrad~~. The data suggests the real far field divergence angle to be ~~.756mrad~~ (half angle) (w<sub>R</sub>/z at that z). This gives:	+	w<sub>R</sub>=.63mm with a theoretical divergence of .69mrad. The data suggests the real far field divergence angle to be 1mrad (half angle) (w<sub>R</sub>/z at that z). This gives:

	'''M<sup>2</sup>≈1.4'''		'''M<sup>2</sup>≈1.4'''

Pranav Rathi: /* Beam propagation factor M2 */

Pranav Rathi — Fri, 08 Feb 2013 20:21:29 GMT

Beam propagation factor M2

←Older revision		Revision as of 20:21, 8 February 2013
Line 113:		Line 113:
	My experimental beam waist is:		My experimental beam waist is:

-	w<sub>R</sub>=.63mm with a divergence of .54mrad. The data suggests the real far field divergence angle to be 1.~~1mrad~~ (w<sub>R</sub>/z at that z). This gives:	+	w<sub>R</sub>=.63mm with a divergence of .54mrad. The data suggests the real far field divergence angle to be .756mrad (half angle) (w<sub>R</sub>/z at that z). This gives:

-	'''M<sup>2</sup>≈1.35'''	+	'''M<sup>2</sup>≈1.4'''

	Now using beam propagation formula with M<sup>2</sup> correction:		Now using beam propagation formula with M<sup>2</sup> correction:

Pranav Rathi: /* Beam propagation factor M2 */

Pranav Rathi — Fri, 08 Feb 2013 20:00:13 GMT

Beam propagation factor M2

←Older revision		Revision as of 20:00, 8 February 2013
Line 115:		Line 115:
	w<sub>R</sub>=.63mm with a divergence of .54mrad. The data suggests the real far field divergence angle to be 1.1mrad (w<sub>R</sub>/z at that z). This gives:		w<sub>R</sub>=.63mm with a divergence of .54mrad. The data suggests the real far field divergence angle to be 1.1mrad (w<sub>R</sub>/z at that z). This gives:

-	'''M<sup>2</sup>≈2'''	+	'''M<sup>2</sup>≈1.35'''

	Now using beam propagation formula with M<sup>2</sup> correction:		Now using beam propagation formula with M<sup>2</sup> correction:

Pranav Rathi: /* Analysis */

Pranav Rathi — Thu, 15 Nov 2012 01:17:57 GMT

Analysis

←Older revision		Revision as of 01:17, 15 November 2012
Line 84:		Line 84:
	Here the plot beam diameter Vs Z is presented. Experimental data is presented as blue and model is red. As it can be seen that model does not fit the data. Experimental beam expands much faster than the model; this proves that the beam waist before the expansion optics must be relatively smaller. And also we are missing an important characterization parameter. The real word lasers work differently in a way that their beam do not follow the regular Gaussian formula for large propagation lengths (more than Raleigh range). So that's why we will have introduce a beam propagation factor called M<sup>2</sup>.		Here the plot beam diameter Vs Z is presented. Experimental data is presented as blue and model is red. As it can be seen that model does not fit the data. Experimental beam expands much faster than the model; this proves that the beam waist before the expansion optics must be relatively smaller. And also we are missing an important characterization parameter. The real word lasers work differently in a way that their beam do not follow the regular Gaussian formula for large propagation lengths (more than Raleigh range). So that's why we will have introduce a beam propagation factor called M<sup>2</sup>.

-	[[Image:Beamwaistexp.png\|700x600px\|~~Diameter~~ Vs Z]]	+	[[Image:Beamwaistexp.png\|700x600px\|Beam waist Vs Z]]

	=====Beam propagation factor M<sup>2</sup>=====		=====Beam propagation factor M<sup>2</sup>=====
Line 126:		Line 126:
	The result is obvious. Plot shows the real experimental data with theoretical data fit with and without M^2 correction.		The result is obvious. Plot shows the real experimental data with theoretical data fit with and without M^2 correction.

-	[[Image:Beam waist experiment with M2.jpg]]	+	[[Image:Beam waist experiment with M2.jpg\|700x600px\|Beam waist Vs Z]]
		+
		+	M<sup>2</sup> is an important parameter and it is good to know it to complete the characterization of a laser.
	[[Category:1064crystalaser]]		[[Category:1064crystalaser]]

Pranav Rathi: /* Beam propagation factor M2 */

Pranav Rathi — Thu, 15 Nov 2012 01:15:31 GMT

Beam propagation factor M2

←Older revision		Revision as of 01:15, 15 November 2012
Line 126:		Line 126:
	The result is obvious. Plot shows the real experimental data with theoretical data fit with and without M^2 correction.		The result is obvious. Plot shows the real experimental data with theoretical data fit with and without M^2 correction.

		+	[[Image:Beam waist experiment with M2.jpg]]
	[[Category:1064crystalaser]]		[[Category:1064crystalaser]]

Pranav Rathi: /* Beam propagation factor M2 */

Pranav Rathi — Thu, 15 Nov 2012 01:10:15 GMT

Beam propagation factor M2

←Older revision		Revision as of 01:10, 15 November 2012
Line 122:		Line 122:

	instead of:		instead of:
-	:<math>w(z) = w_0 \, \sqrt{ 1+ {\left( \frac{z}{z_\mathrm{R}} \right)}^2 } \ . </math>	+	:<math>w_R(z) = w_0 \, \sqrt{ 1+ {\left( \frac{z}{z_\mathrm{R}} \right)}^2 } \ . </math>

	The result is obvious. Plot shows the real experimental data with theoretical data fit with and without M^2 correction.		The result is obvious. Plot shows the real experimental data with theoretical data fit with and without M^2 correction.

	[[Category:1064crystalaser]]		[[Category:1064crystalaser]]

Pranav Rathi: /* Beam propagation factor M2 */

Pranav Rathi — Thu, 15 Nov 2012 01:08:17 GMT

Beam propagation factor M2

←Older revision		Revision as of 01:08, 15 November 2012
Line 117:		Line 117:
	'''M<sup>2</sup>≈2'''		'''M<sup>2</sup>≈2'''

		+	Now using beam propagation formula with M<sup>2</sup> correction:

		+	:<math>w_R(z) = w_0 \, \sqrt{ 1+ {\left( \frac{z M^2}{z_\mathrm{R}} \right)}^2 } \ . </math>

		+	instead of:
		+	:<math>w(z) = w_0 \, \sqrt{ 1+ {\left( \frac{z}{z_\mathrm{R}} \right)}^2 } \ . </math>

		+	The result is obvious. Plot shows the real experimental data with theoretical data fit with and without M^2 correction.
		+
	[[Category:1064crystalaser]]		[[Category:1064crystalaser]]

Pranav Rathi: /* M2 */

Pranav Rathi — Thu, 15 Nov 2012 00:55:25 GMT

←Older revision		Revision as of 00:55, 15 November 2012
Line 86:		Line 86:
	[[Image:Beamwaistexp.png\|700x600px\|Diameter Vs Z]]		[[Image:Beamwaistexp.png\|700x600px\|Diameter Vs Z]]

-	=====M<sup>2</sup>=====	+	=====Beam propagation factor M<sup>2</sup>=====
	The beam propagation factor M<sup>2</sup> was specifically introduced to enable accurate calculation of the properties of laser beams which depart from the theoretically perfect TEM<sub>00</sub> beam. This is important because it is quite literally impossible to construct a real world laser that achieves this theoretically ideal performance level.		The beam propagation factor M<sup>2</sup> was specifically introduced to enable accurate calculation of the properties of laser beams which depart from the theoretically perfect TEM<sub>00</sub> beam. This is important because it is quite literally impossible to construct a real world laser that achieves this theoretically ideal performance level.

Line 114:		Line 114:

	w<sub>R</sub>=.63mm with a divergence of .54mrad. The data suggests the real far field divergence angle to be 1.1mrad (w<sub>R</sub>/z at that z). This gives:		w<sub>R</sub>=.63mm with a divergence of .54mrad. The data suggests the real far field divergence angle to be 1.1mrad (w<sub>R</sub>/z at that z). This gives:
-	::<~~math~~>	+
-	~~M^2≈2~~	+	'''M<sup>2</sup>≈2'''
-	</~~math~~>	+

Pranav Rathi: /* M2 */

Pranav Rathi — Thu, 15 Nov 2012 00:46:42 GMT

←Older revision		Revision as of 00:46, 15 November 2012
Line 92:		Line 92:

	::<math>		::<math>
-	\theta_{th}=\frac{\lambda}{\pi w_0}	+	\theta_{0}=\frac{\lambda}{\pi w_0}
	</math>		</math>
	this is theoretical half divergence angle in radian.		this is theoretical half divergence angle in radian.
	::<math>		::<math>
-	~~M_2~~=\frac{w_{~~exR~~}\~~theta_R~~}{~~w_0~~\~~theta~~}	+	\theta_{R}=M^2\frac{\lambda} {\pi w_0}
		+	</math>
		+	so
		+	::<math>
		+	M^2=\frac{\theta_{R}} {\theta_{0}}
	</math>		</math>
-
	Where:		Where:
	*λ is the laser wavelength		*λ is the laser wavelength
-	*~~w<sub>exR</sub> is the beam waist and~~ θ<sub>R</sub> is the far field divergence angle of the real beam.	+	*θ<sub>R</sub> is the far field divergence angle of the real beam.
	*w<sub>0</sub> is the beam waist radius and θ<sub>0</sub> is the far field divergence angle of the theoratical beam.		*w<sub>0</sub> is the beam waist radius and θ<sub>0</sub> is the far field divergence angle of the theoratical beam.
	*M<sup>2</sup> is the beam propagation factor		*M<sup>2</sup> is the beam propagation factor
Line 110:		Line 113:
	My experimental beam waist is:		My experimental beam waist is:

-	w<sub>~~exp~~</sub>=.63mm with a divergence of .~~5mrad~~. ~~Since we do not know the theoretical beam parameters, we will have to use~~ data ~~to figure out~~ the M<~~sup~~>2</~~sup~~>.	+	w<sub>R</sub>=.63mm with a divergence of .54mrad. The data suggests the real far field divergence angle to be 1.1mrad (w<sub>R</sub>/z at that z). This gives:
-		+	::<math>
		+	M^2≈2
		+	</math>

Pranav Rathi: /* M2 */

Pranav Rathi — Thu, 15 Nov 2012 00:09:24 GMT

←Older revision		Revision as of 00:09, 15 November 2012
Line 100:		Line 100:

	Where:		Where:
-	λ is the laser wavelength	+	*λ is the laser wavelength
-	w<sub>exR</sub> is the beam waist and θ<sub>R</sub> is the far field divergence angle of the real beam.	+	*w<sub>exR</sub> is the beam waist and θ<sub>R</sub> is the far field divergence angle of the real beam.
-	w<sub>0</sub> is the beam waist radius and θ<sub>0</sub> is the far field divergence angle of the theoratical beam.	+	*w<sub>0</sub> is the beam waist radius and θ<sub>0</sub> is the far field divergence angle of the theoratical beam.
-	M<sup>2</sup> is the beam propagation factor	+	*M<sup>2</sup> is the beam propagation factor

	This definition of M<sup>2</sup> allows us to make simple change to optical formulas by taking M<sup>2</sup> factor as multiplication, to account for the actual beam divergence. This is the reason why M<sub></sub>2 is also sometimes referred to as the “times diffraction limit number”.		This definition of M<sup>2</sup> allows us to make simple change to optical formulas by taking M<sup>2</sup> factor as multiplication, to account for the actual beam divergence. This is the reason why M<sub></sub>2 is also sometimes referred to as the “times diffraction limit number”.
Line 109:		Line 109:

	My experimental beam waist is:		My experimental beam waist is:
-	w<sub>exp</sub>=.63mm with a divergence of .5mrad.	+
-	~~Theoratical~~ beam ~~waist calculated from~~ .~~75mrad divergence~~	+	w<sub>exp</sub>=.63mm with a divergence of .5mrad. Since we do not know the theoretical beam parameters, we will have to use data to figure out the M<sup>2</sup>.
		+